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EVALUATION OF SOIL WATER CHARACTERISTIC CURVES AND PERMEABILITY FUNCTIONS FOR
MODELING OF SEEPAGE IN UNSATURATED SOILS
A THESIS
submitted by
TULIN BEATE HOSAGASI FUSELIER
In partial fulfillment of the requirements for a degree of
Master of Science
in
Civil and Environmental Engineering
TUFTS UNIVERSITY
August 2006
ADVISER:
DR. LEWIS EDGERS, PH.D, P.E.
UMI Number: 1436332
14363322006
UMI MicroformCopyright
All rights reserved. This microform edition is protected against unauthorized copying under Title 17, United States Code.
ProQuest Information and Learning Company 300 North Zeeb Road
P.O. Box 1346 Ann Arbor, MI 48106-1346
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ABSTRACT
Accurate modeling of soil behavior usually requires that soil properties be
measured by laboratory or field tests. However, testing of soils on every slope that may
possibly fail due to rainfall is not feasible. Furthermore, measurement of unsaturated
soils hydraulic functions, such as the soil water characteristic curve (SWCC) and the
permeability function, are presently time consuming and difficult. This thesis evaluates
whether unsaturated soil hydraulic functions estimated by a number of published
techniques can be used to predict in-situ pore pressure development in unsaturated soils.
Pore water pressures measured during a field study by Lim et al. (1996), in a
residual soil slope at the campus of Nanyang Technical University, Singapore, were
modeled using detailed site information; including subsurface stratigraphy, rainfall and
evaporation rates, initial pore water pressures, and measured soil hydraulic properties.
The case study was then repeated with estimated hydraulic functions that were based on
models available in the literature and site specific grain size distribution curves. The
computed pore pressures were compared to each other, and to pore pressures measured
during the field study, in order to evaluate how well the estimated functions predict pore
pressure development in unsaturated soils.
The finite element analysis program SEEP/W was used to model pore water
pressures development. The study was limited to one directional flow to estimate pore
pressure response. The results of the study suggest that it is possible to predict pore
pressure development accurately in unsaturated soils using detailed site information and
measured SWCCs and permeability functions. For this case study, computations
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conducted with estimated hydraulic functions did not produce as well an agreement
between the computed and measured field pore water pressures as those conducted with
measured hydraulic functions.
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ACKNOWLEDGEMENTS
I would like to thank my thesis advisor Dr. Lewis Edgers for his advice and
encouragement over the years, and interest in this thesis project. Without his guidance
and timely feedback, this work would have not been completed.
I would also like to thank Dr. Christopher Swan for encouraging me to attend
Tufts University, and for his helpful guidance throughout the graduate program. Special
thanks to John Kastrinos at Haley and Aldrich for his understanding and interest in being
a committee member. Thank you to Dr. Farrokh Nadim at NGI for taking the time to
review our conference paper, which is a significant part of this thesis. Thank you all for
your time and efforts in reviewing my thesis and serving as a committee member.
v
For the people I love the most:
my husband Eric Fuselier,
my sister Aylin Losavio,
and
my parents Beate and Sevki Hosagasi,
you are an inspiration and the reason for the completion of this work.
I would like to especially thank my parents for always giving me the best they can. I am proud to be your daughter.
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TABLE OF CONTENTS ABSTRACT ..................................................................................................................................................II ACKNOWLEDGEMENTS....................................................................................................................... IV TABLE OF CONTENTS........................................................................................................................... VI LIST OF TABLES .................................................................................................................................. VIII LIST OF FIGURES ................................................................................................................................... IX 1 INTRODUCTION ........................................................................................................................... 1-1
1.1 PORE PRESSURES IN UNSATURATED SOILS ............................................................................... 1-1 1.2 MODELING OF FLOW IN UNSATURATED SOILS.......................................................................... 1-4 1.3 THESIS OBJECTIVES .................................................................................................................. 1-4
2 BACKGROUND (LITERATURE REVIEW)............................................................................... 2-1 2.1 FLOW EQUATIONS..................................................................................................................... 2-1 2.2 SOIL WATER FUNCTIONS (SWCCS).......................................................................................... 2-2
2.2.1 Measurement of Water Content vs. Suction......................................................................... 2-4 2.2.2 Best-Fit Curves to Measured Water Content vs. Suction Data............................................ 2-9 2.2.3 Estimation of the SWCC .................................................................................................... 2-14
2.3 PERMEABILITY FUNCTIONS..................................................................................................... 2-17 3 SEEP/W NUMERICAL PERFORMANCE EVALUATION ...................................................... 3-1
3.1 INTRODUCTION ......................................................................................................................... 3-1 3.2 CASE STUDY FOR SEEP/W NUMERICAL PERFORMANCE ANALYSIS ......................................... 3-4
3.2.1 Time Step Size Analysis ....................................................................................................... 3-9 3.2.2 Element Type Study - Effect of 8- versus 4-Noded Elements ............................................. 3-18 3.2.3 Element Size Analysis ........................................................................................................ 3-23
3.3 REVISED EDGERS AND NADIM (2003) CASE STUDY ANALYSIS............................................... 3-28 4 DETAILED CASE STUDY – SINGAPORE NTU SLOPE ......................................................... 4-1
4.1 INTRODUCTION ......................................................................................................................... 4-1 4.2 DESCRIPTION OF FIELD STUDY.................................................................................................. 4-2
4.2.1 Instrumentation.................................................................................................................... 4-2 4.2.2 Subsurface Conditions and Soil Engineering Characteristics............................................. 4-5 4.2.3 Field Monitoring Results ..................................................................................................... 4-9
4.3 MODELING OF NTU SLOPE – PRELIMINARY COMPUTATIONS ................................................. 4-11 4.3.1 Mesh Set Up....................................................................................................................... 4-11 4.3.2 Modification of the Subsurface Profile.............................................................................. 4-19 4.3.3 Modification of the Boundary Flux for Evaporation ......................................................... 4-23 4.3.4 Time Step Size and Element Size Analysis ......................................................................... 4-25
4.4 SINGAPORE SOILS PARAMETERS (LITERATURE REVIEW) ........................................................ 4-28 4.4.1 Measured Grain Size Distribution..................................................................................... 4-30 4.4.2 Measured SWCCs.............................................................................................................. 4-32 4.4.3 Measured Permeability Functions..................................................................................... 4-34
4.5 MODELING OF NTU SLOPE – DETAILED COMPUTATIONS ....................................................... 4-38 4.5.1 Computations with Measured SWCCs............................................................................... 4-38 4.5.2 Computations with Measured SWCCs and Permeability Functions ................................. 4-43 4.5.3 Modeling of the Entire Field Study Period........................................................................ 4-46
4.6 EFFECT OF INITIAL PORE PRESSURES ...................................................................................... 4-48 5 PARAMETRIC STUDY – SINGAPORE NTU SLOPE .............................................................. 5-1
5.1 INTRODUCTION ......................................................................................................................... 5-1
vii
5.2 MEASURED SWCCS AND ESTIMATED K FUNCTIONS (2ND DEGREE).......................................... 5-3 5.3 ESTIMATED SWCCS AND ESTIMATED K FUNCTIONS (3RD DEGREE).......................................... 5-6 5.4 ESTIMATED SWCC AND ESTIMATED K FUNCTION (4TH DEGREE)............................................ 5-12 5.5 COMPUTED PORE PRESSURES AT 1.0 AND 1.5 M DEPTHS ......................................................... 5-24 5.6 MODELING OF THE ENTIRE FIELD STUDY PERIOD................................................................... 5-27
6 SUMMARY AND CONCLUSIONS .............................................................................................. 6-1 6.1 SUMMARY................................................................................................................................. 6-1 6.2 CONCLUSIONS........................................................................................................................... 6-3
6.2.1 SEEP/W Numerical Performance Analysis ......................................................................... 6-3 6.2.2 Detailed Case Study ............................................................................................................ 6-4 6.2.3 Parametric Study ................................................................................................................. 6-4
6.3 RECOMMENDATIONS FOR FUTURE RESEARCH .......................................................................... 6-6 7 REFERENCES ................................................................................................................................ 7-1
viii
LIST OF TABLES TABLE 3-1 SUMMARY OF VOLUME OF WATER INFILTRATING THE FEM DUE TO
RAINFALL...................................................................................................................................... 3-17 TABLE 3-2 SUMMARY OF THE EFFECT OF TIME STEP SIZE AND ELEMENT TYPE ON
COMPUTED PRESSURES ............................................................................................................ 3-19 TABLE 3-3 SUMMARY OF THE EFFECT OF TIME STEP SIZE AND ELEMENT SIZE ON
COMPUTED PRESSURES ............................................................................................................ 3-24 TABLE 3-4 SUMMARY OF THE EFFECT OF TIME STEP SIZE, ELEMENT TYPE, AND
ELEMENT SIZE ON COMPUTED PRESSURES......................................................................... 3-26 TABLE 4-1 GENERAL PROPERTIES OF NTU CAMPUS SOILS (AFTER AGUS ET AL., 2001) .... 4-30 TABLE 5-1 FREDLUND AND XING (1994) MODEL FITTING STATISTICS FOR CLAY LOAM
AND SILTY LOAM SOILS (AFTER SILLERS AND FREDLUND, 2001) ................................. 5-15 TABLE 5-2 VAN GENUCHTEN (1980) MODEL FITTING STATISTICS FOR CLAY LOAM
AND SILTY LOAM SOILS (AFTER SILLERS AND FREDLUND, 2001) ................................. 5-15
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LIST OF FIGURES FIGURE 1-1 SCHEMATIC OF PORE PRESSURES IN SOILS............................................................... 1-3 FIGURE 2-1 A TYPICAL SOIL WATER CHARACTERISTIC CURVE (AFTER FREDLUND ET
AL., 1994).......................................................................................................................................... 2-2 FIGURE 2-2 EFFECT OF SOIL TYPE ON SWCCS (AFTER BARBOUR, 1998). ................................. 2-4 FIGURE 2-3 DIAGRAM OF A PRESSURE PLATE EXTRACTOR (AFTER FREDLUND AND
RAHARDJO, 1993)........................................................................................................................... 2-6 FIGURE 2-4 DIAGRAM OF A FIELD TENSIOMETER (AFTER BRADY ET AL., 1996) .................. 2-7 FIGURE 2-5 TYPICAL FILTER PAPER CALIBRATION CURVE (AFTER MCQUEEN AND
MILLER,1968) .................................................................................................................................. 2-8 FIGURE 2-6 COMPARISON OF THE EFFECT OF A, N, AND M FITTING PARAMETERS ON
THE SHAPE OF THE SWCC......................................................................................................... 2-12 FIGURE 2-7 COMPARISON OF SWCCS BEST-FIT WITH THE VAN GENUCHTEN (1980) AND
FREDLUND AND XING (1994) MODELS................................................................................... 2-13 FIGURE 2-8 COMPARISON OF LABORATORY DATA WITH SWCCS BEST-FIT WITH THE
VAN GENUCHTEN (1980) AND FREDLUND AND XING (1994) MODELS WITH LABORATORY DATA (AFTER SILLERS AND FREDLUND, 2001) ....................................... 2-14
FIGURE 2-9 TYPICAL SWCC AND PERMEABILITY FUNCTION FOR A SILTY SOIL (AFTER FREDLUND ET AL., 1994)............................................................................................................ 2-18
FIGURE 3-1 SWCC AND PERMEABILITY FUNCTION FOR THE TOP SOIL LAYER OF THE EDGERS AND NADIM (2003) CASE STUDY............................................................................... 3-5
FIGURE 3-2 SEEP/W FEM FOR THE EDGERS AND NADIM (2003) CASE STUDY......................... 3-6 FIGURE 3-3 RAINFALL RECORD OF THE OF THE EDGERS AND NADIM (2003) CASE
STUDY.............................................................................................................................................. 3-7 FIGURE 3-4 PORE PRESSURE DEVELOPMENT VS. DEPTH COMPUTED BY EDGERS AND
NADIM (2003). ................................................................................................................................. 3-8 FIGURE 3-5 EFFECT OF TIME STEP SIZE ON COMPUTED PORE PRESSURES VERSUS
TIME ............................................................................................................................................... 3-11 FIGURE 3-6 EFFECT OF TIME STEP SIZE ON COMPUTED PORE PRESSURES VERSUS
DEPTH ............................................................................................................................................ 3-13 FIGURE 3-7 EFFECT OF TIME STEP SIZE ON MODELED RAINFALL INTENSITY..................... 3-14 FIGURE 3-8 CHANGE IN VOLUMETRIC WATER CONTENT IN THE FEM WITH DEPTH
AND TIME...................................................................................................................................... 3-16 FIGURE 3-9 RATE OF INFILTRATION INTO THE SOIL COLUMN AT THE SURFACE. .............. 3-17 FIGURE 3-10 EFFECT OF TIME STEP SIZE AND ELEMENT TYPE ON COMPUTED PORE
PRESSURES VERSUS TIME ........................................................................................................ 3-20 FIGURE 3-11 COMPUTED PORE PRESSURES VERSUS DEPTH 46,000S AFTER START OF
RAINFALL – EFFECT OF 8-NODED ELEMENTS ON COMPUTED PORE PRESSURES...... 3-22 FIGURE 3-12 PORE PRESSURES DEVELOPMENT COMPUTED WITH A 50S TIME STEP AT
VERY DRY INITIAL CONDITIONS ............................................................................................ 3-22 FIGURE 3-13 EFFECT OF ELEMENT SIZE ON COMPUTED PORE PRESSURES VS. TIME......... 3-25 FIGURE 3-14 EFFECT OF TIME STEP SIZE, ELEMENT TYPE, AND ELEMENT SIZE ON
COMPUTED PORE PRESSURES VS. TIME................................................................................ 3-27 FIGURE 3-15 EFFECT OF PERMEABILITY ON COMPUTED PORE PRESSURES VS. TIME. ...... 3-30 FIGURE 3-16 EFFECT OF PERMEABILITY ON COMPUTED PORE PRESSURE VS. DEPTH. ..... 3-30 FIGURE 4-1 INSTRUMENTATION LAYOUT OF NTU SLOPE FIELD STUDY (AFTER LIM ET
AL., 1996).......................................................................................................................................... 4-4 FIGURE 4-2 GENERALIZED SOIL PROFILE OF THE NTU SLOPE (AFTER LIM ET AL., 1996) .... 4-5 FIGURE 4-3 GENERALIZED SOIL PROFILE OF TWO SITES ON NTU CAMPUS (AFTER
RAHARDJO ET AL., 1995).............................................................................................................. 4-6 FIGURE 4-4 VARIATION OF NTU CAMPUS SOILS PROPERTIES WITH DEPTH (AFTER
RAHARDJO ET AL., 1995).............................................................................................................. 4-7 FIGURE 4-5 SWCC FOR JURONG FORMATION RESIDUAL SOILS (AFTER LIM ET AL.,
1996).................................................................................................................................................. 4-8
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FIGURE 4-6 WATER LEVEL MEASUREMENTS AT THE NTU SLOPE (AFTER LIM ET AL., 1996).................................................................................................................................................. 4-9
FIGURE 4-7 MEASURED IN-SITU PORE PRESSURES AT THE CANVAS COVERED AND GRASS SURFACE SECTIONS OF THE NTU SLOPE (AFTER LIM ET AL., 1996) ................. 4-10
FIGURE 4-8 MEASURED IN-SITU PORE PRESSURES AT THE BARE SURFACE SECTION OF THE NTU SLOPE (AFTER LIM ET AL., 1996)............................................................................ 4-10
FIGURE 4-9 PRELIMINARY FEM AND INITIAL PORE PRESSURES FOR CASE STUDY............ 4-15 FIGURE 4-10 COMPARISON OF ESTIMATED PRELIMINARY PERMEABILITY FUNCTIONS
FOR ORGANIC SILTY CLAYS .................................................................................................... 4-16 FIGURE 4-11 COMPARISON OF PORE PRESSURES AT 0.5M DEPTH VS. TIME COMPUTED
USING THE PRELIMINARY PERMEABILITY FUNCTIONS................................................... 4-16 FIGURE 4-12 PRELIMINARY COMPUTED PORE PRESSURES AT 0.5, 1.0, AND 1.5M
DEPTHS VS. TIME ........................................................................................................................ 4-18 FIGURE 4-13 PRELIMINARY COMPUTED PORE PRESSURE DEVELOPMENT VS. DEPTH ...... 4-18 FIGURE 4-14 MODIFIED FEM FOR NTU SLOPE CASE STUDY ...................................................... 4-21 FIGURE 4-15 COMPUTED PORE PRESSURES AT 0.5, 1.0, AND 1.5M DEPTHS VS. TIME
USING THE MODIFIED FEM....................................................................................................... 4-22 FIGURE 4-16 CLOSE-UP COMPARISON OF COMPUTED PORE PRESSURES AT 0.5, 1.0, AND
1.5M DEPTHS VS. TIME USING THE PRELIMINARY AND MODIFIED FEM...................... 4-22 FIGURE 4-17 COMPARISON OF PRELIMINARY AND MODIFIED BOUNDARY
CONDITIONS................................................................................................................................. 4-24 FIGURE 4-18 COMPUTED PORE PRESSURES AT 0.5, 1.0, AND 1.5M DEPTHS VS. TIME
USING THE MODIFIED FEM AND MODIFIED BOUNDARY FLUX...................................... 4-25 FIGURE 4-19 TIME STEP AND ELEMENT SIZE ANALYSES FOR COMPUTED PORE
PRESSURES AT 0.5M DEPTH VS. TIME.................................................................................... 4-27 FIGURE 4-20 CLOSE-UP OF TIME STEP AND ELEMENT SIZE ANALYSES................................. 4-27 FIGURE 4-21 GRAIN SIZE DISTRIBUTION NTU-CSE SLOPE SOILS (AFTER RAHARDJO ET
AL., 2004)........................................................................................................................................ 4-31 FIGURE 4-22 GRAIN SIZE DISTRIBUTION OF SHALLOW NTU SOILS BASED ON AGUS ET
AL. (2001) ....................................................................................................................................... 4-32 FIGURE 4-23 SWCCS OF NTU SOILS (AFTER AGUS ET AL., 2001) ............................................... 4-33 FIGURE 4-24 NORMALIZED (θW/θS) SWCCS OF NTU SOILS BEST-FIT TO A SWCC
ENVELOPE USING THE FREDLUND AND XING (1994) MODEL (AFTER AGUS ET AL., 2001)................................................................................................................................................ 4-33
FIGURE 4-25 SWCC OF NTU-CSE SLOPE SOILS (AFTER RAHARDJO ET AL., 2004) ................. 4-34 FIGURE 4-26 SATURATED PERMEABILITY OF NTU SOILS VS. DEPTH (AFTER AGUS ET
AL., 2005)........................................................................................................................................ 4-36 FIGURE 4-27 PERMEABILITY FUNCTIONS NTU SOILS (AFTER AGUS ET AL., 2005)............... 4-36 FIGURE 4-28 COMPLETE MEASURED PERMEABILITY FUNCTION OF NTU SOILS BASED
ON AGUS ET AL., 2005................................................................................................................. 4-37 FIGURE 4-29 PERMEABILITY FUNCTION OF NTU-CSE SLOPE SOILS (AFTER RAHARDJO
ET AL., 2004).................................................................................................................................. 4-37 FIGURE 4-30 COMPARISON OF NTU SOILS SWCCS OBTAINED FROM LITERATURE ............ 4-39 FIGURE 4-31 THE EFFECT OF THE SWCC ON COMPUTED PORE PRESSURES AT 0.5M
DEPTH VS. TIME........................................................................................................................... 4-40 FIGURE 4-32 SCHEMATIC OF WATER CONTENT VS. PORE WATER PRESSURE CHANGE. ... 4-42 FIGURE 4-33 EFFECT OF THE SATURATED VOLUMETRIC WATER CONTENT OF SOIL
LAYERS ON PORE PRESSURE DEVELOPMENT AT 0.5M DEPTH ....................................... 4-43 FIGURE 4-34 COMPARISON OF PRELIMINARY AND MEASURED PERMEABILITY
FUNCTIONS FOR ALL THREE SOIL LAYERS OF THE MODIFIED FEM ............................. 4-44 FIGURE 4-35 EFFECT OF THE K FUNCTION ON COMPUTED PORE PRESSURES AT 0.5M
DEPTH. ........................................................................................................................................... 4-45 FIGURE 4-36 COMPARISON OF MEASURED AND COMPUTED PORE PRESSURES AT 0.5,
1.0 AND 1.5M DEPTHS WHEN HYDRAULIC FUNCTIONS ARE MEASURED..................... 4-46 FIGURE 4-37 FEM AND INITIAL PORE PRESSURES FOR MODELING OF ENTIRE FIELD
TEST PERIOD ................................................................................................................................ 4-47
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FIGURE 4-38 COMPUTED PORE PRESSURES AT 0.5M DEPTH FOR THE TIME PERIOD OF 1 JANUARY TO 28 FEBRUARY 1994 WHEN HYDRAULIC FUNCTIONS ARE MEASURED ................................................................................................................................... 4-48
FIGURE 4-39 COMPUTED PORE PRESSURES AT 0.5 M DEPTH FOR THE TIME PERIOD OF 27 JANUARY TO 28 FEBRUARY 1994 WHEN HYDRAULIC FUNCTIONS ARE MEASURED BUT INITIAL PORE PRESSURES ARE NOT KNOWN....................................... 4-50
FIGURE 4-40 COMPUTED PORE PRESSURES AT 0.5 M DEPTH FOR THE TIME PERIOD OF 1 JANUARY TO 28 FEBRUARY 1994 WHEN HYDRAULIC FUNCTIONS ARE MEASURED BUT INITIAL PORE PRESSURES ARE NOT KNOWN....................................... 4-50
FIGURE 5-1 SUMMARY OF OPTIONS IN DETERMINING SOIL HYDRAULIC FUNCTIONS WITH SEEP/W.................................................................................................................................. 5-2
FIGURE 5-2 COMPARISON OF PERMEABILITY FUNCTIONS MEASURED, AND ESTIMATED FROM THE MEASURED ‘AVERAGE’ SWCC FOR THE ORGANIC SILTY CLAY SOILS (EL. 138 TO 137.5).................................................................................................... 5-5
FIGURE 5-3 EFFECT OF THE PERMEABILITY FUNCTION ON COMPUTED PORE PRESSURES AT 0.5M DEPTH........................................................................................................ 5-5
FIGURE 5-4 COMPARISON OF SWCCS MEASURED, AND ESTIMATED FROM GRAIN SIZE .... 5-7 FIGURE 5-5 COMPARISON OF PERMEABILITY FUNCTIONS MEASURED, AND
ESTIMATED FROM GRAIN SIZE USING THE ARYA & PARIS (1981) MODEL FOR THE ORGANIC SILTY CLAY SOILS (EL. 138 TO 137.5) .................................................................... 5-8
FIGURE 5-6 COMPARISON OF K FUNCTIONS MEASURED, AND ESTIMATED FROM GRAIN SIZE USING THE MODIFIED KOVACS MODEL FOR THE ORGANIC SILTY CLAY SOILS (EL. 138 TO 137.5).................................................................................................... 5-8
FIGURE 5-7 COMPARISON OF PERMEABILITY FUNCTIONS MEASURED, AND ESTIMATED FROM THE MEASURED ‘UPPERBOUND’ SWCC FOR THE ORGANIC SILTY CLAY SOILS (EL. 138 TO 137.5) ..................................................................................... 5-10
FIGURE 5-8 EFFECT OF THE PERMEABILITY FUNCTION ON COMPUTED PORE PRESSURES AT 0.5 M DEPTH - SWCC ESTIMATED FROM GRAIN SIZE USING THE ARYA AND PARIS (1981) METHOD........................................................................................... 5-11
FIGURE 5-9 EFFECT OF THE PERMEABILITY FUNCTION ON COMPUTED PORE PRESSURES AT 0.5M DEPTH - SWCC ESTIMATED FROM GRAIN SIZE USING THE MODIFIED KOVACS METHOD .................................................................................................. 5-11
FIGURE 5-10 SUMMARY OF OPTIONS IN DETERMINING SOIL HYDRAULIC FUNCTIONS WITH SEEP/W USING DATA BY SILLERS AND FREDLUND (2001). ................................... 5-13
FIGURE 5-11 USDA SOIL CLASSIFICATION PYRAMID AND DETERMINATION OF SOIL TYPES FOR THE NTU SLOPE ..................................................................................................... 5-14
FIGURE 5-12 BEST-FIT CURVES TO MEASURED DATA FOR TWO SOIL SAMPLES (AFTER SILLERS AND FREDLUND, 2001) .............................................................................................. 5-16
FIGURE 5-13 COMPARISON OF SWCCS MEASURED, AND ESTIMATED USING THE FREDLUND AND XING (1994) MODEL FITTING PARAMETERS BY SILLERS AND FREDLUND (2001) (4B) ................................................................................................................ 5-17
FIGURE 5-14 COMPARISON OF K FUNCTIONS MEASURED, AND ESTIMATED FROM PUBLISHED FITTING PARAMETERS USING THE II- FREDLUND ET AL. (1994) MODEL FOR THE ORGANIC SILTY CLAY SOILS (EL. 138 TO 137.5) - SWCCS SHOWN IN FIGURE 5.13.............................................................................................................................. 5-18
FIGURE 5-15 COMPARISON OF K FUNCTIONS MEASURED, AND ESTIMATED FROM PUBLISHED FITTING PARAMETERS USING THE I- VAN GENUCHTEN (1980) MODEL FOR THE ORGANIC SILTY CLAY SOILS (EL. 138 TO 137.5) – SWCCS SHOWN IN FIGURE 5-13................................................................................................................................... 5-18
FIGURE 5-16 COMPUTED PORE PRESSURES AT 0.5M DEPTH WHEN SOIL IS CLAY LOAM – K ESTIMATED USING THE II- FREDLUND ET AL. (1994) MODEL ................................... 5-19
FIGURE 5-17 COMPUTED PORE PRESSURES AT 0.5M DEPTH WHEN SOIL IS SILTY LOAM – K ESTIMATED USING THE II- FREDLUND ET AL. (1994) MODEL ................................... 5-20
FIGURE 5-18 COMPUTED PORE PRESSURES AT 0.5M DEPTH WHEN SOIL IS CLAY LOAM – K ESTIMATED USING THE I- VAN GENUCHTEN (1980) MODEL..................................... 5-20
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FIGURE 5-19 COMPUTED PORE PRESSURES AT 0.5M DEPTH WHEN SOIL IS CLAY LOAM – K ESTIMATED USING THE I- VAN GENUCHTEN (1980) MODEL..................................... 5-21
FIGURE 5-20 COMPARISON OF SWCCS MEASURED, AND ESTIMATED USING THE VAN GENUCHTEN (1980) MODEL FITTING PARAMETERS BY SILLERS AND FREDLUND (2001) (4A) ...................................................................................................................................... 5-22
FIGURE 5-21 COMPARISON OF K FUNCTIONS MEASURED, AND ESTIMATED FROM PUBLISHED FITTING PARAMETERS USING THE II- FREDLUND ET AL. (1994) MODEL FOR THE ORGANIC SILTY CLAY SOILS (EL. 138 TO 137.5) - SWCCS SHOWN IN FIGURE 5.20.............................................................................................................................. 5-22
FIGURE 5-22 COMPARISON OF K FUNCTIONS MEASURED, AND ESTIMATED FROM PUBLISHED FITTING PARAMETERS USING THE I- VAN GENUCHTEN (1980) MODEL FOR THE ORGANIC SILTY CLAY SOILS (EL. 138 TO 137.5) – SWCCS SHOWN IN FIGURE 5-20................................................................................................................................... 5-23
FIGURE 5-23 COMPARISON OF COMPUTED AND MEASURED PORE PRESSURES AT 0.5, 1.0 AND 1.5M DEPTHS FOR THE 2ND DEGREE OF ACCURACY ANALYSIS....................... 5-24
FIGURE 5-24 COMPARISON OF COMPUTED AND MEASURED PORE PRESSURES AT 0.5, 1.0 AND 1.5M DEPTHS FOR THE 3RD DEGREE OF ACCURACY ANALYSIS....................... 5-25
FIGURE 5-25 COMPARISON OF COMPUTED VERSUS MEASURED PORE PRESSURES AT 0.5, 1.0 AND 1.5M DEPTHS FOR THE 4TH DEGREE OF ACCURACY ANALYSIS................. 5-26
FIGURE 5-26 COMPUTED PORE PRESSURES AT 0.5M DEPTH FOR THE TIME PERIOD OF 1 JANUARY TO 28 FEBRUARY - 2ND DEGREE OF ACCURACY ANALYSIS.......................... 5-27
FIGURE 5-27 COMPUTED PORE PRESSURES AT 0.5M DEPTH FOR THE TIME PERIOD OF 1 JANUARY TO 28 FEBRUARY - 3RD DEGREE OF ACCURACY ANALYSIS. ......................... 5-28
FIGURE 5-28 COMPUTED PORE PRESSURES AT 0.5M DEPTH FOR THE TIME PERIOD OF 1 JANUARY TO 28 FEBRUARY – 4TH DEGREE OF ACCURACY ANALYSIS. ........................ 5-28
FIGURE 5-29 COMPARISON OF COMPUTED PORE PRESSURE RESIDUALS.............................. 5-29
1
EVALUATION OF SOIL WATER CHARACTERISTIC CURVES AND PERMEABILITY FUNCTIONS FOR
MODELING OF SEEPAGE IN UNSATURATED SOILS
1-1
1 INTRODUCTION
1.1 Pore Pressures in Unsaturated Soils
One of the key factors for the occurrence of landslides is the infiltration of water
into the unsaturated (vadose) zone above the water table due to precipitation, snowmelt,
or other wetting factors. The infiltration and possible saturation of an unsaturated soil
zone changes the effective stresses for slope stability, and thus the shear strength of soils.
For saturated soils the shear strength of soils is commonly expressed by the Mohr-
Coulomb failure law, defined as:
τ ' ff = c'+σ ' ff tanφ ' Equation (1-1)
where, τ'ff is the shear stress on the failure plane at failure, c’ is the effective cohesion, φ
is the effective angle of shearing resistance due to effective stress, and σ'ff is the effective
stress on the failure plane at failure, defined as:
wu−= σσ ' Equation (1-2)
where, σ is the total normal stress and uw is pore water pressure. An increase in the pore
water pressure, due to infiltration, decreases the effective shear stress (σ') of soils, which
reduces its effective shear strength. A reduction in shear strength, in turn, decreases the
factor of safety for slope stability, possibly leading to slope failure. Therefore,
understanding and evaluating pore pressures in the unsaturated zone is important when
evaluating slope stability.
1-2
The effective shear strength of unsaturated soils has been described (Fredlund and
Morgenstern, 1977) with two independent state variables, defined as:
bffwaffaff uuuc φφστ tan)('tan)(' −+−+= Equation (1-3)
where, ua is pore air pressures, (σ-ua)ff is the net normal stress on the failure plane at
failure, (ua-uw)ff is the suction on the failure plane at failure, and φb is the internal friction
due to suction. Due to the third term in Equation 1-3, representing the strength of soils
due to suction, the shear strength of unsaturated soils is generally greater than that of
saturated soils. Therefore, as unsaturated soils become saturated, the pore air pressure
approaches the pore water pressure, thereby eliminating the suction term in Equation 1-3,
and reducing the shear strength.
It should be noted that not all slopes fail under wetting conditions, which suggests
that a critical combination of hydrologic factors (antecedent moisture, precipitation
intensity, etc.), soil material characteristics (porosity, permeability, shear strength, etc.),
and geologic factors (slope angle, subsurface conditions, etc.) are required for the
occurrence of slope failures (Johnson and Sitar, 1990).
In the unsaturated zone, above the water table, pore pressures are negative with
respect to atmospheric pressures. Generally, the pore pressures become more negative as
distance above the water table increases and are most negative at ground surface. A
schematic of pore pressures above and below the water table is shown for an ideal case of
one subsurface soil layer, in Figure 1-1.
1-3
Figure 1-1 Schematic of pore pressures in soils.
Negative pore pressures in the unsaturated zone develop due to the matrix and
osmotic potentials of soil particles and groundwater. Matrix potential, also called the
matric suction or capillary reaction, is the attraction of the soil matrix (including soil
particles and voids) to groundwater. Osmotic potential, also called the osmotic suction, is
the molecular attraction between water molecules and solutes in groundwater. The
magnitude of osmotic suction depends on the solute chemistry and concentration, and
may or may not be significant with respect to matric suction. The sum of these two
forces is termed total suction. As water is “suctioned” from the water table, air enters the
soil matrix, thereby decreasing its water content and changing its state from saturated to
unsaturated. It is the suctioning effect that is responsible for negative pressures in
unsaturated soils. The magnitude of suction in soils depends greatly on the amount and
intensity of precipitation. Suction increases in the absence of precipitation and decreases
as precipitation infiltrates the ground.
1-4
1.2 Modeling of Flow in Unsaturated Soils
Unsaturated soil mechanics has been a developing field since the 1950’s.
However, most developments in the understanding and application of unsaturated soil
mechanics, including the effects of decreasing soil water content on seepage, shear
strength, and volume change have emerged starting in the 1970’s. Many constitutive
relations for the estimation of seepage, shear strength, and volume change at unsaturated
conditions were developed in the 1970’s. This was followed by the numerical modeling
of the unsaturated behavior of soils in the 1980’s and onward (Fredlund, 2006).
The numerical modeling of flow in the unsaturated zone has been of particular
interest since the mid-1990’s for the prediction of pore pressures, and thus the prediction
of slope stability in rain events. Several commercially available software programs are
available that model the saturated-unsaturated flow interaction in soils. The studies
described in this thesis were performed with SEEP/W, Version 5 (2002) (Geo-Slope
International Ltd.), which is a finite element program for analyzing transient, two-
dimensional, saturated and unsaturated water flow. The program presents seepage
through a system as a function of pressure, head, water content, flux, velocity or gradient
with time or depth.
1.3 Thesis Objectives
Accurate modeling of soil behavior requires that soil properties be measured by
laboratory or field tests. However, testing of unsaturated soils parameters is currently
time consuming and expensive. Therefore, an understanding of modeling flow through
1-5
unsaturated soils by use of measured and estimated soil properties is needed. In this
thesis, in-situ pore pressures measured during a field study are numerically modeled
using soil properties measured by laboratory or field testing, estimated by constitutive
models, or estimated based on published data. The computed pore pressures are
compared to those observed in the field study, and to each other.
The general objective of this thesis is to determine if soil properties measured and
estimated by a number of published techniques can be used to accurately predict pore
pressure development in unsaturated soils. The specific objectives of this thesis are 1) to
evaluate the overall accuracy of numerical modeling of pore pressures, 2) to determine
the detail of site information and soil properties needed to accurately predict pore
pressure response, and 3) to determine if the wealth of published soil hydraulic functions
can be used to predict pore pressure development.
The finite element model in this thesis is limited to one directional flow. The
advantages of this approach are that it is simple, and it will provide useful information
regarding the mechanics of vertically infiltrating rainfall. Even though a one-dimensional
infiltration model is highly idealized, as it neglects any lateral seepage, it will provide an
estimate of the pore pressure response.
Many studies exist that model observed pore pressure response in soils. However,
to the author’s knowledge, a study that compares the effectiveness of using measured
versus estimated soil properties does not exist. In addition, a comprehensive study that
compares the effectiveness of methods used to estimate soil properties for modeling pore
pressures is needed.
1-6
Chapter 2 of this thesis describes the general properties of unsaturated soils, then
gives a summary of common laboratory and field methods used to measure, and
constitutive models used to estimate the unsaturated soil hydraulic functions. A literature
review on the hydraulic characteristics of unsaturated soils is presented. Chapter 3
evaluates the numerical performance of SEEP/W. In Chapter 4, the field study for the
observation of in-situ pore pressures is introduced and field pore pressures are modeled
using measured hydraulic functions. In Chapter 5, pore pressures are modeled using
estimated hydraulic functions that are based on models available in literature and site
specific grain size distribution curves. The results of the study are summarized in
Chapter 6.
2-1
2 BACKGROUND (LITERATURE REVIEW)
2.1 Flow Equations
Transient flow of water through a soil element is governed by the two-
dimensional flow equation as described by Richards (1931) and as shown in
Equation 2-1:
Equation (2-1)
where, h is total hydraulic head; Kx and Ky are permeability coefficients in the x and y
directions; q is the boundary flux from external infiltration; θ is the volumetric water
content; and t is time. Equation 2.1 states that the flow in soil pores must equal the time
rate change of the volumetric water content in the pores. If the change in volumetric
water content is related to the change in pore water pressure, Equation 2-1 can be written
as:
Equation (2-2)
where, mw is a coefficient of volume change related to the relationship between water
content and suction, and γw is the unit weight of water. Since mw is related to the
relationship between water content and suction, and K is related to the relationship
between permeability and suction, the change in water content and permeability with
suction must be specified in a flow model. A brief introduction to the general concept of
these functions, their measurement and their estimation are given below.
∂∂x
(Kx∂h∂x
) +∂∂y
(Ky∂h∂y
) + q =∂θ∂t
∂∂x
(Kx∂h∂x
) +∂∂y
(Ky∂h∂y
) + q = mwγw∂h∂t
2-2
2.2 Soil Water Functions (SWCCs)
The representation of the relationship between water content and suction is
typically termed the Soil Water Characteristic Curve (SWCC). The SWCC is a
continuous sigmoidal function that describes the decrease in water content (volumetric or
gravimetric) with increase in soil suction. A typical SWCC and its variables are shown in
Figure 2-1.
Figure 2-1 A typical soil water characteristic curve (after Fredlund et al., 1994)
The y-axis in Figure 2-1, volumetric water content, is defined as the ratio of the
volume of water (Vw) to the total volume of the soil (V), Vw/V (alternatively, the y-axis is
sometimes plotted as the gravimetric water content, which is defined as the ratio of the
weight of soil water to the weight of soil solids). Again in Figure 2-1, the air entry value
is defined as the suction that must be exceeded for air to enter the soil pores. Up to the
point of air entry, the soil is still in capillary saturation. The residual water content is
defined as the suction, where pore water becomes so sparse that it can not flow between
%
2-3
pore spaces, and further water removal is by evaporation only. The SWCC is a hysteric
curve, where the curve for a drying specimen (desorption) differs from the curve for a
specimen that is being wetted (absorption). However one equation that describes both
curves is appropriate for most engineering practices (Fredlund et al., 1994).
SWCCs generally depend on the grain size distribution, pore diameter
distribution, and structure of soils, and groundwater characteristics. Smaller pore
diameters generate stronger suction, simply based on the capillary rise equation (Equation
2-3) where pore-radius, r, is inversely proportional to h, the height of capillary rise.
Equation (2-3)
Therefore, soils with smaller pore diameters can sustain a higher capillary rise,
and the suction that is required for air to enter the soil system is larger, i.e., the air entry
value increases. The effect of the pore size or grain size distribution on the SWCC is
shown in Figure 2-2 for a range of soil types ranging from sands to clays, where sandy
soils with larger pore diameters have a lower air entry value than clayey soils with the
smaller pore diameters. Moreover, the SWCC is steeper for sandy soils, which indicates
that soils with larger diameter pores lose their suction easier than clayey or compacted
soils.
The measurement of SWCCs is fairly straight forward compared to the
measurement of other unsaturated soil properties. Thus many correlations for the
estimations of other unsaturated soil properties, such as the relationship between
permeability and shear strength with increasing suction, have been based on the SWCC.
rrT
hw
s 15.02==
γ
2-4
As a result, the SWCC is considered to be one of the more important parameters of
unsaturated soil mechanics. SWCCs are either measured in the laboratory or in the field
as described in Section 2.2.1, or estimated based on the grain size distribution of soils as
described in Section 2.2.3.
a) effect of grain size b) effect of compaction
Figure 2-2 Effect of soil type on SWCCs (after Barbour, 1998).
2.2.1 Measurement of Water Content vs. Suction
The SWCC can be determined by measuring the suction of a soil specimen with a
known water content. The measurement is repeated at different water contents until the
measured data points can be connected to form a curve. Some of the common methods to
(a)
(b)
2-5
measure matric and osmotic soil suctions are described herein. For more detail on soil
suction measurement, and the measurement of total suction, refer to Fredlund and
Rahardjo (1993).
a. Measurement of Matric Suction
Matric suction is usually measured with the aid of saturated porous stones (high
air entry disks) or membranes that are brought in to equilibrium with the environment.
The high air entry disks, which are designated according to the air entry pressure they can
withstand when saturated, are used as an interface between the soil specimen and a
suction measuring system. The high air entry disks are used in both field and laboratory
measurements.
In the laboratory, a common method for determining the SWCC is the use of a
pressure plate (or a membrane) extractor, which uses the principle of axis translation in
determining the matric suction of soils. The axis translation principal was first
introduced by Hilf in 1956 and states that matric suction of soils increases as ambient
pressure increases such that their difference is constant. In other words, in a closed
system containing an unsaturated specimen, the difference between the ambient pressure
of the closed system and the negative pressure in the soil is constant, regardless of the
ambient pressure of the system. The axis translation technique, therefore, translates the
reference point for the pore water pressure from standard atmospheric conditions to a
final air pressure in the closed system. Axis translation causes the water pressure in the
closed system to not become highly negative and the problem of cavitations is prevented.
2-6
Although there are several versions of the pressure plate extractor, in its principle,
a specimen sits on top of a saturated high air entry disk in a pressure chamber, which is
kept saturated through a water compartment below it. The pressure in the chamber is
increased so that water is prevented from drawing up to the specimen from the disk. The
pressure difference between the pressure chamber and the water compartment is taken to
be the matric suction. A pressure plate extractor and a schematic cross-section through
one is shown in Figure 2-3.
(a) (b)
a) A ceramic plate extractor b) Schematic of a pressure plate extractor, cross-section
Figure 2-3 Diagram of a pressure plate extractor (after Fredlund and Rahardjo, 1993)
The pressure plate extractor is one of the most commonly used methods in
determining matric suction in the laboratory. Its range in matric suction measurement is
a function of the air entry value of the air entry disk, and is conventionally up to
1,500 kiloPascals (kPa) (Fredlund and Rahardjo, 1993).
2-7
Suction in in-situ soils is commonly measured with a tensiometer. A tensiometer
consists of a high air entry cup connected to a pressure transducer through a small tube.
The high air entry cup is filled with de-aired water and placed in soil to come into
equilibrium with its environment. At equilibrium, the water in the tensiometer is drawn
through the cup into the adjacent soil and has the same negative pressure as the
unsaturated soil, which is measured with the pressure gauge. A field tensiometer and its
schematic are shown on Figure 2-4. The pressures recorded at the ground surface must
be corrected to the elevation head corresponding to the water column in the tensiometer.
(a) A tensiometer, showing a portable gauge (b) Schematic of a tensiometer, cross-section
Figure 2-4 Diagram of a field tensiometer (after Brady et al., 1996)
Tensiometers use sealed devices and contain small water reservoirs to reduce the
possibility of cavitation. There are several types of field tensiometers such as the jet fill,
Gauge to measure tension
2-8
small tip, and quick draw tensiometers that use the same principles as discussed above
but have been improved for specific applications (Fredlund and Rahardjo, 1993).
b. Measurement of Osmotic Suction
Osmotic suction is commonly measured with what is called the filter paper
method. The principle of the operation for the filter paper method is the assumption that
the relative humidity of a filter paper, which has been brought to equilibrium with a soil
specimen in a closed system, will have the same water content as the specimen. When a
dry filter paper is suspended above a soil specimen (with or without contact in a closed
system) the filter paper will increase in water content, establishing equilibrium with the
soil. The soil suction is determined by comparing the water content of the filter paper to
a calibration curve for the filter paper, such as the one shown in Figure 2-5.
Figure 2-5 Typical filter paper calibration Curve (after McQueen and Miller,1968)
2-9
For the measurement, the filter papers are first oven dried. For a contact
measurement 3, stacked filter papers are placed directly in contact with the specimen; the
paper in the center is the one that is usually used for measurement. For a non-contact
measurement a metal ring is placed between the soil surface and the paper. Theoretically,
the equilibrium water content on the paper in contact with the soil corresponds to matric
suction, and the water content with no contact corresponds to total suction. The system is
allowed to equilibrate for a minimum of 7 days. At the end the water content on the
paper is measured by weighing (Fredlund and Rahardjo, 1993).
The laboratory measurement of soil suction is still a developing field since
improvements of the conventional methods are needed to speed the process of
measurement. Ray et al. (1995) suggested a volume-controlled suction test based on the
axis translation principle to measure soil suction continuously and faster. Toker et al.
(2004) suggest a new technique that combines the use of a tensiometer with a laboratory
balance, to speed the testing process and obtain continuous SWCC curves from one
specimen. They conclude that the new method is several times faster and represents the
SWCC for a drying curve better than conventional measurement systems.
2.2.2 Best-Fit Curves to Measured Water Content vs. Suction Data
There have been many studies to best fit the water content versus suction data
obtained in the laboratory to a smooth curve (Brooks and Corey, 1964; McKee and Bumb
1984, 1987; Gardner 1956; van Genuchten 1980, Fredlund and Xing 1994). In this thesis
a general understanding for the best fit models provided in SEEP/W, i.e. the models by
2-10
Fredlund and Xing (1994) and by Van Genuchten (1980), are described as they will be
used in determining the SWCC for the soils in the case study.
The model by Van Genuchten (1980) describes the relationship between
volumetric water content and suction as:
where, Θ is the dimensionless volumetric water content, Ψ is negative pore pressure, θs
and θr are the saturated and residual values of the volumetric soil water content,
respectively, and θw.is the volumetric water content.
The model by Fredlund and Xing (1994) describes the same relationship with a
modification to the Van Genuchten (1980) model, as:
where, e is the base of the natural logarithm (2.718). The parameters a, n, and m in
Equations 2-4 and 2-5 are fitting parameters, where “a” is closely related to the air entry
value and has units of kPa; “m” is related to the residual water content, and “n” is related
to the slope of the SWCC. The effects of the a, n and m parameters in curve fitting for
the Fredlund and Xing (1994) and Van Genuchten (1980) models are parametrically
shown and compared in Figure 2-6. The figure indicates that the effect of an increase in
m
nrs
rw
a⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢
⎣
⎡
⎟⎠⎞
⎜⎝⎛ Ψ
+
=−−
=Θ
1
1θθθθ
m
nrs
rw
ae
⎥⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢⎢
⎣
⎡
⎟⎠⎞
⎜⎝⎛ Ψ
+
=−−
=Θ
]ln[
1θθθθ
Equation (2-4)
Equation (2-5)
2-11
the parameter value is the same for both models, where an increase in the value of ‘a’
shifts the curve to the right, an increase in the value of ‘n’ increases the steepness of the
curves, and an increase in the value of ‘m’ shifts the bottom end of the curve to lower
suctions. However, the pivot point for each parameter is different between the two
models. When the SWCCs are compared between the two models, Figure 2-6 indicates
that the Van Genuchten (1980) model generally results in steeper curves, than the
Fredlund and Xing (1994) model.
2-12
0.0
0.2
0.4
0.6
0.8
1.0
0 1 10 100 1000 10000
Suction (kPa)
Nor
mal
ized
Wat
er C
onte
nt,
θw/θ
s
a=1 kPaa=10 kPaa=100 kPa
0.0
0.2
0.4
0.6
0.8
1.0
0 1 10 100 1000 10000
Suction (kPa)
Nor
mal
ized
Wat
er C
onte
nt,
θw/θ
s
a=1 kPaa=10 kPaa=100 kPa
0.0
0.2
0.4
0.6
0.8
1.0
0 1 10 100 1000 10000
Suction (kPa)
Nor
mal
ized
Wat
er C
onte
nt,
θw/θ
s
n=1n=2n=4
0.0
0.2
0.4
0.6
0.8
1.0
0 1 10 100 1000 10000
Suction (kPa)
Nor
mal
ized
Wat
er C
onte
nt,
θw/θ
s
n=1n=2n=4
0.0
0.2
0.4
0.6
0.8
1.0
0 1 10 100 1000 10000
Suction (kPa)
Nor
mal
ized
Wat
er C
onte
nt,
θw/θ
s
m=1m=2m=4
0.0
0.2
0.4
0.6
0.8
1.0
0 1 10 100 1000 10000
Suction (kPa)
Nor
mal
ized
Wat
er C
onte
nt,
θw/θ
s
m=1m=2m=4
a) Fredlund & Xing (1994) model b) Van Genuchten (1980) model
Figure 2-6 Comparison of the effect of a, n, and m fitting parameters on the shape of the SWCC
a = 100 n = 2
n = 2 m = 1
a = 100 m = 1
a = 100 m = 1
n = 2 m = 1
a = 100 n = 2
2-13
Fredlund and Xing (1994) also incorporate a correction factor to the model
described in Equation 2-5 to prevent the SWCC from becoming asymptotic at high
suction values, by forcing the function to have zero water content at 106 kPa suction, a
value that was determined experimentally. The Correction Factor, CΨ, is defined as:
)}10000001ln(/)1{ln(1rr CC
C +Ψ
+−=Ψ Equation (2.6)
where, Cr is a constant related to the matric suction corresponding to the residual water
content, and is generally in the range of 1,500 to 3,000 kPa. Figures 2-7 and 2-8 show a
direct comparison of the curves fitted with the Van Genuchten (1980) and 'corrected'
Fredlund and Xing (1994) models.
0.0
0.2
0.4
0.6
0.8
1.0
0 1 10 100 1000 10000 100000 1000000
Suction (kPa)
Norm
alize
d W
ate
r C
on
ten
t (θ
w/
θs)
n,m constant; a=10; Fredlund & Xing (1994)
n,m constant; a=10; Van Genuchten (1980)
a,m constant; n=1; Fredlund & Xing (1994)
a,m constant; n=1; Van Genucthen (1980)
a,n constant; m=1; Fredlund & Xing (1994)
a,n constant; m=1; Van Genuchten (1980)
Figure 2-7 Comparison of SWCCs best-fit with the Van Genuchten (1980) and Fredlund and Xing (1994) models.
2-14
Figure 2-8 Comparison of laboratory data with SWCCs best-fit with the Van Genuchten (1980) and Fredlund and Xing (1994) models with laboratory data (after Sillers and Fredlund, 2001)
2.2.3 Estimation of the SWCC
The measurement of soil suction and the corresponding development of a soil
water characteristic curve is a very long process since each point on the curve is
determined separately. Since the measurement of the SWCC is difficult and time
consuming, several empirical models exist that estimate the SWCC based on the grain
size distribution of the soil. The two models that can be used to estimate the SWCC in
SEEP/W are briefly described below. The referenced publications or the SEEP/W
manual should be referred to for more detail on the models.
a. Estimation of SWCC based on Grain Size Distribution
SWCC for Sandy Soils:
Arya and Paris (1981) proposed the use of particle size distribution curve with a
physicoempirical approach to derive the moisture characteristic curve. To do so, the
2-15
grain size distribution curve is divided into many segments so that each segment
describes a particular particle diameter. Each particle is assumed to be spherical in shape
and that the pore space between the particles are cylindrical tubes. Once the pore volume
of soils within a particular segment is estimated based on a cylindrical tubes volume, the
total volume is divided by the section bulk volume (which is the volumetric water content
of the segment). The pore volumes are also used to determine suction by using the
equation of capillarity. The volumetric water content and suction is determined for each
segment of the grain size curve to form the SWCC.
The only input data required for this method is the grain size distribution and the
bulk density of the soil. For use of the Arya and Paris (1981) model, SEEP/W requires
the grain size analysis, but does not require the bulk density, suggesting that it is either a
constant value, or estimated otherwise. The method does not take into account the
packing density, organic matter, and aggregation of the soil into account. Arya and Paris
(1981) state that the model gives a fair estimate of the SWCC. The SEEP/W manual
states that the Arya and Paris (1981) model works well with granular soils when the
entire grain size curve is defined.
SWCCs for Silty and Clayey Soils
SEEP/W uses the methods presented by Aubertin et al. (2003) to estimate the
SWCC for silty and clayey soils. The method by Aubertin et al. (2003) is a modification
to the method presented by Kovacs (1981), and is based on basic grain size analysis
properties such as D10 (particle diameter corresponding to 10% passing) and Cu (the
2-16
uniformity coefficient, D60/D10), pore size distribution, liquid limit, pore pressure, and
void ratio.
In the Modified Kovacs model, SWCC is defined by the degree of saturation for
two parts of the SWCC: one, for water that is stored due to capillary forces, and the other
for water that remains in the pore space due to adhesion. For the determination of both
components, constant curve fitting parameters are used. The model usually provides
SWCCs that have high air entry values.
b. Estimation of SWCC based on Published Data
Although SWCCs are unique, soils with similar grain size distributions and
compaction levels have similar SWCCs. There are many publications available that have
measured SWCCs for various types of soils, which can be used to estimate the SWCC,
for a specific soil type, when site specific laboratory or field data are not available. The
SEEP/W manual states that published data for SWCCs should only be used when site
specific data are not available. The use of published SWCCs in predicting pore pressures
development and its accuracy is investigated in Chapter 5.
Sillers and Fredlund (2001) compiled published measured water content versus
suction data for 200 soils and fit the data to SWCCs using the best-fit models by Van
Genuchten (1980), Gardner (1956), Brooks and Corey (1964), Brutsaert (1966), McKee
and Bumb (1987), and Fredlund and Xing (1994). Since SEEP/W only uses the Fredlund
and Xing (1994) and Van Genuchten (1980) models for curve fitting, the data provided
for the other best-fit models is not be considered further in this study. Sillers and
2-17
Fredlund (2001) present the average, median, and the standard deviation statistics of the
(a, n, and m) curve fitting parameters for the 200 soil samples based the soil type,
classified using the USDA soil classification system. They provide the SWCC fitting
parameters for 8 soil types (clay, clay loam, loam, loamy sand, sand, silt, silty loam, and
sandy loam) based on the relative percent of sand, silt and clay in the soil. It should be
noted that the fitting parameters provided for both models (and not only the model by
Fredlund and Xing, 1994), incorporate the Correction Factor as proposed by Fredlund
and Xing (1994), where the residual water content suction (Cr) was defined as 3,000 kPa
(Equation 2-6). Sillers and Fredlund (2001) specify that the fitting parameters provide an
estimate, and a reasonable range for the SWCC. The Sillers and Fredlund (2001) fitting
parameters for SWCCs are discussed in greater detail in Section 5.4.
2.3 Permeability Functions
As soil water content decreases, water flow between pores becomes discontinuous
and permeability through the soil decreases. The permeability function, which is the
representation of the decrease in soil permeability with increasing suction, can be
measured directly or estimated based on the SWCC. A general comparison of the shapes
of a SWCC and the permeability function for a silty soil is shown in Figure 2-9.
2-18
Figure 2-9 Typical SWCC and permeability function for a silty soil (after Fredlund et al., 1994)
The measurement of the permeability function is more involved than the
measurement of the SWCC, thus it is convenient to be able to estimate the function from
the SWCC. The constitutive models in SEEP/W that estimate the permeability function
(hereafter K function) are discussed below:
Green and Corey (1971) modified a model suggested by Childs and Collis-George
(1950) based on the random variation of pore size to estimate the K function, as:
Equation (2-7)
where kw is the calculated permeability for a specified water content corresponding to the
i’th interval; i, j, n and m are interval related parameters; ks/ksc is a matching factor
(measured saturated permeability/calculated saturated permeability); p is a parameter that
accounts for the interaction of pore classes (see reference or SEEP/W manual); Ts,
)([ ]2
12
2
21230 −
=
−+= Σ j
m
j
p
w
s
sc
sw hij
nT
kk
k εηγ
2-19
ε, and ηw, are the surface tension, porosity, and viscosity of water, respectively; n is the
total number of classes between i and m.
Van Genuchten (1980) used the models proposed by Burdine (1953) and by
Maulem (1976) to derive a closed-form equation for determining the K function, as:
2/
21
])(1[}])(1[)(1{
mn
mnns
w aaak
kΨ+
Ψ+Ψ−=
−−
Equation (2-8)
where, the parameters of a, n and m are the curve fitting parameters for the SWCC.
Fredlund et al. (1994) developed Equation 2-8, and introduce a logarithmic scale
to the model to avoid numerical difficulties. They define the K function as:
where b is ln (1,000,000), a is the fitting parameter in Equation 2-5, θ’ is the derivative of
Equation 2-5 times the correction factor defined in Equation 2-6, and y is the dummy
variable that represents the logarithm of suction. In describing the K function estimation
model, Fredlund et al. (1994) state that the model is generally more accurate for sandy
soils than clayey soils.
Both Fredlund et al. (1994) and Green and Corey (1971) models are solved
numerically, whereas the Van Genuchten (1980) model is a closed-form expression. It
should be noted that the SEEP/W, version 5 (2002), manual states that the constitutive
})(')(
/)(')()({)ln()ln(
dyee
edye
eekk y
b
ay
sy
yb
hy
y
sw θθθ
θθθ∫∫
−Ψ−= Equation (2-9)
2-20
models that estimate K functions are estimates as they do not take into account the
compactive effort used to place the materials and the influence of cracks or fissures on
the system, and that the estimations are generally more accurate for fine granular soils
than for clayey soils.
Measured K function data can be used directly in SEEP/W. However, if the
function is to be estimated using the above constitutive models, SEEP/W requires the
definition of the saturated coefficient of permeability, and the SWCC from which the K
function should be estimated. The SWCC, as described in Section 2.2, can either be
measured and fitted to a curve using the fitting parameters a, n, and m, or estimated based
on grain size analyses. A parametric study showing the effect of using measured or
estimated hydraulic functions is conducted in Chapter 5.
3-1
3 SEEP/W NUMERICAL PERFORMANCE EVALUATION
3.1 Introduction
In a finite element model, the size of the elements or the number of nodes
included in each element can alter the solution. SEEP/W solves transient problems by
discretizing the time domain into smaller time steps where the program is specified to
make a computation. The numerical solution computed can also change depending on the
time step size used during transient analyses. For finite element model programs, it is a
general consensus that the finer the element size in a mesh and the finer the time step the
more accurate a solution will be. However, making these variables too fine may cause
numerical oscillations.
In this chapter the numerical performance of SEEP/W is evaluated prior to
conducting the detailed case study analysis. The objective of this chapter is to understand
the sensitivity of numerical solutions to mesh size, time step size and number of nodes in
an element, to understand oscillation in results, and identify possible limitations of the
program that will prevent accurate calculations of the detailed case study.
The one-directional flow finite element mesh used by Edgers and Nadim (2003)
for a Norwegian debris flow case study is used for this purpose. The effects of time step,
element size, and element type (4- vs. 8- noded elements) on the numerical solutions to
the Edgers and Nadim (2003) case study is studied. This chapter also refines their
results.
3-2
The problems of numerical oscillations and slow numerical convergence of
transient non-linear finite element analyses have been discussed by a number of authors.
Ju and Kung (1997) summarize two basic methods to formulate a mass matrix in finite
element analyses, the mass-distributed and the mass-lumped methods. The mass-
distributed method (also called the mass-consistent) has been the traditional method of
calculation since it results in more accurate solutions than the mass-lumped method.
However, for the modeling of heat or mass transfer into a system where ambient
conditions are very different than what is introduced to the system, the mass-distributed
method has been shown to cause oscillations. Ju and Kung (1997) suggest that for
numerical oscillation to be curbed in a mass-distributed method the element size of the
mesh and time step size cannot be arbitrarily reduced. They present a criterion by
Segerlind (1984) that estimates the minimum time step size that should be used for a
given element size in a one dimensional heat transfer problem. Thomas and Zhou (1997)
expand this criterion to include two-dimensional systems, with four and eight noded
elements. Thomas and Zhou (1997) suggest that for the modeling of heat transfer an
oscillatory response in the numerical solution can be overcome if two conditions are met:
1) if the temperature of an element is equal or higher than the initial temperature of the
same element, and 2) if the temperature of an element further away from the heat source
is equal to or lower than the temperature of an element closer to the heat source
(temperature is to decrease as it moves further from the heat source). Karthikeyan et al.
(2001) apply Thomas and Zhou’s (1997) findings to seepage problems. They suggest the
use of the following equations to determine the minimum time step that should be used to
curb oscillation applicable to seepage flow with non linear hydraulics.
3-3
∆t ≥L2λ2k
for 4 noded elements; Equation (3-1)
∆t ≥L2λ20k
for 8 noded elements. Equation (3-2)
where ∆t is the minimum time step needed to curb oscillation, L is the length of the
element (perpendicular to direction of flow), λ is mwγw where mw is the slope of the soil
water characteristic curve at the most extreme suction in the soil, γw is the unit weight of
water, and k is the permeability at the most extreme suction in the soil.
Pan et al. (1996) give a physical interpretation of the finite element analysis of
infiltration into unsaturated soils and compare the traditional mass-distributed and mass-
lumped methods of establishing the mass matrix for finite element solutions. They
propose two new schemes for the mass-distributed method that are always free of
oscillation.
A second issue with numerical finite element modeling is the issue of slow
convergence to a solution with element size and time step refinement. Tan et al. (2004)
show that for an unsaturated soil column with a constant 0 head boundary on one end and
a constant negative pressure on the other (constant infiltration condition), the wetting
front location changes depending on the element and time step size. Tan et al. (2004)
suggest the use of small elements and time step size, but as large as determined by the
criteria specified by Karthikeyan et al. (2001). They compare their numerical results with
a generalized analytical solution by Warrick et al. (1985). They further suggest a new
under-relaxation technique to accelerate convergence of the finite element computation.
3-4
However, this technique has not been applied to the code of the numerical program used
in this thesis (SEEP/W version 5, 2002).
SEEP/W version 5 (2002) uses the mass-lumped formulation for 3 and 4 noded
elements. It uses the mass-distributed formulation for 6 and 8 noded elements, which
causes numerical oscillations as discussed above. Based upon the earlier discussion, this
chapter investigated the effects of time step, element size, and element type (4 vs. 8-
noded elements) on the pore pressures computed by SEEP/W for the case study reported
by Edgers and Nadim (2003).
3.2 Case Study for SEEP/W Numerical Performance Analysis
Many of Norway’s steep hillsides, partly covered by glacial till and colluviums,
experience debris flows triggered by heavy rainfall, intense snowmelt, or a combination
of both. Edgers and Nadim (2003) modeled the pore pressure response at one of these
debris flows for which detailed hydrologic records existed, but only generalized soil
descriptions, were available. They used a two-dimensional soil column with one
directional flow for their SEEP/W analysis to estimate the pore pressure increase during
the rainfall event and assumed that failure is very likely if pore pressures in a normally
unsaturated zone become positive.
Based on information given in Sandersen et al. (1996) and Jorgensen (1978) on
general Norwegian subsurface soil layers they used a 2m deep soil column with pervious
soils at the top 1m and impervious soils at the bottom 1m of the soil column. The
saturated permeability of the lower soil was 4 orders of magnitude less than that of the
3-5
top soil. The soil was selected from the SEEP/W soil library to be “Well Graded #1”
based on available grain size data for Norwegian soils in the region. The SWCC and the
permeability curve for this soil are shown in Figure 3-1. The finite element mesh (FEM)
created consisted of 4-noded elements, sized 0.1m x 0.1m. The finite element mesh used
in their analysis is shown in Figure 3-2.
a) SWCC (b) K function
Figure 3-1 SWCC and permeability function for the top soil layer of the Edgers and Nadim (2003) case study
Suction0.01 0.1 1 10 100 1000
Con
duct
ivity
1e-013
1e-012
1e-011
1e-010
1e-009
1e-008
1e-007
Suction0.1 1 10 100 1000
Vol
. Wat
er C
onte
nt (x
0.0
01)
200
250
300
350
400
450
(kPa) (kPa)
3-6
Soil: Well Graded #1Sat. Conductivity: 1E-7m/s
Soil: Well Graded #1Sat. Conductivity: 1E-11m/s
0.1m x 0.1m elements
Water Level
Influx Boundary(includes seepage face review)
Distance x-1.0 -0.5 0.0 0.5 1.0 1.5
Ele
vatio
n y
-0.5
0.0
0.5
1.0
1.5
2.0
2.5
Figure 3-2 SEEP/W FEM for the Edgers and Nadim (2003) case study
Edgers and Nadim (2003) modeled the pore pressure increases for two rainfall
events. One of the rain events, for Debris Flow 5 (DF5), was chosen as the focus rain
event for this study. The measured precipitation for the storm that caused DF5 is
illustrated in Figure 3-3. The rainfall record consists of a low-intensity rainfall for a
period of approximately 36,000s (10 hours) followed by a 18,000s (5 hours) period of
almost no rain, followed by another 18,000s (5 hour) period of intense rain with a
maximum intensity of 7.2x10-6 m/sec. The debris flow occurred during this high
intensity pulse at a total elapsed time of approximately 68,400s (19 hours) from the
beginning of the storm.
(m)
3-7
Evaporation or evapotranspiration from the soil column may play an important
role in matric suction of the unsaturated zone, where both would normally decrease pore
pressures especially during the low rainfall-intensity period. Since the low rainfall-
intensity period of the rainfall record is very short, it was assumed that the effect of
evaporation or evapotranspiration in this case study are negligible.
1.0E-07
1.1E-06
2.1E-06
3.1E-06
4.1E-06
5.1E-06
6.1E-06
7.1E-06
8.1E-06
0
3600
7200
1080
0
1440
0
1800
0
2160
0
2520
0
2880
0
3240
0
3600
0
3960
0
4320
0
4680
0
5040
0
5400
0
5760
0
6120
0
6480
0
6840
0
7200
0
7560
0
Time (seconds)
Rai
nfal
l Int
ensi
ty (m
/s)
DF5 Rainfall Intensity
Figure 3-3 Rainfall record of the of the Edgers and Nadim (2003) case study
Edgers and Nadim (2003) assumed that a water table is present 2m below ground
surface (depth). Hence, the initial pore pressures in the soil column were approximately
-20kPa at the surface and linearly increased to 0 kPa at the bottom of the soil column.
Figure 3-4 demonstrates the pore pressure development in the soil column as a “snap
shot” at every 4,000s during the rain event as computed with SEEP/W and presented in
Edgers and Nadim (2003). The plot shows that pore pressures become positive only in
the top soil layer. The permeability of the bottom soil layer is too low for water to
Time for Debris Flow
3-8
infiltrate and water is forced to “back-up” into the top layer. In fact, the lower layer of
the soil column remains mostly in suction throughout the rainfall event.
0.0000e+000
4.0000e+003
8.0000e+003
1.2000e+004
1.6000e+004
2.0000e+004
2.4000e+004
2.8000e+004
3.2000e+004
3.6000e+004
4.0000e+004
4.4000e+004
4.8000e+004
5.2000e+004
5.6000e+004
6.0000e+004
6.4000e+004
6.8000e+004
7.0000e+004
Dep
th (m
)
Pressure (kPa)
0.0
0.5
1.0
1.5
2.0
-5-10-15-20 0 5 10
Figure 3-4 Pore pressure development vs. depth computed by Edgers and Nadim (2003).
The SEEP/W simulation for the above analysis was run using 0.1m, 4-noded
elements and a 1,000s time step size. Figure 3-4 shows that pore pressures in the soil
column become positive between 44,000s and 48,000s after the start of the rainfall event.
The actual debris flow occurred 68,000s after the start of the rainfall event.
The pore pressure development plot may look different than that in Figure 3-4 if a
time step size besides 1,000s, an element length besides 0.1m and more than 4-nodes is
used. The effect of these variables on the pore pressure development for this soil column
was analyzed as discussed below.
Time (seconds)
3-9
3.2.1 Time Step Size Analysis
The study by Edgers and Nadim (2003) for the 4-noded, 0.1m x 0.1m sized
elements was repeated with calculation time steps of 250, 500, 1,000, 2,000, and 4,000
seconds. The time steps were chosen arbitrarily since oscillation is not of concern for 4-
noded elements in SEEP/W (SEEP/W version 5 (2002) uses the mass-lumped
formulation for 4-noded elements). The pore pressure developments versus time plots
determined from all 5 calculations were compared at two locations in the soil column.
The two locations were selected to be immediately below the surface boundary (0.1m
depth) and immediately above the lower soil boundary (0.9m depth).
Figure 3-5(a) illustrates that at a depth of 0.9m pore pressures determined with all
5 time step sizes initially agree until about 46,000s after the start of the rainfall. After
this time, the time step affects the computed pore pressures, which increase most rapidly
for the 250s time step and most slowly for the 4,000s time step. If the pore pressures are
calculated with a 250s time step, the soil at 0.9m depth saturates 50,000s after the start of
the rainfall. If the pore pressures are calculated with a 4,000s time step, the soil saturates
56,000s after the start of the rainfall, a 6,000s (~2 hour) difference. All 5 of the pressure
versus time curves ultimately reach the same pressure, which is the hydrostatic pressure
at saturation. A similar trend of increased rate of pore pressure with decreasing time step
is also observed at a depth of 0.1m depth as shown in Figure 3-5 (b). At 0.1m depth the
initial pressure increase is more or less similar for all time steps until approximately
40,000s after the start of the rainfall. Just as at 0.9m depth, at the 0.1m depth if the pore
pressures are calculated with a 250s time step, the soil reaches hydrostatic pressures
3-10
50,000s after the start of the rainfall; if they are calculated with a 4,000s time step, the
soil saturates 56,000s after the start of the rainfall. Note also that at 0.1m depth, as
shown in Figure 3-5(b) inset, pore pressures decrease slightly before the high rate of pore
pressure increase. This “drying” period coincides with the start of the period where the
rainfall intensity is very low (40,000s); a similar behavior was not computed at 0.9m
depth. This difference in pore pressure development at the two depths can be explained
by the presence of an impervious soil layer at 1m depth. Accordingly, as shown in Figure
3-5, the rate of pore pressure increase is highest where the rainfall intensity is lowest,
between 40,000s and 54,000s (Figure 3-3). This is counterintuitive but occurs because
the soil column needs a certain cumulative amount of water to saturate, and reaches
saturation whether the rainfall intensity is high or low. At a critical time, after enough
precipitation has infiltrated to the soil column, water accumulates in the top soil layer,
above the impervious layer, saturating the top layer and creating a rapid increase in pore
pressures. As the time of the rapid saturation the soils at 0.1m depth have time to “dry”
before the entire layer is saturated.
3-11
Pore Pressure Development 0.9m bgs
-12.0
-8.0
-4.0
0.0
4.0
8.0
0 10000 20000 30000 40000 50000 60000 70000
Time (s)
Pres
sure
(kPa
)
Time Step: 250sTime Step: 500sTime Step: 1000sTime Step: 2000sTime Step: 4000s
Pore Pressure Development 0.1m bgs
-20.0
-16.0
-12.0
-8.0
-4.0
0.0
4.0
0 10000 20000 30000 40000 50000 60000 70000
Time (s)
Pres
sure
(kPa
)
Time Step: 250sTime Step: 500sTime Step: 1000sTime Step: 2000sTime Step: 4000s
a) 0.9m depth b) 0.1m depth (inset: pore pressures between 35,000 and 60,000s, magnified)
Figure 3-5 Effect of time step size on computed pore pressures versus time
-1.2
-0.8
-0.4
0.0
0.4
0.8
1.2
35000 40000 45000 50000 55000 60000
Time (s)
Pre
ssur
e (k
Pa)
(b)
(a)
3-12
The effects of time step on the computed pore pressures are also shown in Figure
3-6, which plots the computed pore pressures vs. depth at 46,000s, 48,000s, and 50,000s.
During this period of rapid change the computed pore pressures diverge, with the greatest
differences occurring for the larger time steps (note that the results for time steps size
4,000s could not be included in the 46,000 and 50,000s plots since they are only
calculated for times that are multiples of 4,000). As shown, when a 250s time step is
used, pore pressures in the top soil layer are nearing hydrostatic pressures, and when a
4,000s time step is used, the pore pressures are mostly negative. Soon after, however,
pore pressures calculated by all time steps merge again as the ultimate hydrostatic
pressure is reached. Figures 3-5 and 3-6 also show that as the time steps are reduced, the
incremental effects become smaller and in fact suggest that the computations are
converging to a stable solution.
3-13
Elapsed Time = 46,000 seconds
0.0
0.5
1.0
1.5
2.0
-10.0 -8.0 -6.0 -4.0 -2.0 0.0 2.0 4.0 6.0 8.0 10.0
Pressure (kPa)
Dep
th (m
)
Time Step: 250sTime Step: 500sTime Step: 1000sTime Step: 2000s
a) Time = 46,000s b) Time = 48,000s c) Time = 50,000s
Figure 3-6 Effect of time step size on computed pore pressures versus depth
Elapsed Time = 48,000 seconds
0.0
0.5
1.0
1.5
2.0
-10.0 -8.0 -6.0 -4.0 -2.0 0.0 2.0 4.0 6.0 8.0 10.0
Pressure (kPa)
Dep
th (m
)
Time Step: 250sTime Step: 500sTime Step: 1000sTime Step: 2000sTime Step: 4000s
Pore Pressures at 50,000 second
0.0
0.5
1.0
1.5
2.0
-10.0 -8.0 -6.0 -4.0 -2.0 0.0 2.0 4.0 6.0 8.0 10.0
Pressure (kPa)
Dep
th (m
)
Time Step: 250sTime Step: 500sTime Step: 1000sTime Step: 2000s
(b)
(a)
(c)
3-14
The difference in the rate of pore pressure increase between the times of 46,000s
and 56,000s when different time steps are used may be due to the fact that the actual
amount of rainfall intensity modeled differs with the calculation time step size, where a
refined time step follows the actual rainfall curve more closely. Figure 3-7 compares the
actual rainfall intensity with the rainfall intensities modeled if a 1,000, 2,000 or a 4,000s
time step is used (250 and 500s time steps follow the actual rainfall intensity very closely
and are not shown for clarity). It is evident from Figure 3-7 that, as the time step size
increases, the amount of rainfall actually modeled deviates from the actual rainfall event.
To confirm whether this difference in rainfall intensity modeling relates to the difference
in the rate of pore pressure increase between time steps, the same analysis was conducted
for a constant intensity rainfall event. The analysis showed that the difference in
computed pore pressures still exists; the rate of pore pressure increase varies with the
time step size used. Accordingly, it is concluded that the difference is due to numerical
issues.
0.0E+00
1.0E-06
2.0E-06
3.0E-06
4.0E-06
5.0E-06
6.0E-06
7.0E-06
8.0E-06
0 10000 20000 30000 40000 50000 60000 70000
Time (s)
Flow
Rat
e (m
/s)
Actual Time Input (3600s)Time Step = 1000sTime Step = 2000sTime Step = 4000s
Figure 3-7 Effect of time step size on modeled rainfall intensity
3-15
As mentioned previously, the solution obtained by using a refined time step size is
generally more accurate. To verify that the solution given by the 250s time step is more
accurate than the other time steps an attempt was made to estimate the amount of water
needed to saturate the soil column. This was accomplished by comparing the volume of
water needed to saturate the system with the volume of water entering the system from
the rainstorm. The volume needed to saturate the system was calculated from the change
in the volumetric water content of the soil before and after the rainstorm. Since
volumetric water content (θ) is described as:
T
w
VV
=θ Equation (3-3)
where Vw is the volume of water in the system and VT is the total volume of the system,
the amount of water to saturate the system can be calculated by:
Tw VV ×∆=∆ θ Equation (3-4)
where ∆Vw is the change in volume of water in the system from initial condition to
saturation, ∆θ is the change in volumetric water content. The initial water content in the
soil column was determined from a steady state run of SEEP/W and the final saturated
water content in the soil column is the water content at the end of the rainfall event.
Accordingly, the increase in the volume of water in the soil column was calculated to be
approximately 0.0144 m3. The change is graphically shown in Figure 3-8.
3-16
0.0
0.5
1.0
1.5
2.0
0.385 0.390 0.395 0.400 0.405 0.410 0.415
Volumetric Water Content
Ele
vatio
n (m
)
Initial Water Content Final Water Content
Figure 3-8 Change in volumetric water content in the FEM with depth and time
The total amount of water entering the system was calculated from the nodal
boundary flux into the system. Freeze and Cherry (1979) explain that infiltration rate
may initially be equal to the rainfall intensity, but it then decreases asymptotically toward
the saturated permeability as the soil approaches saturation at the surface (Figure 3-9).
The volume of water entering the system was determined for all time steps throughout the
rainfall event. Table 3-1 summarizes the volume of rain entering the system for all time
steps. As shown, the volume of water entering the system is higher than the actual
amount of water needed to saturate the soil for the 500s and higher time steps. Table 3-1
shows that the computation conducted with the smallest time step coincided best with the
actual amount of water needed to saturate the soil, reaffirming the fact that the smallest
time step provides the most accurate result.
3-17
Figure 3-9 illustrates the surface flux of the system. As shown, there is a sharp
decrease in the rate of infiltration into the soil approximately 48,000s after the start of
rainfall confirming that the top soil layer becomes saturated as infiltration is ceased.
1.0E-11
1.0E-08
2.0E-08
3.0E-08
4.0E-08
5.0E-08
6.0E-08
7.0E-08
8.0E-08
0 10000 20000 30000 40000 50000 60000 70000
Time (s)
Bou
ndar
y Fl
ux (m
/s)
Time Step : 250sTime Step : 500sTime Step : 1000sTime Step : 2000sTime Step : 4000s
Figure 3-9 Rate of infiltration into the soil column at the surface.
Table 3-1 Summary of volume of water infiltrating the FEM due to rainfall
Time Step Total Water Volume Time to Saturation
seconds m3 seconds250 0.0144 49,000500 0.0145 49,0001000 0.0147 50,0002000 0.0147 52,0004000 0.0148 56,000
Element size = 0.1mx0.1m Element type = 4-nodes
3-18
3.2.2 Element Type Study - Effect of 8- versus 4-Noded Elements
The SEEP/W help manual explains that it uses the Gaussian numerical integration
method for the mass matrix, where the integrals are sampled at specifically defined points
in the elements and then summed for all the points. The number of points in an element
increases as the number of nodes increases. Therefore, for conditions where the variables
are changing rapidly, such as the unsaturated zone, it may be better to use an element
with higher number of nodes (8-noded elements rather than 4-noded elements) and
therefore higher number of integration points. This however, may cause numerical
oscillations as SEEP/W uses the mass-distributed method for 8-noded elements.
The analysis conducted with 4-noded elements showed no oscillation at the
wetting front. Moreover, the wetting front appears to slowly converge to a solution as the
time step is refined. From the above information one can assume that the use of the 250s
time step would provide an accurate numerical solution. However, when the above
calculations were repeated for the same soil column, but for a mesh that consists of 8-
noded elements, the pore pressure versus time curve converges to a different solution. As
mentioned previously, 8-noded elements use more integration points in an element,
therefore giving a more accurate solution, but suffer from oscillations. Figure 3-10
illustrates the difference in pore pressure development at 0.9m depth and 0.1m depth
when 8-noded versus 4-noded elements are used. The plots have been magnified to
emphasize the period of most rapid pore pressure change. The trends of the curves are
very similar to that shown in Figure 3-5 as such the 500s, 1,000s and 2,000s time step
plots were omitted from Figure 3-10 for clarity (the plots for 500s, 1,000s, and 2,000s fall
3-19
between the 250s and 4,000s plots). Table 3-2 summarizes the time to saturation for all
time steps calculated using 4-noded or 8-noded elements. As shown, if 8-noded elements
are used the time for saturation is approximately 3,000 to 4,000s shorter than if 4-noded
elements were used.
Table 3-2 Summary of the effect of time step size and element type on computed pressures
4 noded Elements
8 noded Elements
seconds seconds seconds seconds250 49,000 46,000 3,000500 49,000 46,000 3,0001000 50,000 47,000 3,0002000 52,000 48,000 4,0004000 56,000 52,000 4,000
Time to SaturationTime Step Size
Difference in Time to
Saturation
Element size = 0.1mx0.1m Depth = 0.9m
3-20
Pore Pressure Development 0.9m bgs
-8.0
-4.0
0.0
4.0
8.0
30000 35000 40000 45000 50000 55000 60000
Time (s)
Pres
sure
(kPa
)
Time Step: 250s, Nodes: 4
Time Step: 4000s, Nodes: 4
Time Step: 250s, Nodes: 8
Time Step: 4000s, Nodes: 8
Pore Pressure Development 0.1m bgs
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
30000 35000 40000 45000 50000 55000 60000
Time (s)
Pres
sure
(kPa
)
Time Step: 250s, Nodes: 4Time Step: 4000s, Nodes: 4
Time Step: 250s, Nodes: 8Time Step: 4000s, Nodes: 8
a) at 0.9m depth b) at 0.1m depth
Figure 3-10 Effect of time step size and element type on computed pore pressures versus time
(b)
(a)
3-21
The vulnerability of the 8-noded element mesh to numerical oscillations was then
evaluated by applying the criteria of Karthikeyan et al. (2001), Equation 3-2, for a 0.1m
square element mesh to determine the minimum time step necessary to prevent
oscillations at the wetting front. The permeability and the slope of the SWCC
(Figure 3-1) were determined at -20kPa, the largest suction in this computation.
Accordingly, the minimum time step to avoid numerical oscillations for an 8-noded
element of 0.1m length was determined to be 81s for the upper layer. Therefore, the time
steps that have been used so far were also used for the 8-noded element mesh.
Figure 3-11 illustrates the pore pressure development in the soil column computed
with the 8 noded element mesh for the 250, 500, 1,000, and 2,000s time steps (similar to
that in Figure 3-6). As shown, the wetting front in the top layer does not oscillate.
However there is oscillation at the interface of the two soil layers. Since the conductivity
of the bottom layer is 4 orders of magnitude lower than the upper soil, the minimum time
step to avoid oscillation in this layer is 224.8 hours (809,280s) based on the Karthikeyan
(2001) criterion, a time step much larger than the time steps used in this study, suggesting
oscillation problems for the layer.
Several additional simulations were run with time steps lower than that as
suggested by the Karthikeyan et al. (2001) criterion for the top soil layer. The results
show no oscillation in the top layer even when the time step used is reduced to 50s.
Oscillation was finally observed when the time step was reduced to 50s and the initial
suction in the soil column was arbitrarily adjusted to a constant –80kPa throughout the
soil column. As shown in Figure 3-12, for this condition oscillation occurred in the top
3-22
layer, reaffirming the fact that when small time steps are used, oscillations are more
prominent for very dry initial soil conditions.
Elapsed Time = 46,000 seconds
0.0
0.5
1.0
1.5
2.0
-15.0 -10.0 -5.0 0.0 5.0 10.0 15.0
Pressure (kPa)
Dep
th (m
)
Time Step: 250s, Nodes: 8
Time Step: 500s, Nodes: 8
Time Step: 1000s, Nodes: 8
Time Step: 2000s, Nodes: 8
Figure 3-11 Computed pore pressures versus depth 46,000s after start of rainfall – effect of 8-noded elements on computed pore pressures
4.0000e+003
8.0000e+003
1.2000e+004
2.4000e+004
3.6000e+004
4.2000e+004
4.5000e+004
4.8000e+004
5.1000e+004
6.0000e+004
6.8000e+004
Dep
th (m
)
Pressure (kPa)
0.0
0.5
1.0
1.5
2.0
-20-40-60-80-100 0
Figure 3-12 Pore pressures development computed with a 50s time step at very dry initial conditions
Minor oscillations
3-23
The time step size analysis and the comparison of the 4-noded and 8-noded
element mesh has shown that that as the time step is refined and the number of nodes in
the element are increased, the time to saturation of the soil column decreases. The size of
each element of the finite element mesh is reduced next to determine its effect on the pore
pressure development solution.
3.2.3 Element Size Analysis
Two new soil column meshes were created with element sizes 0.02m x 0.02m,
and 0.05m x 0.05m. The above analyses were repeated for the 250s, 500s, 1,000s and
2,000s time step sizes to see how pore pressure development changes with element size
refinement of the finite element mesh. The 4,000s time step was dropped from
evaluation since the modeling results so far have shown that this time step provided
erroneous results compared to the other time steps. This analysis was conducted on both
4-noded and 8-noded element meshes.
Figure 3-13 compares the difference in pore pressure development at 0.9m depth
and 0.1m depth when different element sizes are used for 250s and 2,000s time steps. As
before, the plots have been magnified to emphasize the period of most rapid pore
pressure change. The overall pore pressure increase for the location is shown in the
insets of Figure 3-13. The Figure shows that as the element size is decreased from 0.1m
to 0.05m to 0.02m, the time to saturation of the soil column becomes shorter. When the
250s time step is used for example, the time to saturation with an 0.1x0.1m element sized
mesh is approximately 49,000s, for the 0.05m element size the time is approximately
47,000s and for the 0.02m element size the time is approximately 46,000s. Table 3-3
3-24
summarizes the time to saturation for all time steps and element sizes used. The table
shows that as the element size is decreased from 0.1m to 0.05m the reduction in time to
saturation is 2000s for all time steps. When the element size is decreased from 0.05m to
0.02m however, the time to saturation is generally only 1,000s shorter. Therefore, the
solution starts to converge to a solution as the element size is being reduced. The overall
behavior of the curves for the different time steps is similar, where the rate of pore
pressure increase is faster if a smaller time step is used. One of the major differences
between the results of computations conducted with different element sized meshes, seen
in Figure 3-13(b), is that for the mesh with 0.02m elements pore pressures continuously
increase without any “drying” at the top surface, whereas when the 0.1m element size is
used there was a distinct “drying” period observed.
Table 3-3 Summary of the effect of time step size and element size on computed pressures
0.1mx0.1m 0.05mx0.05m 0.02mx0.02m 0.1m to 0.05m 0.05m to 0.02m
250 49,000 47,000 46,000 2,000 1,000500 49,000 47,000 46,000 2,000 1,0001000 50,000 48,000 47,000 2,000 1,0002000 52,000 50,000 48,000 2,000 2,000
Time to Saturation (seconds)Time Step Size (seconds)
Difference in Time to Saturation (seconds)
Element type = 4-nodes Depth = 0.9m
3-25
Pore Pressure Development 0.9m bgs
-8.0
-4.0
0.0
4.0
8.0
40000 42000 44000 46000 48000 50000 52000 54000
Time (s)
Pres
sure
(kPa
)
Element: 0.1m, Time Step: 250sElement: 0.1m, Time Step: 2000sElement: 0.05m, Time Step: 250sElement: 0.05m, Time Step: 2000sElement: 0.02m, Time Step: 250sElement: 0.02m, Time Step: 2000s
(a)
Pore Pressure Development 0.1m bgs
-2.0
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
38000 40000 42000 44000 46000 48000 50000 52000
Time (s)
Pres
sure
(kPa
)
Element: 0.1m, Time Step: 250sElement: 0.1m, Time Step: 2000sElement: 0.05m, Time Step: 250sElement: 0.05m, Time Step: 2000sElement: 0.02m, Time Step: 250sElement: 0.02m, Time Step: 2000s
(b)
a) At 0.9m depth, b) at 0.1m depth (insets: entire computation period)
Figure 3-13 Effect of element size on computed pore pressures vs. time
Pore Pressure Development 0.9m bgs
-12.0
-8.0
-4.0
0.0
4.0
8.0
0 10000 20000 30000 40000 50000 60000 70000
Time (s)
Pres
sure
(kP
a)
Pore Pressure Development 0.1m bgs
-20.0
-15.0
-10.0
-5.0
0.00 10000 20000 30000 40000 50000 60000 70000
Time (s)
Pres
sure
(kPa
)
3-26
Figure 3-14 compares the computed results when 4- and 8-nodded elements in
0.1m, 0.05m, and 0.02m element sized meshes are solved with 250 and 1000s time steps.
Table 3-4 summarizes the time to saturation for the time steps shown in Figure 3-14. It
should be noted that the computation time for the 8-noded, 0.02x0.02m element sized
mesh and a 250s time step is approximately 1.5 hours or longer whereas the computation
time for all other analyses were less than 30 to 40 minutes. When the computation for the
0.02m, 8-noded element mesh and 250s time step was underway the program had
difficulty computing as evident from convergence to large residuals on the “residual
versus iteration” plots observed during computation. The computed results for the
analysis showed that the time to saturation was only slightly shorter as compared to the
analysis computed with a 1,000s time step. Thus, the extra time spent on a longer
computation time did not provide a corresponding higher level of accuracy to the
solution.
Table 3-4 Summary of the effect of time step size, element type, and element size on computed pressures
Time Step Size Element Size Time to Saturation
seconds m seconds250 0.1x0.1 4 49,000250 0.05x0.05 4 47,0001000 0.02x0.02 4 47,000250 0.1x0.1 8 46,000250 0.05x0.05 8 45,0001000 0.02x0.02 8 46,000
Number of Nodes
3-27
Pore Pressure Development 0.9m bgs
-8.0
-4.0
0.0
4.0
8.0
12.0
38000 40000 42000 44000 46000 48000 50000 52000
Time (s)
Pres
sure
(kP
a)
Element: 0.1m, Time Step: 250s, Nodes: 4
Element: 0.1m, Time Step: 250s, Nodes: 8
Element: 0.05m, Time Step250s, Nodes: 4
Element: 0.05m, Time Step: 250s, Nodes: 8
Element: 0.02m, Time Step: 1000s, Nodes: 4
Element: 0.02m, Time Step: 1000s, Nodes: 8
Pore Pressure Development 0.1m bgs
-2.0
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
38000 40000 42000 44000 46000 48000 50000 52000
Time (s)
Pres
sure
(kPa
)
Element: 0.1m, Time Step: 250s, Nodes: 4
Element: 0.1m, Time Step: 250s, Nodes:8
Element: 0.1m, Time Step: 250s, Nodes: 4
Element: 0.05m, Time Step: 250s, Nodes: 8
Element: 0.02m, Time Step: 1000s, Nodes: 4
Element: 0.02m, Time Step: 1000s, Nodes: 8
(b)
a) at 0.9m depth, b) at 0.1m depth (insets: entire computation period)
Figure 3-14 Effect of time step size, element type, and element size on computed pore pressures vs. time
Pore Pressure Development 0.9m bgs
-12.0
-8.0
-4.0
0.0
4.0
8.0
12.0
0 10000 20000 30000 40000 50000 60000 70000
Time (s)Pr
essu
re (k
Pa)
Pore Pressure Development 0.1m bgs
-20.0
-15.0
-10.0
-5.0
0.00 10000 20000 30000 40000 50000 60000 70000
Time (s)
Pres
sure
(kPa
)
(b)
(a)
3-28
Table 3-4 and Figure 3-14 show that the use of 8-noded elements instead of 4-
noded elements again slightly shifts the time to saturation to an earlier time, but at the
cost of greatly increased computer time. The difference in the curves computed with the
0.02x0.02m element sized, 4-noded mesh, and a 1,000s time step, and the 0.1x0.1m
element sized, 8-noded mesh and a 250s time step is not large enough to justify the
computation time for the smaller mesh. As discussed earlier, reduced element size and
time steps with 4-noded elements have much greater effect. Therefore, the use of the
smallest time step and element size with 4-noded elements was used for the revised
analysis.
3.3 Revised Edgers and Nadim (2003) Case Study Analysis
Edgers and Nadim (2003) observed that the presence of a deep low conductivity
layer and the antecedent rainfall were important factors in the development of positive
pore water pressures in the case study they presented. If either or both of these factors are
not present, then the potential for the loss of soil suction and the development of positive
pore water pressures is greatly reduced. They observed that the time computed for the
development of full hydrostatic pore water pressures in the upper layer, approximately
50,000s, showed reasonable agreement with the observed time to failure for the debris
flow, approximately 68,400s (19 hours). However, their initial analyses used a time step
of 1,000s and an element size of 0.1 m, with no time step and element size studies as
described in this paper.
The Edgers and Nadim (2003) computations were revised using a time step of
250s and 0.02m square 4-noded elements. Figure 3-13 showed the variation of computed
3-29
pore pressures vs. time for this revised analysis. The revised analysis computes a time of
approximately 46,000s for the development of hydrostatic pressures in the upper 1m
layer, compared to 50,000s initially computed by Edgers and Nadim (2003). The
computations of this study are numerically more accurate than the computations of
Edgers and Nadim (2003), even though their computed time for hydrostatic pressure of
50,000s, quite fortuitously, agrees better with the observed time to failure of 68,400s.
The analysis can be further refined so that the upper layer develops hydrostatic
pressures at a time closer to the observed time of the debris flow. This can be
accomplished by decreasing the permeability of the upper soil layer slightly to
7.0x10-8m/s from 1x10-7m/s. This 30% reduction, simply arrived at by trial and error, is
small compared to the range of uncertainty in permeability that could be expected,
considering, for example, coefficients of variation summarized by Duncan (2000),
especially given the lack of detailed subsurface information and testing. The reduced
permeability produces the pore pressure vs. time and depth variations shown in Figures
3-16 and 3-17, respectively. These figures show that when a permeability 30% lower
than that used by Edgers and Nadim (2003) is used, for the same finite element mesh,
large positive pore pressures develop in the upper layer at about 70,000s, which agrees
very well with the observed time of the debris flow.
3-30
-12.0
-8.0
-4.0
0.0
4.0
8.0
0 10000 20000 30000 40000 50000 60000 70000
Time (s)
Pre
ssur
e (k
Pa)
Edgers and Nadim (2003): Element Size: 0.1m square Time Step Size: 1000s
Revised - Element Size, Time Step Element Size: 0.02m square Time Step Size: 250s
Revised - 30% lower Hyd. Conductivity Element Size: 0.02m square Time Step Size: 250s
Figure 3-15 Effect of permeability on computed pore pressures vs. time.
0.0000e+0004.0000e+0038.0000e+0031.2000e+0041.6000e+0042.0000e+0042.4000e+0042.8000e+0043.2000e+0043.6000e+0044.0000e+0044.4000e+0044.8000e+0045.2000e+0045.6000e+0046.0000e+0046.4000e+0046.8000e+004
Pressure (kPa)
0.0
0.5
1.0
1.5
2.0
-5-10-15-20 0 5 10
(Element Size: 0.02m square, Time Step: 250s, Element Nodes: 4) Figure 3-16 Effect of permeability on computed pore pressure vs. depth.
Time in seconds
Ele
vatio
n (m
)
Element Nodes: 4
3-31
This suggests that, for this case study, uncertainty in the assumed permeability
may be more important than inaccuracies caused by numerical oscillations and slow or
inaccurate convergence. Based on the above results, it is noted that time steps and
element sizes for general use other than to note that site specific time step and element
size studies should be conducted for each case study, in order to achieve accurate
numerical results.
4-1
4 Detailed Case Study – Singapore NTU Slope
4.1 Introduction
In this chapter, variations in in-situ soil pore pressures, as observed during a
detailed field instrumentation study are modeled using the SEEP/W computer program.
As a follow up to the study described in Chapter 3 of this thesis, a two-dimensional finite
element soil column with one directional flow is used. Even though a one-directional
infiltration model is highly idealized as it neglects any lateral seepage, it is a simpler
computation than a two-dimensional model and provides a good approximation of the
pore pressure response. Given that a small change in permeability of soils makes a
significant difference in modeled pore pressure responses (see Chapter 3), it is prudent to
use a simple computation to approximate in-situ behavior. The objective of this chapter
is to evaluate the overall accuracy of computer modeling pore pressures observed during
a detailed field study using measured soil properties, and detail of site information needed
for the process. It should be noted that in this thesis, pore pressures measured in-situ are
assumed to be accurate and any errors associated with field measurements are neglected.
A comprehensive literature search was conducted to find publications describing
field instrumentation studies that monitored in-situ pore pressures in soils during a rain
event. Several studies were considered and compared for the completeness of
information presented. Although many papers present measured in-site pore pressures,
few publications presented a complete set of data for a detailed computer modeling study,
including soil stratigraphy, measured SWCC and permeability functions, precipitation
and evaporation data, grain size analysis, water level elevation, etc.
4-2
After consideration, the field study conducted by Lim et al. (1996) in Singapore’s
Jurong residual soil formation was chosen as the case study for this thesis. The study
gives a clear description of the field tests conducted, and its results. Moreover, Singapore
soils are well-studied soils, which provides the opportunity of finding information not
presented in the paper, in literature. The field study conducted by Lim el al. (1996) is
described below.
4.2 Description of Field Study
Lim et al. (1996) conducted a field study to observe the variations in in-situ pore
pressures at a slope on the campus of Nanyang Technological University, Singapore
(NTU) during the period of January and February 1994. The slope in their study was
approximately 25 m long at an incline of 30 degrees, and a toe incline of 12 to 15
degrees. Lim et al. (1996) divided the slope into three 5m wide (across the slope)
sections to study the effects of different surface conditions on in-situ pore pressure
development, including: 1) a canvas covered surface (canvas placed over grass), 2) a
grass covered surface (unaltered from its natural grass surface), and 3) a bare surface
(stripped of grass and grass roots by removing the top 5 to 10 cm of topsoil). The bare
surface was not compacted after the removal of vegetation.
4.2.1 Instrumentation
Lim et al. (1996) used Jet-Fill tensiometers to measure in-situ matric suction at
four locations on each of the three sections of slope. In each section, the measuring
locations were approximately 7 to 8 m apart, downhill. Each section had one measuring
4-3
location at the top of the slope, two measuring locations on the slope, and one at the toe
of the slope. Three tensiometers were embedded at each measuring location to 0.5m,
1.0m and 1.5m below ground surface. Figure 4-1 illustrates the location and spacing of
the tensiometers in the field. Four standpipe piezometers, two screened at 3.5 and 3.7 m
depths at the top of the slope, and 2 screened at 5.3 and 5.4 m depths at the bottom of the
slope were installed at 4 corners of the study site to monitor water level measurements at
the site.
Rainfall data during the field test was monitored using a hydro logger, which was
connected to a tipping bucket rain gauge located on the top of the slope. The total
number of rain bucket tips within a 10 or 15-minute interval was counted by the logger.
4-4
(b) Plan View
Figure 4-1 Instrumentation layout of NTU slope field study (after Lim et al., 1996)
a) Section View
4-5
4.2.2 Subsurface Conditions and Soil Engineering Characteristics
Soils at the site were characterized as residual soils that decrease in fines content
with increasing depth below ground surface. A generalized subsurface profile for the site
is shown on Figure 4-2. Accordingly, subsurface layers encountered at the site, in order
of increasing depth below the ground surface, are organic silty clays, silty clays, silty
sand and bedrock. No laboratory or field tests for general soil properties were conducted
on the site soils. However, the authors present the general characteristics of NTU campus
residual soils. The authors describe the residual soils (identified as Singapore’s Jurong
formation) as soils that range from silty clay and clayey silt to clayey sand that have
liquid limits between 30 and 60%, plastic limits between 15 and 30%, and fines content
between 50 and 85%. The authors also describe that the water content and plasticity
index of the soils generally decrease with depth.
Figure 4-2 Generalized soil profile of the NTU slope (after Lim et al., 1996)
4-6
Lim et al. (1996) reference a journal article by Rahardjo et al. (1995), which
investigates the engineering characteristics of soils at two NTU campus locations, 300m
apart. The subsurface profiles for the two sites (IHPT91 and IHPT92), and the
corresponding measured water content, plasticity index, density, fines content, Standard
Penetrations Test (SPT) values and Swedish Ram Sounding Test (RST) values are shown
in Figure 4-3 and 4-4, respectively.
Lim et al. (1996) provide measured SWCCs for residual soils on the NTU campus
based on an investigation by Lim (1995). The SWCCs, which were determined for soil
samples from a site other than the field study site, are shown in Figure 4-5.
Figure 4-3 Generalized soil profile of two sites on NTU campus (after Rahardjo et al., 1995)
(a) IHPT91
(b) IHPT92
4-7
Figure 4-4 Variation of NTU campus soils properties with depth (after Rahardjo et al., 1995)
IHPT92
IHPT91
4-8
Figure 4-5 SWCC for Jurong Formation residual soils (after Lim et al., 1996)
Lim et al. (1996) conducted field permeability measurements at the top of slope
and laboratory permeability measurements on samples from depths of 1.7 to 1.9m. The
measured test results indicated a saturated coefficient of permeability of 1x10-6m/s and
1x10-9m/s for the field and laboratory tests, respectively. The methods for the laboratory
and field testing conducted were not specified in the paper. The authors attribute the 3
orders of magnitude difference between the field and laboratory measurements to the
effect of surface cracks near the ground surface, in the field.
Water levels at the site range approximately from 3m below ground surface at the
top of the slope to 5m below ground surface at the toe of the slope. The water level
measurements obtained from the four piezometers on site are shown in Figure 4-6. The
depths of the borehole measurements shown in the figure are unknown, therefore were
ignored in this study.
45 40 35 29 21 12
Volum
etric Water C
ontent, Θ (%
)
4-9
Figure 4-6 Water level measurements at the NTU slope (after Lim et al., 1996)
4.2.3 Field Monitoring Results
Figures 4-7 and 4-8 show the measured daily rainfall rate and measured daily
variation of matric suction at 0.50, 1.0m, and 1.5m depth at two measurement locations
on each of the three sections of the slope. The pore pressures shown are for measurement
locations at the crest for the slope and at the top of the slope. The pore pressures for the
lower slope and toe measuring locations were not presented.
The measured daily rainfall rate throughout the 2-month period consists of
occasional days of low to medium intensity rainfall for a period of approximately 10 days
(1 January to 10 January, 1994) followed by a 16 day period of almost no rain
(11 January to 27 January), followed by another 26 day period of rain almost every day
with a maximum intensity of 35 mm/day (28 January to 21 February), followed by a
another period of no rain for almost 6 days (22 February to 28 February).
4-10
(a) canvas covered (b) grass surface
Figure 4-7 Measured in-situ pore pressures at the canvas covered and grass surface sections of the NTU slope (after Lim et al., 1996)
Figure 4-8 Measured in-situ pore pressures at the bare surface section of the NTU slope (after Lim et al., 1996)
4-11
The measured pore pressures at 0.5m, 1.0m and 1.5m depth indicate that pressures
mostly vary near the ground surface and that the magnitude of variation with weather
conditions decreases with depth. The grass covered and bare surface sections generally
had similar patterns although the variation of suction was most significant in the bare
surfaced sections. Even the canvas covered section showed variation in matric suction
with the changing weather pattern. The figures show that suction increases during dry
weather conditions and decreases immediately after a rain event. Lim et al. (1996)
describe that suctions measured at 1.5 m depth are relatively low and at times become
positive. They suggest that a perched water table may have developed at about 1.5 m
below ground surface throughout the entire site.
4.3 Modeling of NTU Slope – Preliminary Computations
4.3.1 Mesh Set Up
Based on the description of the subsurface profile (Figure 4-2), a 4.5 m deep soil
column was used with organic silty clay at the top 1.5 m, silty clay at the middle 2.0 m,
and silty sand at the bottom 1.0 m of the soil column. Field data collected at the top of
slope of the bare surface section (measuring location P3R1) was selected for analysis in
this thesis. The location was chosen for the reason that a more complete set of suction
data exists for the location, and the bare surface minimizes the effects of
evapotranspiration of soil moisture. Even though only one of the slope sections is
modeled herein, the matric suction presented in Figures 4-7 and 4-8 generally show the
same pattern in variation.
4-12
A finite element mesh consisting of 4-noded, 0.1m square elements was created.
The computation time step was arbitrarily selected as 1800s. However a time-step and
element size analysis similar to that in Chapter 3 was conducted to refine the
computations (see Section 4.3.4). Computations were initially conducted for the time
period of 27 January, the time of the highest recorded suction, thus the start of a wetting
period, to 28 February 1994, the end of the field study. Accordingly, initial pore
pressures of -90kPa, -11kPa, and -2kPa at depths of 0.5m, 1.0m, and 1.5m below ground
surface, respectively, were assigned to the finite element mesh. The “seepage face
review” feature in SEEP/W was activated to exclude the effects of ponding of water
above the soil column. The effects of surface run-off and channeling, which would
reduce the amount of precipitation infiltrating in the soil column were ignored for the
study. Surface run-off from the slope surface is assumed to be negligible since the
average rainfall intensity in the case study is relatively low.
The groundwater level for the soil column was specified to be at 3 m below
ground surface based on data shown in Figure 4-6. Since groundwater level
measurements in piezometers C1 and C3 only show minimal changes in groundwater
elevation throughout the monitoring period, the groundwater level was fixed at elevation
135m by assigning a constant pressure head of zero (0) to that elevation. The initial pore
pressures between those elevations of known suction were estimated by linear
interpolation. The initial pore pressures were used by first running a steady state analysis
with the assigned pore pressures, and then using the results of the steady state analysis as
the initial pore pressures for the Transient analysis.
4-13
Figure 4-9(a) shows the preliminary finite element mesh, consisting of 4-noded
elements sized 0.1mx0.1m, initially used in this study based on the soil profile
information given by Lim et al. (1996). Figure 4-9(b) shows the initial pore pressures
assigned to the soil column based on pore pressures measured on 27 January 1994. The
initial pore pressures at the surface were arbitrarily assumed to be -105kPa. This
assumption was verified by comparing the computed pore pressures when a higher,
-200kPa, surface suction is used. The comparison of the results showed that the initial
pore pressures at the surface do not affect the pore pressure development.
The SWCCs used for this preliminary analysis were those presented in Figure 4-5;
for silty clays the average of the four SWCCs shown was used. Since permeability
functions for the soils were not provided, the functions were estimated from the SWCCs
using the models described in Chapter 2, i.e., by the 1) Van Genuchten (1980), 2)
Fredlund et al. (1994), and 3) the Green and Corey (1971) models. The saturated
coefficient of permeability of the organic silty clays and deeper soils (silty clays and silty
sands) were assumed to be 1x10-6m/s and 1x10-9m/s, respectively based on the results of
the field tests (1x10-6m/s), and laboratory tests conducted on soil samples from depths of
1.7 to 1.9m (1x10-9m/s) by Lim et al. (1996). As mentioned previously, Lim et al. (1996)
attribute the higher saturated permeability measured in the field test to the presence of
cracks near the ground surface. Applying a permeability of 1x10-6m/s for the organic
silty clay layer (top 1.5m) may be too general as surface cracks from de-vegetation
activities likely do not extend to a depth of 1.5m below ground surface; however, the
difference in saturated permeability coefficients between the organic silty clay and silty
clay layer may be helpful in explaining the perched water table at 1.5m depth. The
4-14
estimated permeability functions for the organic silty clay layer are shown on Figure
4-10. Note that the permeability of 1x10-9m/s assumed for the silty sand based on the
laboratory tests reported by Lim et al. (1996) may be too low. However, some very
preliminary SEEP/W runs showed that changes in permeability below the water table had
very little effect on the computed pore pressures in the upper 2m of the soil column.
The change in preliminary computed pore pressures with time at a depth of 0.5 m
are shown in Figure 4-1; the computation was run using a 1,800s time step size. The
computed pore pressures at 1.0 and 1.5m depths were omitted from Figure 4-11 for
clarity of presentation.
4-15
-2-3-4-6-8-11-20-40-60-80-90-95-100-105-105-105
Distance, m0.0 0.5 1.0 1.5 2.0
Ele
vatio
n, m
133.5
134.0
134.5
135.0
135.5
136.0
136.5
137.0
137.5
138.0
(a) Preliminary FEM (b) Initial pore pressures
Figure 4-9 Preliminary FEM and initial pore pressures for case study.
Organic Silty Clay Ksat =1x10-6 m/s K function: estimated from SWCC using the VG method. SWCC: as shown in Figure 4.5
Silty Clay Ksat =1x10-9 m/s K function: estimated from SWCC using the VG method. SWCC: as shown in Figure 4.5
Silty Sand Ksat =1x10-9 m/s K function: estimated from SWCC using the VG method. SWCC as shown in Figure 4.5
Groundwater Elevation
Initial pressure head on 27 January 1994 (kPa).
-120 -80 -40 0 40 Initial Pressure, kPa
4-16
(a) Van Genuchten (1980) (b) Fredlund et al. (1994) (c) Green & Corey (1971)
Figure 4-10 Comparison of estimated preliminary permeability functions for organic silty clays
-100.0
-80.0
-60.0
-40.0
-20.0
0.0
20.0
0 500,000 1,000,000 1,500,000 2,000,000 2,500,000 3,000,000
Time, s
Pres
sure
, kPa
SWCC: Lab. data (Lim et al., 1996); K: Estimated from SWCC using Van Genuchten (1980)
SWCC: Lab. data (Lim et al., 1996); K: Estimated from SWCC using Green & Corey (1971)
SWCC: Lab. data (Lim et al., 1996); K: Estimated from SWCC using Fredlund & Xing (1994)
Field Data, measured
Figure 4-11 Comparison of pore pressures at 0.5m depth vs. time computed using the preliminary permeability functions
Suction0.01 0.1 1 10 100 1000
Con
duct
ivity
1e-011
1e-010
1e-009
1e-008
1e-007
1e-006
Suction.01 0.1 1 10 100 1000
Suction01 0.1 1 10 100 1000
(kPa) (kPa) (kPa)
4-17
Figure 4-10 shows that all three models used to estimate the K function give
different K function curves. For the K function estimated using the Van Genuchten
(1980) model capillary saturation ends (e.g., air enters the system) at approximately
-10kPa. For the K functions estimated using the Fredlund & Xing (1994) and the Green
& Corey (1971) models, capillary saturation ends at approximately -2kPa. Furthermore,
the functions are such that at -100kPa, permeability decreases less than an order of
magnitude when Van Genuchten (1980) and Fredlund et al. (1994) models are used, and
2 orders of magnitude when the Green & Corey (1971) model is used. Both, the
Fredlund et al. (1994) and the Green & Corey (1971) models are truncated at suctions
larger than approximately 500 kPa. However, these differences in the shape of the K
function do not change the outcome of the computed pore pressures as shown in Figure
4-11; especially the computations that use the Fredlund et al. (1994) and the Van
Genuchten (1980) models look very similar. The minimal effect of the K function on the
computed pore pressures is likely due to the high air entry value of the soils, which will
be discussed detail later in this chapter. Thus, the Van Genuchten (1980) model was
selected as the model for estimating K functions in these preliminary computations.
Figure 4-12 compares the computed pore pressure development at 0.5m, 1.0m and
1.5m depths to those measured in the field. As shown, the computed pressures are
generally very similar, and do not vary with depth. Computed pore pressures become
positive within approximately the first 180,000s (2 days) and stay positive thereafter.
The computed pore pressure development versus depth is shown in Figure 4-13.
4-18
-100.0
-80.0
-60.0
-40.0
-20.0
0.0
20.0
0 500,000 1,000,000 1,500,000 2,000,000 2,500,000 3,000,000
Time, s
Pres
sure
, kPa
SWCC: Lab. data (Lim et al., 1996); K: Estimated from SWCC using Van Genuchten (1980) - Depth: 0.5mSWCC: Lab. data (Lim et al., 1996); K: Estimated from SWCC using Van Genuchten (1980) - Depth: 1.0mSWCC: Lab. data (Lim et al., 1996); K: Estimated from SWCC using Van Genuchten (1980) - Depth: 1.5mField Data, measured - Depth 0.5mField Data, measured - Depth 1.0mField Data, measured - Depth 1.5m
Figure 4-12 Preliminary computed pore pressures at 0.5, 1.0, and 1.5m depths vs. time
0.0000e+000
1.8000e+004
3.6000e+004
7.2000e+004
1.0800e+005
1.4400e+005
1.6200e+005
1.8000e+005
2.1600e+005
2.7000e+005
3.6000e+005
4.5000e+005
5.4000e+005
9.0000e+005
1.8000e+006
2.7000e+006
Elev
atio
n, m
Pressure, kPa
133.5
134.0
134.5
135.0
135.5
136.0
136.5
137.0
137.5
138.0
-40-80-120 0 40 80 120
Figure 4-13 Preliminary computed pore pressure development vs. depth
Time, seconds
4-19
Overall, the computed pressures shown in Figure 4-12 do not model observed
field pressures well, as 1) computed pressure curves at all three depths are approximately
constant after a rapid loss of suction and do not show any difference in response to
weather conditions with depth, 2) pore pressures at especially 0.5 m depth do not show
the same fluctuations associated with drying and wetting periods as the observed pore
pressures, and 3) the computed loss of suction occurs much more rapidly than the
measured loss of suction. Some changes to the mesh and boundary conditions to possibly
avert these issues are described below.
4.3.2 Modification of the Subsurface Profile
The differences between the measured and computed suctions described in the
preceding section suggest that the permeability of the organic silty clay should be lower.
Thus, the finite element mesh of the preliminary computations was altered so that the
organic silty clay layer has a saturated permeability of 1x10-6m/s at the top 0.5m, as
before, corresponding to surface cracks due to biological factors, such as roots, worms,
etc., and 5x10-8m/s at the bottom 1m of the layer (0.5 to 1.5m). 5x10-8m/s is the
arithmetic mean of the saturated permeability of the upper (1x10-6m/s) and lower
(1x10-9m/s) layers. The reduction in the saturated permeability is justified by the fact that
surface cracks likely do not extend below 0.5m depth. The saturated permeabilities of the
silty clay and sandy silt layers were not altered from what was used in the preliminary
mesh. In addition to changing the coefficient of permeabilities, the mesh was shortened
to 3.5 m to save on computation time, since pore pressures below the fixed water table
4-20
are constant and do not affect the unsaturated zone pore pressures. The modified finite
element mesh configuration is shown in Figure 4-14.
Figure 4-15 shows the pore pressures computed with the modified mesh. For the
computation with the modified mesh, the SWCCs used previously were not changed. A
comparison between Figure 4-12 and Figure 4-15 indicates that the modifications to the
finite element mesh and the permeability functions changed the rate of pore pressure
development only slightly. The two computed results are compared further in Figure
4-16, where the initial change in computed pore pressures with the two meshes is
magnified. A further reduced saturated permeability for soils at 0.5m to 1.5m depth
might produce better agreement between the computed and measured pore pressures.
However, the objective here is to compute the pore pressures based on known conditions.
Thus, the next section describes some additional modifications that were made to the
applied boundary flux.
4-21
Figure 4-14 Modified FEM for NTU slope case study
-105-105-105-100-95-90-80-60-40-20-11-8-6-4-3-2
Distance, m0.0 0.5 1.0 1.5 2.0
Ele
vatio
n, m
134.5
135.0
135.5
136.0
136.5
137.0
137.5
138.0
Groundwater Elevation
Initial pressure head on 27 January 1994 (kPa).
Organic Silty Clay Ksat =1x10-6 m/s K function: estimated from SWCC using the VG method. SWCC: as shown in Figure 4.5
Organic Silty Clay Ksat =5x10-8 m/s K function: estimated from SWCC using the VG method. SWCC: as shown in Figure 4.5
Silty Clay Ksat =1x10-9 m/s K function: estimated from SWCC using the VG method. SWCC: as shown in Figure 4.5
4-22
-100.0
-80.0
-60.0
-40.0
-20.0
0.0
20.0
0 500,000 1,000,000 1,500,000 2,000,000 2,500,000 3,000,000
Time, s
Pres
sure
, kPa
SWCC: Lab. data (Lim et al., 1996); K: Estimated from SWCC using Van Genuchten (1980) - Depth: 0.5m
SWCC: Lab. data (Lim et al., 1996); K: Estimated from SWCC using Van Genuchten (1980) - Depth: 1.0mSWCC: Lab. data (Lim et al., 1996); K: Estimated from SWCC using Van Genuchten (1980) - Depth: 1.5m
Field Data, measured - Depth 0.5mField Data, measured - Depth 1.0m
Field Data, measured - Depth 1.5m
Figure 4-15 Computed pore pressures at 0.5, 1.0, and 1.5m depths vs. time using the modified FEM
-100.0
-80.0
-60.0
-40.0
-20.0
0.0
20.0
0 50,000 100,000 150,000 200,000 250,000 300,000
Time, s
Pres
sure
, kPa
Computed data - Depth 0.5m - Preliminary Mesh
Computed data - Depth 1.0m - Preliminary Mesh
Computed data - Depth 1.5m - Preliminary MeshField Data, measured - Depth 0.5m
Field Data, measured - Depth 1.0m
Field Data, measured - Depth 1.5m
(a) Preliminary Mesh (b) Modified Mesh
SWCC: Laboratory Data (Lim et al., 1996); K: Estimated from SWCC using Van Genuchten (1980)
Figure 4-16 Close-up comparison of computed pore pressures at 0.5, 1.0, and 1.5m depths vs. time using the preliminary and modified FEM
-100.0
-80.0
-60.0
-40.0
-20.0
0.0
20.0
0 50,000 100,000 150,000 200,000 250,000 300,000
Time, s
Pres
sure
, kPa
Computed data - Depth 0.5m - Modified Mesh
Computed data - Depth 1.0m - Modified Mesh
Computed data - Depth 1.5m - Modified MeshField Data, measured - Depth 0.5m
Field Data, measured - Depth 1.0m
Field Data, measured - Depth 1.5m
4-23
4.3.3 Modification of the Boundary Flux for Evaporation
The pore pressured measured in-situ show suctions increasing during the dry
periods between 1 and 4 February, and 22 and 28 February, 1994, which is largely due to
the effects of evaporation or evapotranspiration (see Figure 4-8). SEEP/W (2002), does
not account for evaporation or evapotranspiration from soils. As a result, the
consideration of evaporation or evapotranspiration is another simple modification that
should be made to the finite element mesh.
The boundary flux was modified by superimposing a negative boundary flux
corresponding to measured evaporation rates. For this modification the Meteorological
Services Department of the National Environmental Agency of Singapore was contacted
to obtain the rate of evaporation in the area during the time period of the field study,
January and February of 1994. The evaporation data in Singapore is collected at the
Changi Meteorological Station, twice a day with a standard World Meteorological
Organization (WMO) “Type A” evaporation pan, 122 cm in diameter and 25.2 cm deep.
The modification included the subtraction of daily evaporation data from the daily
rainfall data measured by Lim et al. (1996). On the days of no to low precipitation there
is a negative flux and moisture flow is out of the soil column. Figure 4-17 compares the
rainfall rate measured by Lim et al. (1996) and the new boundary condition that accounts
for evaporation.
4-24
-10
-5
0
5
10
15
20
25
30
35
Jan27
Jan29
Jan31
Feb2
Feb4
Feb6
Feb8
Feb10
Feb12
Feb14
Feb16
Feb18
Feb20
Feb22
Feb24
Feb26
Feb28
Rainfall rate (mm/day)
Rainfall rate withconsideration of evaporation(mm/day)
Figure 4-17 Comparison of preliminary and modified boundary conditions.
Transpiration, the loss of soil water due to plant activity, was not considered in
this study as the surface of interest is bare. The evaporation from a Type A pan was
assumed to equal that of soil evaporation since when soils are wet, soil evaporation and
pan evaporation are nearly equal (http://www.css.cornell.edu/). However, when soils are
dry, soil evaporation rates are typically lower than pan evaporation rates because water is
less available at the soil surface. The pore pressure development computed when
evaporation rates are included in the edge boundary condition of the soil column is shown
in Figure 4-18.
The figure shows that when evaporation is considered computed pore pressures
show the variation in suction corresponding to weather conditions throughout the testing
period. On the other hand, the computed loss and gain of suction is too extreme when
compared with the measured field pressures. Computed pore pressures, especially at
4-25
0.5m depth, initially increase much too fast and become positive, whereas the observed
field pore pressures at this depth remain in suction throughout the testing time period.
Figure 4-18 also shows that the computed pressures show better agreement with
measured data at 0.5m depth than at 1.0m and 1.5m depths.
-100.0
-80.0
-60.0
-40.0
-20.0
0.0
20.0
0 500,000 1,000,000 1,500,000 2,000,000 2,500,000 3,000,000
Time, s
Pres
sure
, kPa
Computed data - Depth 0.5m - Modified Mesh, Includes Evaporation
Computed data - Depth 1.0m - Modified Mesh, Includes EvaporationComputed data - Depth 1.5m - Modified Mesh, Includes Evaporation
Field Data, measured - Depth 0.5mField Data, measured - Depth 1.0m
Field Data, measured - Depth 1.5m
Figure 4-18 Computed pore pressures at 0.5, 1.0, and 1.5m depths vs. time using the modified FEM and modified boundary flux
4.3.4 Time Step Size and Element Size Analysis
It was determined in Chapter 3 that time step and element size analyses specific to
each case study should be conducted. Accordingly, the time step of 1,800s and the
element size of 0.1m square used for the FEM, so far, were reduced to see their effect on
4-26
the computed pore pressures. The effects of element type were not considered for the
reasons mentioned in Chapter 3.
The computation time step for the finite element mesh used in Section 4.3.2 was
repeated for a time step of 900, 600 and 300s. The computation was also repeated for a
mesh with 0.05m square elements at the top half of the soil column and a time step of
600s. Figure 4-19 compares the computed pore pressures for the time period of 27
January to 28 February when the different time steps and element sizes are used. As
shown, the difference in computed pore pressures is negligible over the time period when
different time steps are used.
Pore pressures computed with the 0.05m square element mesh and 600s time step
varies little from that computed with the 0.1m square element mesh within the first
400,000s. After that, the computed pore pressures are the same as those computed with
the 1,800s time step and 0.1m elements as shown in Figure 4-20.
4-27
-100.0
-80.0
-60.0
-40.0
-20.0
0.0
20.0
0 500,000 1,000,000 1,500,000 2,000,000 2,500,000
Time, s
Pres
sure
, kPa
Tim e Step: 300 secondsTim e Step: 600 secondsTim e Step: 900 secondsTim e Step: 1800 secondsTim e Step: 600 seconds, Elem ent Size: 0.05m
Figure 4-19 Time step and element size analyses for computed pore pressures at 0.5m depth vs. time
-16.0
-14.0
-12.0
-10.0
-8.0
-6.0
-4.0
-2.0
0.0
2.0
4.0
6.0
200,000 250,000 300,000 350,000 400,000 450,000 500,000
Time, s
Pres
sure
, kPa
Tim e Step: 300 secondsTim e Step: 600 secondsTim e Step: 900 secondsTim e Step: 1800 secondsTim e Step: 600 seconds, Elem ent Size: 0.05m
Figure 4-20 Close-up of time step and element size analyses
4-28
For the purposes of this computation, which is a general understanding of
modeled behavior, the minimal difference in computed pore pressures when smaller time
steps and element size are used is not critical. As a result, the time step of 1,800s and
element size of 0.1m will continue to be used.
4.4 Singapore Soils Parameters (Literature Review)
Except for the field and laboratory measurements of saturated permeability, the
soil properties described by Lim et al. (1996) are based on measurements by Rahardjo et
al., (1995) and Lim (1995) for other sites on the NTU campus, and other general
knowledge on the soils; moreover, do not include information for grain size curves and
permeability functions. Accordingly, a literature search was conducted for published
data on Singapore soils to obtain more information on NTU soils SWCCs, permeability
functions, and grain size distribution. The literature search resulted in two articles by
Agus et al. (2001 and 2005), on the SWCCs and permeability functions of Singapore
residual soils, based on the same soil samples obtained from 4 test borings on the campus
of NTU. A third article by Rahardjo et al. (2004) describes the engineering
characteristics of Singapore residual soils, based on soil samples taken from one test
boring on the campus of NTU.
Rahardjo et al. (2004) note that the Jurong formation is highly heterogeneous in
nature and consists of a variety of sharply folded sedimentary rocks, including
conglomerate, sandstone, shale, mudstone, limestone and dolomite, and that large
amounts of tropical rainfall combined with hot and humid climatic conditions favor
weathering of the bedrock to a considerable depth and to a varying degree. For the
4-29
Jurong sedimentary formation they took a complete set of samples with a triple tube core
barrel from one borehole, designated NTU-CSE for its location on the campus of NTU
near Civil and Structural Engineering, to determine the variation of engineering
properties of the Jurong formation soils with depth. The climate in Singapore was
described as hot and humid equatorial, with no marked dry season. The annual average
temperature and relative humidity were given as 26.6 C, and 84% respectively. The
rainfall (2,000 to 2,300 mm/year) was specified to be greatest in the months of November
to January. Rahardjo et al. (2004) also state that the Jurong sedimentary soil profile in
the NTU-CSE slope has a purple clayey silt residual soil surface layer and completely
weathered sandstone at 1m to 2m depth from the ground surface. They tested soil
samples at varying depths for grain size analysis, Atterberg limits, permeability function,
and SWCC among other engineering characteristics.
Agus et al. (2001) describe the Jurong sedimentary formation as grey to black
interbedded mudstone and sandstone, or reddish sandstone and mudstone conglomerates,
and classify the soils as clayey silt, sandy clay of medium plasticity and clayey to silty
sand. They obtain soil samples from depths ranging from 0.3m to 13m from four test
borings (designated as NTU-1 to NTU-4) also drilled using a triple tube core barrel.
However, they do not provide a general subsurface profile so the depth to top of
weathered rock is not clear. The following describe the grain size, SWCC and
permeability functions for the Jurong sedimentary formation obtained from the literature
review.
4-30
4.4.1 Measured Grain Size Distribution
Agus et al. (2001, 2005) summarize the index properties of the samples they
collected in a Table, shown here as Table 4-1. With the exception of samples from
NTU-2 most of the soil samples were collected at depths at least 3m below the ground
surface. Based on the depths of interest for this thesis, samples from shallowest depths
are considered first. Thus, the sample of most interest was NTU-2a, however data from
NTU-2b, NTU-1a, and NTU-3a were also considered.
Table 4-1 General properties of NTU campus soils (after Agus et al., 2001)
Rahardjo et al. (2004) conducted grain size analyses for four soil samples at
3 meters below ground surface and deeper. As with the sample by Agus et al. (2001,
2005) the sample of interest is the shallowest sample at 3m to 4m depth. The grain size
analyses for the samples by Rahardjo et al. (2004) are shown in Figure 4-21.
4-31
Figure 4-21 Grain size distribution NTU-CSE slope soils (after Rahardjo et al., 2004)
Figure 4-22 presents the approximate grain size distribution for all five of the
samples (four samples from Agus et al. (2001, 2005) and one sample from Rahardjo et al.
(2004)). The grain size distribution curves of NTU-2c and NTU-3b (Agus et al., 2001)
are also included in Figure 4-22, for comparison since measured K functions are available
only for these two samples, as described below. As shown in Figure 4-22 the samples by
Agus et al. (2001, 2005) are well graded soils, with 70 to 85% fines (particles <0.075 mm
in diameter), whereas the sample provided by Rahardjo et al. (2004) is poorly graded
with approximately 25% fines. The difference in the fines content suggests that the
samples from both publications should be considered separately.
4-32
0
20
40
60
80
100
0.001 0.01 0.1 1 10
Particle Diameter (mm)
Per
cent
Pas
sing
(%)
NTU 1a
NTU 2a
NTU 2b
NTU 2c
NTU 3a
NTU 3b
NTU-CSE
Figure 4-22 Grain size distribution of shallow NTU soils based on Agus et al. (2001)
4.4.2 Measured SWCCs
Agus et al. (2001) used a pressure plate test for matric suctions, and a salt solution
method for higher suction (>1,500kPa) conditions to determine the SWCC of the soil
samples presented in Table 4-1. Figure 4-23 shows the water content vs. suction data
determined in their laboratory tests and the best fit curves for the data. The best-fit
curves to the data were determined using the Fredlund and Xing (1994) model.
The plots indicate that the shape of the SWCC is very similar for each sample and
that there is no significant change in the shape of the SWCC with the depth of the sample.
Agus et al. (2001) conclude that the depth of the soil does not have a consistent effect on
the SWCC and that likely the parent rock type has a more significant influence on the
SWCC. Accordingly, Agus et al. (2001) plot the SWCCs as normalized volumetric water
content versus matric suction and fit the data within a SWCC envelope estimated using
the Fredlund and Xing (1994) model. The ‘Upperbound’, ‘Average’, and ‘Lowerbound’
SWCCs that fit the data are shown in Figure 4-24.
4-33
Figure 4-23 SWCCs of NTU soils (after Agus et al., 2001)
Figure 4-24 Normalized (θw/θs) SWCCs of NTU soils best-fit to a SWCC envelope using the Fredlund and Xing (1994) model (after Agus et al., 2001)
4-34
The observation of the SWCC not changing with depth is also confirmed by the
SWCC determined by Rahardjo et al. (2004), which also does not show a change in the
shape of the SWCC with depth (Figure 4-25). Rahardjo et al. (2004) used a pressure
plate tests to obtain the SWCC.
Figure 4-25 SWCC of NTU-CSE slope soils (after Rahardjo et al., 2004)
4.4.3 Measured Permeability Functions
Agus et al. (2005) provide the saturated coefficient of permeability for all samples
from the NTU test borings as shown in Figure 4-26. The permeabilities were determined
in the laboratory using a permeameter with the rigid-wall variable head method with
bottom-up flow. Each point on the figure represents and average of 3 to 5 test results.
The variation of the points is less than 35% from the mean value, and does not show a
generalized trend with depth below 3m. Above 3m, saturated permeability is
approximately 1x10-7m/s, decreasing to approximately 2x10-9m/s at 3m depth. Agus et
al. (2005) also measure the permeability function of two samples (NTU-2c and NTU-3b)
by using a flexible wall triaxial permeameter up to a matric suction of 300kPa. The tests
4-35
were conducted using a constant head method and employing the axis translation
technique to control the matric suction in the specimen. The drying unsaturated
permeability functions for the two samples are shown in Figure 4-27. The figure shows
that the permeability functions for the two samples are very similar at suctions greater
than -50kPa even though the samples were collected at two separate depths. The
functions can be completed for the entire suction range by accounting for the measured
saturated permeability of the samples, which was 6.25x10-10m/s for NTU-2c, and
1.21x10-8m/s for NTU-3b. Since the saturated permeability and the general shape of the
K function of NTU soils do not vary largely with depth as shown on Figures 4-26 and
4-27, respectively, an average saturated permeability function is described. Figure 4-28
shows the complete permeability functions, and the average of the permeability
functions, determined based on an average approximate saturated permeability of
5x10-9m/s determined from Figure 4-26.
As a comparison, the permeability functions determined by Rahardjo et al. (2004)
is shown in Figure 4-29, who estimated the permeability function based on the SWCC
and the saturated coefficient of permeability. The saturated coefficient of permeability
was calculated from one-dimensional oedometer test results at an effective stress
corresponding to the in situ depth.
4-36
Figure 4-26 Saturated permeability of NTU soils vs. depth (after Agus et al., 2005)
Figure 4-27 Permeability functions NTU soils (after Agus et al., 2005)
4-37
1.E-11
1.E-10
1.E-09
1.E-08
1.E-07
0.01 0.1 1 10 100 1000
Matric suction (kPa)
Perm
eabi
lity
(m/s
)
NTU-2c: 4.00 to 4.20 m
NTU-3b: 6.00 to 6.45 m
average of NTU-2c and NTU-3b samples
Figure 4-28 Complete measured permeability function of NTU soils based on Agus et al., 2005
Figure 4-29 Permeability function of NTU-CSE slope soils (after Rahardjo et al., 2004)
The literature search provided the permeability functions for the Jurong formation
soils, which in previous computations were estimated using the Van Genuchten (1980)
model based on laboratory SWCC measurements. The search also provided the grain
size distribution for the soils. However, the soil parameters presented by Agus et al.
CL
ML
4-38
(2001, 2005) for the Jurong formation vary from those presented by Rahardjo et al.
(2004). The difference in the presented parameters is most obvious in the grain size and
permeability functions. The grain size distribution curves provided by Rahardjo et al.
(2004) is for sandy soils, whereas all the samples provided by Agus et al. (2001, 2005)
are silty and clayey soils. Lim et al. (1996), as mentioned previously suggest that the
soils on NTU have high percentages of fines. Thus the sample by Rahardjo et al. (2004),
which includes approximately 25% of fines, will not be considered further. The focus for
engineering properties of NTU soils will be those provided by Agus et al. (2001, 2005).
4.5 Modeling of NTU Slope – Detailed Computations
The literature search provided the grain size distribution curves and the K
functions, as well as an additional set of measured SWCCs for NTU campus soils. In this
section the NTU soils engineering characteristics obtained from literature will be
compiled and used to model measured pore pressures of the field study. First, the effect
of using the SWCCs given by Lim et al. (1996) versus those given by Agus et al. (2001)
will be investigated; neither of the SWCCs given are specific to the field study site,
however, Agus et al. (2001) provide the SWCC for at least one shallow (less than 3 ft in
depth) soil sample (NTU-2a), whereas the depth of the sampling for the SWCCs given by
Lim et al. (1996) is not specified.
4.5.1 Computations with Measured SWCCs
Figure 4-30 compares the SWCCs obtained from literature for the 4 shallowest
samples presented by Agus et al. (2001) and the SWCCs presented by Lim et al. (1996).
4-39
As shown, an obvious difference between the SWCC data provided by the two
publications is that the SWCCs provided by Lim et al. (1996) are flatter and have higher
air entry values. Figure 4-30 also shows the ‘Upperbound’, ‘Average’, and
‘Lowerbound’ best fit curves for all the samples collected by Agus et al. (2001) and fitted
using the Fredlund & Xing (1994) model (Figure 4-24). The saturated moisture content
for these best fit curves was assumed to be 0.4 based on the approximate average
moisture contents of the NTU samples (Figure 4-23). As shown the ‘Average’ best-fit
curve, fits the data of NTU-2a, the only sample within the depth of interest for this field
study, relatively well.
0.0
0.1
0.2
0.3
0.4
0.5
0.01 0.1 1 10 100 1000 10000
Matric Suction (kPa)
Volu
met
ric W
ater
Con
tent
Agus et al. (2001): Sample: NTU-1-a; Depth: 3.00 to 3.45m
Agus et al. (2001): Sample: NTU-2-a; Depth: 0.3 to 0.8 m
Agus et al. (2001): Sample: NTU-2-b; Depth: 2.00 to 3.00 m
Agus et al. (2001): Sample: NTU-3-a; Depth: 3.00 to 3.45 m
Lim et al (1996): Organic Silty Clay
Lim et al. (1996): Silty Clay
Agus et al. (2001): Upper bound of envelope
Agus et al. (2001): Average of envelope
Agus et al. (2001): Lower bound of envelope
Figure 4-30 Comparison of NTU soils SWCCs obtained from literature
Pore pressures were first computed using the ‘Average’ SWCC with the finite
element mesh shown in Figure 4-14 to compare the effect of the shape of the SWCC on
computed pore pressures. As such, all soil parameters were kept the same as before,
except the SWCCs. The K functions were kept the same as those shown in Figure 4-14
(i.e., estimated from the SWCC of Lim et al., 1996 using the Van Genuchten 1980
4-40
method) and the saturated volumetric water contents of the organic silty clay and silty
clay layers were assumed to be 0.34 and 0.44 (not 0.4), respectively. The SWCC of both
the organic silty clays and silty clays were assumed to have the same shape, consistent
with Agus et al. (2001) and Rahardjo et al. (2004)’s findings that the shape of the SWCC
does not change with depth.
-100.0
-80.0
-60.0
-40.0
-20.0
0.0
20.0
0 500,000 1,000,000 1,500,000 2,000,000 2,500,000 3,000,000
Time, s
Pres
sure
, kPa
SWCC: Lab. data (Lim et al., 1996)
SWCC: 'Average' SWCC (Agus et al., 2001)
Field Data, measured
K: estimated from the SWCCs given by Lim et al. 1996 using the Van Genuchten (1980) method
Figure 4-31 The effect of the SWCC on computed pore pressures at 0.5m depth vs. time
4-41
Figure 4-31 compares the pore pressures computed when the ‘Average’ SWCC by
Agus et al. (2001) is used versus when the SWCCs by Lim et al. (1996) are used. The
figure shows that when the ‘Average’ SWCC is used, the computed variation of suction
corresponding to weather conditions is not as extreme as when the SWCC by Lim et al.
(1996) is used. This suggests that a higher air entry value, thus a flatter curve in the
suction range of interest for the case study (-20kPa to -100kPa) provides a more
significant response to weather conditions. Thus, for a given change in water content, the
change in pore pressure is inversely proportional to the slope of the SWCC, as depicted in
Figure 4-32. Moreover, soils with high air entry values have permeabilities as high as the
saturated permeability up to the air entry suction. This causes pore pressures to respond
rapidly to a rain event. Similarly, soils with lower air entry values become less
permeable faster and can not respond as fast as a saturated soil.
4-42
0.0
0.1
0.2
0.3
0.4
0.5
0.1 1 10 100 1000
Suction (kPa)
Volu
met
ric W
ater
Con
tent
Figure 4-32 Schematic of water content vs. pore water pressure change.
Based on the above computations, the effect of the saturated water content (θs) of
soils on computed pore pressures was also investigated. The saturated water content of
the organic silty clay used in the above computation was increased to 0.44 to equal that of
the silty clay. Figure 4-33 shows the effect of the increased saturated water content on
computed pore pressures for the computation with the ‘Average’ SWCC. The
comparison of the two pore pressure development curves indicates that a higher water
content increases the overall suction of the system throughout the testing period only
slightly. Thus, for future computations, a saturated volumetric water content of 0.4 will
be assumed for both soil layers for simplicity. This decision is also validated by the fact
Same ∆θ
Small ∆uw
Large ∆uw
4-43
that the ‘Average’ SWCC with a saturated water content of 0.4 fit the measured data for
sample NTU-2c well (Figure 4-30).
-100.0
-90.0
-80.0
-70.0
-60.0
-50.0
-40.0
-30.0
-20.0
-10.0
0.00 500,000 1,000,000 1,500,000 2,000,000 2,500,000 3,000,000
Time, s
Pres
sure
, kPa
'Average' SWCC (Agus et al., 2001) - Water content = 0.34 for OSCs and 0.44 for SCs
'Average' SWCC (Agus et al., 2001) - Water content = 0.44 for OSCs and 0.44 for SCs
Field Data, measured
Figure 4-33 Effect of the saturated volumetric water content of soil layers on pore pressure development at 0.5m depth
4.5.2 Computations with Measured SWCCs and Permeability
Functions
The two permeability functions given by Agus et al. (2005), Figure 4-27, are for
samples (NTU-2c and NTU-3b) that are greater than 4 m deep. Since the saturated
permeability and the general shape of the K function of NTU soils do not vary largely
with depth, the average K function described in Figure 4-28 will be used. However, the
average K function will be modified to have a saturated permeability equal to the
saturated permeability's of the soil layers in this case study i.e., while the shape of the
4-44
function will be that of the average measured, the function will start from a saturated
permeability of 1x10-6m/s for the organic silty clays at elevation 138m to 137.5m,
5x10-8m/s for the organic silty clays at elevation 137.5m to 136.5m, and 1x10-9m/s for the
silty clays at elevation 136.5m to 134.5m. Figure 4-34 shows the average of the
measured K function modified for use in this case study. The figure also shows the K
functions that have been used so far, as estimated using the Van Genuchten (1980) model
based on the SWCCs given by Lim et al. (1996), for comparison purposes. Pore
pressures were computed using the measured 'Average' SWCC and the measured average
K function shown in Figure 4-34. Figure 4-35 compares the computed pore pressures for
this analysis to those of the preliminary analyses.
1.0E-13
1.0E-12
1.0E-11
1.0E-10
1.0E-09
1.0E-08
1.0E-07
1.0E-06
1.0E-05
0.01 0.10 1.00 10.00 100.00 1000.00
Matric suction (kPa)
Perm
eabi
lity
(m/s
)
Measured (Average of NTU-2c and NTU-3b samples by Agus et al., 2005)
Preliminary (Estimated from SWCC by Lim et al., 1996, using Van Genuchten, 1980)
Figure 4-34 Comparison of preliminary and measured permeability functions for all three soil layers
of the modified FEM
El. 138 to 137.5m
El. 137.5 to 136.5m
El. 136.5 to 134.5m
4-45
-100.0
-80.0
-60.0
-40.0
-20.0
0.0
20.0
0 500,000 1,000,000 1,500,000 2,000,000 2,500,000 3,000,000
Time, s
Pres
sure
, kPa
K: Measured by Agus et al. (2005); SWCC: Measured 'Average' by Agus et al. (2001)
K: Estimated from SWCC using VG; SWCC: Measured by Lim et al. (1996)
Field Data, measured
Figure 4-35 Effect of the K function on computed pore pressures at 0.5m depth.
Figure 4-35 indicates that the when the measured ‘Average’ SWCC is used
together with the average of the measured K functions the computed pressures model
those observed relatively well. The computed pore pressures for this analysis at 1.0m and
1.5m are shown in Figure 4-36. Figure 4-36 indicates that, when measured hydraulic
functions are used, computed pore pressures compare well with measured field pressures
even at the higher depths. As a result, it can be concluded that measured SWCCs and
measured K functions provide relatively accurate computations at all three depths.
4-46
-100.0
-80.0
-60.0
-40.0
-20.0
0.0
20.0
0 500,000 1,000,000 1,500,000 2,000,000 2,500,000 3,000,000
Time, s
Pres
sure
, kPa
K: Measured; SWCC: Measured 'Average', Depth: 0.5m
K: Measured; SWCC: Measured 'Average', Depth: 1.0m
K: Measured; SWCC: Measured 'Average', Depth: 1.5m
Figure 4-36 Comparison of measured and computed pore pressures at 0.5, 1.0 and 1.5m depths when hydraulic functions are measured
4.5.3 Modeling of the Entire Field Study Period
The computed pore pressures using measured SWCCs and permeability functions
agree well with the field pressures for the time period of 27 January to 28 February. In
this section, the entire field study period is modeled. As such, the above computations of
the measured ‘Average’ SWCC and measured K function are repeated for the entire field
test period of 1 January and 28 February, 1994.
The in-situ pore pressures observed on 1 January 1994 at depths of 0.5m, 1.0m,
and 1.5m below ground surface were shown on Figure 4-8. As previously, these values
were assigned to the finite element mesh, and the pore pressures at depths between those
known pressures were interpolated for a steady state analysis to provide as the initial pore
pressures for the transient analysis. The initial pore pressures on 1 January used for this
study, -10kPa at 0.5m depth to -2kPa at 1.0m depth, to 2kPa at 1.5m depth, are shown in
-100.0
-80.0
-60.0
-40.0
-20.0
0.0
20.0
0 500,000 1,000,000 1,500,000 2,000,000 2,500,000 3,000,000
Time, s
Pres
sure
, kPa
Field Data, Depth: 0.5m
Field Data, Depth: 1.0m
Field Data, Depth: 1.5m
4-47
Figure 4-37. The results of the computation for the entire field test period is shown in
Figure 4-38, which indicates that field pore pressures are modeled fairly well even for the
“drying” period between 1 January and 27 January, 1994.
-25.0-25.0-25.0-20.0-15.0-10.0-8.0-6.0-4.0-3.0-2.0-1.5-1.00.0
Distance, m0.0 0.5 1.0 1.5 2.0
Elev
atio
n, m
134.5
135.0
135.5
136.0
136.5
137.0
137.5
138.0
Figure 4-37 FEM and initial pore pressures for modeling of entire field test period
-25 -20 -15 -10 -5 0 5 10
Pressure (kPa)
Organic Silty Clay Ksat =1x10-6 m/s K function: measured by Agus et al. (2005) SWCC: measured ‘Average’ SWCC by Agus et al. (2001)
Silty Clay Ksat =1x10-9 m/s K function: measured by Agus et al. (2005) SWCC: measured ‘Average’ SWCC by Agus et al. (2001)
Groundwater Elevation
Initial pressure head on 1 January 1994 (kPa).
Organic Silty Clay Ksat =5x10-8 m/s K function: measured by Agus et al. (2005) SWCC: measured ‘Average’ SWCC by Agus et al. (2001)
4-48
-100.0
-80.0
-60.0
-40.0
-20.0
0.00.0E+00 5.0E+05 1.0E+06 1.5E+06 2.0E+06 2.5E+06 3.0E+06 3.5E+06 4.0E+06 4.5E+06 5.0E+06
Time, s
Pres
sure
, kPa
Field Data, measured
SWCC: 'Average' SWCC (Agus et al., 2001); K: Lab data, average of K functions for NTU-2c and NTU-3b (Agus et al., 2005)
Figure 4-38 Computed pore pressures at 0.5m depth for the time period of 1 January to 28 February 1994 when hydraulic functions are measured
The above results indicate that, even though a one-directional infiltration model is
used, computed pore pressures provide a good approximation of the pore pressure
response. However, determining the soil parameters in the laboratory or in the field is
fairly difficult and time consuming. As a result, the accuracy of computer modeling pore
pressures based on estimated SWCCs and K functions will be investigated in Chapter 5.
4.6 Effect of Initial Pore Pressures
For the above computations, the measured field pressures were modeled based on
measured soil properties and measured initial pore pressures. The question of how well
4-49
pore pressures can be modeled when initial pressures are not available is investigated in
this section.
Accordingly, the above computation was repeated assuming that the initial pore
pressures at 0.5m, 1.0m and 1.5m depths were not known. For this analysis, only the
initial water level was assigned to the finite element mesh at 3m below ground surface.
When initial pore pressured are not defined, SEEP/W calculates the initial pressures
above the water table automatically, as a linear extension of the positive pore pressures
below the water table. Therefore, when only the initial water level is assigned, the initial
pore pressures at 0.5m, 1.0m, and 1.5m depth are approximately -25kPa, -20kPa, and
-15kPa, respectively.
The computation was conducted for both the time periods of 27 January to
28 February 1994, and 1 January to 28 February 2006. The computed pore pressures for
these conditions are shown in Figure 4-39 and 4-40, respectively. The Figures show that,
for both computations, the computed pore pressures at 0.5m depth do not agree well with
measured field data. Figure 4-39 shows that when the initial pore pressures are not
known, the computed pressures over estimate measured data; whereas Figure 4-40 shows
that for the longer time period the computed pressures underestimate the measured data.
4-50
-100.0
-80.0
-60.0
-40.0
-20.0
0.0
20.0
0 500,000 1,000,000 1,500,000 2,000,000 2,500,000 3,000,000
Time, s
Pres
sure
, kPa
SWCC: Measured 'Average' SWCC (Agus et al., 2001); K: Measured, average of K functions for NTU-2c and NTU-3b (Agus et al., 2005)
Field Data, measured
Figure 4-39 Computed pore pressures at 0.5 m depth for the time period of 27 January to 28 February 1994 when hydraulic functions are measured but initial pore pressures are not known.
-100.0
-80.0
-60.0
-40.0
-20.0
0.0
20.0
0 500,000 1,000,000 1,500,000 2,000,000 2,500,000 3,000,000 3,500,000 4,000,000 4,500,000 5,000,000
Time, s
Pres
sure
, kPa
SWCC: Measured 'Average' SWCC (Agus et al., 2001); K: Measured, average of K functions for NTU-2c and NTU-3b (Agus et al., 2005)
Field Data, measured
Figure 4-40 Computed pore pressures at 0.5 m depth for the time period of 1 January to 28 February 1994 when hydraulic functions are measured but initial pore pressures are not known.
5-1
5 Parametric Study – Singapore NTU Slope
5.1 Introduction
In Chapter 4 pore pressures measured during a field study by Lim et al. (1996)
were modeled based on soil parameters measured in the laboratory. However, as
mentioned previously, the laboratory measurements of SWCCs and K functions is
expensive and time consuming. In this chapter the computations of Chapter 4 are
repeated using SWCCs and K functions that are estimated using techniques described in
the literature. This chapter will study the loss of accuracy when the soil parameters are
estimated rather than measured.
Figure 5-1 summarizes the possible ways and methods of estimating soil
hydraulic functions with SEEP/W. The background for each item in Figure 5-1 was
provided in Chapter 2. The Figure also describes the expected degrees of accuracy based
on the assumption that as more estimations are required to determine the hydraulic
functions, the less accurate the computed results. The 1st or highest degree of accuracy
was investigated in Chapter 4 and resulted in relatively well modeled pore pressures. The
2nd degree of accuracy uses measured SWCCs and estimated K functions, where the K
function is estimated from the measured SWCCs. The 3rd degree of accuracy uses
measured grain size distribution curves and estimated SWCC and K functions, where the
SWCC is estimated from the grain size analysis, and the K function is estimated from the
SWCC. Finally, the 4th degree of accuracy uses either the grain size distribution curve or
the percentage of sand, silts and clays compared to published data, and estimated SWCC
and K functions similar to the 3rd degree of accuracy.
5-2
Figure 5-1 Summary of options in determining soil hydraulic functions with SEEP/W.
Expected Degree of Accuracy
1o
2o
3o
4o
Unsaturated Soil Hydraulic Soil Parameter
Measured SWCC
Measured K Function
Measured SWCC
Best-Fit Curve (a, n, m)
Van Genuchten(1980)
Measured Grain Size
Estimated K Function
Estimated K Function
Measured Grain Size
I - Van Genuchten(1980)
II - Fredlundet al. (1994)
III - Green & Corey (1971)
Estimated K Function
2B
2C
2A
3A
3B
I - Van Genuchten(1980)
II - Fredlundet al. (1994)
III - Green & Corey (1971)
SWCC Determination K Function Determination
Best-Fit Curve (a, n, m)
Fredlund&Xing(1994)
Sandy Soils Arya&Paris
(1980)
Clayey Soils Modified Kovacs (2003)
Published Data Sillers & Fredlund(2001)
I - Van Genuchten(1980)
II - Fredlundet al. (1994)
III - Green & Corey (1971)
5-3
Agus et al. (2005) describe a similar hierarchical system for the determination of
the K function of Singapore soils. They define the direct measurement of the K function
as Level 1, as it provides the most reliable result, and the estimation of the K function
from a known SWCC and a known saturated permeability as Level 2. They conclude that
the general shape of the K function determined from a Level 2 study is generally the
same as that determined from a Level 1 study, and that for Singapore residual soils Level
2 gives a satisfactory prediction of the permeability function with variation of less than
one order of magnitude. Agus et al. (2005) also define a Level 3, where the saturated
permeability is estimated from grain size using the Hazen's, Terzaghi's and Kozeny-
Carman's formulations, and the K function is best fit with fitting parameters similar to a,
n, and m parameters for SWCCs, equal to 'a', n=0.48, and m=27 for Singapore soils.
They conclude that estimating the saturated permeability from grain size curves shows
deviations within one order of magnitude from the experimental data. However, if the
measured saturated permeability is used instead of that estimated, the Level 3 prediction
actually provides better agreement with measured K functions than Level 2. The 2nd
degree of accuracy in Figure 5-1 estimates the K function similar to Level 2 defined by
Agus et al. (2005). For the computations in this chapter the one-dimensional finite
element mesh of Figure 4-9 is used.
5.2 Measured SWCCs and Estimated K Functions (2nd Degree)
The ‘Average’ measured SWCC by Agus et al. (2001), Figure 4-30, with a
saturated volumetric water content of 0.4 is used for this analysis. As shown in Figure
5-1, for this 2nd degree of accuracy, the measured water content versus suction data can
5-4
either be input to SEEP/W directly (2A) or the data can be fitted with fitting parameters
(2B or 2C). The ‘Average’ SWCC provided by Agus et al. (2001) had already been fitted
to a SWCC using the Fredlund & Xing (1994) model (2C).
The K function can be estimated using the I) Van Genuchten (1980), II) Fredlund
et al. (1994), or III) the Green and Corey (1971) models based on the SWCC. Figure 5-2
compares the measured permeability function for the organic silty clay to those estimated
by using the three models. As shown, none of the K functions estimated from the
‘Average’ SWCC agree well with the measured K function. The K function estimated
using the Van Genuchten (1980) method becomes less than the saturated permeability at
approximately -0.1kPa, whereas the K functions estimated using the Fredlund et al.
(1994) and Green & Corey (1971) models becomes less than the saturated permeability at
approximately -2kPa. At -100kPa, the K functions estimated using the Van Genuchten
(1980) and Green & Corey (1971) models are approximately 2.5 orders of magnitude less
than the K function estimated using the Fredlund et al. (1994) model, which decreases
less than one order of magnitude within the initial 100kPa of suction.
The pore pressures computed using the 'Average' measured SWCC and the K
functions estimated from the three models, are shown in Figure 5-3. For these analyses
the saturated water content of the average SWCC for all soils was assumed to be 0.4
except when the SWCC given by Lim et al. (1996) was used, where the water contents
were 0.34 and 0.44 for the top and bottom layer respectively. The computations were
initially conducted for the period of 27 January to 28 February 1994, and then extended
to include the entire testing period.
5-5
1.0E-11
1.0E-10
1.0E-09
1.0E-08
1.0E-07
1.0E-06
1.0E-05
0.01 0.10 1.00 10.00 100.00 1000.00
Matric suction (kPa)
Perm
eabi
lity
(m/s
)
Measured K function: Average of NTU-2cand NTU-3b samples
I - Estimated using Van Genuchten (1980)based on 'Average' SWCC
II - Estimated using Fredlund et al. (1994)based on "Average' SWCC
III - Estimated using Green & Corey (1971)based on 'Average' SWCC
Figure 5-2 Comparison of permeability functions measured, and estimated from the measured ‘Average’ SWCC for the Organic Silty Clay soils (El. 138 to 137.5)
-100.0
-90.0
-80.0
-70.0
-60.0
-50.0
-40.0
-30.0
-20.0
-10.0
0.00 500,000 1,000,000 1,500,000 2,000,000 2,500,000 3,000,000
Time, s
Pres
sure
, kPa
I - K: Estimated from SWCC using Van Genuchen (1980); SWCC: Measured 'Average' by Agus et al. (2001)
II - K: Estimated from SWCC using Fredlund et al. (1994); SWCC: Measured 'Average' by Agus et al. (2001)
III - K: Estimated from SWCC using Green & Corey (1971); SWCC: Measured 'Average' by Agus et al. (2001)
Field Data, measured
Figure 5-3 Effect of the permeability function on computed pore pressures at 0.5m depth.
5-6
Figure 5-3 shows that for the 2nd degree analysis computed pore pressures do not
model the observed pressures as well as when both functions are measured (Figure 4-36).
The Figure also shows that for the same SWCC, the flat K function curve estimated using
Fredlund et al. (1994) predicts that pore pressures respond more rapidly to weather
conditions. This occurs because of the higher permeabilities associated with this
estimate.
5.3 Estimated SWCCs and Estimated K Functions (3rd Degree)
For the 3rd degree of accuracy, where the SWCC is estimated from grain size, the
grain size distribution curve for sample NTU-2a, Figure 4-22, was used since the sample
is the shallowest of those available, and therefore the most representative of field study
soils.
The SEEP/W manual recommends the use of the Arya and Paris (1981) model for
estimating the SWCCs of sandy soils, and the Modified Kovacs model for estimating the
SWCCs of clayey soils as described in Section 2.2.3. The grain size distribution of
sample NTU-2a (Figure 4-22) shows that the soil contains approximately 65% of fines.
Thus the Modified Kovacs method is the preferred method. However both models will
be used here to observe their difference in computation. It should be noted that the
SEEP/W manual recommends the use of these models only as a general estimate of actual
conditions.
Figure 5-4 shows the SWCCs estimated using the Arya & Paris (1980), and the
Modified Kovacs methods, and compares the curves to the measured ‘Average’,
5-7
‘Upperbound’ and ‘Lowerbound’ SWCCs. The curves were estimated from the grain
size distribution curve assuming a saturated water content of 0.4. The liquid limit of the
soil was specified to be 39 (Table 4-1) for the determination of the SWCC using the
Modified Kovacs method. As shown, the estimated SWCC functions agree relatively
well with the measured SWCCs. The air entry values for both of the estimated SWCCs
are higher than the air entry values of the measured ‘Average’ and ‘Lowerbound’
SWCCs (see Figure 5-4 inset).
0.0
0.1
0.2
0.3
0.4
0.5
0.01 0.1 1 10 100 1000 10000
Matric Suction (kPa)
Volu
met
ric W
ater
Con
tent
Agus et al. (2001): Average of envelope
Agus et al. (2001): Upper bound of envelope
Agus et al. (2001): Lower bound of envelope
Estimated using Arya & Paris (1981) - sandy soils
Estimated using Modified Kovacs - clayey soils
,
(inset: close-up of SWCCs at saturation)
Figure 5-4 Comparison of SWCCs measured, and estimated from grain size
The SWCCs in Figure 5-4 were then used to estimate the K functions using the I)
Van Genuchten (1980), II) Fredlund et al. (1994), and III) the Green & Corey (1971)
models. Figures 5-5 and 5-6 show the resulting K functions and compare them to the
measured K function (1st degree), and the K function estimated from the measured
SWCC by Lim et al. (1996), which was the K function used for the Preliminary study in
Chapter 4.
Upper bound
Lower bound
0.36
0.38
0.40
0.01 0.1 1 10 100 1000
Matric Suction (kPa)
Volu
met
ric W
ater
Con
tent
5-8
1.0E-11
1.0E-10
1.0E-09
1.0E-08
1.0E-07
1.0E-06
1.0E-05
0.01 0.10 1.00 10.00 100.00 1000.00
Matric suction (kPa)
Per
mea
bilit
y (m
/s)
Measured K function: Average of NTU-2c and NTU-3b
Prelim inary K Function - Es tim ated us ing VanGenuchten (1980) based on SWCC by Lim et al.(1996)
I - Es tim ated us ing Van Genuchten (1980) from SWCC es tim ated us ing Arya and Paris (1981)
II - Es tim ated us ing Fredlund et al. (1994) from SWCC es tim ated us ing Arya and Paris (1981)
III - Es tim ated us ing Green and Corey (1971) fromSWCC es tim ated us ing Arya and Paris (1981)
Figure 5-5 Comparison of permeability functions measured, and estimated from grain size using the Arya & Paris (1981) model for the Organic Silty Clay soils (El. 138 to 137.5)
1.0E-11
1.0E-10
1.0E-09
1.0E-08
1.0E-07
1.0E-06
1.0E-05
0.01 0.10 1.00 10.00 100.00 1000.00
Matric suction (kPa)
Perm
eabi
lity
(m/s
)
Measured K function: Average of NTU-2c and NTU-3b
Prelim inary K Function - Es tim ated us ing VanGenuchten (1980) based on SWCC by Lim et al. (1996)
I - Es timated us ing Van Genuchten (1980) from SWCC estimated us ing Modified Kovacs
II - Es tim ated us ing Fredlund et al. (1994) from SWCC estimated us ing Modified Kovacs
III - Es tim ated us ing Green and Corey (1971) from SWCC estimated us ing Modified Kovacs
Figure 5-6 Comparison of K functions measured, and estimated from grain size using the Modified Kovacs model for the Organic Silty Clay soils (El. 138 to 137.5)
5-9
Even though the estimated SWCCs agreed well with measured SWCCs (Figure
5-4), the K functions estimated using both the Arya & Paris (1981) (Figure 5-5) and the
Modified Kovacs models (Figure 5-6) do not agree well with the measured K function.
Not surprisingly, since especially the measured ‘Average’ and ‘Lowerbound’ SWCCs
agreed well with the SWCC estimated using the Arya and Paris (1981), model the
estimated K functions in Figure 5-5 agree well with those shown in Figure 5-2. When the
K function estimated from the measured ‘Average’ SWCC (Figure 5-2) is compared to
the K function estimated from the estimated SWCC (Figure 5-5) with a slightly higher
air entry value (Figure 5-4 inset), Figure 5-5 shows that the K function estimated using
the Van Genuchten (1980) and Green & Corey (1971) models have shapes similar to that
in Figure 5-2, whereas the K function estimated using the Fredlund et al. (1994) model
has a much larger suction range of capillary saturation. To determine whether the Van
Genuchten (1980) and Green &Corey (1971) models will estimate similar K functions as
Fredlund et al. (1994) model for SWCCs with higher air entry values, the ‘Upperbound'
SWCC with an even higher air entry value (Figure 5-4) was used for the estimation of the
K function. The K functions estimated from the 'Upperbound' measured SWCC using the
three models (I to III) are shown in Figures 5-7.
Figure 5-7 shows again that the K functions estimated using the Van Genuchten
(1980) and Green & Corey (1971) models have similar shapes, and the K function
estimated using the Fredlund et al. (1994) model maintains a saturated permeability up to
about -400kPa, which is questionably high. These findings confirm that the Fredlund et
al. (1994) model does not perform well for clayey soils.
5-10
1.0E-11
1.0E-10
1.0E-09
1.0E-08
1.0E-07
1.0E-06
1.0E-05
0.01 0.10 1.00 10.00 100.00 1000.00
Matric suction (kPa)
Perm
eabi
lity
(m/s
)Measured K function: Average of NTU-2cand NTU-3b sam ples
I - Es tim ated us ing Van Genuchten (1980)based on 'Upperbound' SWCC
II - Es tim ated us ing Fredlund et al. (1994)based on 'Upperbound' SWCC
III - Es tim ated us ing Green & Corey (1971)based on 'Upperbound' SWCC
Figure 5-7 Comparison of permeability functions measured, and estimated from the measured ‘Upperbound’ SWCC for the Organic Silty Clay soils (El. 138 to 137.5)
The K functions estimated from the SWCC estimated using the Modified Kovacs
method (Figure 5-6), show that the higher air entry value of the SWCC affects all 3
models the same way, maintaining saturated permeabilities to approximately -9kPa,
-200kPa, and -15kPa, for the Van Genuchten (1980), Fredlund et al. (1994), and Green &
Corey (1971) models, respectively. The -200kPa high capillary saturation of the K
function estimated with Fredlund et al. (1994) model is, again, questionable since this
suction is much higher than the cavitation suction of water (approximately -90kPa).
The pore pressures computed using the SWCCs estimated from the grain size
distribution curve, and K functions estimated using the three models are shown in Figure
5-8 for the estimations that used the Arya & Paris (1981) method, and Figure 5-9 for the
estimations that used the Modified Kovacs method.
5-11
-100.0
-80.0
-60.0
-40.0
-20.0
0.0
20.0
0 500,000 1,000,000 1,500,000 2,000,000 2,500,000 3,000,000
Time, s
Pres
sure
, kPa
I - K: Estimated using Van Genuchten (1980); SWCC: Estimated using Arya and Paris (1981)
II - K: Estimated using Fredlund et al. (1994); SWCC: Estimated using Arya and Paris (1981)
III - K: Estimated using Green and Corey (1971); SWCC: Estimated using Arya and Paris (1981)
Field Data, measured
Figure 5-8 Effect of the permeability function on computed pore pressures at 0.5 m depth - SWCC estimated from grain size using the Arya and Paris (1981) method
-100.0
-80.0
-60.0
-40.0
-20.0
0.0
20.0
0 500,000 1,000,000 1,500,000 2,000,000 2,500,000 3,000,000
Time, s
Pres
sure
, kPa
I - K: Estimated using Van Genuchten (1980); SWCC: Estimated using Modified Kovacs
II - K: Estimated using Fredlund et al. (1994); SWCC: Estimated using Modified Kovacs
III - K: Estimated using Green and Corey (1971); SWCC: Estimated using Modified Kovacs
Field Data, measured
Figure 5-9 Effect of the permeability function on computed pore pressures at 0.5m depth - SWCC estimated from grain size using the Modified Kovacs method
5-12
Figure 5-8 shows that pore pressures computed using the Van Genuchten (1980)
and the Green & Corey (1971) models are similar and respond to weather conditions
more slowly than the observed pressures. The pressures computed using the Fredlund et
al. (1994) model on the other hand responds much faster. Figure 5-9 shows that pore
pressures computed using all three of the models are very similar, but have smaller
reduction of soil suction pressures that those measured.
Both Figures show that neither one of the modeling methods, in which the grain
size analysis was used to estimate the SWCC and the K function provide good agreement
of measured data. Of the above results, the combination where the SWCC is estimated
by the Arya & Paris (1981) model, and the K function is estimated using the Fredlund et
al. (1994) model (Figure 5-8) arguably provides the best agreement. However, there are
three issues associated with this combination: 1) the Arya and Paris (1981) method for
the determination of the SWCC provides better results for sandy soils, 2) the Fredlund et
al. (1994) method is generally more accurate for sandy soils, and 3) the use of the
combination provides a K function with a capillary saturation much higher than the other
estimations.
5.4 Estimated SWCC and Estimated K Function (4th degree)
The SWCC and K functions may also be estimated from the correlation of the
grain size distribution curve with published data. The following discuss the effectiveness
of using published fitting parameters to estimate the SWCC in computer modeling of
pore pressures. The 4th degree of accuracy options of estimating the SWCC and K
functions are summarized in Figure 5-10.
5-13
Figure 5-10 Summary of options in determining soil hydraulic functions with SEEP/W using data by Sillers and Fredlund (2001).
Sillers and Fredlund (2001) compiled published water content versus suction data
for various soils classified based on the USDA soil classification pyramid, Figure 5-11.
Based on the average grain size analyses of the four shallow soil samples collected from
the campus of NTU, the soils in the field study consist of 23% sand, 48% silt, and 30%
clay, corresponding to Clay Loam on the USDA soils pyramid shown in Figure 5-10. If
the grain size analysis for the shallowest sample NTU-2a, consisting of 28% sand, 55%
silt, and 17 % clay, is used alone, however, the soils would be classified as Silt Loam.
4A
4B
Estimated K Function
Measured Grain Size
SWCC Determination K Function Determination
I - Van Genuchten(1980)
II - Fredlundet al. (1994)
III - Green & Corey (1971)
Best-Fit Curve (a, n, m)
Fredlund&Xing(1994)
Best-Fit Curve (a, n, m)
Van Genuchten(1980)
Published Fitting Parameters by Sillers & Fredlund (2001):
5-14
Figure 5-11 USDA soil classification pyramid and determination of soil types for the NTU slope
The fitting parameters for both soil types were provided by Sillers and Fredlund
(2001). Tables 5-1 and 5-2 summarize the fitting parameters statistics of the two soil
types to be used in the Van Genuchten (1980) (4A) and Fredlund and Xing (1994) (4B)
models. The coefficients of variation for each parameter, shown in Tables 5-1 and 5-2,
are rather large, especially for the parameters for the Fredlund and Xing (1994) model.
Unfortunately, Siller and Fredlund (2001) do not provide a full statistical analysis for the
fitting parameters; however, they specify that the fitting parameters provide an estimate
for the initial parameter guesses, and a range of reasonable results for the fitting routine.
The fitting parameters given by Sillers and Fredlund (2001) are for SWCCs best
fit using the Correction Factor (CΨ) proposed by Fredlund and Xing (1994). The
5-15
Correction Factor, as mentioned in Chapter 2, forces the water content to be zero at
1x106kPa. The residual suction (Cr) used by Sillers and Fredlund (2001) is 3,000kPa. It
should be noted that SEEP/W incorporates the correction factor in the Fredlund and Xing
(1994) model, but does not incorporate it in the Van Genuchten (1980) model.
Table 5-1 Fredlund and Xing (1994) model fitting statistics for clay loam and silty loam soils (after Sillers and Fredlund, 2001)
Soil Sample Size Statistic a (kPa) n m
Mean 172.6 2.418 0.492Std. Deviation 210.3 6.308 0.28
Median 92.3 0.864 0.535Coeff. Variation 1.218 2.609 0.569
Mean 63.14 2.188 0.665Std. Deviation 153.6 1.987 0.323
Median 9.656 1.294 0.626Coeff. Variation 2.433 0.908 0.486
Clay Loam 24
Silty Loam 23
Table 5-2 Van Genuchten (1980) model fitting statistics for clay loam and silty loam soils (after Sillers and Fredlund, 2001)
Soil Sample
Size Statistic a (kPa) n m
Mean 0.700 3.554 0.092Std. Deviation 1.821 7.282 0.070
Median 0.030 1.400 0.081Coeff. Variation 2.601 2.049 0.761
Mean 0.42 3.323 0.142Std. Deviation 0.468 2.815 0.132
Median 0.266 2.136 0.080Coeff. Variation 1.114 0.847 0.930
Clay Loam 24
Silty Loam 23
Review of Tables 5-1 and 5-2 show that the 'a' parameter ranges from 63.14 to
172.6 in Table 5-1, and 0.42 to 0.7 in Table 5-2, a large difference to represent the same
soil type. This large difference in the 'a' parameters may be partially explained by the
different fits of curves to experimental data, as shown in Figure 5-12, where the different
5-16
curves that fit the measured water content versus suction for a silty loam and a sandy
loam sample is shown. In Figure 5-12 (a) when the Van Genuchten model is used as the
best fit model, the SWCC water content starts decreasing with suction almost
immediately, whereas when the Fredlund and Xing (1994) model is used, the air entry
value is much higher. One should keep in mind that the SEEP/W manual suggests that
the Fredlund and Xing (1994) model provides better fits for granular soils rather than
clayey soils. Although it is not known if that statement refers to a specific part of the
SWCC, it is possible that when the Fredlund and Xing (1994) model is used, the air entry
value is overestimated as in Table 5-1.
Figure 5-12 Best-fit curves to measured data for two soil samples (after Sillers and Fredlund, 2001)
a) Silty Loam
b) Sandy Loam
5-17
Figure 5-13 shows the SWCCs for the clay loam and silty loam soil types
estimated using the fitting parameter provided by Sillers and Fredlund (2001) for use in
the Fredlund and Xing (1994) SWCC best fit model, and compares the curves to the
measured 'Average' SWCC. The curves were estimated assuming a saturated water
content of 0.4. As shown all estimated SWCCs are very different in their overall shapes,
and do not model the measured ‘Average’ SWCC well. The K functions that are
estimated from these SWCCs using the Fredlund et al. (1994) and Van Genuchten (1980)
methods are shown in Figure 5-14 and 5-15, respectively. The Green and Corey (1971)
model for the estimation of the K function is omitted from the Figure 5-10 for simplicity.
0.0
0.1
0.2
0.3
0.4
0.5
1.00E-02 1.00E-01 1.00E+00 1.00E+01 1.00E+02 1.00E+03
Matric Suction (kPa)
Vol
umet
ric
Wat
er C
onte
nt Agus et al. (2001): Average of envelope
SWCC of Clay Loam Mean
SWCC of Clay Loam Median
SWCC of Silty Loam Mean
SWCC of Silty Loam Median
Figure 5-13 Comparison of SWCCs measured, and estimated using the Fredlund and Xing (1994) model fitting parameters by Sillers and Fredlund (2001) (4B)
5-18
1.0E-11
1.0E-10
1.0E-09
1.0E-08
1.0E-07
1.0E-06
1.0E-05
0.01 0.10 1.00 10.00 100.00 1000.00
Matric suction (kPa)
Per
mea
bilit
y (m
/s)
Measured K function: Average of NTU-2c andNTU-3b
K of Clay Loam Mean; estimated using II - Fredlund et al. (1994)
K of Clay Loam Median; estimated using II - Fredlund et al. (1994)
K of Silty Loam Mean; estimated using II - Fredlund et al. (1994)
K of Silty Loam Median; estimated using II - Fredlund et al. (1994)
Figure 5-14 Comparison of K functions measured, and estimated from published fitting parameters using the II- Fredlund et al. (1994) model for the Organic Silty Clay soils (El. 138 to 137.5) - SWCCs
shown in Figure 5.13
1.0E-11
1.0E-10
1.0E-09
1.0E-08
1.0E-07
1.0E-06
1.0E-05
0.01 0.10 1.00 10.00 100.00 1000.00
Matric suction (kPa)
Per
mea
bilit
y (m
/s)
Measured K function: Average of NTU-2c andNTU-3b
K of Clay Loam Mean; es tim ated us ing I - Van Genuchten (1980)
K of Clay Loam Median; es tim ated us ing I - Van Genuchten (1980)
K of Silty Loam Mean; es tim ated us ing I - Van Genuchten (1980)
K of Silty Loam Median; es tim ated us ing I - Van Genuchten (1980)
Figure 5-15 Comparison of K functions measured, and estimated from published fitting parameters using the I- Van Genuchten (1980) model for the Organic Silty Clay soils (El. 138 to 137.5) – SWCCs
shown in Figure 5-13
5-19
As shown in Figure 5-14, with the exception of the K function that was based on
the median fitting parameters of silty loam, the estimated K functions remain near
saturated values of suction pressures of -200 kPa, which are unreasonable. When the K
functions are estimated using the I -Van Genuchten (1980) model (Figure 5-15) the K
functions show reduction from saturated values at smaller capillary pressures, but again
do not model the measured values well.
Figures 5-16 through 5-19 show the computed pore pressures for the combination
of the SWCC and the K functions corresponding to clay loam and silty loam soil statistics
shown in Tables 5-1 and 5-2.
-100.0
-80.0
-60.0
-40.0
-20.0
0.0
20.0
0 500,000 1,000,000 1,500,000 2,000,000 2,500,000 3,000,000
Time, s
Pres
sure
, kPa
II - K: Estimated using Fredlund at el (1994); SWCC: Estimated - Clay Loam (Mean)
II - K: Estimated using Fredlund at el (1994); SWCC: Estimated - Clay Loam (Median)
Field Data, measured
Figure 5-16 Computed pore pressures at 0.5m depth when soil is Clay Loam – K estimated using the II- Fredlund et al. (1994) model
5-20
-100.0
-80.0
-60.0
-40.0
-20.0
0.0
20.0
0 500,000 1,000,000 1,500,000 2,000,000 2,500,000 3,000,000
Time, s
Pres
sure
, kPa
II - K: Estimated using Fredlund at el (1994); SWCC: Estimated - Silty Loam (Mean)
II - K: Estimated using Fredlund at el (1994); SWCC: Estimated - Silty Loam (Median)
Field Data, measured Figure 5-17 Computed pore pressures at 0.5m depth when soil is Silty Loam – K estimated using the
II- Fredlund et al. (1994) model
-100.0
-80.0
-60.0
-40.0
-20.0
0.0
20.0
0 500,000 1,000,000 1,500,000 2,000,000 2,500,000 3,000,000
Time, s
Pres
sure
, kPa
I - K: Estimated using Van Genuchten (1980); SWCC: Estimated - Clay Loam (Mean)
I - K: Estimated using Van Genuchten (1980); SWCC: Estimated - Clay Loam (Median)
Field Data, measured
Figure 5-18 Computed pore pressures at 0.5m depth when soil is Clay Loam – K estimated using the I- Van Genuchten (1980) model
5-21
-100.0
-80.0
-60.0
-40.0
-20.0
0.0
20.0
0 500,000 1,000,000 1,500,000 2,000,000 2,500,000 3,000,000
Time, s
Pres
sure
, kPa
I - K: Estimated using Van Genuchten (1980); SWCC: Estimated - Silty Loam (Mean)
I - K: Estimated using Van Genuchten (1980); SWCC: Estimated - Silty Loam (Median)
Field Data, measured
Figure 5-19 Computed pore pressures at 0.5m depth when soil is Clay Loam – K estimated using the I- Van Genuchten (1980) model
The computed pore pressures shown in Figures 5-16 through 5-19 indicate that
when the median fitting parameters given for the Fredlund and Xing (1994) model are
used to estimate the SWCC and either the Fredlund et al. (1994) or the Van Genuchten
(1980) model is used to estimate the K function, the predicted pore pressures compare
fairly well to the measured field data.
Figure 5-20 shows the SWCCs estimated using the Van Genuchten model fitting
parameter as given by Sillers and Fredlund (2001), and compares the curves to the
measured 'Average' SWCC. As before, the curves were estimated from the grain size
distribution curve assuming a saturated water content of 0.4. As shown all estimated
SWCC are very different in their overall shapes, and do not model the measured SWCC
5-22
well. The K functions that are estimated from these SWCCs using the Fredlund et al.
(1994) and Van Genuchten (1980) methods are shown in Figures 5-21 and 5-22,
respectively.
0.0
0.1
0.2
0.3
0.4
0.5
1.00E-02 1.00E-01 1.00E+00 1.00E+01 1.00E+02 1.00E+03
Matric Suction (kPa)
Volu
met
ric
Wat
er C
onte
nt
Agus et al. (2001): Average of envelope
SWCC of Clay Loam Mean
SWCC of Clay Loam Median
SWCC of Silty Loam Mean
SWCC of Silty Loam Median
Figure 5-20 Comparison of SWCCs measured, and estimated using the Van Genuchten (1980) model fitting parameters by Sillers and Fredlund (2001) (4A)
1.0E-11
1.0E-10
1.0E-09
1.0E-08
1.0E-07
1.0E-06
1.0E-05
0.01 0.10 1.00 10.00 100.00 1000.00
Matric suction (kPa)
Per
mea
bilit
y (m
/s)
Measured K function: Average of NTU-2cand NTU-3b
K of Clay Loam Mean; estimated using I - Van Genuchten (1980)
K of Clay Loam Median; estimated using I - Van Genuchten (1980)
K of Silty Loam Mean; estimated using I - Van Genuchten (1980)
K of Silty Loam Median; estimated using I - Van Genuchten (1980)
Figure 5-21 Comparison of K functions measured, and estimated from published fitting parameters using the II- Fredlund et al. (1994) model for the Organic Silty Clay soils (El. 138 to 137.5) - SWCCs
shown in Figure 5.20
5-23
1.0E-11
1.0E-10
1.0E-09
1.0E-08
1.0E-07
1.0E-06
1.0E-05
0.01 0.10 1.00 10.00 100.00 1000.00
Matric suction (kPa)
Perm
eabi
lity
(m/s
)Measured K function: Average of NTU-2cand NTU-3b
K of Clay Loam Mean; estimated using II - Fredlund et al. (1994)
K of Clay Loam Median; estimated using II - Fredlund et al. (1994)
K of Clay Loam Mean; estimated using II - Fredlund et al. (1994)
K of Clay Loam Mean; estimated using II - Fredlund et al. (1994)
Figure 5-22 Comparison of K functions measured, and estimated from published fitting parameters using the I- Van Genuchten (1980) model for the Organic Silty Clay soils (El. 138 to 137.5) – SWCCs
shown in Figure 5-20
As shown in Figures 5-21 and 5-22 the K functions, when estimated using the
Van Genuchten (1980) fitting parameters given by Sillers and Fredlund, do not even
define the entire suction range of interest for this study. This may or may not be related
to the fact that SEEP/W does not consider the correction factor for its Van Genuchten
(1980) model computations. The Van Genuchten (1980) model fitting parameters will
not be considered further.
Overall, when the median fitting parameters given for the Fredlund and Xing
(1994) model (Table 5-1) are used to determine the SWCC for Clay Loam (Figure 5-13),
together with the Van Genuchten (1980) model (Figure 5-15) to estimate the K function,
the computed pore pressures model the observed data relatively well (Figure 5-18).
However, most pore pressures computed did not provide good agreement with the
measured data.
5-24
5.5 Computed Pore Pressures at 1.0 and 1.5 m depths
The computed pore pressures above at a depth of 0.5m showed varied degrees of
accuracy. In order to determine which degree of accuracy provides computed pore
pressures that are in better agreement with measured field pore pressures, the computed
pressures at 1.0m and 1.5m should also be reviewed.
a. 2nd Degree of Accuracy
The computed pressures that agreed best with the measured field pressures in the
2nd degree of accuracy computations (Figure 5-3) was that where the K was estimated
using the I- Van Genuchten (1980) model. The computed pore pressures at all three
depths for this computation is shown in Figure 5-23.
-100.0
-80.0
-60.0
-40.0
-20.0
0.0
20.0
0 500,000 1,000,000 1,500,000 2,000,000 2,500,000 3,000,000
Time, s
Pres
sure
, kPa
K: Estimated; SWCC: Measured (2nd Degree); Depth: 0.5m
K: Estimated; SWCC: Measured (2nd Degree); Depth: 0.5m
K: Estimated; SWCC: Measured (2nd Degree); Depth: 0.5m
Figure 5-23 Comparison of computed and measured pore pressures at 0.5, 1.0 and 1.5m depths for the 2nd degree of accuracy analysis
-100.0
-80.0
-60.0
-40.0
-20.0
0.0
20.0
0 500,000 1,000,000 1,500,000 2,000,000 2,500,000 3,000,000
Time, s
Pres
sure
, kPa
Field Data, Depth: 0.5m
Field Data, Depth: 1.0m
Field Data, Depth: 1.5m
K: estimated using I- Van Genuchten (1980) SWCC: Measured ‘Average’
5-25
b. 3rd Degree of Accuracy
As discussed above, the II- Fredlund et al. (1994) model over estimates the
capillary suction region, defined as the range of suction pressures over which the water
content and permeability are close to the saturated values of the case study clayey soils.
However, the computed pressures agreed best with the measured field pressures for the
3rd degree of accuracy computations (Figures 5-8 and 5-9) when the K was estimated
using the II- Fredlund et al. (1994) model, and the SWCC was estimated using the Arya
and Paris (1981) model. The computed pore pressures at all three depths for this
computation is shown in Figure 5-24.
-100.0
-80.0
-60.0
-40.0
-20.0
0.0
20.0
0 500,000 1,000,000 1,500,000 2,000,000 2,500,000 3,000,000
Time, s
Pres
sure
, kPa
K: Estimated; SWCC: Estimated (3rd Degree); Depth: 0.5m
K: Estimated; SWCC: Estimated (3rd Degree); Depth: 1.0m
K: Estimated; SWCC: Estimated (3rd Degree); Depth: 1.5m
-100.0
-80.0
-60.0
-40.0
-20.0
0.0
20.0
0 500,000 1,000,000 1,500,000 2,000,000 2,500,000 3,000,000
Time, s
Pres
sure
, kPa
Field Data, Depth: 0.5m
Field Data, Depth: 1.0m
Field Data, Depth: 1.5m
Figure 5-24 Comparison of computed and measured pore pressures at 0.5, 1.0 and 1.5m depths for the 3rd degree of accuracy analysis
K: Estimated using II- Fredlund et al. (1994) SWCC: Estimated using Arya & Paris (1981)
5-26
c. 4th Degree of Accuracy
Finally, Figure 5-25 compares computed pore pressures at all three depths for the
clay loam. The pressures at 0.5m depth are shown in Figure 5-18.
-100.0
-80.0
-60.0
-40.0
-20.0
0.0
20.0
0 500,000 1,000,000 1,500,000 2,000,000 2,500,000 3,000,000
Time, s
Pres
sure
, kPa
K: Estimated; SWCC: Estimated (4th Degree) - Depth: 0.5m
K: Estimated; SWCC: Estimated (4th Degree) - Depth: 1.0m
K: Estimated; SWCC: Estimated (4th Degree) - Depth: 1.5m
Figure 5-25 Comparison of computed versus measured pore pressures at 0.5, 1.0 and 1.5m depths for the 4th degree of accuracy analysis
The computed pore pressures shown in Figures 5-23 through 5-25 model
observed field pressures fairly well as 1) computed pressure curves at the three depths
show a difference in the rate of response to weather conditions, in agreement with
measured data, 2) pore pressures show fluctuations associated with drying and wetting
periods, and 3) the computed losses of suction occurs more or less at the same rate as
those measured. However, overall, none of the computed pore pressure using estimated
hydraulic parameters model the measured field data as well as the 1st degree of accuracy
computations (Figure 4-37). Based on the above results, one can rate the above from
-100.0
-80.0
-60.0
-40.0
-20.0
0.0
20.0
0 500,000 1,000,000 1,500,000 2,000,000 2,500,000 3,000,000
Time, s
Pres
sure
, kPa
Field Data, Depth: 0.5m
Field Data, Depth: 1.0m
Field Data, Depth: 1.5m
K: Estimated using I- Van Genuchten (1980) SWCC: Estimated using published fitting parameters with Fredlund & Xing (1994)
5-27
order of best to worst based on the agreement between measured and computed pore
suctions pressures as 1st, followed by 2nd, and followed equally by both 3rd and 4th degree
of accuracies.
5.6 Modeling of the Entire Field Study Period
As in Chapter 4, the entire rain event is modeled using the combinations of SWCC
and K functions of Section 5.5. The same finite element mesh used in Section 4.5 is also
used in this section. The results of the computation for the entire field study period using
the combinations for the 2nd, 3rd, and 4th degree of accuracies are shown in Figures 5-26,
5-27 and 5.28, respectively. The figure also shows the pore pressured computed using
the 1st degree of accuracy curve presented in Section 4.5 for comparison purposes.
-100.0
-80.0
-60.0
-40.0
-20.0
0.0
20.0
0.0E+00 5.0E+05 1.0E+06 1.5E+06 2.0E+06 2.5E+06 3.0E+06 3.5E+06 4.0E+06 4.5E+06 5.0E+06
Time, s
Pres
sure
, kPa
K: Estimated; SWCC: Measured (2nd Degree)
K: Measured; SWCC: Measured (1st Degree)
Field Data, measured
Figure 5-26 Computed pore pressures at 0.5m depth for the time period of 1 January to 28 February - 2nd degree of accuracy analysis.
5-28
-100.0
-80.0
-60.0
-40.0
-20.0
0.0
20.0
0.0E+00 5.0E+05 1.0E+06 1.5E+06 2.0E+06 2.5E+06 3.0E+06 3.5E+06 4.0E+06 4.5E+06 5.0E+06
Time, s
Pres
sure
, kPa
K: Estimated; SWCC: Estimated (3rd Degree)
K: Measured; SWCC: Measured (1st Degree)
Field Data, measured
Figure 5-27 Computed pore pressures at 0.5m depth for the time period of 1 January to 28 February - 3rd degree of accuracy analysis.
-100.0
-80.0
-60.0
-40.0
-20.0
0.0
20.0
0.0E+00 5.0E+05 1.0E+06 1.5E+06 2.0E+06 2.5E+06 3.0E+06 3.5E+06 4.0E+06 4.5E+06 5.0E+06
Time, s
Pres
sure
, kPa
K: Estimated; SWCC: Estimated (4th Degree)
K: Measured; SWCC: Measured (1st Degree)
Field Data, measured
Figure 5-28 Computed pore pressures at 0.5m depth for the time period of 1 January to 28 February – 4th degree of accuracy analysis.
5-29
-50.0
0.0
50.0
100.0
150.0
200.0
250.0
0 1,000,000 2,000,000 3,000,000 4,000,000 5,000,000
Time, s
Res
idua
l
1st degree of accuracy2nd degree of accuracy3rd degree of accuracy4th degree of accuracy
Figure 5-29 Comparison of computed pore pressure residuals
The computed pore pressures shown in Figures 5-26 through 5-28 again model
observed field pressures fairly well. Figure 5-29 shows the residual difference between
pressures measured and computed using the 1st through 4th degrees of accuracy. Based
on the above results, one can rate the above from order of best to worst based on the
agreement between measured and computed pore suction pressures as 1st, followed by
2nd, followed 3rd and followed by the 4th degree of accuracies for this case study.
6-1
6 Summary and Conclusions
6.1 Summary
Accurate modeling of soil behavior usually requires that soil properties should be
measured by either laboratory or field tests. However, testing of soils on every slope that
may possibly fail due to rainfall is not feasible. Furthermore, measurement of the
relevant hydraulic parameters (SWCC and permeability functions) is expensive, time
consuming and difficult. As a result, an understanding of modeling flow through
unsaturated soils by using estimated soil properties is needed. In this study, pore water
pressures measured during a field study on a slope at the NTU campus, Singapore were
modeled using detailed site information, including rainfall rate, subsurface stratigraphy,
initial pore pressures, and measured soil hydraulic properties. The case study was then
repeated with estimated soil hydraulic properties, and the results compared to determine
if soil properties estimated by a number of published techniques can be used to predict
pore pressure development in unsaturated soils. The finite element analysis program
SEEP/W was used to model pore water pressures. The study was limited to one
directional flow to estimate pore pressure response.
Chapter 3 evaluated the numerical performance of SEEP/W to gain an
understanding of the numerical oscillation and slow or inaccurate convergence issues in
finite element analyses of transient non-linear phenomena. Earlier studies were
continued by analyzing the effects of time step, element size, and element type (4- vs. 8-
noded elements) of a finite element mesh on the numerical solutions to a case study by
Edgers and Nadim (2003).
6-2
In Chapter 4 the NTU slope field study was introduced, and the detailed site
information including subsurface profile, groundwater levels, evaporation levels, rainfall
data, and initial pore pressures levels were used and measured soil hydraulic functions
were described. Pore pressures were initially computed using the information presented
in one publication, then expanded to include the results of other publications on NTU
soils. Pore pressures were modeled using hydraulic functions measured in the laboratory.
These computations were repeated assuming that initial pore pressures are not known.
In Chapter 5, a parametric study was conducted to compare computed pore
pressures with measured field pressures using estimated hydraulic functions. Expected
degrees of accuracy were defined for computations using various estimated soil hydraulic
functions. The case where the SWCC is known and the K function is estimated from the
SWCC was described as a 2nd degree of accuracy. The case where the SWCC is directly
estimated from the grain size curve, and the K function is estimated from the SWCC was
described as a 3rd degree of accuracy. Finally, the case where the SWCC is indirectly
estimated from the grain size curve, and the K function is estimated from the SWCC was
assigned a 4th degree of accuracy. Pore pressures were computed with the various
estimated soil hydraulic functions. The computed pressures were compared to each
other, as well as to pressures computed with measured hydraulic soil functions of Chapter
4. Some conclusions that can be drawn from the study are described below.
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6.2 Conclusions
6.2.1 SEEP/W Numerical Performance Analysis
a. Time Step and Element Size Studies: Overall, the pore pressure development for all
time steps and element sizes were similar until pore pressures began to increase
rapidly. Computed pore pressures increased most rapidly for the smallest time step
and element sizes and most slowly for the largest time step and element sizes. As the
time steps and element sizes are reduced, the incremental effects become smaller and
in fact suggest that the computations are converging to a stable solution.
b. 4- vs. 8-Noded Elements: The use of the higher order elements produced numerical
oscillations consistent with the criteria of Karhtikeyan et al. (2001) of the bottom
layer and also greatly increased execution time. Non-oscillating computations using
the 8-noded elements produced reductions in the times for hydrostatic pressures in the
upper layer similar to the reductions produced by reducing time steps and element
size. However, this was accomplished at the expense of much greater execution time.
c. It is not possible to recommend time steps and element sizes for general use other
than to note that site specific time step and element size studies should be conducted
in order to achieve accurate numerical results.
d. The results of Edgers and Nadim (2003) were revised first by incorporating the results
of these time step and element size studies. However, a reduction in the saturated
permeability of 30 percent, greatly improved the agreement between the time
computed for the development of hydrostatic pressures in the upper layer and the
observed time of the debris flow. This suggests that for this case study, uncertainty in
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the assumed permeability may be more important than inaccuracies caused by
numerical oscillations and slow or inaccurate convergence.
6.2.2 Detailed Case Study
a. When measured hydraulic functions were used the computed pore pressures agreed
well with measured field pressures. Thus, it was possible to model the seepage case
study using detailed site information, including subsurface profile, groundwater level,
rainfall and evaporation data, initial pore pressures levels and measured SWCC and K
functions. It should be noted that this thesis assumed that the pore pressures
measured in-situ are accurate, and neglect errors associated with field measurements.
b. The computations showed that evaporation has to be considered for accuracy in
unsaturated seepage models. Without its consideration, the computed and measured
pore pressures would have shown poor agreement.
c. For computed pore pressures to show good agreement with measured pressures, the
initial pore pressures have to be known. This suggests that to be able to predict
increase of pore pressures during a rain event, for example to predict slope stability,
initial pore pressures have to be known. The author is not aware of a method that can
be used to estimate initial pore pressures other than to use high suction values for
periods following dry weather conditions, and to use low suction values for periods
following wet weather conditions.
6.2.3 Parametric Study
a. Pore pressures computed using a measured SWCC and a K function estimated from
the measured SWCC (2nd degree of accuracy) showed that pore pressures agreed well
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with measured field data, however, not as well as the pressures computed with both
measured hydraulic functions.
b. Pore pressures computed using SWCC and K functions estimated from the grain size
analysis directly (3rd degree of accuracy) showed fair agreement with measured data.
Overall, the computations conducted based on the model for sandy soils (Arya and
Paris, 1980) provided results that are in better agreement with measured pore
pressures than computations conducted based on the model for clayey soils (Modified
Kovacs), even though the case study soils were clayey soils. The agreement between
the measured and computed pore pressures is coincidental for this degree of accuracy
as the estimated hydraulic functions do not agree well with the measured hydraulic
functions.
c. Four of the 8 combinations of computations conducted using the published SWCC
fitting parameters (for the 4th degree of accuracy) computations agreed fairly well
with measured field pressures, and the remaining 4 of the 8 combinations did not
show good agreement with measured data. One of the 4 combinations that agreed
well with field data was used to compute the entire rain event. The computation for
the long rain event was the combination that deviated most from measured field pore
pressures.
d. For this case study, the estimated hydraulic functions did not agree with the measured
hydraulic functions. However, the pore pressures computed using the estimated
SWCCs and K functions coincidentally agree with the measured pore pressures.
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6.3 Recommendations for Future Research
Topics on the modeling of pore pressure development and rainfall-induced
landslides that should be considered for future research include:
a. Two dimensional modeling of the same case study to observe the effects of lateral
flow in the predicted pore pressure development. If the two dimensional modeling
shows that the effects of lateral flow are negligible, the computations of the
numerically simple one-directional flow model would be validated.
b. Evaluation of the correlation between evaporation and initial pore pressures in
unsaturated soils.
c. Sensitivity analysis of computed pore pressure development to the saturated
permeability of soil layers.
d. Comparative studies of permeability functions estimated using the Van Genuchten
(1980), Fredlund et al. (1994) and Green and Corey (1971) models.
e. Similar studies that are based on sandy soils instead of clayey soils.
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