Volume II

Proceedings of the Conference on

Analysis and Design in GBOTECRIICAL EIGIIEERIIG June 9-12, 1974 University of Texas • Austin, Texas

Jointly sponsored by University of Texas • College of Engineering Texas Section • ASCE Geotechnical Engineering Division • ASCE

Published by American Society of Civil Engineers 345 East 47th Street New York, N.Y. 10017

$10.00

ANALYSIS AND DESIGN RELA'TING TO EMBANKMENT'S

By Stanley J. Johnson1

UiTRODUCTIOH

General

As a basis for subsequent discussions, it is appropr.iflte +>o first direct attcntJon to three .fine state-of-the-art talks nnd pnpcrs on embankment design. One was given by John Lowe (29) in 1966 at the ASCE Slope Stability Conference at Berkeley on "Stability Analysis of Embankments." The second was given by Laurits Bjerrum (10) in 1972 at the ASCE Purdue Conference on "Embankments on Soft Ground." The third was given by Sl<emptcm and Hutchinson (51) at Mcx i "'" Ci i.y in I C)(,l) '"' "fJLabLl.Lty ur NuLun.d ~.Jlopc~:i Utld Enlbu.nkrnc·nL l•'uu!lrlu.Li.un~. !1 Hc~J'C:rf::.'nCl.'

should also be made to the excellent paper by Bishop and Bjerrum (9) at the ASCE Boulder Shear Conference in 1960. The subject is covered extremely well by these papers, permi·tting discussion of only certain aspects in this paper.

A review of analysis and design relating to embankments seems ap­propriate at this time because the computer age has been with us long enough so that we are realizing economic benefits, in terms of cost, time, and labor saving, and are beginning to comprehend what technical benefits can be achieved. New computer-oriented techniques such as the finite element method have been with us long enough so that we are beginning to realize their potential and utility. The widespread availability of computers makes it possible to use practically a.ny conventional method for stability analysis that we desire. In addi­tion, we can now begin to predict the deformation behavior of founda­tions and embankments in a way that was hardly dreamed of even a decade ago. An incidental benefit of the use of computer-oriented techniques is their role in defining instru.rnentation requirements for reco,:ding embanJc.ment and foundation behavior.

Tl;i s seems, therefore, like a good time to examine our perspec­tive and to (a) a.ssess recent developments, both theoretical, computa­b.cnaJ., and laboratoocy; (b) identify what aspects need prindpal

1 Special Assistant, Soils and PavemE:r..ts I:o.boratory, U. S. Army Engineer Wat,erways :2:xperiment Station, CE, Vicksburg, Miss., F'ello1<, ASCE.

2 GEOTECHNICAL ENGINEERING

emphasis; and (c) determine when and if refined investigations and analyses are worthwhile or essential and when procedures normally used are adequate.

There is another aspect. This concerns problems for which pres­ent methods of design cannot be expected to be adequate. While it may be almost heresy in this computer age, some problems still are only slightly ammenable to state-of-the-art design techniques and must be solved by engineering judgment and adequate safety factors.

Experience and Safety Factors

Local experience in constructing embankments should, of course, be ascertained before site explorations are made and in many cases be­fore a site is selected. At this stage, engineering geologists have special value. While many engineers properly stress the variability in subsoils that occurs from site to site, it seems equally appropri­ate to stress the similarity of certain geologic formations over wide areas. This often makes it possible to utilize embankment design and construction experiences from larger areas. While generalizations are dangerous, it may be equally dangerous to fail to make generalizations where they can reasonably be made.

While it is impracticable to discuss embankment design in detail, it seems appropriate to review the relationship of design factors to safety factors. First, let us assume that a good engineering geology investigation has been made, local embankment construction experience has been evaluated, and appropriate subsurface explorations have been completed. Embankment design factors, see Table 1, include items which we choose to ignore when making conventional analyses and using moderate safety factors, such as 1.5 or higher.a The widespread availability of computers has made it practicable to use complex sta­bility analyses that satisfy static equilibrium requirements. Also, techniques have been developed for compensating for sample distur­bance, provided the samples are not excessively disturbed. Such de­velopments, and others, may appear to justify lower safety factors. This is not necessarily true, however, because when one portion of an integrated and interdependent design chain is refined, one is forced to look at the need for considering additional factors and for refin­ing others. A safety factor is a working component of a design pro­cess; it is not idle, waiting to be called upon only in emergencies. We can overwork our safety factors.

At the 1960 ASCE Conference on Shear Strength of Cohesive Soils, Peck (40) presented an interesting plot relating safety factors

a Table 1 implies that low safety factors are justified or result if refined analyses are made and that conventional analyses require higher safety factors. This generalization has many exceptions; i.e., a refined analysis for an embankment on soft clay may result in higher safety factors than used for conventional analyses. Similarly, a sand embankment and conventional analyses do not require high safety factors.

EMBANKMENTS 3

TABLE 1.--EMBANKMENT DESIGN FACTORS

Factor

(1)

Corrections for slight sample disturbance

Rate of straining in laboratory tests

Creep tests at constant load

Effect of anisotropic consolidation stresses

Effect of failure plane orientation in laboratory tests, i.e. material anisotropy

Types of shear test equipment: Triaxial compression Triaxial extension Direct simple shear Plane strain compression Plane strain extension Residual shear

Stability analyses

Refined Analyses -Low Safety Factors

(2)

X

X

X

X

X

X X X X X X

X

Conventional Analyses and

Safety Factors

(3)

X

X

X

Creep and creep-rupture analyses X

Deformation analyses, end of construction X

Settlement analyses

Progressive failure

X

X

X

computed from undrained analyses, where failures had occurred, with the liquidity index, see Fig. 1. This figure illustrates the impor­tance of experience and is a useful empirical guide for determining if one should expect success in predicting the stability of an embankment and its foundation using conventional approaches.

The state of our current design ca­pabilities, meaning conventional testing and analysis, seems to be about as shown in Table 2. While our ability to under­stand and explain failures has improved enormously, our predictive capability is still in process of development. This table indicates that our design capabil­ities are deficient in some areas; nev­ertheless, good engineering judgment is generally able to compensate for our de­sign limitations.

FIG. 1.--FACTOR OF SAFETY VERSUS LIQUIDITY INDEX FOR FAILED SLOPES (AFTER PECK, REFERENCE 40)

WnoT- We WQ.- vJf

\-...) MIJ - W f­p..,-·

4 GEOTECHNICAL ENGINEERING

TABLE 2.--EMBANKMENT DESIGN CAPABILITIES

Design Aspect

(1)

Embankments on soft foundations: 1. Overall stability 2. Deformations at end of construction 3. Creep deformations--postconstruction

Embankments on intact, overconsolidated clay foundations: 1. Overall stability 2. Deformations

Embankments on highly overconsolidated clay shales: 1. Overall stability 2. Pore pressure development 3. Deformations

Behavior Prediction Capability

Good Fair

(2)

Being developed

Good Generally not

important

Poor Poor Poor

CONVENTIONAL SLOPE STABILITY ANALYSES

General

Techniques for making slope stability analyses of the conven­tional or limiting equilibrium types have been highly developed and are well described in various references. Wright (63) has recently made an especially comprehensive study of methods of current interest and has compared their merits and shortcomings.

It is convenient to classify conventional stability analyses into circular arc and sliding wedge types of failure modes, but some are capable of handling both types of failure mechanisms. Circular arc and other procedures for making stability analyses can be grouped broadly into three classes as illustrated in Table 3. The various methods differ principally in the equilibrium requirements they sat­isfy (Table 4) and in the manner in which they handle interslice forces (see Fig. 2). Wright discusses equilibrium conditions satis­fied by 21 different analysis procedures.a

The general characteristics of some currently used procedures for making stability analyses are listed in Table 5, according to Wright. Some of the newer more detailed procedures can accommodate any type of

a See Reference 63, Table 2.3, page 79.

EMBANKMENTS 5

TABLE 3.--CLASSIFICATION OF STABILITY ANALYSES PROCEDURES

Class Description

(1) (2)

I Approximate procedures: (as good as rigorous procedures for ~ small or zero) :

Ordinary method of slices (61)

II Intermediate procedures (generally work well for design purposes):

Simplified Bishop (6,8) Taylor~-Lowe (55,29) Taylor--U. S. Army Corps of Engineers (CE) (55,61,60)

III Rigorous procedures:

Morgenstern and Price (34) Janbu (23) Spencer (52) Sarma (43)

TABLE 4.--STATIC EQUILIBRIUM REQUIREMENTS

General Requirements

(l)

Moment equilibrium

Vertical and horizontal force equilibrium

Point of application of inter­slice forces

Magnitude of interslice shear forces

Detailed Requirements

(2)

1. Overall moment equilibrium

2. Individual slice equilibrium

1. Overall equilibrium

2. Individual slice equilibrium

1. Must be reasonable; many ac­ceptable solutions

1. Must not exceed available shear resistance; should be checked

6

Q) ;.;

~ Q) rl ()

0 ;.;

P-<

GEOTECHNICAL ENGINEERING

m m m w 00 00 w 00 00 00 00

~ ~ ~ ~ ~ ~ ~ ~

0 g;

0 0\ \0 C\J

" rl l1"\ \0 l1"\

Q)

C\J "'

l1"\ l1"\

l1"\ 0 1'1 ,_;j u (Y") I I ~

H I I QJ H ;.; u o o m c rl rl ~

~ ~ ~ ~

(I] Q) (I]

m ()

~ 0 (I]

EMBANKMENTS

R

FIG. 2.--FORCES IN METHOD OF SLICES

sliding surface but require a computer. the various procedures is shown in Table depend largely upon personal familiarity availability of computer programs.

Circular Arc Analyses

A subjective evaluation of 6, but ratings of this type with the methods and local

7

Ordinary Method of Slices.--The ordinary method of slices, see Table 7, for circular failure surfaces is generally considered crude, but Wright and others have shown that this is not the case where 0 is zero or small. For such cases normal stresses on the base of the failure surface do not influence the available shear strength, and the ordinary method of slices is no more conservative than more detailed methods.

Where 0 is appreciably more than slices is overly conservative and there its use except for quick checks and for ous experiences.

zero, the ordinary method of ll seems little justification for . comparing designs with previ-

Some engineers reason that the conservatism of the ordinary method of slices makes it unnecessary to consider progressive failure, creep, and other aspects of soil behavior not accounted for in normal design. As pointed out by Duncan (15), in a lecture at the U. S. Army Engineer Waterways Experiment Station (WES), such material behavior is demonstrated most strongly when the soil has a low friction angle in undrained shear, and this is when the ordinary method of slices is ap­proximately correct and gives about the same result as more detailed methods.

Simplified Bishop.--The Simplified Bishop analysis occupies a special place in engineering practice because of its wide adoption and long usage. For evaluation purposes, it can be considered as the most suitable procedure for routine purposes despite its failure to satisfy all equilibrium requirements (see Table 5). Numerous compari­sons between it and more involved procedures that satisfy more equi­librium requirements indicate that about the same results are achieved. The justification for using the Bishop analysis is largely empirical, in the sense that comparisons show that it is almost invariably

8 GEOTECHNICAL ENGINEERING

TABLE 6.--EVALUATION OF STABILITY ANALYSES PROCEDURES

Characteristic

(l)

1. Results achieved

2. Practicality of hand computation

3. General suitability for most purposes with circular surfaces and computer solution

4. For evaluating proposed methods

Remarks

(2)

(a) For c large and ¢ small:

All methods give about same result, in­cluding ordinary method of slices, except that Taylor-Lowe and Taylor­CE occasionally give slightly high safety factors

(b) For c small and ¢ large:

Ordinary methods of slices are too con­servative. Others give about same results

(c) For circles extending beyond toe:

Taylor-Lowe give slightly high safety factors; Taylor-CE must assume hori­zontal interslice forces beyond toe

Approximate order of preference:

Ordinary method of slices; Simplified Bishop, Taylor-Lowe, or Taylor-CE

Approximate order of preference:

Use any method except ordinary method of slices; Simplified Bishop, Taylor­Lowe, or Taylor-CE are suitable

Use Morgenstern-Price, but recent pro­gram improvements make it suitable for routine use if desired

TABLE T.--ORDINARY METHOD OF SLICES--CIRCULAR FAILURE SURFACE

l. Satisfactory for ¢ = 0 or small ¢ : a. Use for clay foundations and embankments

b. Use for clay foundations and embankments with ¢ i 0 if circular arc is used only in clay (see Navy Manual, DM-7, Reference 14)

2. Unsatisfactory for ¢ > 0 , yields too low safety factors

a. Do not use for sand foundations

b. Do not use for sand embankments

3. For ¢ = 0 or small ¢ materials, method is no more conservative than "correct" methods

EMBANKMENTS 9

satisfactory, seldom being more than a few percent different than more rigorous procedures. The ordinary method of slices can be easily ex­tended to the Simplified Bishop analysis if hand solutions are made; computer programs are also available.

Force Equilibrium Methods.--Taylor's force equilibrium method (55) has been extended by Lowe (29) for shear strengths corresponding to anisotropic consolidation stresses. Lowe assumes interslice forces that have an inclination equal to the average of the slope of the failure surface and of the overlying ground surface. This assumption gives results close to other more detailed methods (63) but gives in­consistent interslice force directions in the central part of the embankment.

The U. S. Army Corps of Engineers adopted Taylor's method (60,61), as one alternative procedure, suggesting interslice force inclinations equal to the average embankment slope after comparative checks dis­closed that horizontal interslice force inclinations near the center line beneath the crest had little effect. (The computer program, un­published, developed by the Corps can use any desired interslice force inclination for all slices.) The Corps' program gives about the same result as the Taylor-Lowe procedure, but interslice force directions for circles emerging beyond the toe should be assumed as horizontal beyond the toe to avoid excessive passive resistance resulting from downward directed interslice forces. This is in accordance with the Corps' usage although not discussed in Reference 60.

Rigorous Methods.--A number of procedures have been developed that satisfy practically all static equilibrium requirements (see Table 5). These methods are sometimes referred to as accurate methods, but this is misleading in the sense that safety factors they produce are not necessarily accurate. It is difficult to characterize these methods, but the term rigorous may be appropriate from the standpoint that they satisfy static equilibrium requirements (see Tables 5 and 8). Nevertheless, even these procedures, which are somewhat more difficult to use and require a computer, oftentime3 are not carried sufficiently

TABLE 8.--RIGOROUS METHODS FOR STABILITY ANALYSISa

1. Satisfy static equilibrium requirements

2. Difficult to simultaneously satisfy all requirements for magnitude, direction, and location of interslice forces

3. Must be considered approximate--do not consider soil stress-strain characteristics

4. Use for research and comparing other methods

a Morgenstern-Price (34), Janbu (23), Spencer (52), and Sarma (43).

10 GEOTECHNICAL ENGINEERING

far to satisfy all static requirements for interslice forces. These more detailed methods give results so close to the Simplified Bishop analysis, and generally to the force equilibrium method of Taylor, that they cannot be considered superior for practical design pur­poses (62).

Sliding Wedge Analyses

There are many cases where a wide berm, upstream blanket, flat slopes, or a confined, thin layer of soft soil in the foundation indi­cates that a sliding wedge is more appropriate than a circular arc failure surface. One of the earliest references (1944) to sliding wedge analyses relates to the Pendleton levee failure (20,32,56) and contains a graphic description of the mechanism of failure and result­ing movements (see especially the discussion by Terzaghi (56)). Nu­merous procedures are available for making translational or sliding­wedge analyses (see Table 9). The newer, more detailed types of anal­yses, such as Morgenstern-Price, etc. (see Table 5), are capable of accommodating either circular arc, sliding wedge, or combinations of circular arcs or other failure surfaces with plane sections. A sim­plified version of a sliding wedge analysis was developed for use in the Lower Mississippi Valley Division (LMVD) of the Corps of Engi­neers in which the definition of the safety factor was made to cor­respond as closely as possible to that used in conventional circular arc analyses. This procedure, Reference 59, is also presented in the Navy Design Manual DM-7 (Reference 14).

Selection of Method of Analysis

The geometry of a situation governs whether a c·ircular arc, a sliding wedge, or a composite failure surface of curved and plane seg­ments should be selected. This is a first requirement and determines

TABLE 9.--TRANSLATIONAL OR SLIDING WEDGE STABILITY ANALYSES

Procedure Reference No.

(1) (2)

CE 1944 20 CE 1952 61 CE 1961 59, 14

CE 1970 60 Morgenstern-Price 34 Janbu 23

Spencer 52 Seed and Sultan 44, 53 Sarma 43

EMBANKMENTS 11

which types of stability analysis procedure should be considered.

Since even the most detailed of the conventional or limiting equilibrium methods is relatively crude and neglects stress-strain properties of embankment and foundation materials, the simplest suit­able procedure should be adopted. Under limited conditions, i.e., 0 = 0 , the ordinary method of slices is appropriate, but in general the Simplified Bishop, the Taylor procedure with somewhat smaller side force inclinations than used by the Corps of Engineers, and Spencer's procedures seem more satisfactory for practical purposes. However, it is essential that a method be used that the engineer has carefully re­viewed and understands, and this is perhaps more important than other requirements. Since computers are routinely used on large projects and running times are low, it is practicable to use several methods, rather than only one.

Credibility of Computer Solutions

The widespread use of computer programs requires understanding and agreement about their potential credibility. As a basis for using computers, the following is suggested:

a. The engineer is responsible for establishing the credibility of computer solutions.

b. Assume that a computer program (1) written by a competent programmer, (2) carefully checked out on check problems whose answers are known, and (3) used successfully on a variety of problems may still give an unreliable answer. Reasons for this are the difficulty of completely "debugging" large pro­grams and changes in subroutines that are made periodically in the computer itself.

c. Establish the credibility of computer output by: (1) Criti­cally examining the results to determine if they look reason­able. (2) Use two or more entirely independent computer programs, i.e. force equilibrium, Simplified Bishop, etc.

General

(3) Make a hand solution for the critical circle. This re­quires the Simplified Bishop, Taylor's force equilibrium, or other procedures. This should be required for dams. (4) Use charts and approximate solutions.

PORE PRESSURES AND SHEAR STRENGTHS

While conventional procedures for performing stability analyses produce generally comparable results, with the exception of the ordi­nary method of slices for a c,rf; material, this refers only to the technique for performing the analysis. The use of total stress versus effective stress analyses and the various ways in which design shear strengths can be selected produce a wide range of safety factors and

12 GEOTECHNICAL ENGINEERING

are more important than the method for analyzing stability.

The importance of shear strengths used for design and of effec­tive versus total stress analyses is illustrated in Table 10 for Test Section No. 2 constructed by the New Orleans District, Corps of Engi­neers. This and other test sections (24) were analyzed extensively by Ladd and his colleagues at Massachusetts Institute of Technology (MIT) (27,18) for the District. Table 10 shows that the end of con­struction safety factor varied from 1.0 to 1.9, depending upon shear strengths assumed. This range far exceeds differences resulting solely from stability analyses techniques.

Field Vane Tests

Field vane tests sometimes indicate shear strengths that check closely values determined by sampling and testing and correlation with actual failures. In other cases, vane strengths may be too large, by as much as 100 percent. Bjerrum's correction factors (10) were utilized by MIT in a Simplified Bishop stability analysis, as were uncorrected field vane shear strengths, with results as shown in Table 10. It appears likely, on the basis of the various analyses and especially from the behavior of the test section, which underwent

TABLE 10.--LEVEE TEST SECTION NO. 2--NEW ORLEANS DISTRICT, CE

End-of-Construction Stability Analyses

Method of Analysis

(l)

Simplified Bishop

CE sliding wedge

Simplified Bishop

Morgenstern-Price

Simplified Bishop

Interpretation of slope indicators

Simplified Bishop

Simplified Bishop

Shear Strengths

(2)

SHANSEPa--MIT (2i)

CE--design approach (27)

MIT--creep report (18)

Wedge--MIT strengths (21)

Field vane--with Bjerrum's correction (21)

Comparison of laboratory direct simple shear (Geonor) shear stress-shear strain data and field shear strains

Effective stress analysis (21)

Field vane (21)

Safety Factors

(3)

0.97

1.05

1.15

1.15

l. 30

1.3

l. 56

1.92

a Stress history and normalized soil engineering properties.

EMBANKMENTS

large creep deformations finally resulting in cracking but not fail­ure, that the safety factor at the end of construction was probably not much more than 1.1 to 1.3.

Uncorrected field vane strengths are obviously inapplicable.

13

Since correction factors of the type proposed by Bjerrum vary for dif­ferent soil types, it appears necessary to conclude that field vane strengths should be used with the utmost discretion, if used at all, as the only basis for designing embankments. While field vane strengths are not always dependable, such tests have value_ for de~e~­mining differences in subsoil conditions because the vane lS sensltlve to rapid and minor changes in subsurface conditions. It also is use­ful for determining strength increases from consolidation during stage construction.

Compression, Simple Shear, and Extension Tests

Almost all practical design stability analyses utilize results from triaxial compression tests. This has generally been satisfactory where conventional safety factors have been used but may not be satis­factory when attempts are made to use low safety factors or when a re­fined analysis is desired that corresponds as closely as possible to field conditions.

The simplified field con­ditions shown in Fig. 3 illus­trate that the soil may fail by compression, simple shear, and extension. Further, compres­sion and extension tests can be performed using triaxial or plane strain equipment. Dif­ferences between the results of

EXTENSION__.... \

it_SIMPt..E SHEAR

LABORATORY TEST CONDITIONS RELATIVE TO FIELD CONDITIONS

FIG. 3.--LABORATORY TEST CONDITIONS RELATIVE TO FIELD CONDITIONS

triaxial compression and extension tests are illustrated in Fig. 4, prepared from data cited by Bjerrum (10) and_Ladd,_et al .. (27). As­suming that the average of triaxial compresslon, dlrect Slmple shear,

J: 0>-~t.J 1.4 J:z

t;~ 1.2 Z<n l:iz 1.0 t;~ a:ti'J 0.8 j~ ~~0.6

-·-·-·-·-·-; LEGEND • X --, /

X~-.,.. ..... ~- X ','<¥...--·tl/ -·-TRIAXIAL COMPRESSION, TC --- DIRECT SIMPLE SHEAR+ TC

UNDRAINED {GEONOR) X :: (OSS + TC + TE) X !/3

TC --TRIAXIAL EXTENSIQN-;-TC

~~0.4 Q~ 0.2

~~ L--~--------------------~~------~~----­o:::= 0

CASES CITED BY BJERRUM {10) LADD ET AL.(27)

FIG. 4.--COMPARISON OF TRIAXIAL COMPRESSION AND EXTENSION TESTS AND DIRECT SIMPLE SHEAR TESTS, NORMALLY CONSOLIDATED CLAYS

14 GEOTECHNICAL ENGINEERING

and triaxial extension tests approximates the average st-rength along a railure surrace, the conventional use or triaxial compression tests ror the entire railure surrace may result in average shear strengths that are 20-30 percent too high. The suggestion is sometimes made (Ladd) that direct simple shear tests represent a suitable average ror an entire typical railure surrace. As illustrated in Fig. 4, this may be reasonably valid, but it does not seem practicable to rely only on direct simple shear tests.

Typical railure conditions are plane strain rather than triaxial, although this is not always the case. Plane strain tests generally give about 5 percent larger strengths than triaxial compressions tests.

This discussion or the inrluence of test conditions is intended to illustrate the uncertainity that exists in determining the shear strength or soils, considering only test type and equipment. Unless these efrects are evaluated, it is evident that the sarety ractor must compensate for tangible and possibly substantial uncertainties.

Back-Pressure Saturation Errects

The use or back pressure to secure saturation in triaxial com­pression tests was presented by Lowe in 1960 (30) and again in 1967 (29). His ideas met ready acceptance and probably by about 1965 most, but not all, laboratories were using back pressure to achieve saturation and hence,they believed, more conservative test results that better represented ultimate rield conditions.

When using back-pressure saturation, Kaufman and Weaver (unpub­lished data), in the LMVD of the CE, found much higher strengths at low stresses than had previously been obtained ror some materials when only seepage saturation was used. Further, the shear strength at low stresses, producing a high cohesion intercept value, was much greater than developed under rield conditions. While such results were dis­counted in design, an investigation of the effect of back-pressure saturation was made at the WES. Consolidated-undrained triaxial com­pression tests were perrormed on both compacted and undisturbed mate­rials. The results ror a compacted ML silt (see Fig. 5) show that the maximum deviator stress for high back pressures was nearly twice that developed when no back pressure was used. Similarly, an undisturbed silt (ML) tested at a conrining stress or 1 tsr in triaxial compres­sion had a deviator stress under 80-psi back pressure that was 46 per­cent larger than ror a back pressure of 40 psi.

A high back pressure prevents pore water cavitation, which would ~ otherwise occur at low stresses on compacted soils and on overcon­solidated in situ materials tested at stresses less than their pre­consolidation stress. The shear strength is greater than the drained strength because tension, in erfect, is permitted to develop in the pore water. This excess shear strength at low normal stresses should not be used in design, according to Lowe (29), but this restriction has not been consistently observed. Its errect will be discussed subsequently.

EMBANKMENTS

~ ISr---------------------------------------------, ~ w 0: t-

0:~ 10

~~~

- 100 - 90 - 83

t­z w

~ ... v ~~ a• - 52~ ::;.§:: 5 :> ::; x < ::; oL-----L-----L---~----~----~----~----_J

o zs so 75 roo rzs rso 175 BACK PRESSURE, P.S I

0.

FIG. 5.--EFFECT OF BACK PRESSURE ON DEVIATOR STRESS

Plotting and Use of Consolidated-Undrained Test Data

15

When isotropically consolidated-undrained triaxial compression tests are performed, the usual practice ror presenting the test data is to construct a Mohr circle for failure conditions with a cr 3 cor­responding to the chamber or consolidation pressure and a cr1 equal to the chamber pressure plus the deviator stress at railure. An en­velope is constructed tangent to the various stress circles or joining the points on the stress circles representing the shear strength de­veloped on the failure plane. The latter is normally preferred (see Fig. 6), but a tangent envelope is orten used, especially for undis­turbed specimens as a means of compensating ror sampling disturbance. This is a total stress method ror presenting the test data, and en­velopes constructed in this manner are routinely used in design.

According to the usual test envelope, the shear strength corre- ~ sponds to point B for a specimen isotropically consolidated under a ~~

stress indicated by point A in Fig. 6. A peculiar situation has de- ~ veloped, however, in which the test envelope is used by designers in a. .. manner inconsistent with the way the envelope was prepared. Designers .. ·

~ ~ w :: 2 ~

0:

"' w I <nl

LAB SHEAR STRENGTH

DESIGN SHEAR

0 L_ ____ L_ ____ L_ ____ L_ __ ~~--~L__J~J_--~~--~8 0 2 3 4 5

DEVIATOR STRESS AT FAILURE

FIG. 6.--CONSOLIDATED-UNDRAINED TEST ENVELOPE, ISOTROPIC CONSOLIDATION

16 GEOTECHNICAL ENGINEERING

use the test envelope as a relationship between shear strength and ef­fective normal or consolidation stress on the failure plane prior to undrained shear. Thus, the designer uses a shear strength correspond­ing to point C. Obviously, the designer and the laboratory should both agree that the shear strength corresponds to point B. The latter strength is 15-20 percent more than the strength actually used in de­sign, as 0cu or ¢R is often equal to one-hal

The inconsistency between the laboratory and the designer can be simply resolved by plotting test data as proposed by Taylor (54) in which the shear strength at failure on the plane of failure, tak~n as 45 + 0'/2, is plotted versus the effective normal consolidation stress (see Fig. 7) on the failure plane. This procedure has been

3 l- DESIGN SHEAR

C~VENTIONAL R ENVELOPE

DEVIATOR STRESS AT FAILURE

FIG. 7.--CONSOLIDATED-UNDRAINED TEST ENVELOPE, ISOTROPIC CONSOLIDATION

strongly advocated by Lowe (29). While not frequently done, it seems reasonable that this method of plotting should be used to avoid a com­mon but unsupportable inconsistency, but further discussion is de­ferred until the effect of using isotropically consolidated tests for design is considered.

Effect of Anisotropic Consolidation on Consolidated-Undrained Strengths

Conventional laboratory testing procedures utilize isotropically ... consolidated triaxial compression tests for determining undrained ~

shear strengths, i.e. consolidated-undrained, CU , or R tests. As pointed out by Lowe (31) and others (28), anisotropically consolidated specimens conform better to probable field conditions and are claimed to yield somewhat higher shear strengths. It may be practicable on a few large projects to perform anisotropically consolidated tests, but this is generally impracticable. Fortunately, possible effects of anisotropic consolidation can be examined in several approximate and preliminary ways even if only isotropic consolidation was used.

EMBANKMENTS 17

A procedure was developed by Taylor, described in detail by Lowe (31), to approximate the effects of anisotropic consolidation from isotropically consolidated-undrained tests with pore pressure measurements, i.e. R tests. The procedure assumes that the ratio of principal effective stresses crl~ at any point during undrained shear represents the starting cond~tions for a test consolidated to that ratio of principal effective stresses. The results of using this approach, by the WES, is shown in Table ll for two materials. It ap­pears from this and other data that Taylor's approximation is slightly conservative but probably useful as a means for estimating effects of anisotropic consolidation, as a basis for determining if anisotropic­ally consolidated tests should be performed.

A second alternative for estimating anisotropically consolidated shear strengths is to compute them, after Skempton and Bishop, Refer­ence 50, from results of isotropically consolidated tests. This al­ternative uses Skempton's pore pressure parameter at failure, A , for isotropically consolidated tests and the appropriate values ~f 0' and consolidation stress ratio, Kc , where Kc = cr1c~3c . This al­ternative for saturated soils; i.e. B = l , is given in Fig. 8 for c' assumed negligible and can be modified for c' > 0 . The value of

TABLE 11.--MEASURED AND COMPUTED TOTAL STRESS ENVELOPE ANGLES ANISOTROPICALLY CONSOLIDATED TRIAXIAL COMPRESSION TESTS

Envelope Angle for Total Stresses for Consolidation Principal Effective Stress

Ratio of

Material '1.0 1.5 2.0

(l) (2) (3) (4)

Normally consolidated "buckshot" clay:

(l) Test value 16.2° 19.3° 23.9°

(2) Values computed from isotropic-ally consolidated tests using Taylor's method 16.2° 18.5° 22.3°

Normally consolidated EABPLa clay:

(l) Test value l3.7o 16.4° 20.8°

(2) Values computed from isotropic-ally consolidated tests using Taylor's method 13.7° 16.0° 19.7°

a East Atchafalaya Basin Protection Levee, Louisiana

18

i

GEOTECHNICAL ENGINEERING

-- -+(1--)A 1"1 SIN 41' COS 41' [ I I J O:c- lt(2A(I)SIN ill' Kc Kc f

FIG. 8.--EFFECT OF ANISO­TROPIC CONSOLIDATION CU (OR R) TESTS (c' AS­SUMED NEGLIGIBLE OR ZERO)

Af can be readily computed if pore pressures during shear are measured. Transducers provide a simple means for doing this in routine testing. If pore pressures were not measured they can be estimated if 0' has been de­termined, see Fig. 9. Drained direct shear tests provide a simple means for determining c' and 0' .

Still another alternative for es­timating anisotropically consolidated­undrained shear strengths is based upon the frequently used c/p ratios. The use of c/p ratios or s /p ratios for estimating shear s¥reXgths of normally consolidated and overcon­solidated clays implies that the shear strength depends only on o1c and is independent of Kc . If this assump­tion is made, it is easy to prepare plots of shear strength versus consol­idation stress on the failure plane for various ratios of principal effec­tive stresses during consolidation. This approach, in effect, stipulates a

specific stress path, but this may not be the same as achieved in lab­oratory testing or in field behavior.

Embankment Strengths.--In analyzing embankment stability using consolidated-undrained tests, it is important to note that the de­signer normally uses laboratory test envelopes for isotropically con­solidated triaxial compression tests as a relationship between shear strength on the failure plane and the effective normal stress on the failure plane at the start of undrained shear. The influence of anisotropic consolidation stresses is generally not considered but is illustrated in Fig. 10, which was computed according to Fig. 8. These effects can be summarized about as follows: (a) if large positive pore pressures are developed during shear, isotropic consolidation is conservative, i.e. gives smaller shear strengths than for ,rsotropic ..(--· 1

consolidation hrc < 'AcJ; (b) if small positive or negative pore 1

pressures are developed during shear, isotropic consolidation ls un­conservative (-rrc > 'AC ; and (c) isotropic consolidation can be con­servative or unconservatlve dependlng upon the effectlve stress path and varies with consolidation stress ratio~, a;;;ro}c .

These remarks can also be stated as follows: If Skempton's pore pressure parameter at failure, Af , is more than 1/2(1 - sin 0') , isotropic consolidation is conservative (-rrc < !£c), but lf less than thls value lSotroplc consoildatlon ls unconser vo. Ive ( trc > LAC) . This dividing value for Af is 1/4 for 0' 30° and_I/3 fo~ 0' = 20° . Compacted materials often develop small positive or neg~­tive pore pressures in-consolidated-undrained testsL-i.e. Ar is small or negative. For such cases, isotropically consolidated tests

EMBANKMENTS

A =__A_!!__ f (IT1-IT3)

1

liU I

1::=1/7 ill' FROM DRAINED TEST

~~----~~~~--~--------------~-a

l.i'J3c=cr,c=crc

FIG. 9.--ESTIMATING Af FOR CU )OR R) TESTS IN WHICH PORE PRESSURES ARE NOT MEASURED (ISOTROPIC CONSOLIDATION)

1.5 At= I

t I. C. CONSERVATIVE

ILC.< IA.C.

At=O

I.e. UNCONSERVATIVE ILC. > IA.C.

o.5L--------_j_ _______ ---L------'-----:!2

5 1.0 1.5 2~ -

FIG. 10.--EFFECT OF ANISTROPIC CONSOLIDATION ON -rf/crfc , CU (OR R) TESTS

19

20 GEOTECHNICAL ENGINEERING

give substantially too high shear s_:tre.ngths _and. are. unc.onser_vati ve for embankment design.

If the designer were to select embankment shear strengths from plots of Tff versus o1 , instead of using plots of Tff versus of as commonly done, is8tropic consolidation would give too high sfigar strengths for Af < 1.0 , see Fig. 11. The various considera­tions discussed are summarized in Table 12. Anisotropic consolidation

~.~~Jt io V~..U

"'CH II ~ Cf.fc. ..., > ~ ~ 5 roc( ~ " 8 ~ :z -:::>1-0 -'

FIG. 11.--EFFECT OF ANISOTROPIC CONSOLIDATION ON Tf/Olc CU (OR R) TESTS

effects on embankment shear strength merits considerably more study than has been given them. Until such studies are made, it seems ad­visable, if isotropically consolidated tests are performed, to retain our present inconsistent method of plotting and using test data to offset, at least partially, unconservatism in the use of isotropic consolidation. A better procedure would be to plot and use test data in a consistent manner and to perform isotropically and anisotropi­cally consolidated tests.

Foundation Shear Strengths.--The preceding remarks apply also in principle to foundation shear strengths. However, foundation strengths are often determined using c/p ratios, especially for soft clay foundation soils. The shear strength on the failure plane for both normally consolidated and overconsolidated soils can be plaited versus o1 , the maximum consolidation stress, normally taken as the vertical effective stress, p . For test data plotted in this manner, the effect of anisotropic consolidation stresses is illustrated in Fig. 11, for results computed according.to Fig. 8. It is obvious that the c/p approach in conjunction with isotropically consolidated R or CU test data is satisfactory only lf hlgh pore pressures are de­veloped, i.e. for Af = l . These considerations are summarized in Table 12.

The c/p concepts are used in SHANSEP (27) and similar tech­niques as a means of correcting for disturbance of undisturbed samples. This is done by consolidating test specimens to sufficiently large stresses to overcome disturbance effects and normalizing the shear strengths with respect to major principal consolidation stress. It is evident that isotropic consolidation is satisfactory if Af = 1.0 but anisotropic consolidation is evidently required for smaller values

U)

8 U) 1"1 8

:::0 0

p::; 0

p::; I I

:« 0 H 8 ~ ~ H H 0 U) :« 0 0

0 H p.. 0 p::; 8 0 (/) H :« ~

(/)

:::0 (/) p::; 1"1 > 0 H p.. 0 p::; 8 0 (/) H I I

N .-l

1"1 H P'l ~ E-<

~

< m

B. Q

0\ •rl .-0- "'

'H .-l ~ (Y)

(\J

" -..... <]) .-l +' <I!

@ v"vv"'

" 'H m ~ p..

<])

" ;:s "' ~~J "' <I!

" p..

~ ~ <I!

" "!-._...._, 0 p..

'&

"' Q Q ·rl 0 "' +' @' <I! .-l (\J

~ (/)

(\J -..... .-l

A V\\.

""" ~ I I

.-o <])

Q(}+' c m

··rl .-o +' ·rl <1!..-l

" 0 P,t/0 " Q m <]) 0+' +'Om Q IC1 H:>, .-l

rl+' 'H.-l "' 0 m <I!

CJ8 .-o ·rl 0 P<

..c: 0 +' " <!!+' ;;;; 0

"' H

EMBANKMENTS

"' Q <I! 0 :> Q ·rl

·rl m •• +' I QO ..c: c m +'Oco

~ •r-l •r-i

$~~~I -1-)-i-Jro'CI.l m QO ·rl c coC.-lO • 0 •rl Q) 0 CJ Q) .-i .-l""' :> 0 f.) ~ C) rl

"' "' 0 ·rl +' v lf"\ Q (.) P<m 0 " 0 :> 'H (.) m (.) " " ~

<lJ ·.-1 +' <I! CJ..C: P<O "' ·rl "' 0 "' Q P< "•rl 0 0 "+' (.)

" <]) 0 ~ § +'..C: "' 0 QO ·rl <])

"'•rl Q "' H..C: cd •rl •rl

" I <]) Q :> 0 0 (.) (.)

.-l ·rl P<CJ

"' 0 •rl <I! " P< :>+' 0

·rl 0 " <]) Q(}t/0+' :>

·rl 0 ·rl Q Q "'+' 0 m ·rl m

·rl :> 0 +' Q " h .-i m m

cV <I!

co..C: "' •rl +' Q II .-0-.-l ·rl 0 0 "' (.) 'H uo..C: ~ C+' Q "' 0 QO 0 ·rl (.) Q ·rl

<!!+' Q (.) h m 0

·rl +' rd ·rl Pi CJ1 ·rl +' 0 .-l m h ~ oco +' "'·rl 0 <I! Q.-l uo..C: 0 0

H "' () "' I

" "' I .-o <I! "'·rl s <])

:> w..c: <I! "' <]) <l.l8 ;:s :> h~"

;:s •rl +' 0 "' "' "+' "' 'H <]) m (.) • s <]) <]) Q <]) .-o ·rl

"..C:'H 0 @ <!!+' 0 CQ if.; ·r-l "' <I!

<!!+'rl;:JS '" mP< o~

<H • "' .-o :>, "' "' '1 <]) ;:s •rl <]) .-l Q ~ •Cf.lriHrlrdO

··rl h o ;:s m c ·rl w "' rl s m +'

"" •• :> <=: ·rl " m o 1 o m o "'.-o

~i::JCJ"-<<=1~§ +' 0 b IQO rl <!! '1:J <!! o

.-l ~~::J.-2.&!"" P<

"' " " +' <=I " "' ;:J+'o<=:wmo ~ WW<=IOS.O'H

H

21

"' Q <I! 0 :> Q •rl

·rl m '=: +'

QO..C: m +' Oco

Q •r-i •r-i 0 "'+' .-l

•rl ..c: m 0 +'+' co "' m •rl Q co Q.-j 0 ·rl <I! 0 (.) <I! .-l " "' :> 0+' Q (.) •rl

·t/0 "' 0 ·rl +' Q (.) m 0 " 0 :> (.) m (.) " " <]) •rl +' <]) CJ..C: P,O "' •rl "' 0 "' Q P< "·rl 0 0 "+' (.) 0

" <]) 0 § 0 +'..C: "' <Ii

(\J

0 •rl "'·rl Q "' H m ·rl ·rl

B.

I " •rl 0 .-l "' 'H o..c: UO+' Q QO (Y)

0 Q -..... (.) <I! .-l

" CJ+' ·rl "' co P< @ 0 " " m +' <]) o..c: 0

"' "' 0 ·rl (Y) Q <!!· m @

co "' Q '& m <])

:> (.) •rl " •rl QO 0 P< 'H 0 Q

" 0 +' ·rl .-0-0+' -..... "' m .-l HCO

II

'H I Q .-o I ~

" 0 <1!..-l <]) ·rl "' <I! :> +' IP< ;:s "' wm-.....

:> .-o (.) Q +' 0)

;:s •rl •rl <]) ;:s +' B. "'"+'rl +'.0<1 m CJ o <ll "-< <])

"ll~~::JO,.':'j,&i Q

·rl OW'HO ..C:•rl<=l "' Q) () Cf.l CJ 0 oj

~r ·rl m t/0,0 I

if.;. Cl) r-1 0 Q ~ <ll ;:s m "' " .-l

l-' 0 Ul Pi •rl P<O ·rl H •r-1 ,..r::: P< •rl " <]) CJ8 m+' 0 (\J

'H '" :> <=:~ m"-< -..... 0 ·rl co .-l

CJ.<=~ " IP< § co +' I f'-' P< • -..... <ll 0 b.till u:J. ;:so "' II

.-j IQ "t/0 "'"" ;:s P< <I! 0 <]) 'H

"' H •r-::~ H " s ~

"' ;:$+' m+' " 0 0 ~ "' "' s "' O'Hcc:J

" 0

"" H H m

--~~-~.,;ltw~:;'_·~"'~!!i-ililillljllllllllllllll----------lll!\1.~-------------------··········

22 GEOTECHNICAL ENGINEERING

of Af . Isotropically consolidated tests, with corrections to relate them to in situ anisotropic conditions, shou],§_ll_q_t __ p_e __ used in lieu of anisotropic consolidations unless no other alternative is available.

Anisotropic Material Behavior

In addition to the effect of anisotropic consolidation stresses on undrained shear strength, the soil may itself exhibit anisotropic characteristics in which the shear strength varies with the direction of the failure plane (51) . tJJ ke.o ~ , \2_,\l,. ,

Where low safety factors are sought for economic reasons and the consequences of failure permit increased risks, tt is necessary to consider the effects of anisotropic material behavior, as distinct from effects of anisotropic consolidation stresses. This requires trimming specimens at various inclinations to obtain shear planes at different angles, This is burdensome and is rarely done. Some field failures have been ascribed to anisotropic material behavior that was not anticipated, Even relatively uniform soils may have shear strengths' on horizontal failure planes that are 10 percent less than that for usual test conditions. For some soils, the reduction may be far greater, as much as 4o percent of the usual triaxial compressive strength. Since this aspect of material behavior is rarely investi­gated in practical work, safety factors must be adequate to compensate for this effect.

Effect of Strain Rate

It is impossible to perform undrained laboratory tests slow enough to simulate field loading. Nevertheless, we routinely use tests performed at relatively rapid strain rates for stability analy­ses. Obviously we depend on adequate safety factors to cover a de­ficiency in testing. Many materials are sensitive to strain rate effects (51), as shown in Fig. 12 for tests made at MIT on specimens

0.36

DATA FROM LADD ET AU27) REPORT TO C E.

-" 0.32 b' !=t [ti' "' :0

J:lit3'

0.24

0.20 0.5 5

STRAIN RATE € 0/o / HR

FIG. 12.--EFFECT OF STRAIN RATE ON SHEAR STRENGTH TRIAXIAL COMPRESSION TESTS, NORMALLY CONSOLIDATED CLAY

EMBANKMENTS

from the Atchafalaya Basin in Louisiana. This plot shows that if a specimen were to reach peak deviator stress at 5 percent strain in 15 minutes, it would be 20 percent stronger than a specimen reaching failure in 10 hours. The effect of strain rate is obviously of much importance, particularly where low safety factors are used.

For San Francisco Bay mud, Duncan and Buchignani (16) state

23

"For loads maintained a week or longer, the shearing resistance is only about 70 percent of the value measured in conventional triaxial tests." Much other data (51) corroborates these findings. While the Bay mud and Louisiana clays are typical of only some soils, the ef­fects of strain rate on them is typical. Obviously usual testing times leave much to be covered by safety factors.

Tensile Testing for Cracking Studies

Cracking, as distinct from shear displacement, implies that the tensile strength of the embankment material has been exceeded. Obvi­ously tensile strength and stress-strain characteristics a~e of major importance in cracking studies.

Finite element studies (11,13,19) of development of tensile zones in embankment dams generally utilize moduli of deformation in tension that are much less than corresponding moduli in compression. The moduli in tension have to be assumed because adequate test infor­mation has not been available. Tests at the WES (1,2) show that moduli of deformation in tension, using a hollow cylinder device, were larger than moduli in compression using unconfined compression tests for comparably compacted soil specimens. This surprising result was also found at Cambridge University (Parry, Reference 38) using both beams and uniaxial compression tests with deformations measured by x-radiographic techniques with lead-shot markers.

Failure conditions in which one principal stress is tensile while the others are compression correspond to field conditions of cracking in dams but have not been studied to any significant degree under con­trolled laboratory conditions. Limited tests at the WES (1) show that when one principal stress was tension, its value increased when the magnitude of the other principal stresses, which were compressive, increased. While this result, which is rather surprising, appears in­consistent with conventional failure theories, it may reflect the im­portance of the mean or octahedral normal stress on the tensile strength of soils. The octahedral normal stress can be positive even though one principal stress is negative and an increase in the com­pressive principal stresses may permit the principal stress in tension to be larger. It is obvious that the subject of cracking requires ex­panded laboratory research of the behavior of soils under various com­bined stress conditions.

24 GEOTECHNICAL ENGINEERING

APPLICATIONS OF STABILITY ANALYSES

General

Stability analyses are generally made for limiting conditions such as (a) end of construction, (b) sudden drawdown and steady seep­age for embankment dams, and (c) long-term conditions. Where founda­tion materials are highly overconsolidated, they may contain joints, faults, and other weakened surfaces along which only residual or mod­erately higher shear strengths may be realized. For such conditions, selection of appropriate shear strengths and pore water pressures may be so difficult that stability analyses are of marginal value. This difficulty may be partially overcome by field in place tests and by testing large specimens, but the substantial cost of such tests gen­erally precludes definitive investigations.

End-of-Construction Stability

Stability at the end of construction is a minor factor for low embankments on good foundations but is of major importance for high embankments, such as dams, and for all embankments on soft foundations. The practice at the present time is to use either total stress or ef­fective stress approaches, with shear strength bases as summarized-in Table 13.

Total Stress Analyses.--The total stress approach uses a shear strength determined from unconsolidated-undrained tests. Compacted materials are tested at a range of placement densities and moisture contents to determine placement requirements consistent with available borrow materials and climatic environment. No drainage during con­struction is usually assumed. Where embankment materials are of a cohesive nature, the shear strength envelope has a substantial cohe­sion intercept and a relatively low friction angle, as illustrated in Fig. 13. If such an envelope is used for design, the shear strength corresponding to low normal stresses is partially developed from ten­sion in the pore water. The result is that a portion of the embank­ment (see Fig. 14) is, in effect, assumed to develop negative pore pressures while the remainder develops positive pore pressures. Field observations on conventional piezometers (12,48) generally show negli­gible positive pore pressures to significant depths below the embank­ment surface, implying negative pore pressures at higher elevations. It may not be conservative to rely upon negative pore water pressures because of the effect of adverse climatic conditions, especially if construction requires several years. Quite possibly, some cases where the rate of fill placement had to be decreased because of excessive movements during construction should be attributable to a design con­cept that partially relies upon negative pore water pressures, rather than to a deviation of placement moisture contents from design values. This would, of course, depend on climatic conditions.

While there is much evidence to suggest rather strongly that end­of-construction stability can be satlsfactorily determlned ln the usual manner using UU or Q envelopes, lt-·a:_ppearsd.esirahl.:enot'-to

G-< 0 "' .,.;

"" "'

(Y)

0 :>, (\J ,S::rl +' (1j

~.)il

"' <V 'M +' .,.; Ul >:: <V

"" +' >:: <V s <V CJ (1j rl p,

"" rl <V

·rl G-<

H <V <V "' ~ ;:J 0

0 +' :>, CfJ ro <V

u

+'

"' §

EMBANKMENTS

~ .,.;

+' "' CJ "' <V <V

G-< H "-<+' l'il "'

CJ

"' <V H

<V ;:J

H "' 0 "' p, <V

H p,

0 +'

"" >=: 0 p,

"' <V H H 0 CJ

<V ~ .,.; +' Ul

CJ "' <V <V G-< H "-<+' l'il "'

u

<V H 0 p,

H <V

"" .,.; <V CfJ H >=: ;:J Orl CJ .,.;

(1j +'"-< 0 >=: 0

+' 0

"" ;;; "' <V <V.S::

"' "' CfJ <V s >-< 0 +' H Ul'H

>-< bD (1j >=: <V 'M .S::+> Ulrl

;:J ""CfJ

§ ~ <V "' ~ <V

'M bD +' >=: CJ (1j <V.S::

G-< CJ G-<

<V <V H

"";:J <V CfJ

+' "' ;:J <V P<>-< s p, 0

0

<V ~ 0

~

rl

CJ

25

26

': "'3

"' "' a: >-"'

GEOTECHNICAL ENGINEERING

2 3

" [2_ !CL.O M LA 0'1 i) t () tr FA-1 L-v.,rti: '81\v~L-oPG-

//

SHEAR STRENGTH USING Q ENVELOPE

4 5 6 NORMAL STRESS 1 cr.-

FIG. 13--UNCONSOLIDATED-UNDRAINED OR Q TEST ENVELOPE END OF CONSTRUCTION CONDITION

FIG. 14.--DESIGN FOR CONSTRUCTION CONDITION USIN~ Q STRENGTH

lower safety factors below l. 5 and certainly not less than abont 1 3 unless the possibility of decreased shear strength at low stresses is carefully considered.

Sudden Drawdown Stability Analyses

In total stress procedures for analyzing partial or complete sud­den drawdown, the assumption is usually made that the effective normal stress on the failure surface after drawdown is the same as the effec­tive normal stress prior to drawdown (29,60). This is basically equiv­alent to the procedure suggested by Bishop (5-8). Both procedures neglect the effect of pore pressures associated with shear during un­drained load reduction, which is conservative according to Bishop (6). The mechanics of pore pressure and stress changes during sudden draw­down (6) are sometimes misunderstood. These changes involve a de­crease in total stresses, cr1 and cr3 . Since cr

3 decreases more

rapidly than crl , shear stresses increase. External water pressfres decrease as a consequence of drawdown, thereby increasing the over­turning forces tending to cause loss of equilibrium. Conventional approaches are generally rather conservative (4,39,41) because dissi­pation of pore water pressures as drawdown occurs is neglected.

EMBANKMENTS 27

The total stress approach for sudden drawdown formerly used the envelope for consolidated-undrained tests (see Fig. 15), even at low confining stresses. This envelope is still sometimes used, although it results in a substantial shear resistance at low confining stresses from tension in the pore water. The current practice of the Corps of Engineers and of others is to use a combined envelope, normally ferred to as an S R envelo e to avoid reliance on she - ) sociated with negative pore water pressures. l.\J /T.:>II't l.. 51~~ l'>v>~'St<;.

"' "' "' a: >-"' a: ;:'i J:

"'

j'

cat.isou~ATE(),-UNDRArNm -c__u- r2-ENVELOPE .

COMBINED s~TNi/ELOPE

EFFECTIVE STRESS ENVELOPE

NORMAL STRESS , {y

FIG. 15.--SHEAR STRENGTH RESULTING FROM NEGATIVE PORE PRESSURES IN UNDRAINED SHEAR

The need for an S-R combined envelope is avoided if an effective stress analysis is used, since shear strengths associated with nega­tive pore pressures are automatically excluded because the effective stress envelope is used in association with positive effective normal stresses.

The use of a combined S-R envelope for sudden drawdown analyses introduces special problems when the upstream slope consists of rela­tively impervious soils. Where this occurs, the critical sliding sur­face becomes shallow, and the analysis approximates drawdown for an infinite slope. This results in relatively flat slopes, although the safety factors for interior sliding surfaces that would affect the safety of the embankment would be large. This poses the following question: Should the embankment be designed to permit shallow slides that involve small quantities of material or only for deep interior sliding surfaces that affect the safety of the embankment? In con­sidering this question, it is, perhaps, relevant that sudden drawdown and an infinite slope analysis correspond closely to a steady seepage condition out of the upstream slope, as occurs following drawdown.

Engineering judgment is an essential element in selecting design criteria for the conditions described since the cost of effecting re­pairs is significant. Even shallow slides of an upstream slope dis­rupt the riprap and require repairs under adverse conditions. The reservoir may rise and interfere with the work. Also, riprap may be

28 GEOTECHNICAL ENGINEERING

difficult to obtain and expensive in the small quantities required. Some engineers faced with repair of shallow upstream slides have con­cluded that embankment design should be based on shallow failure sur­faces if analyses show them to be critical. While other engineers conclude that shallow slides should not be taken this seriously, and constitute an acceptable maintenance problem, the differing views il­lustrate the advantages of using a zone of free-draining material beneath the outer slope if it is available. A pervious zone in only the upper part of an embankment is advantageous where drawdown is re­stricted to the upper part of the reservoir. The most severe drawdown conditions probably occur at pumped storage projects.

Effective Stress Analyses for Nonfailure (Design) Conditions

Effective and total stress analyses of failures should both be made where practicable. Effective stress analyses contribute greatly to an understanding of embankment and foundation behavior and have much to recommend them as supplements to total stress analyses, or vice versa according to one's viewpoint.

While effective stress analyses of failure conditions are valu­able and straightforward, the manner in which they should be used for nonfailure conditions is not so obvious. Effective stress analyses in conjunction with pore pressures measured in piezometers or computed from undrained one-dimensional compression or other analyses assume the stress path to failure is along vertical line OB in Fig. 16. As pointed out by Barron (3), other stress paths are possible, such as OA and OC, and is not logical nor necessarily safe to assume that the >£­fective stress path is OB. This was previously stated by Gould in Navy DM-7 (14) in the following way: "Where ... pore pressures are de-veloped during shear ... utilize pore pressures ... in effective stress analysis with strength c and 121 from CU tests." Also, "In mate­rials where no (large) pore pressures are developed during shear ... evaluate pore pressures ... and apply them in effective stress analysis with c' and 121' strengths." This approach considers measured pore pressures in determining the effective normal stress prior to shear. Pore pressures developed during shear are accounted for by using c

"' "' w a: 1-

"' a: < w :r

"'

EFFECTIVE STRESS PATH USED IN EFFECTIVE STRESS ANALYSES /

Ar=l/2 Q-SIN ¢')(STRESS PATH OB) :}?/POSSIBLE STRESS ¢' At A PATHS

20° 0.33 -~ ...._ / 25° o. 29 t0~1N SITU STRESSES 30° 0.25 :

NORMAL STRESS

I I I

J CfN=ON-J.L

FIG. 16.--EFFECTIVE STRESS ANALYSES

EMBANKMENTS 29

and 121 from undrained tests. This is reasonable. The effective stress principle as presented by Terzaghi (57) requires that shear stress, pore water pressure, and effective normal stres~ re~ate to_ conditions at failure. The shear strength may be too hlgh lf posslble pore pressure increases resulting from shear are neglect~d (58).

Effective stress analyses are often used to evaluate stability of unfailed embankments during or after construction, using pore water pressures measured by piezometers to compute effective no~mal . stresses, and this is frequently considered one of the maJor beneflts from installing piezometers. Effective stress analyses assume that the stress path to failure from point 0, Fig. 16, corresponds to path OB, which has an Af value of 1/2(1- sin 121'! . This may not coincide with actual Af values developed in undralned shear.

The ratio of the shear strength normally assumed in effective stress analyses to the actual strength available is illustrat~d in Fig. 17, using computational procedures given in Fig. 8. It lS

2.0

1.5 2.0

\9--<-~t A{-

T

l£.__r;____,._.. (} fc Ts IS NORMALLY USED IN

EFFECTIVE STRESS ANALYSES

2.5

K - iJ, c c- U3c

3.0

Ts (UNCONSERVATIVE), 'Ys>'YA

Ar=l/2 (I-SIN¢')

T8 (cONSERVATIVE), 'Y8 < "l'A

3.5 4.0

FIG. 17.--SHEAR STRENGTH ALTERNATIVE--EFFECTIVE STRESS STABILITY ANALYSES

apparent that the usual effective stress approach give~ lower shear strengths than will actually develop if smal~ or n~gatlve pore pres­sures are developed during undrained shear, l.e., lf Af _values_are less than about 1/4 to 1/3 Af ~ 1/2(1 - sin 121') for lsotroplcally consolidated tests. However, if substantial pore pressures are de­veloped during shear (Af > l/4 to 1/3), the usual effect~ve stres~ approach gives too high shear strengths. This may result ln excesslve computed safety factors, especially for embankments on soft foundations.

The effect of using the conventional effective stress approach is further illustrated by the effective stress path shown in Fig. 18 for a laboratory test having Af about 0.8. Points A, B, and C c~rre­spond to possible field shear and effective no~mal str~ss comblna­tions, while point D gives the shear strength lf undralned shear

30

"' ~ 0: .... "' 0:

~ I en

GEOTECHNICAL ENGINEERING

¢'

NORMAL STRESS CYt

11EFFECTIVE STRESS 11

ANALYSIS SAFETY FACTOR, SAFETY FACTOR, C', ¢'STRENGTHS CU STRENGTHS

A

B

c D

3.37

1.89

1.40

1.00

EFFECTIVE STRESS PATH

2.02

1.31

1.13

1.00

FIG. 18.--EFFECT OF STRENGTH ASSUMPTIONS ON SAFETY FACTOR

f~ilure were to develop. The safety factors for conventional effec­tJ.ve__§,nd_iotal stress approaches summarized on this figure indicate that the conventional effective stress approach gives much too high safety factors -~L _ _Af-..~~rge, -~:!E-_this ~

. ~he data presented suggests that the usual effective stress anal­ysJ.s J.s conservative for well-compacted embankments, but this probably depends on t~e embankment height. T_hese data also suggest that the usual effectJ.ve stress approach is unconservative, i.e. computed safety factors are_too high, for embankments constructed of wet clay or on soft foundatJ.ons. This shortcoming of effective stress analyses for nonfailure conditions can be overcome by explicitly including pore pressure developed during shear.

I~ may be argued that the difference between total and usual effectJ.ve stress approaches results from a difference in the defini­tion of"the safety fa~tor. However, both approaches define the safety factor ·:.as the r~tJ.o of the available shear strength of the soil to that requJ.red to maJ.ntain equilibrium," Bishop (6,8). It appears, therefore, that total and usual effective stress analyses for nonfail­ure conditions have different concepts of available shear strength. I~ ~lso appears that many effective stress analyses do not relate suf­fJ.cJ.ently closely to soil behavior during undrained shear.

SPECIAL PROBLEMS

Creep Movement

Slope indicator measurements show that substantial lateral move­ments in embankments and foundations occur more frequently than had been expected. This is especially the case where consolidation occurs slowly, as where clay foundations are thick without intermediate drainage layers. As previously mentioned, such conditions ·caused tfie Corps of Engineers, New Orleans District, to construct various test sections (24,27) to determine reasons for adverse field behavior. Slope indicator observations indicated lateral movements of as much as 3 ft, resulting in substantial vertical subsidence of th~ levee crown. These lateral movements occurred with only a small amount of

~-

EMBANKMENTS 31

consolidation, indicating that the problem of lateral defor­mations was important and long-continuing.

An empirical relationship between safety factors and lateral deformations of the test sections is illustrated in Fig. 19 relating lateral movements from slope indica­tors and design safety factors computed by a sliding wedge analysis by the New Orleans District for the initial or as-constructed condition. As a result of the type of in­formation shown in Fig. 19, the safety factor for new levees constructed on thick, soft clay foundations was in­creased to 1.4 and more re­cently to 1. 5.

40

x~Nll,FLOODWAY SIDE :i MAl? 1 .: 30 2

X l!, LANDSIDE z ' "' ][, FLOODWAY SIDE X\ ::1

w >

20 0 ::1 .J In,LANDSIDE X < 0:

"' .... 10 < NOTE' LATERAL MOVEMENTS .J

MEASURED AT El-20, 55' FROM 'f.

0~-----L----~L------L----~----~ 1.0 1.1 1.2 1.3 I. 4 1.5

FACTOR OF SAFETY

FIG. 19.--LATERAL MOVEMENTS VERSUS SAFETY FACTOR, WEST ATCHAFALAYA BASIN PROTECTION LEVEES, TEST SEC­TIONS II AND III (NEW ORLEANS DIS­TRICT, CE)

Because of the large. creep deformations observed in the test sec­tions, the New Orleans District sponsored extensive research, being done under Ladd at MIT, to determine if creep can be predicted. This work (18,21,27), and additional creep studies performed by Palmer-ton (36) at the WES using finite element analyses, are still in the re­search stage. Nevertheless, experimental techniques and finite ele­ment and other computational procedures being developed now permit creep deformations under undrained shear loadings to at least be esti­mated. The results are promJ.sJ.ng, but empirical observations such as illustrated in Fig. 19 may be more reliable for some time.

While only postconstruction creep deformations have been dis­cussed, excessive deformations may occur during construction even though conventional safety factors may be adequate. Nevertheless, postconstruction creep deformations may be more important.

Clay Shale Foundations

Clay shale foundations have been especially troublesome and con­ventional testing and analyses may have little value. Large-diameter test shafts are about the best means for interpreting subsurface con­ditions. While preconsolidated clays develop low pore pressures for loadings less than their preconsolidation stress, this is not true for clay shales. Some, but not all, clay shales develop high pore pres­sures on loading and consolidate extremely slowly. The high pore pressures combined with preexisting weakened surfaces have caused many construction difficulties.

Some engineers are convinced that horizontal and other drains are effective, but drainage may be difficult to achieve since abnormally

32 GEOTECHNICAL ENGINEERING

high pore pressure gradients near drainage faces are often found, making it difficult to relieve pore pressures at moderate distances from drainage faces.

While testing and analyses have their place, final design may have to be based on empirical observations of similar materials.

Clay Shale Embankments

. Shale has been used successfully in embankments, but an increas-lng number of such embankments are giving serious problems. The Federal Highway Administration is studying problems with shale embank­ments and has much unpublished data available. Until the results of this study are complete, shale should be used with caution and it seems advisable to place and compact clay shale as soil and not as un­compacted rock fill.

Dispersive Clays

Some clays erode, disperse, or deflocculate in a remarkable and unexpected manner. This behavioral characteristic was discussed by Sherard, et al., at the 1972 ASCE specialty conference held at Purdue University (45,46) and by others (47). While this behavior is still being studied, principally by the Soil Conservation Service and more recently by the Corps of Engineers, it appears of sufficient impor­tance to use the simple criteria and soil test developed by the Soil Conservation Service and Sherard. It is not yet clear how widespread or serious dispersive clay problems are, nor if they can be modified by placing on the wet side or through use of admixtures. Mitchell and Woodward (33) investigated the possibility that dispersive clays were involved in California landslides but only 5 of 16 slides were pos­sibly of this category.

Embankments on Soft Foundations

The construction of embankments on soft foundations (10) presents a ;ariet~ of special problems including (a) stability, (b) strength galn durlng construction, (c) benefits of incremental construction with a consolidation phase between increments, (d) possible use of low safety factors dur~ng c~nstruction,. (e) creep deformations and crrep rupture, (f) two-dlmenslonal consolldation effects, and (g) means for treating or replacing soft foundations. The Highway Research Board is concerned with embankments on soft foundations and will soon publi~ a report on this subject.

The importance of embankments on soft foundations was evidenced at the Austin ASCE Specialty Conference, June 1974, by the workshop sessions and by the papers on (a) "Finite Difference Analyses for Sand Drain Problems," by Olson et al. ( 35); (b) "Precompression Analysis for Highway Embankments," by Krizak and Krugmann (25); and (c) "Design of Embankments on Peat," by Raymond (42).

EMBANKMENTS 33

FINITE ELEMENT ANALYSES

The rapid development of the finite element method (15,17,21,22, 26,37) is making it possible to estimate stresses and deformations in embankments and their foundations using nonlinear stress-strain prop­erties and variable Poisson's ratios to account for soil volume changes. While finite element analyses are expensive and somewhat time consuming for most purposes, the acceptance of seismic design procedures, incorporating as an initial step a static finite element analyses of an embankment and foundation, makes it practicable to uti­lize finite element analyses for both dynamic and static design for many projects. However, the technique has probably advanced beyond our knowledge of soil behavior.

Finite element analyses can be used to compute distributions of shear stresses, major and minor principal stresses, ratios of princi­pal stresses, and deformations. This makes it possible to determine if limiting equilibrium analyses are reasonable, and this approach has been used to evaluate limiting equilibrium methods by Wright,- Kulhawy, and Duncan (64). While finite element analyses are probably not needed or justified for most embankment design problems, their utility is great and they probably should be performed for the final section of major embankments such as high or critical dams. The cost of per­forming static finite element analyses is not large if adequate com­puters and experienced personnel are available.

APPRAISAL OF CURRENT TECHNIQUES

Because of the numerous factors that affect final evaluation of the stability of an embankment and its foundation, embankment analysis

" and design must be regarded as partially an empirical process. The empiricism involved can be reduced, or at least better understood, by studying the influence of individual factors involved. Duncan and Buchignani (16) did this in connection with an investigation of a slope failure and more efforts of this type are needed. Their evalua­tion for soft San Francisco Bay mud, summarized in Table 14, is that usual laboratory tests indicate shear strengths 20 to 30 percent higher than in situ values, although laboratory strengths determined in the usual manner were only 15 percent higher than strengths back­figured from failure conditions. Progressive failure was not con­sidered significant for these soils.

Evaluations of the type shown in Table 14 can be extended to cover additional factors for embankment design. Admittedly, such ef­forts are extremely subjective and hardly defensible; nevertheless, they appear worthwhile if only to focus attention on factors involved; see Table 15. An effort of this type suggests the following: For well-compacted embankments on good foundations, safety factors from conventional total stress analyses may be about 5 percent low to 15 percent too large; if Taylor's method of plotting R test data is used, safety factors may be 10 to 30 percent too high. Effective

34 GEOTECHNICAL ENGINEERING

TABLE 14.--FACTORS AFFECTING STABILITY ANALYSES

(After Duncan and Buchignani, Reference 16)

Effect is to:

Factor

(l)

Sample disturbance

Used rough caps and bases in triaxial compression tests, too much end restraint

Used vertically oriented test specimens, neglecting an­isotropic material behavior and lower shear strengths for other failure plane orientations

Used triaxial instead of plane strain equipment

Laboratory triaxial tests performed too fast (usual practice)

Underestimate In Situ Strength

Percent

(2)

10-20

5

Summation 15-25

Net effect

~estimate In Situ Strength

Percent

(3)

5

10

30

45

20-3.Q

(Lab strength too high)

stress analyses for compacted embankments may give saf~y factors that are about 5 percent low for Af less than l/4 to l/3 and 50 percent high for Af more than these values. The latter might occur only for very high embankments and would probably be unusual. When the ~ame approach was tried for clay embankments for soft foundations, the safety factor from total stress analyses was 20 percent too high to 20 percent too low while the safety factor from effective stress anal­yses was up to 40 percent too high. The total stress approach seems preferable for this case.

Evaluations of this type have little meaning unless they are done for a specific site and conditions, but even then required data are not usually available to permit reliable conclusions. Nevertheless, such efforts have value if their primary purpose is to suggest that

I I f

EMBANKMENTS 35

TABLE 15 .--FACTORS INFLUENCING DESIGN SHEAR STRENGTHS~ Factor

(1)

Sample disturbance of foun­dation materials

Effect of fissures in clays, especially highly overcon­solidated clays and clay shales--effects not reflec­ted in tests on small samples

Rough caps and bases in lab­oratory tests

Triaxial compression instead of compression, simple shear, and extension tests

Triaxial instead of plane strain tests

Back-pressure saturation

Conventional plotting of R or CU test data, as total stress envelopes

Isotropic, instead of anisotropic, consolida­tion in R or CU triaxial compression tests

(a) Af > 1/4 to 1/3

(b) Af < 1/4 to 1/3

Anisotropic material behavior--use of verti­cal instead of inclined test specimens

Conventional rates of shear in laboratory testing

Progressive failure

Conventional effective Stress design shear strengths

(a) Af < 1/4 to

1/3 ; i.e. embanlunent

(b) Af > 1/4 to

1/3 ; i.e. soft foundations

Influence, percenta

(2)

-(5-20)b

+(25-1000)

+5

+(20-30)

-(5-8)

Depends on embankment height (significant)

-(l5-20)

-(0-30)

+(0-20)

+(10-40)

+(5-200)

+(0-20)

-(0-30)

+(0-50)

Effect: + = unconservati ve; causes too high strength; -strength.

b For relatively good undisturbed samples.

Remarks

(3)

Remolding may increase strength of slickensided specimens. Disturbance is greatest for deep borings and soft soils

Generally a factor only for highly overconsolidated soils

Especially important for foundation soils

May cause grossly excessive strengths in R tests at low confining stresses; conser­vative at high confining stresses

Does not apply for Taylor plotting

Values shown assume test enve­lopes for isotropic consoli­dation interpreted as 'f versus Ore ; i.e. as used by designers in stability analyses

Effect depends on rate of test­ing, soil type, rate of con­solidation in field, etc.

Depends--on soil; mainly a fac­tor for foundation soils· May be more serious than shown for some soils

Values shown are for non­failure or design conditions only; not for failure conditions

conservative; causes too low

36 GEOTECHNICAL ENGINEERING

usual safety factors are working and not reserve elements of embank­ment design. Such efforts suggest that the common experience that 2resent embankment design procedures are satisfactory for safety fac­tors around l. 5 is quite reasonable. __ However ~._:iJ: ... J..9ii"~"T--:Sai"~.iL.:iic.:.tW:.s are used_, ___ §.<l<O_qll!i.i;€_S.j;ability and tol~...§,ble deforll)g_j;_:h_0_rl,'Lcann_oj; __ bg ____ _ taken for granted and the effect of individual factors should be ev-;;:Iliated-:- -------- ---

It is perhaps remarkable that usual embankment design procedures succeed as well as they do. For an embankment on a soft foundation, for example, the practical design procedures of the New Orleans Dis­trict of the Corps of Engineers were about as satisfactory as highly sophisticated st·ate-of-the-art procedures, as illustrated in Table 10. This statement refers to total stress analyses only. The usual type of effective stress analysis was disappointing. This is probably be­cause usual effective stress analyses represent an extension of effec­tive stress principles to nonfailure conditions without considerin& ore pressures associated with undrained shear. This shortcoming does

not apply a to failure conditions, b where pore pressures used in effective stress analyses are estimated for failure conditions, or (c) where effective stress analyses are used with consolidated­undrained strength parameters, as suggested by Gould (14).

Since we must regard design procedures as partially empirical, it may be well to recall past design practices and changes that have gradually been made in them. This is especially important in evaluat­ing proposed changes in embankment design practice. Design experience seems to be about as follows. Between about 1940 and 1960 or 1965, total stress embankment design used (a) the ordinary method of slices, (b) consolidated-undrained strength envelopes with seepage saturation, and (c) the full CU orR test envelope. Effective stress analyses (where used) neglected pore pressures resulting from undrained shear to failure. Changes have been and are being made in some or all of these aspects (see Table 16) making it somewhat difficult to relate current design practices with experiences gained during the period 1940 to 1965 or 1970. It is quite apparent that some of the changes are unconservative while other changes, back-pressure saturation for tests at high confining stresses and S-R combined envelopes, are con­servative. On balance, total streqs design changes probably-are-con­servative and have reduced computed safety factors while effective stress design changes are unconservative and are increasing apparent, but not actual, safety factors.

While we sometimes sanctify our procedures by relating them to previous experience, this table shows that we are gradually chang~g the base of our experience. Changes made, and changes to be made, strongly suggest that we need to evaluate as part of design, the role of individual factors affecting embankment analysis and design. Theo­retical studies have progressed enormously rapidly and have left our understanding of soil shear strength and deformation behavior far be­hind. It seems timely to urge that we devote more effort to experi­mental investigations of soil behavior, considering creep, anisotropy, rate of strain, and other factors.

EMBANKMENTS 37

TABLE 16.--EMBANKMENT DESIGN CHANGES

Factor Approximate

Date of Changes

(l)

Stability analysis method:

(a) Ordinary method of slices

(b) Improved methods giving higher safety factors

Laboratory testing:

(a) Seepage saturation of consolidated-undrained tests

(b) Back-pressure saturation

Design shear strengths:

(a) CU or R test envelopes for drawdown analyses

(b) Combined S-R envelopes for drawdown analyses

SUMMARY AND CONDLUSIONS

General

(2)

To 1960-1968

After 1960-1968

To 1960-1965

After 1965

To 1968

After 1968

Analysis and design procedures relating to embankments need t~ em hasize improved understanding of the effect of variables whose ln­fl;ence is compensated by safety factors. The use of com~lex s~a- . bility analyses made possible by computers does not constltutedJUStl-fication for considering the results to_be mo~etac~ur~t;~ no~heo~:thod their use constitute a reason_for lowerlng sa et~ acfosh~ar strengths.

sis is not nearly as lmportant as selec lon o of a~al~actors compensate for the influence of relevant factors that Safen~t explicitly considered in normal design procedures. Safety are have alwa s been and currently are, working elements of em-~:~~~~t design a~d constitute more than a reserve of unused strength.

Conventional Stability Analyses

Conventional or limiting equilibrium types ~f stabi~ity anal~ses · te and even the most advanced lS relatlvely cru e, are all approxlma , · f t t• equi-

k rkably well. These procedures satls Y sa lC. yet they wor rema . l"f · assumptlons librium requirements to varying degre~s.f~r Slmp ~ Ylng but none satisfy stress-strain compatlblllty requlrements.

l h Probably been developed Conventional stability ana yses ave f needed. Even the most about as far as practicable, or as ar as

38 GEOTECHNICAL ENGINEERING

advanced are not normally carried sufficiently far to satisfy all static equilibrium requirements, but the consequences are negligible.

The ordinary method of slices satisfies moment equilibrium and assumes that the resultant of forces on the sides of a slice are par­allel to the base. It gives about the same result as the most ad­vanced techniques for 0 = 0 or 0 small. Hence, for these cases the ordlnary method of slices is appropriate and does not compensate for aspects not explicitly considered, such as creep and other fac­tors .. For 0 large, t?e o~dinary method of slices is not logical, especlally for steeply lnCllned portions of the failure surface. For c '. 0 materials with 0 substantial, there is no reason to use the ordlnary method of slices for final design. It can be used for com­parative purposes and should be used when relating.current techniques to design procedures previously in use.

F?r c , 0 materials and circular failure surfaces the Simpli­fied Blshop procedure is attractive because it gives about the same results as more complex procedures and is simple to use in manual com­putations. It is only slightly more time consuming than the ordinary ~ethod of slices. Taylor's force equilibrium procedure does not sat­lsfy moment equi~ibrium but generally checks closely more complete methods that satlsfy both moment and force equilibrium requirements. The inclination of interslice forces can be assumed too large for some conditions, giving somewhat high safety factors; hence, this method should be used with caution.

_T?e widespr~ad availability of computers means that virtually any stablllty analysls technique desired is practicable, even Morgenstern and Price, which is widely considered to be the most advanced. How­ever, Simplified Bishop and Spencer's methods seem the simplest, but a~y of t~e common methods can be used in accordance with the subjec­tlve deslres of the designer and the availability of appropriate com­puter programs. Fortunately, computer programs for all methods have been developed. Also, computer running times are small for all programs.

Sliding wedge analyses probably should be used more widely than presently done. Simple wedge analyses or more advanced programs such as the Morgenstern-Price, Janbu, Spencer, Taylor, Sarma, etc., can be used.

Credibility of Computer Solutions

The wides~read use of computers requires understanding and agree­ment about thelr potential credibility. The user of a program, no~ its developer, is responsible for establishing the credibility of com­puter solutions. The user should assume that a computer program (a) written by a competent programmer, (b) carefully checked out on check problems whose answers are known, and (c) used successfully 0~ a variety of problems may still give an unreliable answer. Reasons for this are the difficulty of completely "debugging" large programs and changes in subroutines that are made periodically in the computer itself.

EMBANKMENTS

The credibility of computer output can be established by:

a.

b.

Careful examination of results to determine if they look reasonable.

Using two or more entirely independent computer programs, i.e. force equilibrium, Simplified Bishop, Spencer, Morgenstern-Price, etc.

39

c. Making a hand solution of the critical circle. This requires use of the Simplified Bishop, Taylor's force equilibrium, or other procedures. This should be required for dams.

d. Using charts and approximate solutions.

Pore Pressures and Shear Strengths

Selection of appropriate design shear strengths is more variable and is more important than differences in currently used techniques for making stability analyses.

Triaxial compression tests are commonly used for determining the design shear strength along the entire failure surface. Shear condi­tions along different segments of the failure surface normally corre­spond to compression, simple shear, and extension tests. The use of triaxial compression tests to represent average shear strengths along the failure surface may result in design strengths that may be as much as 20-30 percent too large.

This effect is partially offset because plane strain better ap­plies to most field conditions than does triaxial compression. In this aspect, triaxial compression is conservative by perhaps 5 percent.

Back pressure saturation can result in too high shear strengths at low normal stresses in R or CU tests. For some materials, i.e.

"--.those that dilate during shear, the results can be grossly in error. This is avoided if S-R or CD-CU combined test envelopes, or effective stress analyses, are used.

Conventional plotting of R or CU test data is inconsistent with the way designers use test envelopes. The effect is that design strengths are 15-20 percent too low. This inconsistency is avoided by plotting test data as suggested by Taylor, also by Lowe.

Isotropic consolidation stresses are normally used in R or consolidated-undrained triaxial compression tests, even though field conditions correspond to anisotropic consolidation stresses. Taylor's method can be used to evaluate approximately this effect, or computa­tions for anisotropic strengths can be made using Skempton's A and B parameters at failure (49).

For embankments, and occasionally for foundations, designers use laboratory test envelopes as a relationship between shear strength and effective normal consolidation stress on the failure surface. If

40 GEOTECHNICAL ENGINEERING

Skempton's Af value for saturated soils is larger than l/2(1 -.sin 0') , isotropic consolidation gives lower shear strengths than anlsotropic consolidation for the same normal consolidation stress. However, if Af is smaller than l/2(1- sin 0') , isotropic consolidation gives too high shear strengths and is unconservative. This dividing value for Af is l/4 for 0' = 30° and l/3 for 0' = 20° .

If laboratory test data are regarded as a relationship between shear strength and effective major principal consolidation stress as done in SHANSEP (27) and c/p concepts, shear strengths for isot;opic and anisotropic consolidation are the same if Af = 1.0 . However, for smaller values of Af , isotropic consolidation gives too high shear strengths if the soils in situ are anisotropically consolidated. This was pointed out by Skempton and Bishop in 1954 (50).

Anisotropic material behavior may cause the shear strength of in­clined specimens to be 10 to 40 percent less than for conventional vertically oriented specimens.

The rate of shear or strain in conventional far too rapid to correspond to field conditions. strengths to be 5 to 200 percent too high.

Application of Stability Analyses

laboratory testing is This may cause shear

Conventional analyses have limited or no value for designing em­bankments on clay shale and similar foundations containing fissures slickensides, faults, and other geologic defects unless these featU:es are explicitly considered.

End-of-construction stability using total stress methods normally rely on a shear strength at low normal stresses that is associated with pore water tension. This is generally satisfactory but may not always be conservative.

Sudden-drawdown stability using total stress methods should use S-R or CD-CU test envelopes to avoid reliance on pore water tension. A possible alternative is to use seepage saturation (4 days or longer) without back pressure for tests at low normal stresses.

Effective Stress Analyses \

Effective stress analyses for nonfailure (desi n) as normally made assume a vertical effective stress path correspo ding to a value for Af of l/2(1 - sin 0') . Actual stress paths may yield higher or lower shear strengths.

If Af is less than l/2(1 - sin 0') , effective stress analyses as normally made are conservative; if Af is more than this value, such analyses are unconservative and give excessive safety factors. Alternatively, if Af is less than l/4(0' = 30°) or l/3(0' = 20°) , ~onventional effective stress analyses are conservative, but if Af ls more than l/4 or l/3 they are unconservative.

EMBANKMENTS 41

Approximately, effective stress analyses are conservative or sat­isfactory for well-compacted embankments but not for soft foundations. and possibly not for high or wet embankments, for which Af may be larger than l/4 to l/3.

Effective stress analyses for failure conditions are satisfactory and beneficial.

Safety Factors

In conventional embankment design the safety factor must compen­sate for many factors not explicitly considered. Consequently, safety factors are working elements of the design process and do not consti­tute a reserve of unused strength.

While adequate stability can often be achieved at low safety fac­tors, excessive deformations may occur for safety factors less than about 1.5. This depends upon the rate of foundation consolidation.

If analyses yield high safety factors, such as 2, 3, or more, Peck's 1960 safety factor chart should be reviewed (40). It may sug­gest that field conditions may be more complex than assumed and that unsuspected geologic weaknesses may be present.

Evaluation of Current Embankment Analysis and Design

Presently used embankment analysis and design procedures work re­markably well when safety factors of about 1.5 or more are used. When safety factors are less, the influence of relevant factors that are commonly ignored should be considered, not only as they affect sta­bility but also as they influence deformations.

ACKNOWLEDGMENTS

It is a pleasure to acknowledge the many benefits of stimulating discussions with Reginald A. Barron, George E. Bertram and John Lowe III. Special appreciation is owed Mr. Bertram for reviewing the paper and making many constructive comments. The same appreciation is due the writer's colleagues at the U. S. Army Engineer Waterways Ex­periment Station, CE, especially Messers. Don Banks, Walter Sherman, and Willian Strohm.

GEOTECHNICAL ENGINEERING

APPENDIX I.--REFERENCES

l. Al-H:'ssaini, M. M. and Townsend, F. C., "Investigation of' Tensile TestJ.ng of' Compacted Soils," Miscellaneous Paper S-74-10 Jun 1974, U. S. Army Engineer Waterways Experiment Stati~n CE Vicksburg, Miss. ' '

2. Al-:-Hussain~, M. M. an~ To;;nsend, F. C., "Tensile Testing of' SoJ.ls, A LJ.ter~ture VJ.ew, Miscellaneous Paper S-73-24, May 1973, U. S. Army EngJ.neer Waterways Experiment Station, CE, Vicksburg, Miss.

3.

4.

5.

Barron, R. A., Discussion of' paper by Bishop and Morgenstern "Stability Coeff'ic~ents for Earth Slopes," (Geotechnique 10:4: 129-150), GeotechnJ.que, Vol XIV, No. 4, Dec 1964, pp 360-261.

Bazett, D. G., Discussion, Proceedings of Conference on Pore Pressure and Suction in Soils, Butterworths, 1961, pp 134-135.

Bishop, A. W., "Some Factors Controlling the Pore Pressures Set Up Durin~ the Construction of Earth Dams," Proceedings, Fourth InternatJ.onal Conference on Soil Mechanics and Foundation Engi­neering, Vol II, London, 1957, pp 294~300.

Bishop, A. W., "The Stability of' Earth Dams " Ph. D. thesis sub­mitted to the Imperial College, University ~f' London, May 1952.

Bishop, A. W., "The Use of Pore-Pressure Coefficients in Prac­tice," Geotechnigue, Vol IV, No. 4, Dec 1954, pp 143-147.

Bishop, A. W., "The Use of the Slip Circle in the Stability Analysis of' Slopes," Geotechnigue, Vol V, No. l, Mar 1955, PP 7-17.

Bishop, A. W. and Bjerrum, L., "The Relevance of the Triaxial Test to the Solution of Stability Problems," Proceedings of ASCE Research Conference on Shear Strength of Cohesive Soils, Boulder, Colo., Jun 1960, pp 437-501,

Bjerrum, L., "Embankments on ence on Performance of' Earth ASCE, Vol II, 1972, pp l-54.

Soft Ground, " Proceedings, Confer­and Earth-Supported Structures,

Casagrande, A. and Covarrubias, S. W., "Cracking of Earth and Rockf'ill Dams: Tension Zones in Embankments Caused by Conduits and_Cutoff Walls," Contract Report S-70-7, Jul 1970, U. s. Army EngJ.neer Waterways Experiment Station, CE, Vicksburg, Miss.

Clough, G. W. and Snyder, J. W., "Embankment Pore Pressures During C~nstruction," Technical Report No. 3-772, May 1966, U. s. Army EngJ.neer Waterways Experiment Station, CE, Vicksburg, Miss.

13.

14.

15.

16.

17.

18.

19.

20.

21.

22.

23.

24.

EMBANKMENTS 43

Covarrubias, S. W. , "Cracking of' Earth and Rockf'ill Dams: ·A Theoretical Investigation by Means of the Finite Element Method," Contract Report S-69-5, Apr 1969, U. S. Army Engineer Waterways Experiment Station, CE, Vicksburg, Miss.

Department of the Navy, Bureau of Yards and Docks, "Soil Me­chanics, Foundations and Earth Structures," NAVDOCK Design Manual DM-7, 1961.

Duncan, · J. M., "Finite Element Analyses of' Stresses and Movements in Dams Excavations and Slopes, State-of-the-Art," Applications of the Finite Element Method in Geotechnical Engineering, Pro­ceedings of a Symposium held by the U. S. Army Engineer Waterways Experiment Station, 1-4 May 1972, C. S. Desai, ed., Sep 1972, pp 267-326.

Duncan, J. M. and Buchignani, A. L., "Failure of Underwater Slope in San Francisco Bay," Journal of Soil Mechanics and Foundation Division, ASCE, Vol 99, No, SM9, Sep 1973, pp 687-703.

Duncan, J. M. and Chang, Chin-Yung, "Nonlinear Analysis of' Stress and Strain in Soils," Journal of Soil Mechanics and Foundation Division, ASCE, Vol 97, No. SMll, Nov 1971, pp 1597-1615.

Edg~rs, L., Ladd, C. C., and Christiani, J. T., "Undrained Creep of' Atchafalaya Levee Foundation Clays, Vols I and II, Research Report No. R73-16, Soil Pub. 319, Feb 1973, to U. S. Army Corps of Engineers.

Eisenstein, z., Krishnayya, A. V. G., and Morgenstern, N. R., "An Analysis of Cracking in Earth Dams," Applications of the Finite Element Method in Geotechnical Engineering, Proceedings of a Symposium held by the U. S. Army Engineer Waterways Experiment Station, l-4 May 1972, C. S~esai, ed., Sep 1972, pp 431-455.

Fields, K. E. and Wells·, W. L. , "Pendleton Levee Failure," Trans­actions, ASCE, Vol 109, 1944, pp 1400-1413.

Foott, R. and Ladd, C. C., "The Behavior of' Atchafalaya Test Em­bankments During Construction," Research Report R73-27, Soils Pub. 322, May 1973, to U. S. Army Corps of' Engineers.

Hoeg, K., "Finite Element Analysis of Strain-Softening Clay," Journal of' Soil Mechanics and Foundation Division, ASCE, Vol 98, No. SMl, Jan 1972, pp 43-58.

Janbu, N. , "Slope Stability Computations," Embankment-Dam Engi­neering, Casagrande Volume, Wiley, 1972, PP 47-86.

Kaufman, R. I. and Weaver, F. J., "Stability of Atchafalaya Levees " Journal of Soil Mechanics and Foundation Division, ASCE, Vol 93, No. SM4, Jul 1967, pp 157-176.

44 GEOTECHNICAL ENGINEERING

25. JC;izak, R. J. and Kru~ann, P. K., "Precompression Analysis for HJ.ghwa;: Ernbankme~ts, :• Proceedings, Specialty Conference on AnalysJ.s and DesJ.gn J.n Geotechnical Engineering ASCE A t· Tex, 9-12 Jun 1974. ' , us J.n,

26. Kulh~wy, F. H;, and Duncan, J. M., "Stresses and Movements in OrovJ.lle Dam, Journal of Soil Mechanics and Foundation Division

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ASCE, Vol 98, No. SM7, Jul 1972, pp 653-666. '

Ladd, C. C. et al., "Engineering Properties of Soft Foundation Clays ~t Two South Louisiana Levee Sites," Research Report R72-26, SoJ.ls Pub. 304, Dec 1972, to U. S. Army Corps of Engineers.

Lee? K. L. and Morrison, R. A., "Strength of Anisotropical 'y Con­s?lJ.da~e~ ?ompacted Clay," Journal of Soil Mechanics and F~unda­tJ.on DJ.VJ.sJ.on, ASCE, Vol 96, No. SM6, Nov 1970, pp 2025-20h3.

Lowe, John, III, "Stability Analysis of Embankments " Journal of Soil Mechanics and Foundation Division, ASCE, Vol 93 No. SM4, Jul 1967, pp l-34. '

Lowe, John, III, and Johnson, T. C., "Use of Back Pressure to crea~e Degree of Saturation of Triaxial Test Specimens," Pro­ce:dJ.ngs, Research Conference on Shear Strength of Cohesi~ SoJ.ls, ASCE, Boulder, Colo., Jun 1960, pp 819-836.

In-

Low:, J?hn, III, and Karafiath, L., "Effect of Anisotropic Con­solJ.datJ.on on the Undrained Shear Strength of Compacted Claj's " Pr?ceedings, Research Conference on Shear Strength of Cohesiv~ SoJ.ls, ASCE, Boulder, Colo., Jun 1960, pp 837-858.

Middleb:;ooks, T. A., Discussion of "Pendleton Levee Failure" by K. E. FJ.elds and W. L. Wells, Transactions, ASCE Vol 109 1944 PP 1421-1424. ' ' ,

Mitchell, J. K. and Woodward, R. J. "Clay Chemist and Slo-.:-e Stb"l"t "J ' ry " a J. J. y, ournal of Soil Mechanics and Foundation Division, ASCE, Vol 99, No. SMlO, Oct 1973, pp 905-911.

Morgenstern, N. R .. and Price, V. E., "The Analysis of the Sta­bility of General Slip Surfaces," Geotechnique, v l 15 N -Mar 1965, pp 77-93. - 0

' 0

• .L,

Olson, R. E., Daniel, D. E., and Liu, T. K., "Finite Differenc\ Analyses for Sand.Drain Pro~lems," Proceedings, Specialty Con­ference on AnalysJ.s and DesJ.gn in Geotechnical Engineering ~. Austin, Tex., 9-12 Jun 1974. '

P~lme~ton, ~· B:, "Creep Analysis of Atchafalaya Levee Founda­tJ.o~, A?plJ.catJ.ons of the Finite Element Method in Geotechnical Eng~neerJ.ng, Proceedings of a Symposium held by the u. s. Army EngJ.neer Waterways Experiment Station, l-4 May 1972, c. s. Desai ed., Sep 1972, pp 843-862. '

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EMBANKMENTS 45

Palmerton, J. B. and Lefebvre, G., "Three-Dimensional Behavior of a Central Core Dam," Research Report S-72-l, Dec 1972, U. S. Army Engineer Waterways Experiment Station, CE, Vicksburg, Miss.

Parry, R. H. G., Lecture at U. S. Army Engineer Waterways Experi­ment Station, CE, Vicksburg, Miss., 15 Mar 1974.

Paton, J. and Semple, N. G., "Investigation of the Stability of . an Earth Dam Subject to Rapid Drawdown Including Details of Pore Pressures Recorded During a Controlled Drawdown Test," Confer­ence on Pore Pressure and Suction in Soils, Butterworths, 1961, pp 85-90.

Peck, R. B. and Lowe, John, III, "Moderators' Report, Session 4-Shear Strength of Undisturbed Cohesive Soils," Proceedings, Con­ference on Shear Strength of Cohesive Soils, ASCE, Boulder, Colo., 1960, pp ll37-ll40.

Pope, R. J. , "Evaluation of Cougar Dam Embankment Performance," Journal of Soil Mechanics and Foundation Division, ASCE, Vol 93, No. SM4, Jul 1967, pp 231-250.

Raymond, G. P., "Design of Embankments on Peat," Proceedings, Specialty Conference on Analysis and Design in Geotechnical Engi­neering, ASCE, Austin, Tex., 9-12 Jun 1974.

Sarma, S. K., "Stability Analysis of Embankments and Slopes," Geotechnique, Vol XXIII, No. 3, Sep 1973, pp 423-433.

Seed, H. B. and Sultan, H. A., "Stability Analyses for a Sloping Core Embankment," Journal of Soil Mechanics and Foundation Divi­sion, ASCE, Vol 93, No. SM4, Jul 1967, pp 69-84.

Sherard, J. L., Decker, R. S., and Ryker, N. L., "Hydraulic Frac­turing in Low Dams of Dispersive Clay," Vol l, Part l, '!;roceed­ings, Specialty Conference on Performance of Earth and Earth­Supported Structures, Soil Mechanics and Foundation Division, ASCE, Purdue University, Jun 1972, pp 653-689.

Sherard, J. L. , Decker, R. S. , and Ryker, N. L. , "Piping in Earth Dams of Dispersive Clays," Vol l, Part l, Proceedings, Specialty Conference on Performance of Earth and Earth-Supported Struc­tures, Soil Mechanics and Foundation Division, ASCE, Purdue Uni­versity, Jun 1972, pp 589-626.

Sherard, J. L. et al., Discussions of References 45 and 46, Vol III, Proceedings, Specialty Conference on Performance of Earth and Earth-Supported Structures, Soil Mechanics and Foun­dation Division, ASCE, Purdue University, Jun 1972:

a. Edward D. Graf and Harpal S. Arvra, p 105. b. Aldo R. Reginatto, p 107. c. 0. G. Ingles, pp lll, 119. d. Gordon R. Bell, p 127.

46 GEOTECHNICAL ENGINEERING

e. R. A. Rallings, p 131. f. Aurelio B. Vizcaino and Vicente C. Lattuade, p 135. g. Authors' Closure, p 143.

48. Sherman, W. C. and Clough, G. W., "Embankment Pore Pressures During Construction," Journal of Soil Mechanics and Foundation Division, ASCE, Vol 94, No. SM2, Mar 1968 (see closing discus­sion, Vol 95, No. SM6, Nov 1969, pp 1546-47).

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I I l '

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47

Wright, S. G., KulhawY, F. H., and Duncan, J. M., "Accuracy of Equilibrium Slope Stability Analyses," Journal of Soil Mechanics and Foundation Division, ASCE, Vol 99, No. SMlO, Oct. 1973, PP 783-792.

APPENDIX II.--NOTATION

The following symbols are used in this paper:

S-R

AC anisotropic consolidation;

Skempton's pore pressure parameters;

c = cohesion, total stresses;

c' cohesion, effective stresses;

cu IC

K c ML

p

Q

R

R

s u envelope

uu

consolidated-undrained test;

isotropic consolidation;

consolidation stress ratio; Kc a1c!a3c

silt, Unified Soil Classification System;

effective vertical stress;

unconsolidated undrained test;

consolidated-undrained test;

consolidated-undrained test with pore pressure mea­surements;

l/2(a1 - a3

) ;

combination of S-test envelope and R envelope such that for any normal stress the lower of the S or R strengths is used in design;

unconsolidated undrained test;

48

(Jl

01

(J3

(J3

Tf

TAC

GEOTECHNICAL ENGINEERING

major principal total stress;

major principal effective stress;

= minor principal total stress;

minor principal effective stress;

shear stress on the failure plane at failure;

shear strength on failure plane, anisotropically consolidated test;

shear strength on failure plane, isotropically con­solidated test;

angle of internal friction, total stresses; angle of internal friction, effective stresses;

angle of internal friction from consolidated­undrained tests; and

angle of internal friction from consolidated­undrained tests.

ANALYSIS AND DESIGN OF LIGHTLY-LOADED FOUNDATIONS

by

George F. Sowers, F., ASCE*

1 . INTRODUCTION

1.1 Foundation Engineering Overview

The narrow strip of land lying between Egypt on the south and Syria and Lebanon on the north has been the source of two contradictory cultural attributes for at least four milleniums: warfare and wisdom. The first has been almost continuous; the second climaxed nearly 2000 years ago, Although foundation engineering emerged only recently in technical literature of the region, it must have been on men's minds

·as they wandered across the sandy waste lands long ago because the following two quotations have come down to us from that past:

"A wise man bu i 1 t his house upon the rocks and the rain fell and the floods came and the winds blew and beat upon that house, but it did not fall because it had been founded on the rock. The foolish man built his house upon (loose) sand and the rain fell and the floods came and the winds blew and beat against that house and it fell and great was the fall of it."

Jesus of Nazareth as related by Matthew, 7:24

"Which of you desiring to build a tower does not first sit down and count the cost, whether he has enough to comp·lete it. Otherwise, when he has laid a foundation and is not able to finish, all who see it will begin to mock him ... "

Jesus of Nazareth as related by Luke, 14:28-30

These two quotations capsul ize foundation engineering. First, are the technical requirements of resistance to all the forces acting on the structure; if the foundation fai Is, all else fails with it. Second, is the impact on the total cost; until the foundation cost has been determined (and it may be a major part of the uncertainties facing a bui Jder) the cost of the structure cannot be properly eval­uated. Foundation engineering consists of reconciling these two con-

*Chairman of the Board/Consultant, Law Engineering Testing Company Regents Professor of Civil Engineering, Georgia Institute of Technology

49