interpreting pore-water pressure changes induced by water table fluctuations and mechanical loading...

Interpreting pore-water pressure changes inducedby water table fluctuations and mechanical loadingdue to soil moisture changes

Collins Ifeanyichukwu Anochikwa, Garth van der Kamp, and S. Lee Barbour

Abstract: Pore pressures within saturated subsurface formations respond to stress changes due to loading as well as tochanges in pore pressure at the boundaries of the formation. The pore-pressure dynamics within a thick aquitard in responseto water table fluctuations and mechanical loading due to soil moisture changes have been simulated using a coupled stress–strain and groundwater flow finite element formulation. This modelling approach isolates the component of pore-pressure re-sponse of soil moisture loading from that caused by water table fluctuations, by using a method of superposition. In thismanner, the contributions to pore-pressure fluctuations that occur as a result of surface moisture loading (e.g., precipitation,evapotranspiration) can be isolated from the pore-pressure record. The required elastic stress–strain properties of the aquitardwere obtained from the measured pore-pressure response to barometric pressure changes. Subsequently, the numerical simu-lations could be calibrated to the measured response by adjusting only the hydraulic conductivity. This paper highlights thesignificance of moisture loading effects in pore-pressure observations and describes an efficient technique for obtaining insitu stress–strain and hydraulic properties of near-surface aquitards.

Key words: soil moisture changes, elastic modulus, hydraulic conductivity, pore-pressure changes, piezometers.

Résumé : Les pressions interstitielles à l’intérieur des formations sous la surface sont affectées par les variations decontraintes dues aux charges ainsi que par les variations de pression interstitielle aux frontières de la formation. La dyna-mique des pressions interstitielles à l’intérieur d’un aquitard épais répondant aux fluctuations de niveau phréatique et auxcharges mécaniques causées par les variations d’humidité du sol a été simulée à l’aide d’une formulation couplée decontrainte-déformation et d’écoulement d’eau souterraine par éléments finis. Cette approche de modélisation isole la compo-sante de la réponse des pressions interstitielles à un chargement par l’humidité du sol de celle causée par les fluctuations dela nappe phréatique, et ce, à l’aide d’une méthode de superposition. De cette façon, les contributions aux fluctuations depression interstitielle causées par les charges de l’humidité de la surface (ex. précipitation, évapotranspiration) peuvent êtreisolées de la mesure de pression interstitielle. Les propriétés en contrainte-déformation élastiques de l’aquitard nécessairesont été obtenues par des mesures de variations de pression interstitielle causées par les changements de pression baromé-trique. Par la suite, les simulations numériques ont pu être calibrées sur les réponses mesurées en ajustant seulement laconductivité hydraulique. Cet article présente l’importance des effets de chargement par l’humidité sur les observations depression interstitielle et décrit une technique efficace pour obtenir les propriétés de contrainte-déformation et hydrauliques insitu d’aquitards situés près de la surface.

Mots‐clés : variations d’humidité du sol, module élastique, conductivité hydraulique, variations de pression interstitielle, pié-zomètres.

[Traduit par la Rédaction]

Introduction

A change in the volume of water stored near the groundsurface, whether as soil moisture, surface water or snow, rep-resents a change in the total weight acting on underlying for-mations and will be reflected in changes of pore-fluidpressure (van der Kamp and Maathuis 1991; van der Kamp

and Schmidt 1997; Bardsley and Campbell 2007). Thismechanical loading, referred to as “moisture loading” in thispaper, induces a pore-water pressure response within theunderlying saturated formations in the same manner as thatproduced by construction of an areally extensive surface fill(Bishop 1954; Skempton 1954). Changes in pore pressurewithin a confined aquifer in response to changes of total

Received 14 December 2010. Accepted 22 November 2011. Published at www.nrcresearchpress.com/cgj on 28 February 2012.

C.I. Anochikwa* and S.L. Barbour. Department of Civil and Geological Engineering, University of Saskatchewan, 57 Campus Drive,Saskatoon, SK S7N 5A9, Canada.G. van der Kamp. Environment Canada, National Hydrology Research Centre, 11 Innovation Boulevard, Saskatoon, SK S7N 3H5,Canada.

Corresponding author: Garth van der Kamp (e-mail: [email protected]).*Present address: MDH Engineered Solutions, Member of the SNC-LAVALIN Group, 232-111 Research Drive, Saskatoon, SK S7N 3R2,Canada.

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Can. Geotech. J. 49: 357–366 (2012) doi:10.1139/T11-106 Published by NRC Research Press

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mechanical load at the ground surface have also been recog-nized in the groundwater literature for such cases as tidalloading of subsea aquifers and barometric pressure changes(Jacob 1940). There is an extensive body of literature dealingwith the analysis of such effects (e.g., Rojstaczer and Agnew1989; Rasmussen and Mote 2007), which have been ob-served to depths of kilometres (Schulze et al. 2000). In spiteof this early work in both hydrogeology and geotechnical en-gineering, the influence of surface moisture loading on pore-pressure fluctuations has not been generally recognized. Theeffects may be subtle, but recognition and analysis of pore-pressure responses induced by moisture loading can be usefulin interpreting pore-pressure changes and can potentially beused to enhance understanding of the site hydrology (Marinet al. 2010). Under appropriate site conditions and hydrogeol-ogy, the pore-pressure responses can also provide a measureof the in situ compressibility and permeability of the forma-tions (Jacob 1940).Changes in the elevation of an overlying water table will

induce transient flow in an underlying formation that willproduce fluctuations in pore pressure. Such changes are com-monly observed in shallow observation wells and piezome-ters. Where such effects are observed within shallow low-permeability formations such as clays and clay-rich glacialtills, they can be modelled with analytical or numerical ap-proaches (e.g., Keller et al. 1989) to provide estimates of thein situ coefficient of consolidation (also known as hydraulicdiffusivity). In shallow formations these pore-pressure changesare generally large and tend to dominate the observed pore-pressure changes. Pressure changes due to groundwater pump-ing and other artificial influences may also further obscure theeffect of moisture loading. However in deeper undisturbed for-mations, moisture loading may be the major cause of pore-pressure change (van der Kamp and Maathuis 1991).The main purpose of this paper is to introduce the concept

of moisture loading and explore its significance in the con-text of geotechnical engineering. The methodology and mate-rial characterization rely heavily on geotechnical methods andhave the potential to provide a valuable tool in geotechnicalpractice. In particular, the paper illustrates how the analysisof water table effects and moisture loading effects, includingresponses to barometric pressure loading, allows determina-tion of in situ values of compressibility (e.g., elastic modu-lus) and vertical hydraulic conductivity of near-surfaceaquitards.The theoretical model developed in the paper is applied to

a dataset of long-term measurements of pore-pressure changewithin a thick, low-permeability aquitard. A method is devel-oped to separate the effect of water table fluctuations withinan overlying unconfined aquifer from the pore-pressure dy-namics within the aquitard so that the effect of moisture load-ing can be isolated. The methodology utilizes a coupledstress–strain and seepage finite element formulation to predictpore-pressure dynamics in response to mechanical loadingand transient groundwater flow processes (Anochikwa 2010).

Study site and field observationsThe study site is located in the southern part of Prince Al-

bert National Park, Saskatchewan, Canada, geographically lo-cated at 53.7°N, 106.2°W (Black et al. 1996; Barr et al.2000) at an elevation of 600 m (Fluxnet-Canada 2009). The

site is near the Fluxnet-Canada Old Aspen site, which has aneddy flux tower and climate station (Fluxnet-Canada 2009).The vegetation of the entire area is dominated by maturetrembling aspen (Populus tremuloides) with scattered smallopenings.The soil profile at the site is 20 m of a surficial, uncon-

fined aquifer of sand, gravel, and some silt overlying a stiffunoxidized clay till that is at least 22 m thick. The total thick-ness of the clay till was not determined as drilling met withrefusal on what was probably a boulder. The nearest deepstratigraphic test hole is about 15 km distant, but regionalstratigraphic data suggest that thin sand and gravel aquiferlayers may be present at various depths and that the base ofthe glacial deposits occurs between 360 and 400 m elevation(Judd-Henrey et al. 2008), indicating that the total thicknessof glacial deposits at the site is likely in excess of 200 m.Two piezometers were installed for this study. Each of

them was instrumented with a sensitive, nonvented, 50 psi(1 psi = 6.9 kPa), Geokon 4500H vibrating-wire pressuretransducer, with a resolution of better than 1 mm water. Piez-ometer P1 was installed within the clay till at a depth of34.6 m and was placed in a 2.2 m long cavity filled with sa-turated sand and sealed with bentonite to the surface (Barr etal. 2000). The second pressure transducer was placed in anopen polyvinyl chloride (PVC) standpipe (piezometer P2) in-stalled below the water table in the upper sand and gravel.The standpipe was installed to a depth of 6.26 m belowground and had a 1 m long slotted screen. The pressuretransducers were connected to a data logger that continuouslyrecorded the 30 min average of pore pressure measured every30 s (Barr et al. 2000). Other instrumentation details are pro-vided by Barr et al. (2000). The site profile and piezometricinstallations are shown in Fig. 1.Barometric pressure was measured at the piezometer site

using a sheltered barometer as discussed by Barr et al.(2000). Precipitation, P, was measured at the Old Aspenflux tower site, located about 1 km west of the piezometersite, using a Belfort 5915 accumulation gauge and a TexasElectronics TE525M tipping bucket rain gauge as discussedby Barr et al. (2000). Actual evapotranspiration data (ET) forthe site were available from Fluxnet Canada and were ob-tained using an eddy covariance instrument mounted on theOld Aspen eddy flux tower, 39.5 m above ground level overthe 21 m tall aspen forest stand (Black et al. 1996). The ETdata are adjusted to force closure of the energy balance forthe site (Barr et al. 2011). Lateral runoff by surface or sub-surface flow was not measured at the piezometer site. At theflux tower site, runoff was determined from water balancecalculations to be very small during dry periods, such as2001–2004, but is a significant part of the water budget ofthe site during wet periods such as June 2004 to December2006 and later (Barr et al. 2011).The pore-pressure data from piezometer P1 were corrected

for barometric response by subtracting the changes of baro-metric pressure multiplied by a correction factor that was ad-justed by trial and error to eliminate barometric effects asdetermined by visual inspection of the corrected data. Vari-ous mathematical data analysis methods are available for de-termining the barometric influence on pore-pressure records(e.g., Butler et al. 2011), but due to the interfering influenceof other ill-defined effects, such as rainfall events, evapo-

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transpiration, and seasonal changes of the water table, the re-sults of such automated analyses tend to be ambiguous. Thevisual inspection method (see example given in Fig. 2), wasfound to be relatively objective in that different observers, us-ing records covering a range of different seasons over theyear, arrived at very similar results for the optimum correc-tion factor. This correction factor represents the loading effi-ciency, “B-bar” (B), as discussed in a following section. Earthtide effects were eliminated by calculating the earth tide grav-ity changes using the TSOFT software package (van Campand Vauterin 2005; Royal Observatory of Belgium 2010),then multiplying these by another correction factor, again op-timized by trial and error based on visual inspection, andsubtracting the resulting values from the pore-pressure data.Figure 2 shows details of the data for a 20 day period in

2003, including the changes of barometric pressure, the rawpore-pressure data for the deep piezometer (P1), the porepressure for P1 with barometric pressure and earth tide ef-fects removed, and the cumulative values of P – ET (S(P –ET)) that equal the change of total moisture at the site if thenet lateral moisture movement (runoff) is very small. Theoptimum value of loading efficiency for barometric loadingwas determined to be 0.91 with an uncertainty range ofabout ±0.01, and it may be seen that with this factor thebarometric loading effects are virtually entirely removedfrom the piezometer record (Fig. 2b). It should be noted thatcorrection for barometric effects only is sufficient for practi-cal purposes of estimating material properties. Figure 2cshows the piezometer pressure record corrected for earthtides as well as for barometric effects, together with the accu-mulated atmospheric moisture input S(P – ET) measured atthe flux tower. The pore-pressure response due to moistureloading by a ∼30 mm precipitation event on 3 August canbe clearly seen in the piezometer record. Daily decreases insoil moisture of a few millimetres due to evapotranspirationcan also be seen in the record of S(P – ET). These small

daily changes are reflected in the piezometer record, but arepartly obscured by other daily fluctuations, likely due to im-perfect removal of the effect of earth tides. The steeper declineof the piezometer pressure as compared with S(P – ET) isdue mostly to pore-pressure fluctuations caused by transient

Fig. 1. Site soil profile and instrumentation. Fig. 2. (a) Change in barometric pressure. (b) (i) Raw response ofpiezometer P1 and (ii) raw response of piezometer P1 corrected forbarometric effects. (c) (i) Response of piezometer P1 corrected forbarometric earth tides effects and (ii) cumulative net atmosphericwater input, S(P – ET), from the Old Aspen flux tower, 18 July – 7August 2003, both set at zero initial offset.

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fluctuations in the overlying water table, which was declin-ing during that period. This combined effect of water tablechanges and soil moisture loading is the main focus of theanalysis presented in this paper.The full 1998–2006 data record for piezometers 1 and 2 as

well as S(P – ET) are shown in Fig. 3. The site experiencedsevere drought conditions from 2001–2003 and extreme wetconditions from 2004–2006, as indicated by the decline inS(P – ET) from 2001 to early 2004 and the subsequent riseby about 500 mm. These dry and wet conditions are reflectedin the decline and subsequent rise of the water table. In nor-mal years, melting of the winter’s snow accumulation in lateMarch or April leads to a rise of the water table at the end ofwinter with a secondary rise later in summer or in the au-tumn if there is heavy rainfall (e.g., June 2004). The plot ofS(P – ET) shows the accumulation of snow in winter as agradual rise, with a subsequent decline in most summerswhen transpiration by the trees is at a maximum. The deeppiezometer P1 exhibits a delayed and damped response tothe longer-term water table fluctuations. Inspection of a smallstream at the lower portion of the watershed showed thatthere was no runoff at all in the autumn of 2003, but thatthere was strong runoff in 2005 and 2006. These observa-tions are corroborated by the annual water balance data forthe site reported by Barr et al. (2011), which show essentiallyzero runoff from the flux tower site from late October 2000to September 2004. Precipitation, P, was lower than normalfrom October 2000 to September 2003 and water losses byevapotranspiration, ET, were matched by precipitation, bychanges of soil moisture, and by snow accumulation and thawover the winter seasons. From October 2004 onward the waterbalance indicates that much of the rise in S(P – ET) repre-sents runoff from the site rather than moisture accumulation.

Theoretical backgroundBiot (1941) and Nur and Byerlee (1971) present three-

dimensional generalized constitutive relationships for coupledstress-strain and pore-water pressure response of a saturated,isotropic linearly elastic porous media. These equationswere further developed by van der Kamp and Gale (1983)for a laterally constrained domain subject to a spatially con-tinuous surface loading (e.g., barometric pressures). Theyshowed that the pore-pressure change in response to an in-stantaneous change in surface load, referred to as the load-ing efficiency, can be described as follows:

½1� B ¼ Du

DsB

where B is the loading efficiency, also known as Skempton’sB coefficient (Skempton 1954), u is pore pressure, and sB isthe barometric pressure. In the case of a linear, elastic, isotro-pic, saturated soil, the loading efficiency is described by thefollowing expression:

½2� B ¼ 1=EC

1=EC þ n=EW

where EC is the drained constrained modulus of elasticity, nis porosity, and EW is the bulk modulus of elasticity of water.Jacob (1940) and Skempton (1954) developed similar expres-sions.

The drained constrained modulus, Ec, can be obtainedfrom the barometric response if it can be assumed that thebarometric response is undrained; that is, not altered by tran-sient flow through adjacent formation boundaries. Rewritingeq. [2] produces

½3� EC ¼ EW � BEW

Bn

The specific storage, at zero lateral deformation (Jacob 1940)can be calculated with

½4� Ss ¼ rwg1

EC

þ n

EW

� �

where rw is the density of water and g is gravitational accel-eration. The value of Young’s modulus, E, can be obtainedusing the relationship between E, Ec, and Poisson’s ratio, n(Poulos and Davis 1974; van der Kamp and Gale 1983):

½5� E ¼ ECð1þ vÞð1� 2vÞð1� vÞ

If the Poisson’s ratio equals 1/3, as is commonly assumed,then

½6� E ¼ 2

3EC

van der Kamp and Gale (1983) also presented the equationdescribing the pore-pressure response to mechanical loadingand transient flow for a one-dimensional vertical column ofa saturated, linearly elastic, porous medium from which thefollowing equation can be derived:

½7� @u

@t¼ B

@sL

@tþ D

@2u

@z2

where sL is the mechanical load (total stress) acting at thetop of the column [ML–1T–2] and D is the hydraulic diffusiv-ity [L2T–1], t is time [T], and z is elevation [L]. The hydraulicdiffusivity is the ratio of the vertical hydraulic conductivity,Kv, to specific storage, Ss, and is equivalent to the coefficientof consolidation (Cv) in geotechnical engineering.

Fig. 3. Field observations of responses of deep (P1) piezometer cor-rected for barometric and earth tide effects and shallow water table(P2) piezometer corrected for barometric effects, and cumulative at-mospheric water balance S(P – ET), 1998–2006.



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The term B@sL=@t represents the undrained pore-pressureresponse to changes in mechanical load, while D@2u=@z2 rep-resents the vertical transient flow of groundwater that occursin response to the induced changes in pore pressure, u. Sim-ulation of the pore pressure changes within the domain,based on eq. [7], requires specification of stress–strain andhydraulic (flow or pore pressure) boundary conditions andinitial conditions within the domain being simulated.The linearity of the governing equation allows the equa-

tion, boundary conditions, and primary variables to be splitor merged mathematically by the method of superposition,so that the effects of stress changes and of pore-pressurechanges at the upper boundary can be simulated and exam-ined separately. Consequently, the pore-pressure changes, u,can be expressed as the sum of the incremental pore-pressurecontributions resulting from pore-pressure fluctuations at thetop boundary, uW, and from transient moisture loading, uL

½8� uðz; tÞ ¼ uLðz; tÞ þ uWðz; tÞEquation [7] can then be re-expressed by substituting eqs. [8]and [9] as

½9� @ðuL þ uWÞ@t

¼ B@sL

@tþ D

@2ðuL þ uWÞ@z2

The isolated case of pore-pressure response to mechanicalloading associated with changing total soil moisture aloneand the accompanying transient drainage is

½10� @uL

@t¼ B

@sL

@tþ D

@2uL

@z2

The effect of a changing hydraulic head boundary condi-tion, such as that arising from water table fluctuations, canbe described with eq. [11] assuming no total stress change

½11� @uW

@t¼ D

@2uW

@z2

If uL and uW satisfy eqs. [10] and [11], respectively, andthe appropriate boundary conditions, then their sum u (u =uL + uW) represents the sought-for solution to eq. [9]. Thisseparation and superposition is justified if the material withinthe domain is relatively stiff and incompressible so that den-sity changes and dilation or compaction of the material arevery small. In this case the density changes within the do-main due to changes of pore pressure and externally imposedstress will be small and the resulting changes of total stresswithin the modeled domain will be small compared to theimposed stress.For the purposes of simulating the pore-pressure changes

below the water table, the modeling domain can be chosensuch that the top boundary of the domain lies below the low-est position of the water table and the domain remains fullysaturated at all times. This selection of the domain avoids thecomplexity of having to account for the distribution of mois-ture in the unsaturated zone between the water table and theground surface. The total moisture above the saturated do-main equals the sum of all water above the domain includingall subsurface moisture above the domain and below theground surface, water ponded on the ground surface, snowaccumulation above the ground surface, and moisture held in

the canopy of the vegetation. The change of total moisturemust equal the net water flux into the site (P – ET – R) ex-pressed as a height of accumulated water per unit time inter-val [LT–1], where R is the net lateral runoff of water from thesite, whether by surface or subsurface flow. The site waterbalance can be estimated by measurement of P, ET, and Ror by measurement of the above-surface and subsurfacemoisture; for example, by means of soil moisture sensorsand by tracking snow accumulation.The soil moisture loading at the top of the domain is ex-

pressed as a stress–strain boundary condition

½12� @sLð0; tÞ@t

¼ rwgðP� ET� RÞ

where rw is in [ML–3] and g is in [LT–2]. The mathematicalsolution of eq. [9] for the domain also requires specificationof pore-pressure changes or flows at the top and bottom ofthe domain. The pore-pressure changes can be measured bymeans of suitably placed piezometers above and below thedomain.In cases where site conditions allow both B and D to be

determined by analysis of the pore-pressure records, it be-comes possible to arrive at in situ values for Ss and Kv, usingthe foregoing equations and an assumed (or known) value ofthe porosity, n.

Modelling methodologyThe commercially developed program SIGMA/W (GEO-

SLOPE International Limited 2008) implements a coupledstress-strain and seepage finite element formulation that sol-ves the partial differential equations presented by Biot(1941). Figures 4a and 4b present the simulated domain andthe boundary conditions used in the model, respectively.Only the clay aquitard was included in the analysis. The ap-plied top hydraulic boundary condition was obtained fromthe piezometer P2 as changes in pore pressure associatedwith the fluctuating water table elevation. The stress-time ser-ies specified at the top boundary was obtained using the cu-mulative site water balance monitored at the flux tower,S(P – ET), assuming that runoff, R, is negligible, so that thesoil moisture load is given by the (cumulative) value of rwgS(P – ET) against time,. The model utilized the stresschange generated from the difference between the specifiedstress at the given time and the stress at the preceding time.The lower boundary was assumed to be a zero deflection andzero water flux boundary.The one-dimensional domain extends from the base of the

upper aquifer to the drilled depth. Unfortunately, there wasinsufficient stratigraphic information to determine the actualthickness of the clay till. The modelled domain was assumedto be 22.5 m of clay till with uniform elastic properties andhydraulic conductivity and an assumed impervious lowerboundary. The boulder that terminated drilling at 22.5 mcould be part of a thin granular intertill material (e.g., Math-eson et al. 1987) separating the domain from an underlyingtighter and less permeable till. However, sensitivity testswere carried out to assess the influence of varying the aqui-tard thickness for the simulations along with the materialparameters, particularly the elastic parameters. Sensitivitychecks were also performed with other possible conceptual



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multi-layer domain configurations up to an assumed depth tothe bedrock (Anochikwa 2010).The material properties for the model include the drained

elastic modulus (Young’s modulus E), porosity (n), saturatedhydraulic conductivity (K), and Poisson’s ratio (n) (assumedto be 1/3). The SIGMA/W stress model also incorporates a“load-response ratio,” which can be used to represent theloading efficiency B described previously, provided that thevalues of B, porosity, Young’s modulus, and Poisson’s ratioare consistent with the relationships described in eqs. [2] to [6].The estimated Young’s modulus of elasticity obtained from

the barometric correction was 528 MPa, as calculated from aloading efficiency B of 0.91 determined by analysis of theobserved barometric response with an assumed porosity of0.26 and a Poisson’s ratio of 1/3. The specific storage coeffi-cient Ss (eq. [4]) then equals 1.36 × 10–5 m–1.The model was calibrated by keeping E constant at

528 MPa, the pore-pressure load-response function at 0.91,and varying the hydraulic conductivity, Kv, to obtain the bestmatch to the measured pore-pressure response for piezometerP1. Lateral runoff was not measured, but can be assumed tohave been very small during the drought when the water ta-ble was low, as corroborated by the water balance estimates

of Barr et al. (2011). Therefore, the records for the periodJanuary 2002 to December 2004 were used for the calibra-tion because the error due to neglecting runoff would besmall during that period.It was assumed for the purpose of the simulation that the

water table, the moisture load S(P – ET – R), and the porepressure within the domain were constant before 1 January1998. This is of course, highly unlikely. An initial calibrationshowed that the final value of Kv would be approximately2 × 10–5 m/day. This means that the time required for fulldissipation (about 99.9%) of an excess pore pressure acrossthe full depth (22.5 m), based on Terzaghi’s (1943) expres-sion for time factor with one-way drainage, is approximately3 years. This was confirmed by modeling the response of thedomain to step changes of stress (Anochikwa 2010). A steppore-pressure change at the upper boundary would propagateacross the entire domain in the same time frame. Thereforethe first 3 years — 1998 to 2000 — were considered a“spin-up” period and not used for calibration because thepiezometer record would still have some transient “memory”of the unknown changes of the water table and of P – ET – Rprior to January 1998. Any such memory of moisture load-ing prior to January 1998 would be completely dissipatedby 2001 and the piezometer P1 pressure would reflect onlythe water table and the moisture load changes after January1998. Changes in pore pressure measured in piezometer P1were based on a start date of 1 January 1998. However, atthis point the record still incorporated an undefined re-sponse to an earlier water table that would propagate toequilibrium by 2001. Therefore it is to be expected that thebest-fit simulation for the period 2002 to 2004 should in-clude a constant offset, which would represent the unknowneffect of prior water table changes on the pore pressurewithin the aquitard as of 1 January 1998.With these considerations in mind, the value of Kv was

varied until a best-fit between the simulated and measuredpiezometer P1 pressure was achieved. The definition of best-fit is somewhat subjective, depending on the criteria that areused (e.g., Dawson et al. 2007; Krause et al. 2005). Using amaximum value of the coefficient of determination, (R2) (e.g.,Krause et al. 2005) of 0.995 gave a Kv value of 1.6 × 10–5m/day. Using other best-fit criteria, including the index ofagreement (d) of 0.958 and Nash–Sutcliffe’s efficiency coef-ficient (CE) of 0.832 (e.g., Krause et al. 2005; Dawson etal. 2007) yielded slightly higher values of Kv, up to a valueof 2.5 × 10–5 m/day. The observed and simulated responsesfor Kv of 1.6 × 10–5 m/day, which were considered to givethe best overall match during 2002–2004, are shown inFig. 5a. The constant offset between the modelled and ob-served responses during the calibration period 2002–2004was determined to be 114 mm by means of linear regres-sion (as an intercept). Applying this offset to the observedpiezometer response gives the very close match shown inFig. 5b, with a low root-mean-squared error (RMSE) (e.g.,Dawson et al. 2007) of 14.8 mm change of pore-pressurehead. For the subsequent period, when net lateral runofffrom the site was likely significant, the fit is less satisfac-tory, but still close considering that the modelling approachassumes that lateral flow is zero.Sensitivity studies were carried out to examine the influ-

ence of varying the material parameters, geometry (thickness)

Fig. 4. One-dimensional numerical model: (a) conceptual model ofclay–till aquitard; (b) boundary conditions. h, pore-pressure or hy-draulic head; qz, vertical flux; s, stress.



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of domain, and the off-setting of the pore-pressure boundaryconditions over the simulation period by changing theirinitial (1 January 1998) values (Anochikwa 2010). As thethickness of the clay–till was not determined, evaluating theinfluence of linear variation of elastic parameters in domainsof different thicknesses was a key sensitivity assessment.Also, in each case of varying elastic properties with thick-ness, the respective best-match Kv value was determined. Inaddition, the influence of deeper intertill sand aquifer layersthat might exist at the site (Judd-Henrey et al. 2008)) were eval-uated using multi-layer clay–till models (Anochikwa 2010).The obtained range of Kv values for this site is somewhat

uncertain because the full thickness of the aquitard and theactual boundary condition at the bottom of the aquitard arenot known. In fact, there is even a possibility that if the aqui-tard in this site is actually much thicker, the Kv could behigher by up to a factor of 3 (Anochikwa 2010). The ob-tained Kv, 1.6 × 10–5 m/day (1.9 × 10–10 m/s), is consistentwith in situ values for glacial clay–till measured at other sitesin Saskatchewan (Keller et al. 1986, 1988, 1989; Shaw andHendry 1998), which typically lie in the range of 10–11 to10–8 m/s.

The simulation of the pore pressures at piezometer P1 inresponse to water table fluctuations alone and to moistureloading S(P – ET) alone are shown in Figs. 6 and 7, respec-tively. It is clear that the long-term pattern of pore-pressurefluctuations is dominated by the influence of the water table,while short-term transients are mostly due to moisture loadchanges. The coupled stress-flow model was run assumingthat density changes within the domain were negligible,which is consistent with the assumptions required for theprinciple of superposition. As expected, the separately mod-eled pore-pressure changes in response to water table fluctua-tions and to mechanical loading by S(P – ET) add up exactlyto the modeled response to the combined inputs shown inFig. 5 (Anochikwa 2010).To check how well the site water balance is approximated

by the decomposition of the pore-pressure dynamics, themodelled piezometric response to loading S(P – ET) wascompared with the observed pore-pressure response to thesite water balance (Fig. 8), isolated by subtracting the mod-eled response to the water table (Fig. 6) from the observedpore-pressure record for piezometer P1. The two results arein reasonable agreement during the dry years (2001–2004)with increasing disparity during the wet periods, likely due tothe occurrence of lateral flow during periods 2005 and 2006.

Fig. 5. Calibration of simulated to observed pore-pressure responsesat piezometer P1 (January 2002 to December 2004) obtained using(a) zero initial offset for all observations; (b) observed responsesoffset by 114 mm.

Fig. 6. Simulated pore pressures at piezometer P1 in response towater table fluctuations at piezometer P2 in overlying aquifer.

Fig. 7. Simulated pore-pressure changes at piezometer P1 in re-sponse to loading by S(P – ET).



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DiscussionThe amplitude of the pore-pressure response to water table

fluctuations diminishes with depth, while the amplitude ofthe instantaneous pore-pressure response to areally extensivesoil moisture loading (initial, undrained, excess pore pres-sure; e.g., Terzaghi et al. 1996, p. 226) extends to all depths(van der Kamp and Maathuis 1991). Therefore, it is increas-ingly important to consider the effect of soil moisture loadingin the analysis of pore-pressure fluctuations in deep aqui-tards. This concept is illustrated in Fig. 9, which presents theresults from a simulation of an aquitard with a diffusivity(Cv) of 1.18 m2/day (i.e., Kv of 1.6 × 10–5 m/day and Ss of1.36 × 10–5 /m). At a depth of 15 m, the pore-pressure fluc-tuations are dominated by the water table fluctuations, whilethe response to surface loads is highly dissipated. The reverseis true at greater depths where the water table fluctuations arenearly fully damped, while the response to loading fully re-flects the surface loading.The site water balance can be characterized by the cumula-

tive sum S(P – ET – R) if each of these water balance com-ponents can be measured or estimated with acceptablereliability. This is true for the case described in this paperfor the dry years. Alternatively, the site water balance can beestimated if sufficient data on total moisture changes areavailable, including snow accumulation and changes of mois-

ture in the deeper vadose zone and at the water table. Forpore-pressure changes at shallow depths, the water table in-fluences predominate and even a rough approximation of thesite water balance may suffice to account for moisture load-ing effects.For pore-pressure changes at depth, where water table in-

fluences are small, the observed pore-pressure changes mayprovide a measure of the site water balance (Marin et al.2010) that can be useful in the evaluation of hydrologicalmodels.If evaluation of the in situ hydraulic and mechanical pa-

rameters is of primary interest, then it would be good prac-tice to install and monitor several piezometers at different

Fig. 8. Piezometer P1: (i) observed response minus modelled re-sponse to water table; and (ii) modelled response to water balanceS(P-ET) loading for (a) all responses at zero initial offset and(b) observed responses offset by 114 mm.

Fig. 9. Simulated pore-pressure fluctuations at 15 and 100 m depths:(a) due to water table fluctuation alone; (b) due to soil moistureloading alone; (c) combined effects of water table fluctuations andsoil moisture loading.



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depths. Simulation of each of the observed responses is likelyto greatly constrain the possible range of values of the pa-rameters and their variation with depth. Keller et al. (1989)provided an example of such an approach. In addition, it ishighly desirable that the site stratigraphy be determined to adepth considerably greater than the intended depths of thepiezometers. Typically if the formation of interest is an aqui-tard, it is recommended that the full thickness of the aquitardbe determined and a piezometer be located in the underlyingformation. If this is not done, there is likely to be consider-able uncertainty in the results of the simulation. Soil moistureloading effects are likely to occur for any formation in whichthe pore fluid is isolated from the water table, including con-fined aquifers and thick low-permeability aquitards. If thepore pressure is influenced by barometric pressure changes,it is likely that soil moisture loading effects will also occur,although they may be obscured by other larger pore-pressurefluctuations such as those due to barometric pressurechanges.Equation [3] shows that when B approaches a value of 1,

the use of a barometric loading response to determine Ec be-comes problematic, requiring highly accurate determinationsof B. This would be the case for softer soils with values ofEc much less than Ew (eq. [2]), i.e., Ec less than about100 MPa. Under such conditions, applications of the baro-metric response method would require accurate on-site bar-ometers and pressure transducer installations (preferablyusing vented transducers) that respond very rapidly and accu-rately to changes in pore pressure. The trial and error methodof determining B by visual inspection of the pore-pressure re-cords has the merit of being simple and appears to be robustfor piezometers installed deeply within thick aquitards, How-ever for cases where this method turns out to be ambiguous,as might be the case for shallow piezometers, more sophisti-cated numerical methods may be necessary such as the ap-proach described by Butler et al. (2011).The numerical modelling approach described here can be

extended to the analysis of pore-pressure responses and hy-draulic parameters of soil under loading by ponded water,such as mine tailings ponds, reservoirs, and lakes. In suchcases, the water head equivalent of the mechanical loadingand hydraulic head changes are the same. Similarly, Boutt(2010) discusses analysis of loading of an aquifer by a streamwith changing water level.

ConclusionsThe pore-pressure responses induced by water table fluctu-

ations and by surface loading due to changes in soil moisturewere simulated using a coupled stress–strain and seepage fi-nite element model. Both of these processes should be takeninto account for the interpretation and simulation of pore-pressure changes in saturated formations beneath a water ta-ble. At shallow depths near the water table, the pore-pressurechanges due to the fluctuations of the water table are usuallyconsiderably greater than the moisture loading–induced changes.However, at greater depths the moisture loading responses,though small, may predominate in the observed pore-pressurechanges. Failure to recognize the moisture loading effects inthe observed pore pressures could lead to misinterpretationof the observations and erroneous values for the hydraulic

parameters determined by calibration of the model to fit theobservations. The isolated pore pressure response to soilmoisture loading potentially offers applications for monitoringsite water balances and the associated hydrological processes,such as precipitation, evapotranspiration, and runoff.Simulation of the observed pore-pressure fluctuations can

provide robust values for the consolidation coefficient (or hy-draulic diffusivity) of the formation under favourable circum-stances. If the loading efficiency (or Skempton’s B (B-bar)pore-pressure coefficient) can be determined from the ob-served response to barometric pressure changes, then thestorage coefficient, Ss, and the vertical hydraulic conductivity,Kv, can be determined separately.

AcknowledgementsData obtained at the Fluxnet Canada Old Aspen site were

provided by Fluxnet Canada with the assistance of Alan Barrand Erin Thomson whose assistance is gratefully acknowl-edged. Randy Schmidt’s contributions with regard to installa-tion and operation of the piezometers were critical to thisstudy. Curtis Kelln provided advice during the simulationsand his comments helped clarify and strengthen the manu-script. Brenda Bews provided welcome assistance with edit-ing and formatting of the paper. Funding for this study wasprovided by the Canadian Foundation for Climate and At-mospheric Studies (CFCAS) through its support of the Prai-rie Drought Research Initiative (DRI), and by University ofSaskatchewan scholarships awarded to C.I. Anochikwa. Apreliminary version of this paper was published in the pro-ceedings of the 2009 Canadian Geotechnical Conference(Anochikwa et al. 2009).

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interpreting pore-water pressure changes induced by water table fluctuations and mechanical loading...

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