Engineering Geology 100 (2008) 27–42

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Engineering Geology

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Regional land subsidence simulation in Su-Xi-Chang area and Shanghai City, China

Xiaoqing Shi a,⁎, Jichun Wu a, Shujun Ye a, Yun Zhang b, Yuqun Xue a, Zixin Wei c, Qinfen Li c, Jun Yu d

a Department of Hydrosciences, Nanjing University, Nanjing 210093, Chinab Department of Earth Sciences, Nanjing University, Nanjing 210093, Chinac Institute of Geology Survey of Shanghai, Shanghai 200072, Chinad Geological Survey of Jiangsu Province, Nanjing, 210018, China

⁎ Corresponding author. Tel.: +86 25 83592326; fax: +E-mail address: shixiaoqing@nju.org.cn (X. Shi).

0013-7952/$ – see front matter © 2008 Elsevier B.V. Aldoi:10.1016/j.enggeo.2008.02.011

A B S T R A C T

A R T I C L E I N F O

Article history:

Su-Xi-Chang area and Sha Received 25 July 2007Received in revised form 20 February 2008Accepted 26 February 2008Available online 18 March 2008

Keywords:The Southern Yangtze DeltaRegional land subsidenceDeformation featuresNumerical simulation

nghai City, located in the south of Yangtze Delta, China, has subsided due togroundwater overpumping. Because of the regional scale of the groundwater exploitation, cone of depressionand land subsidence at present, Su-Xi-Chang area and Shanghai City are treated as a single area for landsubsidence study to avoid the uncertainty of boundary condition due to the regionalism. The characteristicsof aquifer system compaction are complex because of the difference in the types, compositions andstructures of the soils that the hydrostratigraphic units are composed of, and in the histories of groundwaterlevel change the hydrostratigraphic units have experienced. Considering the fact that different hydrostrati-graphic units have different kinds of deformation and that an identical unit may also present differentdeformation characteristics, such as elasticity, elasto-plasticity, and visco-elasto-plasticity, at different sites ofthe cone of depression or in different periods, corresponding constitutive laws have been adopted. Thisavoids the shortcomings of the previous research that the same constitutive law was adopted in all thehydrostratigraphic units during the entire time period. A coupled flow and subsidence model, which includesa three-dimensional flow model with variable coefficients and a one-dimensional (vertical) subsidencemodel, is built according to the complicated hydrological condition in the region. The simulation model iscalibrated using observed data, which include compression of individual strata from groups of extensometersand groundwater levels from observation wells from 1995 to 2002. The model reproduced that the primarysubsidence layer in Shanghai shifts from the shallow aquitard to the fourth confined aquifer because of thegroundwater yield variations and the change of exploitation aquifers. However the third aquitard was theprimary subsidence layer in Su-Xi-Chang area and the compaction deformation of the sandy aquifers wasremarkable. The simulation results could provide some reasonable advice about groundwater exploitation inthe future.

© 2008 Elsevier B.V. All rights reserved.

1. Introduction

Land subsidence caused by excessive groundwater withdrawal canbe explained through the principle of the effective stress (Poland andDavis, 1969; Galloway et al., 1999). In the recent 30 years, it has beenextensively investigated quantitatively and qualitatively by manyprevious researchers (Gambolati and Freeze, 1973; Gambolati et al.,1974; Helm 1975, 1976; Neuman et al., 1982; Bravo et al., 1991;Gambolati et al., 1991; Shearer, 1998; Larson et al., 2001).

The Su-Xi-Chang area (including Suzhou, Wuxi and Changzhoucities) and Shanghai City are located in the Southern Yangtze Delta inthe eastern part of China. The area is about 12,000 km2 and 5000 km2

for the Su-Xi-Chang area and Shanghai City, respectively. It is an areaof intensive groundwater development for domestic and industrialuses. Groundwater has been extracted for over 100 years in the area,which resulted in severe land subsidence. Currently, excessive

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exploitation of groundwater across the provincial boundary forms ahuge regional cone of depression. Consequently, the land subsidencecone is also regional, centering in the downtowns of Shanghai and Su-Xi-Chang areas.

Shanghai is the first city in which land subsidence was found andreported in 1921 and its effect and damage were the greatest. In 2002,the maximum cumulative subsidence of Shanghai and Su-Xi-Changarea were 2.63 m and 2.00 m, respectively (Sun, 2002). Merely in Su-Xi-Chang, the area with subsidence larger than 0.2 m has reached5000 km2 in 2000 (NCCGS et al., 2003). With the regional scale of thegroundwater exploitation, the existence of cone of depression andland subsidence at present, thus it is necessary to break through theprovincial boundary for studying land subsidence.

An integrated numerical groundwater and land subsidence modelfor land subsidence simulation is proposed. In the previouslydeveloped land subsidence models, either the study area was usuallytens to hundreds of square kilometers, the simulation involved onlyone or two hydrostratigraphic units, or the same soil deformationfeature was assumed throughout the study area. The model in this

28 X. Shi et al. / Engineering Geology 100 (2008) 27–42

paper deals with the regional land subsidence in tens of thousands ofsquare kilometers and involves several deformation features of thewholeaquifer system.Thismodel is improvedas to thepreviousones (Gambolatiet al., 1974; Helm, 1975, 1976; Larson et al., 2001; Chen et al., 2003).

Some new issues are involved in this model. The first and the mostimportant issue is that not only the complicated geological conditions,but also the complex deformation features of different hydrostrati-graphic units are considered due to the large study area. An identicalunit may also present different deformation characteristics, such aselasticity, elasto-plasticity, and visco-elasto-plasticity, at differentsites of the cone of depression or in different periods (Ye et al.,2005; Shi et al., 2007, in press; Zhang et al., 2007). Differentsubsidence models are employed according to the deformationfeatures in different locations and over different periods whenestablishing the regional land subsidence model. Many previousland subsidencemodels assumed the same deformation models for allthe hydrostratigraphic units, such as subsidence model based onelastic deformation (Chen et al., 2003), subsidence model based onvisco-elastic deformation (Corapcioglu and Brutsaert, 1977), subsi-dence models based on elasto-plastic deformation (Gambolati andFreeze, 1973; Gambolati et al., 1974; Helm, 1975, 1976; Neuman et al.,1982; Gambolati et al., 1991), and subsidence model based on visco-elasto-plastic deformation (Gu and Ran, 2000).

Secondly, the parameters in most of the previous subsidencemodels are constant (Gambolati and Freeze, 1973; Gambolati et al.,1974; Helm, 1975; Gambolati et al., 1991; Li et al., 2000). In fact, thehydrogeological parameters, such as the hydraulic conductivity andspecific storage, changed along with the compression of hydrostrati-graphic units. Rudolph and Frind (1991) investigated the transienthydraulic behavior of highly compressible aquitards through bothnumerical analysis and field studies. They found the hydraulicparameters of an aquitard varied during consolidation. Chen et al.

Fig. 1. The geographic location of the study are

(2003) also found the reduction in the hydraulic properties using thenumerical model for Suzhou City. In order to represent groundwaterflow under the condition of land subsidence, the flow model shouldhave variable parameters.

Thirdly, coupling the flow model and the subsidence model torepresent the impact of subsidence to the hydrological parameters is anew issue. The ground water flow model and subsidence modelshould be solved together in theory, which is called fully coupled landsubsidence model, such as Biot model. However, the fully coupledmodel is hard to be used because of too many parameters and thecomplicationwhen considering non-elastic deformation. Hence the socalled ‘Two Steps’ model or ‘uncoupled model’ was developed, whichcalculated the hydraulic heads firstly and then calculates thedeformation (Gambolati and Freeze, 1973). Since the deformation ofhydrostratigraphic units and the changes in hydraulic heads actuallyoccur simultaneously, the ‘two steps’ model cannot accuratelydescribe the physical mechanism of land subsidence. Another coupledmethod should be applied to overcome the disadvantages of ‘fullycoupled’model and ‘two steps model’. In this research, a ‘coupled twostep’ model (Chen et al., 2003) is used. The flow model and the landsubsidence model are coupled by changing parameters as functions ofthe hydraulic heads and deformation, and then the hydraulic headsand deformation are calculated by two steps in the model.

Last but not least, for the regional land subsidence simulation, thehorizontal scale is much more than the vertical scale. The verticalthickness of each hydrostratigraphic unit is generally not larger thantens meters and the thinnest is only a few meters, while the layerextends tens of thousands of square kilometers in the horizontal scale.If we discretize the aquifer units by finer mesh according to thevertical scale, a surprisingly large CPU time and computationalmemory are required in the conventional finite element method.Otherwise, if we discretize the aquifer units by coarser mesh

a with the indication of the extensometer.

Fig. 2. The hydrogeological profile in the study area (the location of the section line a–a′ is indicated in the Fig. 1).

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according to the horizontal scale, the very thin and deformedelements should be faced, which would increase the errors of results.

Themain objectives of this paper are to introduce the developmentof regional land subsidence model based on complex differentdeformation features and to calibrate the model using observed dataincluding compression of individual strata from groups of extens-ometers and groundwater levels from observation wells. The objec-tives can be accomplished through the following three steps. (1) Studyon the groundwaterflowmodels based on elastic, elasto-plastic, visco-elastic and visco-elasto-plastic constitutive laws. (2) Study on thesubsidence model based on elastic, elasto-plastic, visco-elastic andvisco-elasto-plastic constitutive laws. (3) Apply the multiscale finiteelement method (MsFEM) to solve the land subsidence model.

2. General situation of the study area

2.1. The geographic location

The study area is located in the Taihu Lake plain in the south of theYangtze Delta. It borders Mogan Moutain and Maodong Plain in thewest, the East Sea and the Yellow Sea in the east, the Yangtze River inthe north, and Zhejiang Province in the south, as illustrated in Fig. 1.The study area includes Suzhou, Wuxi and Changzhou cities in JiangsuProvince (except Taihu Lake) and Shanghai City (except Chongming,Changxing and Hengsha islands). The elevation decreases from thewest to the east.

2.2. The hydrogeological condition

The study area consists of Quaternary deposits. The ground surfaceis flat, with a mean elevation of 3 to 5 m and a gentle inclination fromwest to east. The Quaternary deposits are alluvial, lacustrine, marine,and palustrine, including clay, silty clay, silt, sand, and gravel. Based onthe geological era, hydrodynamic conditions and the formation types,the quaternary deposits are considered as six aquifers: an unconfinedaquifer, the 1st, the 2nd, the 3rd, the 4th and the 5th confined aquifersdenoted from top to bottom as A0, A1, A2, A3, A4 and A5 in Fig. 2,respectively. The confining aquitards interbedded between aquifersare called aquitard 1 to aquitard 5, denoted from top to bottom as B1 toB5 in Fig. 2, respectively. The aquitards are composed of clay and siltyclay. All of the aquifers are continuous across the entire study areaexcept the fifth confined aquifer, which is primarily restricted to thenorthern part of Shanghai and the northeastern part of Suzhou. Thefirst aquitard, which occurs mainly beneath Shanghai and Suzhou

Fig. 3. History of groundwater pumping from the confined aquifers in the c

cities, is mainly composed of soft clay. The other four aquitards consistof mainly stiff to hard clay and silty clay. Fig. 2 shows the conceptualhydrogeological cross section of the Southern Yangtze Delta. Thelocation of the cross section is also shown in Fig. 1.

3. Change in piezometric level and aquifer system deformation

3.1. Groundwater exploitation and resultant change in piezometric level

Groundwater extraction from the aquifer system below theSouthern Yangtze Delta began in 1860 and became extensive in the1950s. In the beginning, several separate cones of depression werecentered in the areas of pumping overdraft. Then the cones extendedand exceeded the boundaries of provinces when the groundwaterpumpage increased. Currently, they have joined together and formed alarge and regional coalesced cone of depression in the SouthernYangtze Delta. The groundwater pumping histories, main exploitedaquifers and the amount of pumpage varies spatially in this area. Thegroundwater in the unconfined aquifer and the 1st confined aquiferare mainly unexploited because of bad groundwater quality. Thus thetwo aquifers are not presented in the following content.

Fig. 3 shows the amount of net groundwater pumpage fromindividual confined aquifer in Shanghai from 1961 to 2001. Fig. 4indicates the representative changes in piezometric level in Shanghai.Large-scale extraction in Shanghai occurred in the late 1950s and thegroundwater withdrawal from the 2nd and 3rd confined aquifersaccounted for 80.5% of the total pumpage. The piezometric level in thetwo aquifers declined to the historical lowest values in the early 1960s.The lowest piezometric level was lower than −30 m, which causedland subsidence in Shanghai to increase rapidly from 1957 to 1961,with the average annual subsidence rate of 110 mm. In order toprevent the piezometric level from declining continuously and tocontrol land subsidence, the amount of groundwater pumpagedecreased significantly and artificial recharge was carried out after1966. Themainly exploited aquifers were gradually adjusted to the 4thand 5th confined aquifers after 1972. The piezometric levels in the 2ndand 3rd confined aquifers increased rapidly to higher than −5m by theearly 1970s and then fluctuated within a certain range with theconstant average. The rate of land subsidence correspondingly sloweddown and even some recovery occurred over the period 1966–1971.After the middle of the 1980s, more groundwater was needed due tothe economic development. The 4th and 5th confined aquifers werethe main exploitation units, so the groundwater levels in those twoaquifers declined continuously. In 2000, the groundwater pumpage

ity of Shanghai from 1961 to 2001 (modified form Shi et al., in press).

Fig. 4. History of groundwater level (m asl) for four confined aquifers in the Shanghai area (modified form Shi et al., in press).

31X. Shi et al. / Engineering Geology 100 (2008) 27–42

from the 4th and 5th confined aquifers accounted for 70% and 15% ofthe total amount of Shanghai, respectively (Wei, 2002). This causedthe piezometric level in the 4th confined aquifer to declinecontinuously till 1998 when the exploitation decreased substantially.After 1998, the piezometric level in the 4th confined aquifer remainednearly constant and even rose a little. The piezometric level in the 5thconfined aquifer changed in a similar pattern to that in the 4thconfined aquifer. The piezometric level in the 2nd and 3rd confinedaquifers also declined in the late 1980s as a result of the increasingexploitation and the rapid decrease of piezometric level in theunderlying 4th confined aquifer. However, the levels were muchhigher than the previous lowest values that occurred in the 1960s.

In the Su-Xi-Chang area, groundwater extraction started in 1927.Intensive extraction occurred after 1983 when the town industrydeveloped rapidly. The 2nd and 3rd confined aquifers were the mainlyexploited aquifers in the area (as shown in Fig. 5). The groundwaterlevels in these aquifers declined continuously (as shown in Fig. 6) untilthe middle of the 1990s, when the groundwater exploitation wasgreatly restricted. The strict restrictions led to a substantial exploita-tion reduction, which results in a gradual rise in the piezometric level.The depth of the piezometric level at the center of the depression coneof the 3rd confined aquifer in Changzhou decreased from 20 m in the1960s to 82.3 m in 1994. Then, the piezometric level rose graduallyfrom the previous lowest value −75.53m in 1994 to −58.63m in 2003.Although the 4th confined aquifer was not largely pumped in Su-Xi-Chang, its piezometric level experienced a similar changing pattern tothat of the 3rd confined aquifer, due to the leakage to the 3rd confined

Fig. 5. History of groundwater pumping from the confin

aquifer. The center of the depression cone of the 4th aquifer waslocated in north of Changzhou, with the piezometric level approxi-mately at −60.0 m in 2003.

3.2. Compaction of hydrostratigraphic units

Groundwater overdraft has caused regional depression cones in theconfined aquifers. Each of them contains several local cones ofdepression. Accordingly the land subsidence cone is also regional,centered in Shanghai and Su-Xi-Chang areas. At present, land subsidencehas affectedmore than 1/3 of the entire region. The development of landsubsidence was coincident with that of the groundwater cone ofdepression spatially and temporally. The characteristics of aquifer systemcompaction are complex because of the differences in the types,compositions and structures of the soils that the hydrostratigraphicunits are composed of, and in the histories of groundwater level changeswhich the hydrostratigraphic units have experienced (Ye et al., 2005; Shiet al., in press; Zhang et al., 2007). An identical unit may also presentdifferent deformation characteristics, such as elasticity, elasto-plasticity,and visco-elasto-plasticity, at different sites of the cone of depression orin different periods (Zhang et al., 2007; Shi et al., 2007, in press).

Taking the 4th confined aquifer in the F10 extensometer inShanghai for example (Fig. 7), it exhibited visco-elasto-plasticbehavior under certain changing patterns of piezometric level. Thecompaction of this aquifer lagged behind the change in piezometriclevel. The features are similar to that of the aquitards consisting of softclay, although the aquifer is composed of sands.When the piezometric

ed aquifers in Su-Xi-Chang area from 1980 to 2000.

Fig. 6. History of groundwater level (m asl) for three confined aquifers in Su-Xi-Chang area where extensometer F00 is located (modified from Shi et al., 2007).

32 X. Shi et al. / Engineering Geology 100 (2008) 27–42

level decreased but was above its previous lowest level, the aquifercompacted and expanded closely following the declining and rising ofthe piezometric level. There was irrecoverable plastic compaction ineach yearly cycle. The aquifer exhibited elasto-plastic behavior, asshown by the curve within 1989 to 1991 in Fig. 7. When thepiezometric level decreased below its previous lowest value theaquifer had experienced, the aquifer did not expand but compactedcontinuously in yearly rises. The compaction of aquifers laggedbehind the change in piezometric level. The aquifer exhibited visco-elasto-plastic mechanical behavior, as shown by the curve after 1991in Fig. 7. More detailed deformation features of the hydrostratigraphicunits are presented by Shi et al. (2007). Analysis of the deformationfeatures of each unit provides an important basis for the application ofthe deformation model used in the numerical modeling.

4. The conceptual model

4.1. The hydrogeological conceptual model

The simulated aquifer system is loose Quaternary deposit. Becauseof the influence from the basal structures and paleotropography, the

Fig. 7. The deformation-groundwater level (m asl) curve of the 4th confined aqu

thickness of the Quaternary deposits increases from the western partto the southeastern part. It is thinner than 100 m in Changzhou Cityand greater than 300 m in the north of Shanghai. There are more than250 observation wells in the study area. They provide fairly detailedinformation on the spatial distribution of each hydrostratigraphic unitand are an important basis for aquifer parameter zonations in thenumerical modeling.

Most of the boundaries of the study area are the watershed of thehydrogeological units. It is an advantage to treat Su-Xi-Chang area andShanghai City as a single study area, which can avoid the boundaryuncertainty due to the administrative division. Part of the boundariescontaining observationwells with full observation data series are set tobeDirichlet boundaries (constant-headboundary). Lakes or rivers insidethe model area or at the boundaries are also treated as known-headboundaries. Part of the boundarieswithout observationwells are treatedas Neumann boundary. The flux is determined at the model calibrationstage to reproduce the available head observations. Since the bottom ofthe Quaternary deposits contacts with bedrock directly, it is regarded asan impermeable boundary in the study area. The south boundary (theborder to ZhejiangProvince) is thegroundwater shed andhas little effecton the study area. Therefore, it is treated as no-flow boundary. Limited

ifer in the F10 extensometer in Shanghai (modified from Shi et al., in press).

33X. Shi et al. / Engineering Geology 100 (2008) 27–42

by the paper length, only the boundary condition and the locations ofobservationwells of the 3rd confined aquifer are demonstrated (Fig. 8).

Located in the subtropical monsoon zone, the study area is mildand humid, with abundant rainfall in the autumn. Rain is an importantsource of recharge to the groundwater system. There aremany surfacewater bodies in the study area. The major ones are Taihu Lake in thewest and the Yangtze River in the north. Theses surface water bodiesprovide direct recharge to the shallow unconfined aquifer, and eventhe 1st confined aquifer.

The main groundwater drainage in the study area is artificialexploitation in deep aquifers. Groundwater also discharges to surfacewater. The location and the pumpage of pumping wells in differentaquifers are allotted to the corresponding nodes in the numericalmodeling.

A groundwater level monitoring system in this area has been inoperation since the 1960s. There are no observation wells in theunconfined aquifer or the 1st confined aquifer. The number of theobservational wells in the 2nd, the 3rd, the 4th and the 5th confinedaquifers is 67, 127, 50 and 16, respectively.

A land subsidence monitoring system, using bench mark observa-tions, was introduced and started working in Shanghai in 1921. Landsubsidence in Su-Xi-Chang area was not discovered and measureduntil the 1960s. There are 27 extensometer groups in Shanghai and 5extensometer groups in the Su-Xi-Chang area. The extensometers aresurveyed in every month and most of them are located in thedowntown of the cities. The locations of the extensometers randomlychosen for comparing the observed and simulated settlement aredemonstrated in Fig. 1. These extensometer groups provide aninvaluable historical record of the vertical deformation of differenthydrostratigraphic units. Together 162 extensometer marks of the 32

Fig. 8. The boundary condition and the locations of

extensometer groups are used in the model calibration andverification.

4.2. Deformation model of the soil

As to land subsidence due to groundwater withdrawal, the relation-ship between groundwater level change and soil compaction is oftenderived based on the principle of effective stress developed by Terzaghi(Craig, 1995). The aquifer units were often treated as linear elasticmaterials, and the aquitard units were treated as bi-linear materials(Bouwer 1977; Pacheco et al., 2006). However, field monitoring data ofcompaction and piezometric level records from the extensometergroups andobservationwells in the studyarea indicate thatdeformationof hydrostratigraphic units is complex. It is greatly related to both theproperties of soils and the piezometric level changing patterns (Ye et al.,2005; Shi et al., 2007, in press; Zhang et al., 2007).

Considering the complicated temporal and spatial deformationfeatures of the hydrostratigraphic units, it is not appropriate to use thesame deformation model for all the hydrostratigraphic units during allthe time steps as the traditional way does. It is necessary to applyrelevant soil deformationmodels indifferent zones andperiodsbasedonthe soil properties and the change patterns of groundwater level. For the4th confined aquifer discussed above, an elastic deformation model canbe used at first. An elasto-plastic deformation model should be adoptedwhen the groundwater level falls continuously above the previouslylowest values. Finallyavisco-elasto-plastic deformationmodel shouldbeconsidered when the groundwater level falls continuously below theprevious lowest values. In the followingwewill discuss how to adopt thecorresponding deformation models in the mathematical model accord-ing to the deformation features of the hydrostratigraphic units.

observation wells of the 3rd confined aquifer.

34 X. Shi et al. / Engineering Geology 100 (2008) 27–42

5. Mathematical model

5.1. The flow model based on different constitutive laws

The general expression of flow governing equation (Gambolati andFreeze, 1973) is:

jd KdjH½ � ¼ g/bAHAt

þ AeAt

ð1Þ

where H is hydraulic head.K is hydraulic conductivity.γ is volume weight of water.β is volume compressibility of water./ is porosity.ε is the vertical strain.

The concrete expression of second term in the right hand of Eq. (1)is different in condition of different constitutive laws. The simplestconstitutive law is elastic. According to elastic stress–strain relation-ship and the effective stress theory, there is an expression:

AeAt

¼ �aAr VAt

¼ gaAHAt

ð2Þ

where α is volume compressibility of soil. σ′ is effective stress, definedas the difference between the total stress (σ), which is the totaloverburden load, and fluid or pore pressure (p). If the total overburdenload to be constant, dσ′=−dp.

Substituting Eq. (2) into Eq. (1), we obtain the traditional flowequation (Bear, 1972):

jd KdjH½ � ¼ g /bþ að ÞAHAt

¼ SsAHAt

ð3Þ

where Ss is specific storage, and Ss=γ(α+ϕβ).In order to describe the visco-elasto-plastic deformation, the

modified Merchant model is adopted to build the corresponding flowand subsidencemodels (Ye, 2004). Merchantmodel (Fig. 9) is composedof aHooke spring and a Kelvin element. The Kelvin element is composedparallel of a Hooke spring and a dashpot. Spring ‘a’ is used to describeelastic deformation of soil. Kelvin element is used to describe creep ofsoil. So themodel can be used to describe visco-elastic deformation. Thedifference between the modified Merchant model and the originalmodel is that the linear springs describing elastic deformation arereplaced by nonlinear springs describing elastic and plastic deforma-tions, similar with the modification by Gambolati et al. (1974), Helm

Fig. 9. Schematic representation of the Merchant model.

(1975, 1976), Neuman et al. (1982) and Gambolati et al. (1991).Laboratory tests on sediment cores and measurements of aquifersystemcompaction obtained fromborehole extensometers indicate thatthe compressibility values can be quite different. They depend onwhether the effective stress exceeds the previous maximum effectivestress, termed the preconsolidation stress (Riley, 1969). Hence thedeformationsof springs ‘a’ and ‘b’ are elastic if the current effective stressis less than the preconsolidation stress. Spring ‘a’ and Kelvin elementtogether can describe instantaneous elastic deformation and creep.Otherwise the deformations of the two springs are plastic. Spring ‘a’ andKelvin element together can describe instantaneous plastic deformationand creep. Thus the modified Merchant model can describe instanta-neous elastic, elasto-plastic, visco-elastic and visco-elasto-plastic defor-mation and has the advantage of fewer parameters. The flow functionbased on themodifiedMerchantmodel is (Huang,1983; Ye et al., 2005):

jd KdjH½ � ¼ g/bAHAt

þ ga1AHAt

� A g a1 þ a2ð Þ H0 � Hð Þ þ e� e01þ e0

� �ð4Þ

where α1 is the compression coefficient of spring ‘a’.α2 is the compression coefficient of spring ‘b’.μα2 is the reciprocal of the viscous coefficient λ of the Newton

viscous body in the Merchant model.e is void ratio.e0 is the initial void ratio.H0 is the initial head of every time step.

Note that α1 and α2 are not constant, the values are determined bythe Eqs. (5a), (5b).

a1 ¼ ake1 if HNHpa1 ¼ akv1 if HVHp

ð5aÞ

a2 ¼ ake2 if HNHpa2 ¼ akv2 if HVHp

ð5bÞ

where Hp is the historical lowest groundwater level, termed thepreconsolidation head.

αke1 and αkv1 are coefficients of elastic compressibility andplastic compressibility of spring ‘a’, respectively.

αke2 and αkv2 are elastic compressibility and plastic compres-sibility of spring ‘b’, respectively.

The modified Merchant model includes elastic, elasto-plastic,visco-elastic and visco-elasto-plastic constitutive laws. Differentconstitutive law can be realized by setting different parameters. Forinstance, supposing the deformation features of some zone are elasticand plastic, λ should be set to zero and the parameters of αke1 andαkv1 are chosen to reflect the elastic and plastic deformation of the soilstrata. The different constitutive law in the deformation model isreflected in the same way.

5.2. Deformation model

When only one-dimensional (vertical) deformation is considered,the equation of the soil deformation is:

DL ¼Z L

0edz ¼

Z L

0

e� e01þ e0

dz ð6Þ

Where ε is the vertical strain,L is thickness of the hydrogoelogic unit.ΔL is deformation of the hydrogoelogic unit.

Fig. 10. The flowchart of calculation process.

Table 1Summary of representative hydrogeologic parameters after the model calibration

Aquifer Hydraulic conductivity, m/s Compression index Swelling index

A0 5×10−5 to 1×10−6 0.3 to 0.1 0.06 to 0.02A1 2×10−4 to 1×10−5 0.2 to 0.1 0.04 to 0.01A2 4×10−4 to 1×10−4 0.2 to 0.1 0.04 to 0.01A3 7×10−4 to 1×10−5 0.2 to 0.1 0.03 to 0.01A4 4×10−4 to 3×10−5 0.3 to 0.1 0.08 to 0.01A5 3×10−4 to 2×10−5 0.3 to 0.1 0.08 to 0.02Aquitards 1×10−9 to 5×10−11 0.5 to 0.1 0.09 to 0.02

35X. Shi et al. / Engineering Geology 100 (2008) 27–42

When the modified Merchant model with the visco-elasto-plasticstrain–stress relationship is adopted, the subsidence equation is (Yeet al., 2005):

DL ¼Z L

0

ga1DH þ AgDt a1 þ a2ð ÞDH1þ ADt

dz ð7Þ

Notably, it can be simply applied by setting the parameters in themodel, which can present corresponding elastic, elasto-plastic andvisco-elastic deformation.

5.3. Coupling of the flow and subsidence models

A regional land subsidence model includes a flow model and asubsidence model. A ‘coupled two step’ model is proposed in thepaper. The model can calculate the hydraulic heads and deformationby two steps and also couple them by changing parameters asfunctions of the hydraulic heads and deformation. The parameters inthe models are the functions of effective stress and porosity ratio, andkeep changing during subsidence. Therefore, the regional landsubsidence model is nonlinear. The solution process is that: 1) Thepore water pressure and the deformation are calculated separately,which is the same as that in an uncoupled model. 2) According to theeffective stress and the porosity ratio, all the parameters arerecalculated. Then the new pore water pressure and deformation areobtained in the flow and subsidence models based on the newparameters. 3) Examine the convergence of pore water pressure andthe deformation values by comparing the new values with theprevious iteration values. 4) Determine if the next iteration is needed.If convergence has been reached for all the two models, thecomputation of the next time step is performed. Otherwise, the

present iteration values are updated by relaxing the new and theprevious iteration values. The coupling iteration process (step 2 andstep 3) continues after the updating. The numerical process isillustrated in Fig. 10.

5.4. Parameters in the flow and subsidence models

When a hydrostratigraphic unit keeps compressing and theporosity keeps decreasing, they result in a continuous change ofhydraulic conductivity and specific storage. The empirical equationbetween hydraulic conductivity and porosity is listed below (Lambeand Whitman, 1979; Rivera et al., 1991).

K ¼ K0/ 1� /0ð Þ/0 1� /ð Þ

� �mð8Þ

where ϕ0 stands for the initial porosity.K0 is the initial hydraulic conductivity.m is an empirical coefficient. In this case, it is about 2 to 3.

The relationship between the specific storage Ss and the porositycan be obtained as follows: the definitions of specific storage andporosity ratio are Ss=γ(α+ϕβ) and / ¼ e

1þe, respectively. The waterbulk density γ and the water volumetric compression coefficient β aretreated as constant. The soil volumetric compression coefficient αchanges with effective stress and void ratio. According to thedefinitions of the compression coefficient Cc and the swelling indexCs (Huang, 1983), the relationship among soil volumetric compressioncoefficient α, effective stress and porosity ratio is as follows:

a ¼ �de= 1þ e0ð Þdr V

¼ ln 10ð Þ�de=d log r Vð Þ1þ e0ð Þr V ¼ 0:434

Cc

1þ e0ð Þr V HbHp� �

ð9aÞ

a ¼ �de= 1þ e0ð Þdr V

¼ ln 10ð Þ�de=d log r Vð Þ1þ e0ð Þr V ¼ 0:434

Cs

1þ e0ð Þr V HzHp� �

ð9bÞHydraulic conductivity and specific storage are always changingduring the entire simulation period. The parameters that need to becalibrated and verified are: the initial porosity ratio e0, the historicalmaximum preconsolidation pressure σp, compress index Cc, reboundindex Cs, initial hydraulic conductivity K0 and the parametersm and μ.In the numerical model, the initial hydraulic conductivity and specificstorage values are derived from pumping tests. The initial mechanicalparameters of clays and silts are obtained from laboratory tests. Thetrial and error method is used for calibration by matching thecalculated and observed values of piezometry and subsidence. Table 1is a summary of parameter values for the aquifers and aquitards.

6. Model calibration and verification

The solution of a regional land subsidence model is one of thedifficulties in land subsidence simulation. The horizontal scale of the

Table 2Statistics of the relative mean error between the simulated and measured piezometrichead during the entire simulation period (from 1995 to 2002) after the model calibration

The numberof theobservation wells

Therelativemean error

b5% 5%–10% 10%–20% 20%–30% 30%–50% N50%

260 Percent 36.27 25.69 17.02 8.96 7.83 4.23

Note: The relative error is calculated as the ratio of the simulated head and the differencebetween thesimulatedand theobservational head in themodel calibrationandverification.

36 X. Shi et al. / Engineering Geology 100 (2008) 27–42

study area is much larger than the vertical scale and the thicknessdistribution of the aquifer and aquitard are non-uniform. Somehydrostratigraphic units are very thin. If the traditional finite elementmethod (FEM) were adopted, the fine discretization should be used toavoid the distorted elements. It would cost much computer resourceand a very long computer time. Thus the multiscale finite elementmethod (MsFEM) (Hou andWu, 1997; Hou et al., 1999; Ye et al., 2004)is used to solve the coupled subsidence model, which can efficientlyreduce the element number and avoid the distorted element.

In the mesh discretization, the hexahedron element is adopted andthe aquifer system is divided into 6 layers in the vertical with averagethickness about 50m. That is, an aquifer and an aquitard are treated asone layer. Delay of the head dissipation and the deformation arerealized using the modified Merchant model. Therefore, there is noneed to separate the aquifer and the aquitard in order to illustrate thesubsidence delay. The elements are mostly square in the horizontaldirection. They become irregular quadrangle only in some local places,such as observation wells and pumping wells. The size of the elementis about 1200 m×1200 m in the horizontal plane. The numbers of thenodes and elements are 47,912 and 56,146, respectively.

Note only the results of the 3rd confined aquifer, which has thewidest distribution and gets the greatest influence from the exploita-tion, are listed because of the length limitation.

6.1. The initial condition and simulation period

Considering the availability of the data and the seasonal exploita-tion pattern of groundwater, the simulation period is from theDecember, 1995 to the December, 2002, divided into 28 time stepswith 3 months in every step. The model calibration period is from the1st step to the 20th step, and the verification is from the 21st to the28th step.

Fig. 11. Map of the piezometric head (m above mean sea level) of the 3rd confined aq

The initial head of each node is required. In the study area, thereare many observation wells located inside the model area and at theboundaries of each aquifer. Thus the initial heads of all aquifers areobtained directly by kriging interpolation based on the observed data.The initial head of the aquitards are obtained via the calculationbetween the corresponding upper and lower nodes in the aquifers bylinear interpolation. The initial groundwater level contour of the 3rdconfined aquifer is illustrated in the Fig. 11. The initial subsidence timeis 30th December, 1995. The initial relative displacement to theground is zero for all the nodes.

6.2. Simulation results and discussion

Transientflowmodel calibration and verificationwere accomplishedby simulating groundwater level changes in the aquifer in response toclimatic variability (recharge) and groundwater usage (pumping). Thecalibrationwas conductedsuccessively fromthefirst time step to the lastone. In each stress period for which the observation data are available,the observed and model-calculated groundwater levels at a total of 260observation wells were statistically compared. Through this process,model input parameters, i.e., hydraulic conductivity, recharge rates andboundary conditions, were further adjusted to minimize the

uifer as measured in 1995 and used as initial condition in the flow simulations.

Fig. 12. Comparison between measured (circles) and simulated (solid lines) piezometric head (m above mean sea level). A,C,E for Su-Xi-Chang area, B,D,F for Shanghai City.

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Fig. 13. Map of the piezometric head (m above mean sea level) in the 3rd confined aquifer as of March 2000 (A) as measured and (B) computed by the flow model.

38 X. Shi et al. / Engineering Geology 100 (2008) 27–42

Fig. 14. Scatter diagram of observed versus calculated deformation at all observationtimes in F00 extensometer.

39X. Shi et al. / Engineering Geology 100 (2008) 27–42

discrepancy between the observed and calculated groundwater levels.The groundwater level statistics of the relative error at all monitoringwell locations and observation times is listed in Table 2. There is a fairlygood overall agreement between the observed and calculated values. Toexamine the temporal trend of calculated heads as compared to that ofobserved heads, six observation wells (three in Su-Xi-Chang and theother three in Shanghai) with long time series were selected fromdifferent parts of themodeled domain. Fig. 12 shows that the calculatedand observed hydrographs at the selected observation wells havegenerally similar trends, with the calculated heads in good agreementwith the observed over a long period of time. From Fig.12, it can be seenthat the groundwater levels in all the confined aquifers increaseobviously due to the gradual decrease of the groundwater yield (asillustrated in Figs. 3 and 6). Especially the levels in the 4th confinedaquifer in Shanghai and in the 3rd confined aquifer in Su-Xi-Chang, bothof which are the main exploitation units in the local place, recoversobviously as shown in the Fig. 12F and C, respectively. Whereas, thegroundwater level in the 3rd confined aquifer in Shanghai declined (asshown in Fig. 12D) because the 3rd confined aquifer in Shanghairecharges to the corresponding aquifer in Su-Xi-Chang due to theinfluence from the regional groundwater cone of depression. Thecomparison between the observed and the simulated level contours arepresented inFig.13. Thefigure indicates the groundwater level in the3rdconfined aquifer is fairly low all along, because it is always the mainextract aquifer in Su-Xi-Chang area. Besides the deepest groundwatercone of depression in Changzhou, some small ones are developed nearTaicang and Kunshan. The groundwater level in the 3rd confined aquiferin Shanghai is relatively high owing to the small pumpage there.

Similarly, the 162 marks in the 28 extensometer groups are usedfor the deformation model calibration and verification. The statisticsof the subsidence relative error is listed in Table 3. This is moreapparent from Fig. 14 which compares the model-calculated deforma-tions with the observed deformations in F00 extensometer. Thecomparison of the observed and the simulated accumulative sub-sidence is illustrated in Fig. 15. It can be seen from the accumulativesubsidence contour map that the depression cone of land subsidenceis located in Changzhou, Wuxi, Suzhou and the urban district ofShanghai. Besides that, a local depression cone of land subsidence hasbeen developed in Taicang and Kunshan because of the existence ofthe local groundwater cone of depression there. The depression coneof land subsidence is across the administrative boundary, whichimplies the necessity of breaking through the administrative bound-ary in simulation. Comparing Figs. 13 and 15, the location of thedepression cone of land subsidence matches that of the groundwaterlevel depression cone. In the view of local distribution of landsubsidence depression cone, the simulation results illustrated that theoccurrence and the development of the land subsidence are in closerelationship with the groundwater pumping both in time and space.The configuration of the subsidence cone is basically identical withshape of the groundwater depression cone.

To examine the temporal trend of calculated deformations ascompared to that of observed deformations, twomarks with long timeseries were selected from the Su-Xi-Chang area and Shanghai City,respectively (Fig. 16). First, from the view of the whole tendency, thesimulation results showed the land subsidence was developedcontinually. Secondary, comparing Fig. 16A and C, it can be seen that

Table 3Statistics of the relative mean error between the simulated and measured landsubsidence from 1995 to 2002 after the model calibration

The number of theextensometer groups

The relative error b5% 5%–10% 10%–20% N20%

162 Percent 22.3 31.5 29.6 16.6

Note: The relative error is calculated in the same way as that in the Table 1.

the subsidence of the 4th confined aquifer in Su-Xi-Chang becomeslarger with time, although the 3rd aquitard, which is over the maingroundwater exploitation unit (3rd confined aquifer), is still the mainsubsiding unit. This phenomenon implies that the compactiondeformation of the sandy aquifer can not be ignored. However, thesand in the 4th confined aquifer (the main subsiding unit) in Shanghaikeeps compressing, instead of demonstrating the elastic features,although the groundwater level of this aquifer rises annually.This implies that the delay phenomenon of the sandy aquifer isremarkable.

The results indicate that the simulation precision in the modelcalibration and verification reaches the Chinese national standard(NSB, 1993). It is satisfied to get the simulation result precision forsuch a complicated aquifer system with large head variation andcomplex deformation mechanism. The result implies that the modelbuilt can reflect the main characteristic of the studied aquifer systemand the land subsidence, suggesting that the conceptual model candisplay the actual hydrogeologic condition in the study area. Theseresults suggest that the adoption of various types of constitutive lawhas effect on the subsidence simulation. From above, it can beconcluded that the model is reasonable and can be used for predictionaccording to the exploitation scenarios established by the manage-ment division.

7. Conclusion

Based on the regional subsidence simulation in the Su-Xi-Changarea and Shanghai City, the following conclusions can be obtained:

1. Both the spatial heterogeneity of the hydrogeological units and thetemporal and spatial groundwater level variations determine thecomplexity of the deformation features in the regional landsubsidence. The modified Merchant model can describe visco-elasto-plastic deformation of different hydrostratigraphic units.The results indicate that modified model has advantages of fewerparameters and easier application, when it is used for simulatingthe complicated deformation features.

2. The land subsidence model built in this paper includes a three-dimensional flow model with variable parameters and a one-

Fig. 15. Map of the cumulative land subsidence (mm) over the entire simulation period (A) as measured and (B) computed by the subsidence model.

40 X. Shi et al. / Engineering Geology 100 (2008) 27–42

Fig. 16. Comparison between measured (circles) and simulated (solid lines) accumulative land subsidence (mm). A,C for Su-Xi-Chang area, B,D for Shanghai City.

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dimensional (vertical) subsidence model. A ‘coupled two step’method is adopted in the paper. The model can calculate thehydraulic heads and deformation by two steps. It also coupled thegroundwater flow model and land subsidence model by changingparameters as functions of the hydraulic heads and deformation.

3. After the calibration and verification by the observed groundwaterlevel and extensometer groups, the simulation results reveal thatthe model is reasonable and can be used for subsidence prediction.The simulation results indicate the depression cone of ground-water has exceeded the provincial boundary due to greatexploitation, forming a huge regional depression cone. The landsubsidence in the Su-Xi-Chang area and Shanghai City is connectedinto a regional depression cone. Therefore, it is necessary to breakthrough the provincial boundary and have a regional landsubsidence simulation. It will be beneficial for land subsidencemanagement, observation, research and control.

4. The model reproduced that the primary subsidence layer inShanghai shifts from the shallow aquitard to the fourth confinedaquifer because of the groundwater yield variations and thechange of exploitation aquifers. However the third aquitard wasthe primary subsidence layer in the Su-Xi-Chang area and thecompaction deformation of the sandy aquifers was remarkable.The scope of subsidence still keeps extending and the cumulativesubsidence still keeps increasing, because of the deformation delayof aquitards and aquifers. It is very urgent to conduct manage-ments such as restricting groundwater exploitation to control thedevelopment of land subsidence.

5. Although some improvements are made for this regional landsubsidence model, there are still some issues for further researchin land subsidence simulation. A pivotal one is the parametersdetermination of aquifers in the land subsidence simulation, forinstance, accurate determination of the preconsolidation head (thecritical groundwater level) of each aquifer in different geologicalzones. Because of the lack of data, the preconsolidation heads inthis paper are estimated based on the location and thickness ofaquifers, the structure of the aquifers and aquitards, and the initialgroundwater levels of each aquifer. Then the preconsolidationheads are adjusted during the model calibration, which bringsuncertainty of the model to some extent. The porosity is anotherimportant issue. In this paper, it is determined in the same way asthe preconsolidation heads. In the further research, it would behelpful if geological statistics is adopted to make complement.

Acknowledgments

The authors would like to express appreciation to the editors andtwo anonymous reviewers for their valuable comments and sugges-tions. Thepaper isfinancially supported by theNational Nature ScienceFoundation of China grants No. 40335045, 40702037 and 40725010.

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