Ground settlements and drawdown of the water table around an excavation
Ground settlements and drawdown of the water table around an excayation J. P. HSI AND J . C. SMALL School of Civil and Mining Engineering, The University of Sydney, Sydney, NSW 2006, Australia Received December 16, 1991 Accepted April 7, 1992 In the vicinity of an excavation in a saturated soil, ground settlements are often caused by the combined effects of stress release and drawdown of the water table. These settlements may be crucial if the excavation is carried out in a congested area. A case history of excavation adjacent to closely constructed blocks of buildings is discussed in this study. Ground settlements and water-surface levels were monitored during the excavation period, as the settlement of the surrounding area was of concern. The authors have previously developed a fully coupled numerical method that allows the computation of the displacements and pore pressures in a soil taking account of the drawdown of the water table which may accompany excavation. This method is used here for back-analysis of a full-scale excavation that has been comprehensively documented. Comparisons between the field measurements and the calculated results are given in this paper. Key words: consolidation, excavation, finite element, seepage, transient unconfined flow. A proximite d'une excavation dans un sol sature, des tassements du sol resultent souvent des effets combines du relschement des contraintes et de l'abaissement de la nappe phreatique. Ces tassements peuvent 6tre cruciaux si l'excavation est realisee dans des zone achalandees. Une Ctude de cas d'une excavation adjacente a des blocs de bgtiments dense- ment construits est discutee dans cette Ctude. Les tassements et les niveaux de la nappe phreatique ont ete mesuris durant la piriode de l'excavation puisque l'affaissement de la zone environnante etait prioccupante. Les auteurs ont dkveloppe anttrieurement une methode numerique complktement appariee qui permet le calcul des deplacements et des pressions interstitielles dans un sol et qui prend en compte le rabattement de la nappe phrCatique qui peut resulter de l'excavation. Cette mkthode est utiliske ici pour l'analyse a rebours d'une excavation a pleine Cchelle qui a CtC pleine- ment ducomentke. Des comparaisons entre les mesures sur le terrain et les resultats calculCs sont donnes dans cet article. Mots C/&S : consolidation, excavation, Clement fini, infiltration, Ccoulement transitoire non confine. [Traduit par la redaction] Can. Geotech. J . 29, 740-756 (1992) Introduction Damage to buildings, roads, and utilities is frequently seen around an excavation site. It is usually caused by excessive ground movements due to excavation. Therefore care needs to be taken when an excavation is to be executed in a con- gested area. An accurate prediction of the behaviour of the soil surrounding an excavation can lead to an improved design and limit any damage around the cut. While the excavation is proceeding, a monitoring system is often needed to provide information about the response of the excavation and give early warning if any unexpected behav- iour is encountered. Two main factors are known to induce ground settlement around an excavation. Firstly, there is stress relief due to overburden removal. The soil that is being removed initially serves as a support to the boundary of the excavation. When it is removed, the soil around the cut starts moving inwards due to the loss of this support, and ground settlement is then generated. Secondly, if the excavation is carried out below the groundwater table and if the soil is permeable or the elapsed time is long enough to allow the water table to drop, an additional ground settlement may occur due to the increase in effective stress in the soil generated by the fall of the groundwater table. Currently most of the methods for excavation analysis in saturated soils have been based on the assumption that the water table remains at a constant level and that pore pres- sures and deformations of the soil can be calculated by use of effective-stress approaches (Osaimi and Clough 1979; Banerjee et al. 1988; Tsui and Cheng 1989; Yong et al. 1989; Bolton et al. 1989; Cheng and Tsui 1991; Finno and Prin~cd in Canada / In~pr~nlC au Canada Harahap 1991). As drawdown of the water table is one of the major factors that contributes to the ground settlement, it should be taken into account in excavation analysis where a drawdown does occur (Walker and Morgan 1977; Debidin and Lee 1980; Moran and Cherry 1981 ; Schroeder et al. 1986; Forster et al. 1991). The authors have successfully developed a fully coupled finite element method (Hsi and Small 1992a, 1992b; J.P. Hsi and J.C. Small, in preparation) for excavation analysis which incorporates aspects of consolidation theory (Biot 1941, 1956; Sandhu and Wilson 1969; Christian and Boehmer 1970; Hwang et a/. 197 1 ; Small et al. 1976), tran- sient free-boundary flow (Desai 1976; Rushton and Redshaw 1979; Bathe 1982; Bathe et al. 1982; Desai and Li 1983; Cividini and Gioda 1984; Gioda and Desideri 1988), and overburden removal theory (Ghaboussi and Pecknold 1984; Brown and Booker 1985). Deformations and pore pressures generated in a soil around an excavation can be evaluated by this method, and since it is fully coupled, changes in water pressure will cause deformation in the soil, and changes in soil deformation can cause changes in water pressure. A vir- tual work formulation is used to determine the out-of- balance forces applied along the boundary of the excava- tion so that overall stress equilibrium is maintained during the excavation process. As presented in the previous work (Hsi and Small 1992a, 1992b; J.P. Hsi and J.C. Small, in preparation), this method is implemented by a finite element program, EXCAZ, that is able to solve plane strain and axisymmetric problems and can be used for elastic or elasto- plastic soils. Can. Geotech. J. Downloaded from www.nrcresearchpress.com by University of Sydney on 09/30/13For personal use only.FIG. 1. Permeability-pressure relationship. k,, permeability of saturated soil. A case history of an excavation for which the ground sur- face settlement and drawdown of the water table were monitored is discussed in this study. The excavation was car- ried out to a depth of about 27 m mainly in silty sands inter- bedded with some thin layers of silty clay. The elastic model was used here to simulate the soil behaviour during excava- tion. Sufficient soil data from site investigations and labo- ratory tests were provided so that reliable soil parameters could be determined for use in the analysis. Fully coupled numerical method The fully coupled method for excavation analysis pre- sented here may be used to compute the movement of the soil due to stress relief and due to water table drop. In the numerical analysis the tractions removed from the finite ele- ment mesh are calculated by using a modified form of Ghaboussi and Pecknold's (1984) or Brown and Booker's (1985) method. This method can correctly evaluate the forces to be removed, unlike many methods used previously (Christian and Wong 1973; Clough and Mana 1976; Osaimi and Clough 1979; Banerjee et al. 1988; Tsui and Cheng 1989; Cheng and Tsui 1991) where the tractions were calcu- lated by integrating only the stresses in the removed soil. The numerical procedure can also predict how the water table will drop as the excavation proceeds and how this will cause deformation in the soil. Governing equations The finite element equation used for excavation analysis taking account of drawdown of the free surface is given by (Hsi and Small 1992a, 1992b; J.P. Hsi and J.C. Small, in preparation) where All terms used here are listed in the appendices, and details are given by Hsi and Small (1992~) and Hsi (1992). SMALL 741 TABLE 1. Soil profile and description Layer Thickness (m) Description I 8.8-12.5 Silty fine to medium sand; grey; containing small amounts of shells; loose to medium dense 2 0.7-3.1 Silty clay or clayey silt; grey; soft to stiff 3 2.5-12.3 Silty fine to medium sand; grey; loose to dense 4 0.0-7.5 Silty clay and clayey silt; grey; soft to stiff 5 16.3-24.0 Silty fine sand with thin layers of sandy silt; grey; medium dense to dense 6 6.9-10.3 Fine sandy silt; grey; with silty clay or clayey silt occasionally; medium dense to dense 7 Unknown Silty clay; grey; stiff to very stiff Equations [I] and  are an extension of the incremental approach for solving consolidation problems using an incre- mental time marching scheme proposed by Small et al. (1976). As both stress removal and drawdown of the free surface are considered for the excavation analysis, the vector - Ag is incorporated for simulating tractions applied along the excavation boundary due to soil removal, and the term CFS is incorporated so as to take account of water flowing from the soil as the water table falls. The significance of these two terms - Ag and CFS is described in the following. By consideration of overall force equilibrium being main- tained in the soil while excavation proceeds, an extended form of Brown and Booker's method (1985) or the method of Ghaboussi and Pecknold (1984) was developed in which the vector of forces - A g to be removed from the finite ele- ment mesh is given by These forces are applied to the nodes of the finite element mesh when elements are removed. The vector is evaluated by integrating pore pressures and effective stresses at the ( j - 1)th stage over the remaining (i.e., the elements that have not been excavated) domain at the jth stage. It is noted that the coupling matrix L involves an integration over the volume of the soil mass, and it is defined in Appendix 1. As drawdown of the water table is considered, the con- cepts of the residual flow procedure proposed by Desai and Li (1983) and Bathe et al. (1982) were adopted. The term CFS may be written as [41 CFS = jr aaT Sy cos p d r This term can be used to calculate the imposed flow along the free surface where the pore pressure is zero. This approach can only be applied, however, when there is no negative pore-pressure zone generated by the excavation above the level of the base of the cut. When a negative pore- pressure zone is produced due to excavation, there may be several zero pore-pressure contours, and so the free surface contour cannot be precisely determined. An alternative method proposed by Cividini and Gioda (1984) has t o be Can. Geotech. J. Downloaded from www.nrcresearchpress.com by University of Sydney on 09/30/13For personal use only.CAN. GEOTECH. J . VOL. 29, 1992 I Can. Geotech. J. Downloaded from www.nrcresearchpress.com by University of Sydney on 09/30/13For personal use only.20 30 SPT N HSI AND SMALL 10 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5 UNIT WEIGHT (tlm 3) -80 I I I I 0 10 20 30 40 50 WATER CONTENT (%) FIG. 3. Relationship of elevation to (a) SPT -80 I I I I I 0.20 0.30 0.40 0.50 0.60 POROSITY unit weight, (c) water content, and (d) porosity. used when this occurs. With this method, the free surface and the size of the time step chosen and is not as accurate is assumed to correspond to the sides of the elements, and as the residual flow procedure, but it has the advantage of its position is calculated from the velocities of the free sur- not depending on the position of the zero pore-pressure con- face. It is therefore dependent on the fineness of the mesh tour. The method is only used if excess negative pore pres- Can. Geotech. J. Downloaded from www.nrcresearchpress.com by University of Sydney on 09/30/13For personal use only.744 CAN. GEOTECH. sures exist above the base level of the excavation, otherwise table drops. The porosity n of a saturated soil is the sum the method of Bathe et al. (1982) is used. of the specific yield and the specific retention; for sandy In , Sy is the specific yield that defines the amount of soils, S,, is slightly smaller than n, whereas for clayey soils, water which can be yielded from the soil when the water Sy is much smaller than n (Walton 1970). GI &pa) FRICTION ANGLE FIG. 3. (continued). Relationship of elevation to (e) plastic and liquid limits for CL/ML, ( f ) plasticity index for CL/ML, (g) c, for CL/ML, and (h) friction angle. CD, consolidated drained triaxial test; CU, consolidated undrained triaxial test; DS, direct shear test. (h) 10 0 -10 -20 h a w 3-30 F u > W -40 a W -50 -60 -70 - 80 90 (9) 10 0 -10- -20 - a w 2-30 2 2 > 112-40 cl w -50 -60 -70 - 80 40 00 00 on q q " q qJuou ,, q - q - - - q q 00 - q - I I I I I I I 10 20 30 40 50 60 70 80 C I ' A+ X - x + +xunt + X - A 0 ++ - 4 - + Lu 0 q CU(CUML) - 0 CD(CUML) A CD(SM) - X DS (CUML) + CD(SM) I I S q I I I 10 15 20 25 30 35 Can. Geotech. J. Downloaded from www.nrcresearchpress.com by University of Sydney on 09/30/13For personal use only.HSI AND SMALL 745 CONST. HEAD (SM) 0 TRIAXIAL (SM) FIG. 3. (concluded). Relationship of elevation to (i) m, and ( j ) permeability. CONST. HEAD, constant head permeability test; FIELD, field permeability test; TRIAXIAL, triaxial permeability test. 0 10 2Om - Scale FIG. 4. Layout plan of the excavation. To eliminate the flow above the free surface, the perme- ability of the soil is reduced according to the levels of negative pore pressure which exist there (Bouwer 1964; Freeze 1971; Cathie and Dungar 1975; Desai and Li 1983; Li and Desai 1983) as shown in Fig. 1. Limit values of permeability klimi, and negative pore pressure Plimi, are defined as the lowest values that the soil can reach. The permeability and pore pressure are reduced in the zone above the free surface according to the perme- ability - pore pressure relationship until the negative pressure reaches Plimi,. Once suctions reach Plimi, they are held at this value and not allowed to become more negative, and the permeability is set to a value of klimit. Finite element programming A finite element program, EXCAZ, was developed by the authors to solve the governing equations. An eight-noded isoparametric element is used in the program. It is able to perform plane strain and axisymmetric analyses in elastic or elastoplastic materials. To ensure the equilibrium of stresses within each incre- ment of excavation and to determine the location of the free surface, iterations are required within each time step so that equilibrium can be achieved. Generally the program was found to give convergent results within five iterations if the implicit Euler backward method (a = 0) was used, and con- vergence of the solution was deemed to have occurred if the change in total water head at each node was less than 1000th of the height of the solution domain. Case history Job nature An excavation was to be carried out in Kaoshung, Taiwan, for the construction of the basement of Chung-Chow Sewerage Intake Pump Station (CSIPS). In the vicinity of the excavation site, there were a number of existing build- ings as shown in Fig. 2. Taipei Civil Engineers' Association was commissioned by Kaoshung Architects' Association to conduct a study on the influences of the excavation on the surrounding area (Taipei Civil Engineers' Association 1985). Can. Geotech. J. Downloaded from www.nrcresearchpress.com by University of Sydney on 09/30/13For personal use only.CAN. GEOTECH. J. VOL. 29, 1992 , I Slurry wall Position of the struts each stage o f excavation -35.7 -40 t FIG. 5. Profile of the excavation. The settlements of the ground surface and the changes in the groundwater table were monitored during the excava- tion period. Site conditions The site of the planned CSIPS was located on reclaimed land at Chijin in Kaoshung. Taiwan Strait was to the south- west, and densely packed buildings lay to the northeast. Farther to the northeast lay one of the shipping channels of Kaoshung Harbour. The location and layout of the exca- vation site are shown in Fig. 2. Soil profile Fourteen boreholes were drilled, and a series of soil tests were conducted by China Engineering Consultants, Inc., Taiwan, on samples taken from the excavation site (China Engineering Consultants, Inc. 1981). Based on the investiga- tion results, the soil profile can be simplified into seven layers, which are summarized in Table 1. The idealized soil profile used in the analysis is shown on the graphic log in Fig. 9. On top of layer 1, fill was found in some areas which varied from 0 to 5 m in thickness. Groundwater conditions During the period of site investigation, wells and piezo- meters were installed to investigate the levels of the ground- water table and the pore-pressure distribution in each layer of soil. Based on the long-term observed data (January to May 1981), it was found that the water pressure was distri- buted hydrostatically throughout the deposit and that the groundwater table varied between an elevation of 0.13 and 0.39 m due to the oscillation of the tide level. Soil characteristics Intensive field and laboratory tests were carried out to investigate the properties of the soils. The results are sum- marized in Figs. 3a-3j. As the deposits at the excavation site are interlayered with sandy (layers 1, 3, 5) and clayey (layers 2, 4, 6, 7) soils, the results in these figures are pre- sented by using different legends according to the soil type; sandy soil is denoted as SM and clayey soil as CL/ML. Excavation procedures The excavation was carried out to a depth of about 27 m if the fill is ignored. The layout plan is shown in Fig. 4. I t Can. Geotech. J. Downloaded from www.nrcresearchpress.com by University of Sydney on 09/30/13For personal use only.HSI AND SMALL Jan Feb Mar Apr May June July Aug Sept Oct Nov Dec Month In 1984 FIG. 6. Excavation rate. was first excavated from the ground surface to an elevation of - 3.7 m at slopes of 1 : 1 and 1 :2, and then shotcrete was applied on the surface of the slopes to prevent erosion caused by the inflow of the groundwater. A slurry wall was later constructed from the base level (elevation - 3.7 m) to an elevation of - 35.7 m. Eight stages of excavation then fol- lowed. The wall was supported by struts installed near the base of each stage of excavation. The excavation profile is shown in Fig. 5, and the excavation rate is shown in Fig. 6. Monitoring system To monitor the drawdown of the water table during exca- vation, 15 observation wells numbered A-0 as shown in Fig. 2 were installed during the period from March to October 1984, and an additional 23 wells numbered from OW-1 to OW-25 (except for OW-11 and OW-15) as shown in Fin. 2 were later installed in November 1984 to obtain moreinformation about the groundwater table. The records showed that most of the drawdown of the water table had occurred during the first two stages of excavation (before building the slurry wall). After the construction of the slurry wall, the drawdown was not so significant due to the fact that the wall had penetrated through some low-permeability layers and effectively cut off the seepage toward the excava- tion. During the entire excavation period, the maximum lowering of the groundwater table was 4.5 m. The ground settlement was measured by use of markers placed in the surrounding area. These were numbered from K1 to K16 as shown in Fig. 2 and were set up during the period from March to May 1984. As settlements were mea- sured after the completion of the second stage of excava- tion, some settlement had already occurred. Therefore, information concerning the total settlement was not avail- able for this case. To be consistent, all the measured settle- ments discussed later were assumed to be measured relative to initial values taken on May 10, 1984. The maximum relative settlement observed was about 3.2 cm. Simulation of excavation Soil parameters for analysis Soil parameters used in the finite element analysis were mainly determined from the field and laboratory test results discussed in a previous section (Soil characteristics), and values chosen are shown in Table 2. The oedometer test results show that the soil was normally consolidated; therefore the coefficients of lateral earth pres- sure at rest KO were calculated by using the Jaky equation (1944), i.e.,  KO = 1 - s i n 4 ' The variation of KO with depth is presented in Fig. 7. To make reasonable estimations of the elastic moduli E' of the soil layers, different approaches were used. (1) Initial tangent moduli were obtained from the stress-strain plots of triaxial consolidated drained tests. (2) Undrained elastic moduli Eu were estimated from values of undrained shear strength c,, plasticity index I,, and overconsolidation ratio based on a chart presented by Duncan and Buchignani (1976), and then the drained moduli E' were calculated from 2(1 + v ' )  E' = 3 E u where Y' is the Poisson's ratio. (3) Drained moduli were obtained from the pressuremeter tests. (4) Drained moduli Can. Geotech. J. Downloaded from www.nrcresearchpress.com by University of Sydney on 09/30/13For personal use only.CAN. GEOTECH. J. VOL. 29, 1992 X n SELECTED + CU(CUML) 0 CD (CUML) A CD (SM) X DS (CUML) + CD(SM) -80 I I I I I I I 0.3 0.4 0.5 0.6 0.7 0.8 0.9 KO FIG. 7. Relationship of KO to elevation. Abbreviations as in Fig. 3. - 80 0 2 4 6 8 10 ELASTIC MODULUS (kPa) FIG. 8. Relationship of elastic modulus to elevation. OED., oedometer (consolidation) test; PRES., pressuremeter test. Other abbreviations as in Fig. 3. Can. Geotech. J. Downloaded from www.nrcresearchpress.com by University of Sydney on 09/30/13For personal use only.HSI AND SMALL I F I G . 9. Finite element mesh used for analysis. Abbreviations as in Table 2. I (in kPa) were estimated from standard penetration test (SPT)Nvalues based on the correlations presented by Webb (1969a, 1969b) for saturated fine to medium sand,  E' = 537(N + 15) and Ohya et al. (1982) for clayey soil,  E' = 1500N (5) Drained moduli were calculated from where m, is the coefficient of volume change for the swell- ing behaviour obtained from one-dimensional consolidation tests. All the evaluated moduli are shown plotted in Fig. 8 for both sandy and clayey soils. The limit negative pore pressure Plimi, was chosen to be - 20 kPa, and the limit permeability klimit was chosen to be 1000th of the permeability of the saturated soil. The soil parameters used for the analysis are presented in Table 2 as determined for the appropriate soil type in Figs. 3a-3j, 7, and 8, and selected values are also presented in the appro- priate figures. In these figures, the following notation is used for the source of the data: CU, consolidated undrained triax- ial test; CD, consolidated drained triaxial test; DS, direct shear test; CONST.HEAD, constant head permeability test; TRIAXIAL, triaxial permeability test; FIELD, field perme- ability test; PRES., pressuremeter test; OED., oedometer (consolidation) test; and SPT, standard penetration test. Finite element mesh From the layout of the excavation site and the neighbour- ing area as shown in Fig. 2, the problem can be considered as being axisymmetric. Equivalent radii rl and r2 for the cut within the wall and the outer boundary shown in Fig. 5 can be calculated by equating the perimeters of the rectangular sections to circular sections with radii r l and r2. It was found that r l = 22.7 m and r2 = 53.9 m. The excavation procedure is simulated by removing the soil in six stages, two before and four after the construc- tion of the slurry wall as shown in Fig. 6. The problem was considered as being axisymmetric, so only one half of the problem needed to be discretized into elements. The finite element mesh shown in Fig. 9 which consists of 384 isoparametric elements and 1233 nodes was used for the analysis. The shotcrete was applied immediately after completion of the simulated second stage of excavation, so the slopes of the excavation were treated as being pervious for the first two stages and impervious thereafter. The wall was built at the end of the simulated second stage of excavation. A very large modulus (2.1 x lo7 kPa) and a very small permeabil- ity (1.0 x lo-'' m/day) were assigned to elements repre- senting the wall at this stage. As there is no further informa- Can. Geotech. J. Downloaded from www.nrcresearchpress.com by University of Sydney on 09/30/13For personal use only.CAN. GEOTECH. J. VOL. 29, 1992 - .- 1 o FlELD MEASUREMENTS 1 I NUMERICALRESULTS 1 I I (b) 1 7 I ! o FIELD MEASUREMENTS i c NUMERICAL RESULTS ~ -5 ' I I 1 0 100 200 300 400 500 600 DISTANCE FROM CENTRE OF EXCAVATION (rn) FIG. 10. Measured and predicted water table on (a) August 20 and (b) December 31, 1984. tion about the force applied through the struts to the wall Groundwater table or the deformation of the wall, horizontal movements of The observed water-surface levels on August 20 and the wall were restricted at the nodes near the level where December 31, 1984, were compared with the results of the the struts were used. This assumption is considered to be analysis and are shown in Figs. 10a and lob. It is seen that satisfactory in this study because as a conventional slurry good agreement was obtained between measured and calcu- wall is concerned, and it was propped with steel beams, the lated positions of the water surface at both stages. The lateral movement of the prop should be very small. numerical results show that there is no significant drawdown of the water table after the construction of the wall, as was Comparisons of field measurement and numerical results The analysis of the excavation was found to converge within three iterations if the time marching integration fac- tor a was chosen to be 0.0 and the convergence criterion was defined as a change in total water head at each node being less than 1000th of the height of the solution domain. The results of the analysis are presented in the following sec- tions where comparisons with field measurements of the ground settlement and drawdown of the water table are also presented. observed at the site. This was due to the fact that the wall penetrated through layers of soils having low permeabilities, and this halts the flow of water into the excavation. Settlements of the ground surface The observed ground settlements around the excavation on August 27, November 14, and December 28, 1984, are shown plotted in Figs. l l a - l l c , respectively. In these figures, numerical results are presented for both the overall settlements from commencement of the excavation and the settlements relative to May 10, 1984, the time at which mea- surement was commenced. The measured values shown on Can. Geotech. J. Downloaded from www.nrcresearchpress.com by University of Sydney on 09/30/13For personal use only.Can. Geotech. J. Downloaded from www.nrcresearchpress.com by University of Sydney on 09/30/13For personal use only.CAN. GEOTECH. J . VOL. 29, 1992 10.0 130.0 80.0 (90.0 1120.0 ( 150.0 FIG. 12. Pore-pressure contours on December 31, 1984. -1.1.2 - Scale: H 1.0 100 - Wall \ p o r e Pressure [kPa) 7 .---.- 4 . . . . < < < r < < < < L L . l _ r r r . . ? ? , h ? ,. * h ,. + h A r . 7 r v r r r r r ,. r ,. * h ). b m h h 1 A * h . . . * L A + * L L * * n A ,. h & 10.0 130.0 1 ~ 0 . 0 1eo.o 11200 ( 1 ~ 0 . 0 FIG. 13. Velocity vectors of flow on December 31, 1984. the plots should therefore be compared with the calculated relative movements. There is some scatter of the measured data as can be seen in Figs. 1 la-1 lc. Since measurements were taken at a num- ber of positions around the excavation (see Fig. 2), inevitably there will be some variations in the soil profile and properties which will influence results. To make predic- tions fit better to measured data, upper bound values of modulus were chosen for the analysis (see Fig. 8). It is seen that the shape of the relative surface settlement profile is fairly close to that measured. Mean values of the modulus (see Fig. 8) were also used here to observe their influence on the surface settlement. The results are also shown in Figs. 1 la-1 lc. By December 28 (see Fig. llc), the maximum settlement differs by about 1.5 cm from the maximum settlement obtained by using the selected moduli. The use of the "mean" moduli gives a predicted surface deflection profile, which is an upper bound to the measured data, whereas use of the stiffer "selected" moduli gives a better fit to the scatter of measured values. The reason for the overprediction of displacements using the mean data could be due to factors such as soil aniso- tropy, or the fact that some settlement markers were placed on structures (e.g., the corners of buildings) where the stiff- ness of the buildings and the type of foundation may affect settlement. However, if a true prediction were made using mean values of modulus, the values of settlement obtained would be conservative. It is also interesting to note that the calculated water table levels are not greatly affected by the change from the "mean" to the "selected" moduli. It was found that the analysis predicted much smaller set- tlements within a radius of about 80 m of the excavation. This is due to heave of the soil in the vicinity of the excava- tion. Unfortunately there were no measured values within 80 m of the excavation, and so the predicted surface- settlement profile cannot be confirmed in this region. Can. Geotech. J. Downloaded from www.nrcresearchpress.com by University of Sydney on 09/30/13For personal use only.HSI AND SMALL 753 1 (a) , ,. -0.5, Displacement in y-direction (cm) FIG. 14. Contours of (a) settlement and (6) heave on December 28, 1984. Scale - 0 20000 m FIG. 15. Ground displacements on December 31, 1984. Further numerical results Some results computed for the end of the excavation (December 3 1, 1984) are presented here without comparison to field measurements to demonstrate the capabilities of pro- gram EXCAZ. The computed pore-water-pressure contours are shown in Fig. 12. The flow-velocity vectors are shown in Fig. 13, where it can be seen that in most of the region the velocities are extremely small except those around the bottom of the wall and near the top of the wall. The con- tours of settlement and heave are presented in Figs. 14a and 14b, respectively. Settlements may be seen to be predicted to occur beyond about 70 m away from the centre of the excavation, whereas within this range heave takes place. The ground movements are also shown in Fig. 15 by displace- ment vectors. Shear stress contours are shown in Fig. 16, where it may be seen that in front of the wall (the passive zone) the shear stresses concentrate between the base of the cut and the bottom of the wall, whereas behind the wall (the active zone) they concentrate around the corner of the excavation. Conclusions The case history of an excavation performed in Taiwan where field measurements of the surrounding ground settle- ments and water-surface levels were recorded has been dis- cussed. Detailed site conditions and soil characteristics are Can. Geotech. J. Downloaded from www.nrcresearchpress.com by University of Sydney on 09/30/13For personal use only.CAN. GEOTECH J. VOL. 29, 1992 (0.0 (30.0 I60.0 /80.0 (120.0 (150.0 FIG. 16. Shear stress contours on December 31, 1984. presented which provide sufficient information for the deter- mination of soil parameters for the analysis. A method previously developed by the authors (Hsi and Small 1992a, 1992b; J.P. Hsi and J.C. Small, in prepara- tion) for evaluating the deformations and pore pressures in a soil during excavation taking into account the drawdown of the free surface was used here. The method of calculating the equivalent tractions to be applied to the excavation boundary to simulate overburden removal is based on a vir- tual work formulation which ensures that the stress equi- librium is always maintained. Simulation of the excavation process is presented, and good agreement between the field measurements and the computed results was found. Acknowledgments The field-measurement data taken during the excavation for Chung-Chow Sewerage Intake Pump Station were pro- vided by Taipei Civil Engineers' Association, Taiwan, Republic of China (R.O.C.), and the site investigation and soil-test results were provided by China Engineering Con- sultants, Inc., Taiwan, R.O.C. The authors are grateful to Dr. Chin-Der Ou, Director General of the National Express- way Engineering Bureau, Taiwan, R.O.C., Mr. Chi-Sheng Chao, Manager of the Geotechnical Engineering Depart- ment, China Engineering Consultants Inc., Taiwan, R.O.C., and Ms Rita K.M. Ho, Secretary of the National Express- way Engineering Bureau, Taiwan, R.O.C., for their help and assistance in collecting the information needed for this study. Banerjee, P.K., Kumbhojkar, A.S., and Yousif, N.B. 1988. Finite element analysis of the stability of a vertical cut using an aniso- tropic soil model. Canadian Geotechnical Journal, 25: 119-127. Bathe, K.J. 1982. Finite element procedures in engineering anal- ysis. Prentice-Hall, Inc., Englewood Cliffs, N.J. Bathe, K.J., Sonnad, V., and Domigan, P . 1982. Some experi- ences using finite element methods for fluid flow problems. Pro- ceedings, 4th International Conference on the Finite Element Method in Water Resources, Hannover, Germany, pp. 9.3-9.16. 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Proceedings, Conference on in situ Investigations in Soils and Rocks, London, session C, pp. 181-188. Webb, D.L. 1969b. Discussion to session C: "Strength and Defor- mation of Soils: In Situ Testing." Proceedings, Conference on in situ Investigations in Soils and Rocks, London, pp. 218-219. Yong, K.Y., Lee, F.H., Parnploy, U., and Lee, S.L. 1989. Elasto- plastic consolidation analysis for strutted excavation in clay. Computers and Geotechnics, 8: 311-328. Appendix 1 Some terms used in the governing finite element equations (eqs. [I] and ) are listed here. (1) Stiffness matrix K: [All K = j , , B T ~ B d v (2) Coupling matrix L: [A21 L = \ " a d T d v (3) Flow matrix @: [A31 @ = \ " E T k E d v (4) Load vector f: Appendix 2. List of symbols vector of shape functions displacement-strain matrix undrained shear strength vector relating nodal displacement to volumetric strain stress-strain matrix matrix relating the nodal total water head to Vh elastic modulus of soil undrained elastic modulus vector of body forces and surface tractions vector of body forces matrix for the imposed flow along the free surface vector of total water heads vector of elevation heads vector of total water heads at the free surface matrix of permeability coefficients stiffness matrix coefficient of lateral earth pressure at rest limit permeability for a soil coefficients of permeability in x, y directions coupling matrix liquid limit coefficient of volume change porosity SPT blow count matrix of element shape functions plasticity index Can. Geotech. J. Downloaded from www.nrcresearchpress.com by University of Sydney on 09/30/13For personal use only.CAN. GEOTECH. J. VOL. 29, 1992 plastic limit Yt total unit weight of a soil limit negative pore pressure for a soil yw unit weight of water surface loaded by tractions 6 vector of nodal displacements specific yield Ag vector of applied tractions due to soil removal time Y' Poisson's ratio vector of external tractions u' vector of effective stresses vector of surface tractions cP flow matrix volume of a soil mass 4' effective friction angle time marching integration factor T angle between free surface segment and horizontal V vector operator = 2 2 2 direction [ax9 a,] vector of body forces i- right-hand side vector of governing equations free surface contour (eq. [ I ] ) Can. Geotech. J. Downloaded from www.nrcresearchpress.com by University of Sydney on 09/30/13For personal use only.