FINITE ELEMENT ANALYSIS OF SIGNIFICANT GROUND DEFORMATION DUE TO PILE DRIVING IN SILTS

Movement of adjacent ground and support-of-excavation structures due to pile driving in non-plastic silts is a significant issue in urban areas of Rhode Island. There have been several cases in which such movements have damaged historic structures and transportation infrastructure. The objective of this research is to perform a finite element analysis of a particular case study involving movement of a sheetpile wallsupported excavation due to the excavation and pile driving activities. The case study involved construction of a pile-supported gate and screening structure that is part of the combined sewer overflow project by the Narragansett Bay Commission. The structure was built by first driving sheetpiles around the site, then excavating in stages to the desired elevation, and then driving piles at the base of the excavation. Geotechnical instrumentation at the site included three inclinometers located behind the sheetpile walls and two piezometers in the excavation. Deformations of the wall were observed during each stage of excavation. Additional significant movements of the wall and elevated pore pressures were measured during pile driving. A 2-Dimensional finite element analyses was performed to model the deformation of the sheetpile walls using the commercial software PLAXIS version 7. Soils at the site were modeled with either a linear elastic, perfectly plastic MohrCoulomb constitutive model or a non-linear hyperbolic model. The excavation sequence was taken from construction records and simulated directly by removing soil in the model. Properties of the soils (strength and stiffness) were varied around values from the literature until the predicted wall movements matched observations. There was good agreement between the modeled displacements and observations for the first two stages of excavation using reasonable values of strength and stiffness for Rhode Island silts. These parameters would be a good place to start in future modeling efforts involving support of excavation projects in Rhode Island The only way to simulate the last stages of excavation and wall displacement was to use unreasonably low values of strength and stiffness. Possible explanations for this poor agreement include: a) loss of ground during pumping reduced the stability in the excavation and led to larger movements; b) the excavation caused significant disturbance (almost liquefaction) of the soil at the base of the excavation; and c) the soil surrounding the inclinometer tubes behind the wall moved or became disturbed and the measured movements are not representative of the actual wall movements. Dynamic loading of the soil from pile driving could not be directly modeled within PLAXIS. Therefore, the effects of pile driving were modeled by reducing the strength and stiffness of the underlying silts to simulate disturbance and possible liquefaction. Again, the properties of the soil were reduced until the predicted movements match field observations. Although this ignores the fact that the actual process is at least partially undrained, the approach used in this thesis is a first step in understanding movement of adjacent structures in Rhode Island silts due to pile driving.

21 Table 2-4: Summary of elasto-plastic parameters for the residual soils (Zornberg et al., 1998) (Kraft et al., 1981) ... 114 INTRODUCTION Non-plastic Rhode Island Silts are very sensitive to construction activities such as pile driving or excavation processes. Vibrations caused by these construction activities can cause pore pressure generation and lateral deformations. This leads to temporary reductions in effective stress and can ultimately lead to a decrease of soil strength and stiffness (Idriss and Boulanger, 2008). In some cases, this can lead to liquefaction of the soil.
Several instances of movement of adjacent ground and cracks in nearby structures have been recorded on Rhode Island construction sites (Davis, 2004;Bradshaw et al., 2007;Trautman, 2009;Taylor, 2011). Unfortunately, the effects of pile driving on the properties of silts is difficult to estimate apriori and contractors and engineers dealing with Rhode Island Silts collect in-situ data with inclinometers and piezometers during construction to monitor these effects. These measurements are useful for determining when problems are occurring, but it would be beneficial to have a method for estimating these problems beforehand.
Such measurements were taken at one construction site in Providence, Rhode Island for a near surface gate and screening structure for a large combined sewer overflow rehabilitation project. Deflections and piezometric heads were measured during the excavation and the pile driving processes and provided an opportunity to study the behavior of Rhode Island silts during excavation and pile driving.
In this study, a finite element analysis is performed to simulate the observed insitu behavior. A commercial finite element program called PLAXIS Version 7 is used.
The objective is to optimize the soil properties in the finite element model in such a 2 way that the simulated deflections during the excavation and pile driving process are similar to the measured defections in the field.
In the first part of the study a literature review is presented. It involves case studies that have used finite element analyses to simulate the behavior of soils due to excavations. Publications that present some basic ideas and problems of finite element simulations for such case studies are also presented.
The second part of this study describes the construction activities and in-situ conditions at the gate and screening structure to be studied. The observed measurements are also presented.
Finally, the finite element analyses and the results are shown in the third part of this study. Analyses are divided into a simulation of the excavation and a pile drivingsimulation. The reason is to highlight the differences but also the similarities between those two construction processes. A discussion of the results and conclusions drawn in this study are presented at the end of the thesis. can be run to improve or verify finite element simulations will also be described.
Section 2.3 describes selected studies that have used finite element simulations to model the behavior of excavation systems.
The following papers and studies summarized herein are listed in Table 2-1: The case studies presented in the following were chosen because of the different constitutive soil models presented, FE-codes or programs used, and relevance to the present study. Brown and Booker (1985) Discription of an FE analysis method Finno et al. (1991) Parametric studies of FE analyses Finno et al. (2007) Effects of geometry on FE analyses Finno and Hashash (2009) In-Situ monitorng and back-analysis methods Whittle et al. (1993) FE analysis of excavation in Boston, USA Zornberg et al. (1998) FE analysis of excavation in Sao Paulo, Brazil Langousis (2007 BOOKER (1985) This paper presented the results of a finite element analysis for an excavation simulation. A method was described that could provide good results when using a linear elastic constitutive model, and additionally for non-linear soil behavior as well as multi-stage excavations.

Content of the Paper/Study
In general the following steps can describe the simulation of an excavation: • The objective of the simulation presented was to remove the shaded portion A of Figure 2-1(a).
• Portion A was replaced by tractions (τ i ) as shown in Figure 2-1(b).
• If the tractions are removed because of simulating the excavation process, the behavior of portion B will change. This could be simulated by applying equal and opposite tractions as presented in Figure 2-1(c).
• This process could be repeated for more excavation stages.  (Brown and Booker, 1985) The authors noted that there were various methods to compute the described simulation process. One example was the approach of Mana (1976) in which the excavation boundary forces were determined by: 208 elastic material by excavation in one stage, this form of simulation is unlikely to be satisfactory when the material behaviour is non-linear.
Hence the authors of this paper sought a method which did not introduce the errors referred to above. This method could be checked for the linearly elastic case as the results should be independent of the number of stages shown in reference [2]. Such a method is presented here, and as is intended as the basis for simulation of excavation in non-linear materials.

EXCAVATION SIMULATION"
The basic aspects of simulation of excavation by the finite element method are summarised as follows. Finite element implementation of this process involves determination where M was the number of elements, B was the displacement strain matrix, σ was the stress vector and f was the vector of nodal forces. This method presumed the direct determination of tractions and nodal forces from known values of stresses.
The authors of this paper proposed an approach in which a virtual work methodology was used. In fact, the nodal forces could be found by adequate numerical integration of stresses, body forces and external tractions throughout the soil mass. It was also assumed that total equilibrium was maintained at each stage of excavation. The aim was to appraise the effects of commonly-made assumptions of the mentioned parameters on the computed deformation behavior of braced excavations.
For the studies a special finite element code was used (Harahap, 1990) that could compute plane strain and axisymmetric stress conditions and could perform drained, undrained loading as well as consolidation and fluid flow analyses. The soil 6 was simulated by eight-node biquadratic isoparamtric elements with pore pressure degrees of freedom in the corner node (for consolidation effects) and without pore pressure degrees of freedom (for cohesionsless soil or fully drained analyses). Sheet piles were simulated by beam elements and struts were simulated by bar elements.
Additionally the interface between sheet pile and soil was coded by six-noded, quadratic isoparametric slip elements.
Parametric studies were performed with two different methods of loading. In the first method detailed in-situ inclinometer measurements of sheet pile displacements were applied as boundary displacements in the computations. It resulted in a certain soil response on the active side on the wall. It was assumed that uncertainties with the simulated excavation process were minimized by this displacement-controlled analysis. Nevertheless the results only provided a basis of comparison of computed response since only the active side of the wall was simulated.
The second method was the more common stress-controlled loading, which included simulations of excavation of pilot trenches, sheet-pile installation and alternating steps of excavation and strut installation. Comparisons between computed responses and measured responses were made during sheet-pile installation, the deepest excavation stage and after installation and preloading each strut level (4 levels in total).
Three different constitutive soil models were compared: a modified isotropic plasticity (i.e. modified cam clay) model (MCC) (by Roscoe et al., 1968), an anisotropic bounding surface model (ABSM) (by Banerjee et al., 1985) and an isotropic bounding surface model (IBSM) (by Harahap, 1990). All models were based 7 on effective stress response and were coupled with fluid flow equations to simulate pore pressure changes. Inputted soil parameters were determined from laboratory tests and from the literature. Table 2-2 summarizes the studies performed.  (Finno et al., 1991) The results of the displacement-controlled simulation showed that there is little effect of either the sheet-pile installation or the soil model on the actual results (changes in stress). The authors concluded that the models only responded to active loadings, that is why their responses (stress path plots) looked quite similar.
More important were the results of the stress-controlled simulations since here an accurate simulation of sheet-pile deflection was attempted. There were many differences investigated, including the soil models, the finite element procedure, sheetpile installation effects and construction sequences. Because of that, the authors tried to investigate the effects of the relevant parameters in more detail. It was concluded that for isotropic models the deformations were greatly affected by the elastic constants (smaller values of shear or bulk moduli lead to higher deformation) used in the analysis. Also, these kinds of models lead to more accurate results if passive loadings dominate the behavior. Nevertheless, finding the right parameters required considerable judgment to obtain reliable predictions of deformation.
The second point of interest was the effect of sheet-pile installation. Different stress conditions at the excavation wall induced by the installation caused different deformations. It was observed that not including the sheet-pile effect in computations lead to 35% less deformations compared with computations that included the installation of sheet pile. This difference was mainly caused by a reduction of available passive resistance because of changing the pore water pressures in the soil throughout pile installation.
The third aspect that was studied was the mesh effect. Three different analyses were run incorporating the ABSM soil model. This includes a full mesh model (both excavation walls were modeled) and a centerline symmetric mesh model (one half of the excavation was modeled). The full mesh analysis includes the sheet-pile effect whereas the centerline symmetric mesh was analyzed with and without sheet-pile effect, respectively. It was shown that the displacements in the half mesh analysis were overestimated, especially when the sheet-pile effect was incorporated. The other two analyses showed better, but still different results, which highlight the importance of a proper accounting of sheet-pile effects.
Furthermore, the effect of construction procedures was evaluated. Therefore a complete simulation of construction was computed including the activation of modeled strut levels as the excavation reached the proper elevation. Overexcavation was minimized. Also the real construction order and time was maintained to demonstrate the influence of construction sequence. Similar trends compared with former analyses were evaluated, but the final excavation stage predicted a 2.3 times smaller deflection of the piles than observed. The authors emphasized the importance of correctly simulating the real construction sequence and limiting the overexcavation.
Finally the authors concluded that incorporating all facts mentioned above in finite element analyses would significantly increase the quality of the results.

THREE-DIMENSIONAL EFFECTS FOR SUPPORTED EXCAVATIONS IN
CLAY BY FINNO ET AL. (2007) This paper presented results of finite-element simulations to define the effects of excavation geometry. Factors investigated included length, width, and depth of excavation, wall system stiffness and factor of safety against basal heave. All these factors lead to development of a plane strain ratio (PSR), defined as the maximum movement in the center of an excavation wall computed by three-dimensional analyses and normalized by plane strain analyses. = The authors first summarized observations that were made in different finite element studies: • Smaller movements developed at the corners, compared with the center of the excavation wall.
• 2D calculations mostly overpredicted the movements near the center of the excavation wall for large distances between rigid stratum and excavation bottom and also for smaller ratios of length to height of the wall.
• In contrast, 3D simulations matched more closely with field responses.
Since no systematic evaluations of excavation geometry had been made previously, this paper addresses these influences in a parametric study.
PLAXIS 3D Foundation and PLAXIS 2D version 8.0 were used as the threedimensional and plane strain geotechnical finite element software, respectively. A hardening soil model (non-linear elastic) was used to describe the soil behavior.
Modeled excavations varied from 20 m by 20 m (L x B) to 160 m by 80 m. Excavation depths H e ranged from 9.8 to 16.3 m. Consequently the ratio L/H e varied from 0.5 to 12. Also, mesh boundaries were located more than 120 m from the excavation wall, that was more than the 5 times H e recommended by Roboski (2004). Values of wall system stiffness S from 32 (flexible wall) to 3200 (stiff wall) were used to investigate stiffness effects.

11
The simulations showed that the computed movements of 3D analysis were less than those computed by plane strain simulations especially for smaller excavations.
For larger excavations the observed movements were almost the same. To evaluate the effects of excavation size and depth, PSR values of normalized geometric parameters were compared. These were the ratio of primary wall length to elevation depth L/H e and the ratio of primary wall length to secondary wall length L/B. It could be shown that a L/H e ratio greater than 6 resulted in a PSR value of approximately 1. That means 3D and 2D analyses lead to similar wall movements. In contrast, large differences between 3D and 2D simulations were observed for L/H e ratios smaller than 2 (see An investigation of the wall stiffness effect lead to the result that L/H ratios less than 2 caused lower PSR values, whereas the PSR of the flexible and medium walls increase faster for higher excavation depths than the stiff wall. This indicated a higher corner restraint for stiff wall systems.  (Finno et al., 2007) Moreover it was observed that the factor of safety FS BH against basal heave could have an influence on the PSR. In particular the PSR of stiff walls decreased for smaller FS, while flexible walls were not much affected by the FS. Nevertheless for L/H e ratios of 6 or higher the PSR remained 1 regardless of stratigraphy and stability.
Finally an empirical equation was developed from the finite-element parametric study data: where the factor C depended on the factor of safety against basal heave and could be determined by: ve insensitivity of the PSR to the description of the parameters used 3D is presented by Blackburn and rizes the wall stiffness parameters. ss is computed assuming that the le in the horizontal direction ͑the ting the direction along the length rection͒ to account for the rotations ile wall and the lack of continuity direction. Fig. 3 shows lations for both the 20 m by 20 m s. The lateral deformations repre-ments. The movements computed by the 3D analysis are less than those computed by plane strain simulations for the smaller excavations but are almost the same for the larger excavations.

Effects of Excavation Size and Depth
The influence of excavation geometry on lateral soil displacement is evaluated by comparing the PSR values for several normalized geometric parameters. Fig. 4͑a͒ shows the relationship between PSR and the ratio of primary wall length to elevation depth, L / H E based on all cases shown in Table 2. While a variety of wall stiffness, soil stratigraphy, and soil models were employed to develop these results, the general trends in the PSR are similar. The trends indicate that L / H E ratios greater than 6 result in an excavation response which has a PSR approximately equal to 1, thus suggesting that results of plane strain and 3D analyses will yield the same maximum wall displacement in the center of the excavation. Large differences between plane strain and 3D responses are apparent when L / H e is less than 2, implying that as the excavation gets deeper relative to its length, more restraint is provided by the sides of the excavation. Fig. 4͑b͒ shows the same results plotted versus L / B ratio. When this ratio is less than or equal to 2, L / H E must be taken into consideration for determining the PSR. Smaller values are apparent for L / B values less than 1, indicative of movement on the shorter side of the excavation. Note that there is less scatter in the PSR-L / H e plot in Fig. 4͑a͒ than in the PSR-L / B plot in Fig. 4͑b͒ suggesting that of these two geometric parameters, L / H is more influential in defining the behind the wall: plane strain versus 13 Furthermore the value of k depended on the support system stiffness and could be taken as: where S could be determined by:   (Finno et al., 2007) The authors concluded that despite of different soil models and assumptions used in this study, the trends in the finite-element results could be reasonably represented by computed limits of Equation 2.3 (see Figure 2-3). Also the proposed largest effects at small values of L / H e . As L / H e gets larger, the effects of wall stiffness become less pronounced.
The value of C in Eq. ͑3͒ depends on the factor of safety against basal heave, FS BH , and is taken as This relation is illustrated in the results shown in Fig. 9 where C values are based on Eq. ͑2͒ for all cases where the PSR was less than 0.9. The trends in the computed responses are reasonably represented by Eq. ͑5͒. A comparison of the predictions made via Eq. ͑2͒ and results of all parametric studies presented herein and those presented in literature is made in Fig. 10. In the figure, the solid line represents a base case with the k and C constants equal to 1. This corresponds to a flexible support system ͓where the 0.0001S term is negligible in Eq. ͑3͔͒ and a factor of safety against basal heave ͑FS BH ͒ greater than or equal to 1.8.
The dashed lines in Fig. 10 represent upper and lower bounds of Eq. ͑3͒. The upper bound shown in Fig. 10 corresponds to a base curve ͑k and C equal to 1͒ with an excavation geometry term ͑L / B͒ greater than 4. This geometry approximates plane strain conditions and, therefore, a PSR value close to unity for all L / H e values would be expected. The lower bound curve is calculated with a combined kC equal to 0.5 reflect influence the PSR, material ͑FS BH = 1.8 material ͑FS BH = 0.8 a value of 0.0375 f corresponds to a lo where the length o secondary wall. La pected for this case values. In spite of d making the finiteelement results are from Eq. ͑3͒.
In summary, the the geometry of the system, and the fac greater corner effe tions, as evidenced two walls, as eviden and for lower facto when L / H e is larger same maximum mo range of conditions    presented. The aim was to introduce a monitoring program during construction to record ground movement and use this data to control the process of construction and constantly update predictions of excavation movements.

Computed Horiz
According to the authors it was necessary to simulate all aspects of the construction process, like installation of supporting walls, hydrodynamic effects or material responses, which could affect the stresses around the excavation. This could increase the accuracy of predicted behavior. Moreover the plane strain ratio, PSR, described in section 2.2.3 had to be taken into consideration if the L/H e ratio was less than 6.
Inclinometers, laser scanning systems, webcams, automated total surveying station and remote access tiltmeters, produce real time data. For typical elasto-plastic constitutive models inclinometer data based on measurements close to a support wall was the most useful. Horizontal displacements, settlements and pore water pressures 15 were also recorded. The construction process could be tracked by a three-dimensional laser scanning method called LIDAR (Light Detection and Ranging) and internet accessible webcams. Furthermore optical surveying stations were installed to monitor the displacement of optical prisms placed at different locations around an excavation site. Additional tiltmeters were attached to adjacent buildings to compute angular distortions (related to settlements). All monitoring stations included data transmission communication system, like RS232 serial interfaces or radio transceivers that allows for collecting collecting of data on a remote host computer.
This data was then used in an inverse analysis. In this analysis parameter values and other aspects of the model were adjusted until the computed results of the model matched the observed results of the system. The advantage was the ability to calculate parameter values automatically. In contrast the disadvantages were complexity, nonuniqueness of the solution and numerical instability. Two different types of inverse analysis had to be distinguished; gradient methods and artificial intelligence methods like artificial neural networks or generic algorithms. The computed results (of a "first" finite-element analysis) were compared with field results by means of a weight least-squared objective function. This function provided a quantitative measure of accuracy of the predictions. By the weight function the parameters used for further analysis was chosen by its reliability (e.g. errors associated to measurements were minimized). Furthermore a sensitivity matrix was produced by a forward difference approximation. As a result optimized parameters like soil properties were obtained that were used in a final finite-element computation.
It was now possible to get good agreement between computed and measured excavation behavior and to update predictions of movements.  (Finno and Hashash, 2009) Another inverse analysis method presented in this paper was the SelfSim selflearning engineering simulation. This analysis extracted relevant constitutive soil information directly from field measurements like deformations or settlements. After a certain learning process described below the resulting soil model, used in the final finite-element analysis, provided deformation results that were consistent with observed field behavior. This updated model could then also be used for predictions of similar excavations (similar soil layers, construction method, supporting structure, etc.). and surface settlements were measured in the field (step 1). The measured deformations and the known excavation stages were then traded as complementary sets, which had to be computed in a numerical model. The key of this method is a neural network based model that had to simulate the soil response. This model was 16 can be written in a windows environment to couple UCODE with any application software.

Fig. 7. Flow chart for inverse analysis
where b is a vector containing values of the parameters to be estimated; y is the vector of the observations being matched by the regression; y (b) is the vector of the computed values which correspond to observations; is the weight matrix wherein the weight of every observation is taken as the inverse of its error variance; and e is the vector of residuals. This function represents a quantitative measure of the accuracy of the predictions. A sensitivity matrix, X, is then computed using a forward difference approximation based on the changes in the computed solution due to slight perturbations of the estimated parameter values. This step requires multiple runs of the finite element code. Regression analysis of this non-linear problem is used to find the values of the parameters that result in a best fit between the computed and observed values. In UCODE, this fitting is accomplished with the modified Gauss-Newton method, the results of which allow the parameters to be updated using: used to compute the soil response using stress-strain data (initially from laboratory tests or stress history of the soil). In a second step a finite-element analysis using the initial neural network soil model was performed with a numerical model that represented the investigated construction sequence (step 2a).  (Finno and Hashash, 2009) Another finite-element analysis was done with a second numerical model where measured wall deflections and settlements were imposed as additional al results shown in the observed data, likely caused by the n does not include iffness degradation select moduli that the soil mass, and e average modulus es not consider the he parameters used larger deformations tate site, and hence n were observed at application of the meters to both the sonable agreement ments, within the tion of the inverse improved fit with chea 2006). ering Simulations: d, self-learning in , is introduced to rical simulations. ve soil information ts of excavation ations and surface odel, used in a und deformations r of the current the prediction of he soil model can l field information. xcavation problems ash et al., 2003, , 2006). In a typical ations and surface d excavation stages mations and the given excavation stage. SelfSim stipulates that due to equilibrium considerations and the use of correct boundary forces due to soil removal, the corresponding computed stress field provides an acceptable approximation of the "true" stress field experienced by the soil. In step 2b of SelfSim a parallel FE analysis using the same NN soil model is performed in which the lateral wall deflections and surface settlements are imposed as additional displacement boundary conditions. The computed equilibrium strain field provides an acceptable approximation of the "true" strain field experienced by the soil.
The stress field from step 2a and the strain field 18 displacements boundary conditions (step 2b). The neural network model was also used for this simulation. Subsequently the stress field of step 2a and the strain field of step 2b were extracted to build stress-strain pairs, which were used to train the neural network soil model. It was assumed that these stress-strain pairs represented an approximated constitutive soil response. The analyses of step 2 were repeated until analyses of steps 2a and 2b provided similar results. Finally the resulting and "trained" constitutive soil model could be used for predictions of later construction steps or even for other excavations with similar ground conditions (step 3).
The authors concluded that their integrated tool to predict, monitor and control ground movements provided good results between predictions and observed performance of excavations. In particular, the calibration of numerical models (by means of parameter optimization) throughout inverse analysis could minimize the errors between measured and predicted results. Two different soil models were used to model the soil behavior. The stressstrain-strength properties of fill, sand, till and argillite were described by an elastoplastic model using a Drucker-Prager failure criterion with a nonassociated flow rule (EP-DP). Initial parameters were obtained from laboratory data or from the literature (Table 2-3). The MIT-E3 effective stress soil model by Whittle (1990) was used to describe the behavior of the clay layer. The parameters used in this model were validated by laboratory data. Table 2-3 summarizes the input properties used for the finite element analysis.  (Whittle et al., 1993) Successive "stages" in the analysis were used to simulate different construction sequences at the site. The repetitive sequence of excavating and building each floor was simulated by three stages in the analysis. First an undrained excavation to the associated elevation (beneath each built floor) was computed. Then a time delay was incorporated to simulate curing of the concrete and partial drainage. Finally a structural prop that corresponded to the installed floor slab was simulated. Any computed deformations were then relative to an initial equilibrium state (stage 5 of  (Whittle et al., 1993) The predictions of the base case analysis were compared with measured field data. This data was constantly recorded by inclinometers (lateral movements of the diaphragm wall and lateral soil displacement), optical surveys (surface settlement and movement of the surrounding buildings), extensometers (relative, vertical displacement of the clay, till and rock) and piezometers (ground-water and piezometric levels). All these measured variables were also computed by the finite-element analysis.
The comparison between prediction and field data showed that there was a significant difference in computed and real behavior. In particular, the predicted settlements caused by piezometric elevations were overestimated. Also, the lateral wall deflections were not accurate because of shrinkage and expansion effects of the floors that were not incorporated in the analysis before.
The first analysis was then modified significantly. Floor slab shrinkage was incorporated and the lower boundary was changed into a constant pore pressure boundary condition. After these changes, the computed deflections matched much 24 better with the field data. Figure 2-9 presents the base case analysis, the modified analysis and measured data:  (Whittle et al., 1993) This case study showed that it is possible to make a reasonable prediction of deformations due to a top-down construction project in soft clay. Nevertheless there are some remarks of the author that described some solutions for occurred difficulties: 1. Not only lateral wall deflections should be recorded and compared with predicted values. Additional information provided by measurements of soil deformation show the effects of excavation procedures much better and are essential to validate the model predictions.
2. Uncertainties of soil properties need to be be minimized as model complexity increases.
3. Concrete shrinkage, important for cast-in-place floor systems, should be taken into consideration to compute more trustable wall deflections.
4. Defined boundary conditions can affect significantly the change in piezometric elevations.
5. An improved characterization of small strain nonlinear behavior of soils can improve the predictive capabilities of a finite element model.  Lade (1977Lade ( , 1979 was calibrated from results of laboratory tests. The aim was to predict the displacement of the excavation, including the stress 26 fields induced in the residual soil mass during different excavation stages. This model would then be used to predict the performance of adjacent structures.

NUMERICAL PREDICTION OF THE BEHAVIOR OF AN
The analyzed excavation was 31 m deep and was located next to an existing 17-story building with two underground levels. A soldier pile and lagging system, supported by three strut levels, were used to resist lateral forces. 18 m of "Residual Red Clay" underlain by a "Residual Variegated Soil" layer was found on the construction site. Furthermore the water level that was initially located at the base of the red clay layer was lowered to 35 m before the excavation process. Figure (Zornberg et al., 1998) The author mentioned that there is little experience about the application of an elasto-plastic model to represent the behavior of "undisturbed samples of unsaturated soils." Therefore an extensive laboratory-testing program was performed, which 27 included tests at different shear stress paths representative of excavation. A summary of the elasto-plastic parameters used for the residual soil are shown in Table 2-4). Table 2-4: Summary of elasto-plastic parameters for the residual soils (Zornberg et al., 1998) The results of the laboratory tests were compared with the predictions of the nonassociated elasto-plastic model at the element scale. A good agreement between measured and predicted behavior was achieved that supported the applicability of the model to the overall analysis.
The computer code ANLOG (Zornberg and Azevedo, 1990) was used to perform the finite element simulation of the excavation. This code also incorporates Lade's elasto-plastic model, which includes two yield surfaces; a conical shaped plastic expansive surface (characterized by a nonassociated flow rule) and a cap-type plastic collapsive surface (governed by a associated flow rule). Consequently, elastic, plastic expansive and plastic collapsive components were used to describe the total strain increments. Eight-node isoparametric elements were used to model the soil and three-node elements were used to describe struts and anchors. The finite element mesh finally consisted of 481 nodal points and 147 elements.

28
Two sets of analyses were run to simulate the excavation process. First, the state stresses in the soil prior to the excavation were analyzed. This involved four steps as shown in Figure 2-11 and summarized as. • Step 1: Characterization of initial geostatic state, defined by the soil unit weight and the earth pressure coefficient K 0 . • Step 2: Simulation of two underground level excavation of the adjacent building.
• Step3: Application of a distributed loading to simulate the effect of the building foundations. • Step 4: Lowering of the water table.
The final state of stress level describes the initial stress level for the second set of analyses.
Figure 2-11: Analyses performed to define the stress state before the excavation (Zornberg et al., 1998) 29 Four construction phases were simulated for the excavation as shown in Figure   2-12. The first excavation step did not include placement of struts whereas the following phases incorporated struts that were simulated by activating the corresponding bar elements.  (Zornberg et al., 1998) The aim of the analysis was to obtain stress and displacement fields in the soil elements for each stage. Additionally the loads in the structural elements were estimated.
One result showed that the settlements of the adjacent building were negligible.
Moreover, a maximal lateral displacement of 37 mm was predicted at the bottom strut level ( (Zornberg et al., 1998) Unfortunately, the author did not address the issue of the reliability of the results. Since the main reason for the simulation was to predict the performance of adjacent building structures, no extensive in-situ measurements were incorporated.
Only the predicted settlements of the 17-story building were confirmed by several measurements.

AUTOMATED MONITORING AND INVERSE ANALYSIS OF A DEEP EXCAVATION IS SEATTLE BY LANGOUSIS (2007)
The aim of this case study was to test the performance of an automated survey system that was invented to monitor the behavior of a deep excavation. Finite element analyses were performed to predict the wall movements and to compare it with results gained by monitoring data. Several sets of finite element analyses were performed to evaluate the effects of soil stresses, tieback placements and 3-D corner restraint on the predicted displacements.
The construction site was located in Seatle, WA and consisted of a 21.6 m deep excavation for 5 parking levels. Soldier pile walls with wooden lagging and 4 to 5 31 rows of tiebacks were installed on the North, South and East sides of the excavation.
For the West shoring wall a special design by GeoEngineers, consisting of a soldier wall with 9 to 10 rows of soil nails and 4 to 5 rows of tieback, was used to keep the deformation smaller than 1 inch. These West wall piles were part of further investigations (Figure 2-14). The soil consisted of fill, silty sand, clayey silt and very dense sand. The data obtained from these measuring systems was used to provide an early detection of deflections that could potentially damage the nearby structures and to validate a numerical model.    (Langousis, 2007) Since there was a large difference between predicted and observed movement a new numerical model was developed after the excavation was completed.
The new model includes a staged excavation for the Qwest building to simulate the stress history induced by the construction of this building. Therefore, the excavation was computed and the soldier wall was replaced with a rigid wall. The

Summary
1) The construction sequence followed differed from the sequence used in the design.
34 seen in Table 2-5. The constitutive soil models used in the analyses were either the Hardening-Soil (S/H), or the Mohr-Coulomb M/C) models. All the structural elements and the concrete were assumed to behave as elastic materials. Moreover, drained and undrained analyses were run to compute an upper and lower limit of response in the clay layer.  (Langousis, 2007) The finite element mesh (      (Langousis, 2007) The construction process was simulated by successive design stages, which are: the sheet pile installation, followed by alternating stages of excavating and soil nail installation (between 9 to 10 rows of nails), and then alternating stages of excavation and tieback installation (between 4 to 5 rows of tieback). All these steps were simulated after the Qwest excavation was initially computed. Silt layers were still larger than observed. Furthermore the undrained analyses reduced the deflection in the clay layer.
One reason for that difference could be 3-D effects in which stiffening effects of the corners of the excavation are not considered in plane strain analysis. It was investigated that especially the Clayey Silt layer 50 to 75 feet below the surface could not be simulated in plane-strain analyses in a sophisticated way (critical PSR value).
The results obtained from two-dimensional analyses likely over-predicted the movements in this layer.
Another factor that was discussed in the case study was the numerical representation of the tiebacks in the finite element analysis. Tiebacks have a threedimensional geometry but modeling them as two-dimensional elements includes significant approximations. The two-dimensional analysis might cause the stresses transmitted to the soil overlap, reducing the tieback load-bearing capacity and producing excessive displacements. To evaluate this influence tiebacks were modeled as equivalent struts (springs that transmit axial forces) with an equivalent strut length and stiffness. This study had shown that modeling the tiebacks as equivalent struts has little effect on the calculated deflections.
Moreover, two sets of inverse analysis (drained and undrained) were performed to find the soil parameters that provided the best fit to the observed lateral deflections.   (Langousis, 2007) Finally, the author drew the following conclusions: 1. Including the excavation history of the Qwest building in the finite element analysis lead to a displacement profile that was closer to the movements observed in the field.
2. Undrained instead of drained analysis for the Clayey Silt layer resulted in a more accurate deflection profile.
3. The computed deflections in the Clayey Silt layer are higher than observed since the 3-D effect increased the stiffness at the corner of a deep excavation.
4. Since the inclinometers were attached at the soldier piles, they were influenced by the stiffness of the soldier pile. The inclinometer should be located behind the wall so that localized effects to not influence the results.
5. Computing the tiebacks as equivalent struts did not influence the displacement profile.
115 optimizations and they are similar to the observed values. For the upper portion of the wall the three parameter optimization gives slightly better results than the two parameter optimization. This better fit is reflected in the lower final objective function and the higher RFI for the Three Parameter Optimization. Hence, the three parameter optimization gives a better solution, even though the simulation was terminated by the finite element code.    Additional supporting structures were 5 levels of horizontal struts (w-shaped). The soil consisted of silty sand and the groundwater level was at 3.5 m below the surface.

Instruments
Ground instrumentation was used to monitor movements of the ground and adjacent buildings. These included inclinometers inside the diaphragm wall and soils, settlement markers on the ground and adjacent buildings, standpipe and electrical piezometers and vibration wire gauges on the struts. The monitoring plan at O6 is shown in Fig. 2. Measurements taken by the instruments were used to observe the behaviour of the walls and adjacent structures, ensuring that movements were acceptable. They also provided data to validate the numerical model used in this paper.

Soil response to excavation
Ground responses at O6, such as lateral wall movements, surface and building settlement, piezometric levels and prop loads during construction are described in [24]. The measured lateral deformations and surface settlements are compared to the values predicted in this paper. Seven inclinometers were installed in the diaphragm wall and three inclinometers in the soil to measure lateral deformation. Fig. 3 presents the most relevant lateral displacement data from inclinometer SID5. This inclinometer was at the centre of the excavation, and is the closest to plane strain condi- Bulk modulus (B) and shear modulus (G) are determined by in which l is Poisson's ratio.
It is possible that there could have been a delay in str installation and slab construction that might have induced add tional displacements [24]. Therefore it was concluded [18] th the soil could experience larger strains because of the lack support during the delay, and assumed a 40% reduction of and G in the analyses as an additional test to examine the effe of delayed construction on the elastic response.  40 from the modeled excavation minimized the effects of themselves. It was also assumed that the installation of walls and struts had no effect on the surrounding soil. The elastic-plastic "Mohr-Coulomb" model was used and the soil parameters were estimated from laboratory tests, standard penetration tests (SPT) and measurements of shear wave velocity on site (Table 2-7).   (Hsiung, 2009) The analyses showed that the determination of the soil stiffness from shear wave velocity (denoted "WV") compared to estimates from the standard penetration test (denoted " SPT" and "SPTR") lead to different predictions of wall movement.
Moreover settlements were underestimated and did not match with observations.
A different computer program (PLAXIS) was used for the purpose of comparison. This program incorporated an interface element between the wall and the Moreover, it was recommended [7] that G at small strains could be determined by where c is the soil density and V 2 s is the measured shear wave velocity of soil from the site.
Thus, the soil bulk modulus (B) is determined by In presenting the test results, analyses delivered using soil stiffnesses determined from the shear wave velocity are denoted ''WV", and those determined from SPT-N values and reduced SPT-N values are called ''SPT" and ''SPTR", respectively. Fig. 5 presents a comparison of lateral wall movements from predictions and observations. It seems that a small strain stiffness based on shear wave velocity measurements predicts displacements more accurately than those derived from the SPT tests for the first stage of the excavation. The opposite is true for the final excavation stage. Fig. 6 indicates the predicted and observed surface settlements B.-C.B. Hsiung / Computers and Geotechnics 36 ( tions. It is also where the largest deformations occurred. The lateral movements indicate that the wall initially behaved as a cantilever, but then behaved as a propped cantilever as the excavation progressed; the movements continued to increase during the excavation. The maximum lateral movement (d hm ) reached 55 mm, as observed at the final excavated level. The ratio of measured d hm to excavation depth (H) was up to 0.3%. Surface settlements induced by the excavation were also monitored; the measurements taken from section A-A at the south side of the excavation (SM08-SM13) are shown in Fig. 3. There are no data within 5 m of the excavation because the excavation was in the middle of a major road and the road had to be kept open. The surface settlement (d vm ) varied from 4 to 7 mm during the first stage of excavation and increased to 17-27 mm upon its completion. The maximum surface settlement was observed 19 m from the excavation, which is similar to the maximum excavation depth. The influence zone at ground level may have extended up to 70 m from the excavation site, but there is little data to support this. The ratio of d vm to H is approximately 0.09-0.14% and d vm /d hm is 0.5-1.0%, as derived from observations. This d vm /d hm is similar to that reported previously in [19].
Two electrical piezometers were installed inside the excavation, but one was damaged during construction. Measurements show that the piezometric level continued to drop during the excavation to approximately 8 m below the final excavation level, but began to rise after its completion.
Standpipe piezometers were installed outside the excavation immediately next to the diaphragm wall at 27 m (PS5 and PS7) depth of the deepest borehole. A two-dimensional symmetric analysis was undertaken, so the centre of the excavation was used as one vertical boundary. The other vertical boundary was set at 200 m from the wall (approximately 10 times the maximum excavation depth), as suggested in [7]. Fig. 4 presents the analytical mesh used in this study.
The properties of the retaining structure and internal struts were the same as those recommended in [17]. The actual groundwater level varied seasonally between 2 and 4 m below the surface; it was thus assumed to be 3 m below the surface for the purposes of the analysis. The analysis was based on a ''wishedin-place" mode; installation effects were ignored.
An elastic-perfect plastic ''Mohr-Coulomb" model was used. The soil parameters, (such as soil density (c) and effective friction angle (/ 0 )) given in [17] were selected. The physical characteristics of the soil (e.g., soil density) were measured in the laboratory. No triaxial consolidated-drained/consolidated undrained tests were carried out, so / 0 was interpreted using [4] N c is determined by where r 0 is the effective overburden pressure and N is the SPT-N value.
The influence of the elasticity of the soil on the behaviour associated with a large-scale cofferdam excavation in Kaohsiung is described in [8]. The recommended stiffness used by [4] was based on the relationship where N is the SPT-N value obtained from the site. soil, which was not available in the FLAC analyses. Seepage analyses were also included in the revised analyses. The stiffness parameters followed the same assumptions like before (shear wave velocity: denoted "E s " and SPT: denoted "E").  (Hsiung, 2009) The PLAXIS simulation predicted smaller movements than those predicted using FLAC (Figure 2-21). Since there is no significant difference in the predicted vertical displacement for FLAC and PLAXIS the author concluded that seepage did not have a significant effect on the movements (PLAXIS allowed seepage, whereas FLAC did not). The influence of the interface element, however, was identified as the main reason for the different predictions of lateral wall movements.
lts, analyses delivered using soil e shear wave velocity are denoted om SPT-N values and reduced SPT-'SPTR", respectively. Fig. 5 presents movements from predictions and mall strain stiffness based on shear predicts displacements more accuthe SPT tests for the first stage te is true for the final excavation d and observed surface settlements predictions match observations, so . influences of elasticity were done gram [17] for the purpose of comm PLAXIS [2] was used with the om SPT-N values and shear wave nt between the wall and the soil LAXIS (note that this is not avail-C). In order to present test results, ined from shear wave velocity are he SPT-N value are denoted ''E". It eepage in the analyses. d and observed movements at the ation and at the end of the excad shape of the wall based on the s " prediction) and that based on diction) both under-estimate the he initial stage of excavation. The e observed deflected shape than nal excavation stage. In the case E s " prediction is better than the initial stage and the final stage, rate. The ''E" prediction for longignificantly greater than the obt the observed rate of change of nce from the wall is much greater elated to the fact that the elastic ear. The fact that this is less critnts could be due to the fact that y the average stiffness of the ele-The FLAC simulation predicted larger movements (see Fig. 5) at the end of the first stage of the excavation than those predicted using PLAXIS (see Fig. 7). It is suspected that the use of interface elements in the PLAXIS simulations is the reason for this difference.
There were no significant differences in the predicted vertical movements using FLAC and PLAXIS (see Figs. 6 and 8). This suggests that seepage has little effect on predicted movements (PLAXIS allows seepage; FLAC does not). In this case, the difference in horizontal displacements is unlikely to be affected by seepage, so the conclusion that the interface element is the reason for the difference is probably correct.

Influence of soil creep
Soil creep may affect deep excavations and contribute to the ground response [15]. It has also been reported [24] that a delay in installing struts and constructing the slab could induce additional ground movements at O6. In order to evaluate the effects of soil creep on the ground response, the built-in creep models in esh used in this study. FLAC were used. The simplest creep model, the classical visco-elastic model, was selected for the analyses because of the limited data available on the creep properties of the soils. Input parameters for this model include the elastic bulk modulus, the mass density, the elastic shear modulus and the dynamic viscosity [11]. Section 5.1 shows that small strain parameters can be used to back-analyse deep excavations in sand. Thus, elastic bulk and shear moduli interpreted from shear wave velocities were used. Various values of dynamic viscosity (D v ) were used in the analyses to predict the movement of the wall and surface settlements. The creep function was only applied at the 3rd level prop installation stage and construction of the base slab because of the speed of construction prior to that stage. Fig. 9 shows predicted and observed lateral wall movements based on different values of D v . First, it appears that variance of D v does not contribute significantly to Fig. 9a because there was no further delay of strut installation at this stage. There is a clear difference in predicted wall displacement at the end of excavation depending on the value of D v . The back-analyses indicate that the viscosity model for creep simulation is able to predict lateral wall deformations successfully, and that 1.5 Â 10 15 -2.0 Â 10 15 Pa should be applied for D v for excavations at O6. The values of D v will depend on the soil properties and the time of construction. Fig. 10 presents the predicted and observed surface settlement at the end of the first stage of excavation and at the end of the excavation. Comparing analyses that do not consider creep (see Fig. 6), no significant differences are seen at shallow excavation depths. The predictions at the end of excavation that allow for creep show results that are more consistent with observations at the final excavation depth (see 1.5 Â 10 14 of D v on Fig. 10b) than the simple elastic analyses. The analyses still predict settlement some distance from the wall, although this does not occur. This is partly due to the model chosen.
A ratio of maximum lateral wall movement (d vm ) to excavation depth is 1.45% at the end of the first stage of excavation was found at an excavation in Taipei, CPC, which is about 1.5-3 times the ratio obtained from another site, TNEC [7]. It took a long time to cast the concrete slabs at the CPC site, which might be the reason for the    (Hsiung, 2009) n. As shown in Table 1, the installam below ground level) took a longer endent (creep) behaviour induced in . A previous study [14] provided an ate the effects of the rate of creep d stage of an excavation. This is f maximum wall deflection between

Influence of the soil-wall interface
The ratio of maximum vertical movement (dvm) to maximum lateral movement (dhm) has been reported in the range of 0.5-1.0 [21]. However, the ratio of dvm/dhm from predictions described in Section 5.1 is much less than values reported in [21]. Vertical movements tend to be under-estimated, possibly due to assumptions regarding the behaviour of the soil-wall interface. Thus, a study of the influence of soil-wall interface elements is presented in this paper. In the analyses, the interface parameters, including redicted surface settlements: (a) 3.4 m of tion depth. Finally, lateral mo pletely different at s proof of the effectiven using an elastic-perfe A comparison of p shown in Fig. 13. It ap on assumptions of 3 with the observation while a value of 3 Â 1 nal excavation stage. the analyses of latera still recommended t 3 Â 10 6 Pa be used to  Nevertheless, the predictions of surface settlement were under-estimated due to missing assumptions regarding the behavior of the soil-wall interface. Further analysis incorporated changing interface parameters (friction angle Φ sw , normal and shear stiffness K n and K s ). The final results showed that analyses not using a soil-wall interface under-estimate surface settlements.
Finally, the author made the following conclusions: 1. Predictions based on constant soil elasticity over-estimated the lateral wall movements below the excavation level. Furthermore, the predictions of surface settlement did not match at locations close or far from the excavation.
2. An elastic-perfect plastic model provides more consistent predictions for the use of small strain parameters.
3. The effect of an excavation-induced seepage had a limited effect on vertical displacement.

Creeping (time-dependent behavior of soils) caused by late installation of struts
affected the vertical movement and could be addressed by using a special dynamic viscosity "D v " parameter.

Limits of the applied constitutive model caused inconsistencies between
predictions and observations in surface settlements.
6. The use of a soil-wall interface lead to more reliable predictions of surface settlement. A certain factor of normal and shear stiffness K n and K s was used to address this issue. 44

SUMMARY AND FINDINGS OF CASE STUDIES
It has been demonstrated that stress-controlled loading (simulating excavation and strut installation) leads to more reliable results than the displacement-controlled loading (in-situ measurements applied as boundary conditions) since the latter only simulates the active side of the wall (Finno et al., 1991). Also, different constitutive soil models have been used with varying degrees of success. Quite simple linear soil models (e.g. constant soil elasticity) mainly overestimate lateral movements (Finno et al., 1991;Hsiung, 2009) whereas more complex models like the Hardening-Soil model (Langousis, 2007) or an effective stress soil model (Whittle et al., 1993) lead to better results.
The influence of sheet pile wall installation was addressed although there seems to be no satisfactory method to incorporate this into the simulation (Finno et al., 1991). Therefore all finite element studies presented above assumed that the wall was "wished in place" and have no influence on the computed results. An interface element between soil and wall could provide something like a proper simulation (Hsiung, 2009) of pile driving.
An influencing fact was the boundary conditions. Simulations containing water flows (like settlement and dewatering problems) had to deal with this in particular. For example Whittle et al. (1993) changed the lower boundary conditions from non-flow to static water head boundary condition and the results changed favorably. All other studies created boundary conditions that are at least 5 times the excavation depth away from the excavation wall to minimize any influence.

45
Furthermore, simulation phases/ sequences similar to the real construction activities on site were used in all studies to compute different movements in different construction phases. This process was mostly used to simulate the change in stress during certain construction activities or even ground water lowering.
The mesh effect addressed by Finno et al. (1991) was not considered in every study (e.g. Whittle et al., 1993 andHsiung, 2009) although the influence of opposite walls connected with struts or concrete slabs was recognized by some authors (e.g. Langousis, 2007).
Another issue addressed in some studies is the stiffness effect at the corners of an excavation. All studies presented above used two-dimensional simulations instead of three-dimensional simulations. For this reason it could be that the simulated deflections near the corner of an excavation were much higher than measured in the field. Finno et al. (2007) developed an equation that incorporates excavation dimensions and wall stiffness to calculate a PSR-ratio (defined as deflections calculated with three-dimensional analysis normalized by deflections calculated with two-dimensional analysis). It was found that an excavation-length/excavation depth ratio higher than six will probably lead to comparable results in 3-D and 2-D simulations. In contrast L/H e values smaller than 2 will definitely lead to different results.
Back-analyses were used to improve the simulation results, and both artificial intelligence methods (Finno and Hashash, 2009) or inverse-analyses were used (Langousis, 2007).        It was also noticed that data from piezometers (PZ-1 and PZ-2) showed a response that was likely related to the pile driving activity. The data suggests that the installation of the piles caused pore pressures to increase. According to the pile-driving journal there was a trend where pore pressures increased most when the pile-driving activity was close to the piezometer, whereas there was less, as the pile installation was farther away. This trend was confirmed by Bradshaw et al. (2007), where the pore pressure ratio r u was calculated from the ratio of the excess pore pressure to the initial vertical effective stress. Since r u did not reach a ratio of unity (=1), there was no indication of liquefaction, although pore pressure ratios of 60 % were calculated.
Nonetheless, excess pore pressures dissipated fairly quickly, mostly within a few hours.

Excavation
57 Figure 3-11 shows the time history for piezometric head recorded at PZ-1 during pile driving. It can be seen that pore pressures increased rapidly during installation of pile. Also, the trend of increasing excess pore pressures with decreasing distance from pile driving is visible.  15-node triangular elements were used to represent the soil. Structural elements like the sheet pile wall or the struts were modeled as elastic materials. The mesh was 59 refined inside and around the excavation to get more accurate estimates of the deflections.
Since three inclinometer locations (4, 10, 5) existed, three analysis sections were modeled. These are named sections A, B and C. Each section varied slightly in terms of soil layer thickness and excavation steps.  To generate the finite element mesh described above the following assumptions were made beforehand and verified by several test simulations: 1) Using 15-node triangular elements provided more accurate results than the Plaxis default 6-node elements although the calculation time was increased by a factor of 2.5 (the calculation time for each design section was enlarged from 4 minutes to approximately 10 minutes). The 6-node element provides a second 7) The mud mat that was constructed after excavating to final grade was not incorporated in the finite element model. The reason for that was that the influence (gravity load, stiffness element) of the mat was assumed to be small for the in-situ soil behavior, whereas the influence in the finite element model would be very high. In preliminary simulations the soil inside the excavation was "pushed" upwards, but the mud mat -which added additional gravity load -would push the soil back in an excessive manner and affected the results greatly.

CONSTITUTIVE MODEL
Modeling an excavation problem in non-plastic silts was considered to be a drained analysis. That means no pore pressures, caused by rapid loading and low permeable soils, will be generated.  The HS-model uses a more advanced approach to simulate soil behavior. The

Hardening-Soil Model is a non-linear hyperbolic model similar to the well-known
Duncan-Chang model (Schanz et al., 1999). Basic input parameters are stiffness for primary loading !" !"# , stiffness for primary compression !"# !"# , stiffness for un-/reloading !" !"# , stress dependent stiffness according to a power law m and the basic parameters c', φ', Ψ. In contrast to the MC-model, the yield surface is not fixed in principal stress space, but can expand due to plastic straining (Plaxis, 1998). This is called "hardening" and consists of two main types: shear hardening due to primary deviatoric loading and compression hardening to primary compression in oedometer loading and isotropic loading. The stiffness moduli used for the HS-model are stress dependent and can be calculated with: Actual values of modulus consequently depend on the minor principal stress ! ! which can be determined by a triaxial test and also depends on a reference confining pressure !"# which is usually 100 kPa. The power m shows the amount of stress dependency. PLAXIS suggests using m around 0.5 for normal soils and increase m to 1.0 for soft soils. For most calculations in this study it was assumed !"# !"# = !" !"# and !" !"! = !" !"# .

INPUT PARAMETERS
Finding the right input parameters was hindered by the limited set of soil data.
A geotechnical boring was performed at the north (BS98-7) and south (BD98-12) end of the excavation to investigate soil properties. The distribution of uncorrected blow counts (SPT-values) is presented in Figure 4-4.  The estimated parameters were then compared to soil parameters that were suggested in the "Geotechnical Base Line Report" (Haley and Aldrich, Jacobs Civil, 2002). The report assumed three soil layers for the entire construction side without any variances between the north and the south side of the excavation. Because the initial estimates differed so much, it was decided to use a certain set of parameters for each design section including modified values from the initial estimates and Geotechnical Base Line Report soil parameters. These values are shown in Table 4-4. Identical unit weights for all design sections were chosen to minimize the gravity effect (see also section 4.1.4) and to provide reproducibility. Nevertheless, to account for the different soil densities investigated in the two boring logs, the effective stress friction angles and subsequently the K o values were varied.
Furthermore, stiffness parameters (E, !" !"# , !"# !"# ) had to be estimated. There are some methods in the literature to determine E using SPT-values. Most methods use corrected SPT-values called N 60, which can be calculated as with: E m -hammer efficiency C B -borehole diameter correction C S -sampler correction C R -rod length correction For this study those values were:  Typical stiffness parameter for !" !"# , !"# !"# or correlations between those parameters and SPT-values are harder to find in the literature. Tjie-Liong (2011) recommended the following correlation for silty and clayey soils: !" !"# = 292 * !" (4.5) Using Equations 4.4 and 4.5 stiffness parameters for the north side of the excavation were calculated as 6484 kN/m 2 ( !"# !"# ) and 6248 kN/m 2 ( !" !"# ) compared to values for the south side with 2545 kN/m 2 ( !"# !"# ) and 2453 kN/m 2 ( !" !"# ). However, it is part of this study to find parameters that represent the existing site. Consequently, estimates from the literature were only used for basic computations and were changed in a "trial and error" method until fitting.
Besides appropriate soil elements, structural elements were included in the model to simulate sheet pile wall and struts. The stiffness of those structural elements was calculated by means of drawings where dimensions and material were described.
The sheet pile wall consists of CZ-128 sheet piles and was simulated in PLAXIS as a beam element defined by a bending stiffness EI and a normal stiffness EA. Struts were simulated as node-to-node anchor (elastoplastic spring elements with two fixed ends on either side of the excavation wall) and a defined normal stiffness EA. Different dimensions of struts were used for the three strut levels, therefore the normal stiffness had to be adjusted for each level (see Table 4-8). The horizontal strut spacing was 8.1 m whereas the vertical spacing was 3.3 m (1. level to 2. level) and 2.1 m (2. level to 3. level).

SIMULATION PROCESS FOR EXACATION
The simulation process in PLAXIS should represent the in-situ excavation process as presented in Figure 3-5. In general, the simulation started with installing the sheet pile walls by activating the beam elements in the model and was followed by alternating steps of excavation and strut installation. Deactivating the soil cluster in the finite element model simulated an excavation process. Activating the node-to-node anchor simulated struts installation. The detailed construction/simulation activity for each designs section will be shown in section 4.2.
In PLAXIS each of the steps described above was simulated by a plastic calculation (no time effect included). The loading for calculating deformations in the finite element model occurred because of using a staged construction procedure. That

Structural Element Bending Stiffness -EI (kNm 2 /m) Normal Stiffness -EA (kN/m) Element Type
Sheet Pile Wall CZ-128 6.46x10 4 3.25x10 6 Beam 1. Strut Level (W14X90) -3.42x10 6 Anchor 2. + 3. Strut Level (W14X120) -4.56x10 6 Anchor 71 means, changing geometry configurations lead to a changed ultimate state (equilibrium) that had to be calculated by the finite element program. The embankment at the west side of the excavation encountered some problems since it created an asymmetrical problem. Because of the higher load caused by the embankment the entire soil profile was shifting to the east and caused large movements even before the excavation was started. Therefore it was decided to include an initial simulation step where only gravity loading was calculated. For this step, no structural elements were activated or soil was deactivated, just the embankment was allowed to "settle" (this process was not a real settlement calculation since no pore pressure change was allowed). The goal was to create a certain stress history for the soil. After doing this, all displacements (not the stresses) were reset to 72 zero and the next simulation step was applied by activating the sheet pile walls. By doing this procedure the effect of the asymmetrical problem could be reduced.
Groundwater conditions were also simulated in the analysis. The initial water table was situated at elevation 1.8 m, but it decreased because of pumping water out inside the excavation. A "phreatic line" defined the water table level at the beginning of the simulation and was used to calculate initial water pressure. During excavation a prescribed groundwater head was used as left and right boundary conditions (here 1.8 m). Because of the staged construction method and defined impermeable sheet pile walls no water was assumed to be in the excavated areas inside the excavation. Finally, using a groundwater flow calculation could simulate a change in groundwater table and changed water pressure (Figure 4-6). The overall scope of this study was to simulate the soil behavior of Rhode Island Silts due to pile driving. However, simulating the process of pile driving was not trivial. The problem was, driving piles into the ground cannot be simulated with ! PLAXIS directly. Even if it was possible to model piles by means of structural elements, it was not possible to simulate a dynamic motion. Therefore, a special approach was used to solve this problem.
In principle, this approach did not attempt to simulate the pile driving itself, but rather the immediate effect of pile driving on the surrounding soil properties. It is well known in the literature that pile driving installation can lead to degradation of soil strength and stiffness. This effect is called liquefaction. There are numerous definitions of the phenomena, but most of them describe it as a reduction in effective stress due to pore pressure generation leading to loss of strength and stiffness (Taylor, 2011;Wu et al., 2004).
Two different kinds of liquefaction can be distinguished. They depend on the state of the granular soil (contractive or dilative). When the static shear stress of a soil is greater than the shear strength of that soil in a liquefied state then this is called flow liquefaction. Usually this can happen in cohesionless soils (sands and non-plastic silts).
Applying cyclic loads (like pile driving) bring the soil to an unstable state, which causes a dramatic reduction in strength. This happens suddenly and causes large deformations (Kramer, 1996;Idriss and Boulanger, 2008). The second possibility of liquefaction is called cyclic mobility. This occurs when the static shear stress is less than the shear strength of the liquefied soil. Each cycle of load produces a gradually increase of strain and it is driven by cyclic and average shear stresses. Deformations increase proportionally and signalize failure when the strains are unacceptable large.
For the analysis of dynamic degradation the effective strength of the soil element governs the behavior and degradation of the medium. In a standard cyclic triaxial test pore pressures develop due to a lack of drainage within the specimen and as the effective stress decreases the stiffness decreases, which can be seen in increasing strain. Figure 4-7 and Figure 4-8 present typical cyclic triaxial test results, including an increasing pore pressure ratio until reaching r u =Δu/σ' = 1 as failure criterion. Typical pore pressure increase with resulting increase in pore pressure ratio for stress controlled cyclic triaxial tests (Taylor, 2011) A shown in Figure 3-11 excess pore pressures were measured during pile driving and therefore supports the assumption of decreasing effective stress with increasing excess pore pressures. The question arises how to relate the loss of strength  to the build-up of excess pore pressures? In general the liquefaction potential is evaluated by relating the cyclic shear stress induced by the source (earthquake, pile driving activity) to the cyclic resistance (Idriss and Boulanger, 2008).
For this study it was not necessary to calculate any cyclic shear stresses or cyclic resistance, but to assess the strength loss due to pile driving itself. Parameters that could be reduced in PLAXIS to simulate strength loss were the effective stress friction angle φ' and the stiffness E, !"# !"# , !" !"# and !" !"# . Also, there are many attempts in the literature to relate cyclic loading to soil properties, mainly to bulk moduli, K, and shear moduli, G, that can be correlated to Young's modulus and the oedometer modulus (Wood, 1990;Plaxis, 1998). Nevertheless, the approach of this study is to estimate appropriate values of moduli and effective stress friction angle first using a trial and error method and then verifying the optimized parameters later.
In this study, calculations in PLAXIS were executed as effective stress analyses; consequently the input parameters were effective stress parameters. The soil was assumed to behave as a drained material. In contrast, to simulate excess pore water pressure caused by pile driving an undrained soil behavior should have been selected.
But since the excess pore pressures dissipated relatively quickly after pile driving the time dependency was important. Unfortunately, simulating this time dependency was not possible with a staged construction, which had to be used to change the soil parameters (consolidation simulation could have been chosen instead, but this did not account for plastic deformations). Additionally, defining a value of excess pore pressures for certain soil clusters was not possible in PLAXIS. Consequently, the only 76 possibility to simulate the effect of excess pore water pressure due to pile driving was to execute a drained analysis with reduced effective stress parameters.    Since the PSR of case A is smaller than 4, a length to excavation depth ratio L/H e had to be taken into consideration to determine a more accurate PSR. Each excavation step (simulation stage) therefore had a certain H e . Figure 4-12 displays the PSR for different excavation steps of design section B (since this was the midspan location). An L/H e ratio greater than 6 resulted in a PSR of around 1. In contrast, very small PSR were reached for L/H e ratios smaller than 2, which indicated large differences between plane strain and 3-D simulations.  Finno et al., 2007) Consequently, when assuming a smaller L/B ratio like in case A the plane strain simulation would over predict the deflections especially when reaching the 3rd simulation stage. Assuming a bigger L/B ratio like case B, more reliable plane strain calculated deflections could be determined.
In principle, the conical shaped excavations towards the south and north end of the excavations cannot be treated as perpendicular sheet pile walls (like assumed in case A) related to the simulated west sheet pile wall. This supports the assumption ments. The movements computed by the 3D analysis are less than those computed by plane strain simulations for the smaller excavations but are almost the same for the larger excavations.

Effects of Excavation Size and Depth
The influence of excavation geometry on lateral soil displacement is evaluated by comparing the PSR values for several normalized strain versus Also the optimized soil parameters necessary to match simulated with measured movements are summarized.
The soil parameters presented in Table 4-4 were used as default values for the simulation. The only parameters that were adjusted during the simulations were the moduli and the effective stress friction angles of the soils. The moduli of the fill and sand layer were, after an initial adjustment, kept constant, and the modulus and effective stress friction angle of the silt layer was decreased with progressing excavation. This was done to account for some amount of soil disturbance that may have occurred in the silt during excavation (Russell, 2011). Therefore, an area up to 2 m away from the sheet pile walls (east and west) was characterized as disturbed area.
Note that the magnitude of disturbance might differ in this area. For example, the soil inside the excavation could be more disturbed (because of heavy equipment) than the outside area. Further effects of soil disturbance will be discussed is section 4.4.
The design sections used in this study are presented in the following figure. It shows that the 3rd and final excavation stages were simulated in one step. This was done based on field reports that indicated that the contractor excavated the last two stages in one step.   Table 4-9 shows that the moduli of the silt had to be decreased by a significant amount. In detail, the 2nd stage silt moduli were reduced to 40 % (inc. optimized) and 46 % (beam optimized) the initial value. Additionally the friction angle was decreased to 80 %. To simulate deflections measured for the 3rd stage and final stage the moduli had to be set to 1.4 % (inc. optimized) and 2 % (beam optimized) for some clusters.
The friction angle was decreased to 44 %. Also, the power value m was increased to 1.0 to simulate a very soft soil (as suggested in Plaxis, 1998).
It has to be noted that different soil areas depending on their location relative to the "working area" could be subjected to different amounts of soil disturbance. For example, the silt around the sheet pile toe remained undisturbed (see Figure 4-15), whereas the silt right underneath the excavated area and outside the sheet pile wall was assumed to be heavily disturbed. In general, the closer the silt was to the "working area", the more disturbance was assumed. The exact location of disturbed areas can be seen in the plots presented in appendix A.

DESIGN SECTION B
The excavation stages simulated at design section B were: Additional area of disturbance Also, the strut pre-stress was included in this simulation as described in the section before.
Then optimized curves are: As shown in Figure 4-18, the Stage 1 and 2 were simulated well. In contrast, Stages 3 and 4 produced some problems to simulate them correctly. It was solved by adding additional area of disturbance below the already assumed area of disturbance.
Because section B was the midspan location more deflection was expected. Also, the excavation depth was 0.5 m deeper. Therefore, the deflections are double the amount measured at sections A and C. However, as shown in the following table the soil disturbance was assumed to be very high and could not be increased more without creating problems in the finite element calculation.

SUMMARY OF EXCAVATION SIMULATION
Moduli and effective stress friction angle optimizations had been made for the "real" inclinometer location (1 m from the sheet pile wall) and the sheet pile wall itself. Appropriate soil parameters could be found to simulate the deflection of the first and second excavation stage, whereas the moduli and effective stress friction angle for the third and final stage of construction are not reasonable.
Because of soil disturbance the stiffness moduli and the friction angles of the silt layer had to be reduced for each excavation stage to match measured curves.
However, decreasing the soil stiffness up to 99 % is very unrealistic. This fact and other explanations for this issue will be discussed in section 4.4. The following table summarizes the parameters found in this study: The difference between the optimized parameters in each stage is illustrated in  The overall scope of this study was to simulate soil movements due to pile driving. This section presents the results of a parameter optimization to fit finite element simulated curves with measured deflection curves. Calculations were made based on the assumptions presented in section 4.1.5.
It was decided to use a more detailed silt layer system below the already existing area of disturbance due to excavation (see Figure 4-23, Figure 4-28 and Figure   4-31). Consequently each "sub"-layer could be subjected to a different amount of soil disturbance. During the simulation process adjustments were made for each layer and the modulus was decreased in step sizes of 5 %. Below an absolute value of 5 % the step size was decreased to 1 %.
As discussed in section 4.1.1 the mud mat was not included in the simulation.
Doing this would probably result in lesser silt strength and stiffness parameter than presented below, because the mat would push the soil downwards (gravity) and therefore reduced the sheet pile wall moving. Consequently, to obtain the measured deflection curves, even larger reductions in soil properties would be required. As presented in Table 4-13 the stiffness and strength parameter of the silt were not reduced as much as deeper elevations. Since the sheet pile wall ended at elevation -11.9 m it was necessary to provide a certain amount of resistance against moving.
Using lower values than presented above, would have caused the lower part of the sheet pile wall to move excessively. In contrast to the beam-optimized simulation, much better results could be determined for the inclinometer location using the soil profile shown in Figure 4  The main difference between the soil setup presented for the inclinometer location and the sheet pile wall was the reduced soil strength at elevation -13 m to -15 m. A summary of the reduced soil parameters is shown in Table 4-14, and a comparison between the simulated displacements and the measured data is shown in  Using these parameters the following deflection curve was obtained:  Shown in Figure 4-27 is a much better fitting deflection curve for the inclinometer location. Even the movements at elevation -10 m could be simulated quite well. As before, the strength reduction right at the toe of the sheet pile wall could not exceed a certain amount (here 70 % reduction). When using smaller values excessive movement would have occurred.

DESIGN SECTION B
According to construction field reports, inclinometer 10 became unreadable shortly after the beginning of pile driving. Consequently no measured deflections exist to use for optimizing parameters. However, in this study the parameters determined for design section A were applied for this design sections to investigate possible deflection caused by pile driving. Since only the inclinometer location optimized parameters  Therefore the parameters had to be changed until at least some usable deflection curves were obtained. A summary of the reduced soil parameters is shown in Table 4-    The shape of the curve presented in Figure 4-30 shows reasonable agreement with measured results of design section A. Specifically, the peak at elevation -10 m could be simulated well. However, since the deflections at design section B are almost twice that high as design section A, the only goal here was to find a curve that has the right shape not necessarily the right amount of deflection.

DESIGN SECTION C
As with design section B, inclinometer 5 became unreadable shortly after the beginning of pile driving. No measured deflections existed to use for optimizing parameters at design section C. Consequently, optimized parameters (inclinometer location) from design section A were applied to design section C.  Table 4-16, and a comparison between the simulated displacements and the measured data is shown in  Although the shape of the deflection looks reasonable (especially the peak at elevation -10 m), the amount of movement does not. The movement was doubled from 10 cm to over 22 cm, which is not comparable to the real deflections measured at design section A. Therefore, it was decided to use different parameters for design section C. The principle remained the same (dividing the underlying silt into layers), but the percentage of strength and stiffness reduction decreased. This assumption could also be verified by the fact that design section C had a far greater distance from the pile driving activity than the other design sections and was consequently subjected to fewer disturbances. Good results were achieved by using the following setup:

SUMMARY OF PILE DRIVING SIMULATION
The former sections presented an attempt to simulate the effect of pile driving in Rhode Island silts on the movement of the sheet pile walls. The assumptions made in section 4.1.5 regarding reductions in strength and stiffness lead to reasonable agreement between simulated and measured wall movements due to the pile driving.
Actual wall movements were only measured at design section A because of the failure of the inclinometers at sections B and C shortly after driving commenced.
For design section A, the difference between the inclinometer location and the beam-optimized curve suggests that the inclinometer measurements in the field represented mainly the soil behind the sheet pile wall and did not indicate the real deflection of the sheet pile wall itself. Therefore it was decided to optimize the soil parameters of design sections B and C only for this inclinometer location. Since design section B caused some problems in the excavation simulation (extreme soil strength reduction etc.) the goal there was to get a reasonable qualitative curve without necessarily simulating the right amount of deflection due to pile driving.
Consequently, the results there are somewhat questionable. In contrast, for design section C a reasonable deflection curve (both in shape and magnitude) was obtained.

DISCUSSION ABOUT FINITE ELEMENT SIMULATION
Although the wall deformation patterns could be simulated by reducing the strength and stiffness of the soils during excavation, the magnitude of the reductions in some cases are not reasonable. The following discussion is divided into three parts, a 108 discussion about the finite element software itself, the excavation simulation and the pile driving simulation, respectively.

FINITE ELEMENT SOFTWARE PLAXIS
There are a few shortcomings when using the finite element software PLAXIS.
The first problem was that PLAXIS did not provide the possibility to do a displacement-controlled loading like presented in section 2.2.2. Since measured displacement curves were available, the displacement-controlled simulation would probably have resulted in more realistic soil parameters. However, since this was not possible a trial and error method was used to determine the optimized soil parameters, and some combinations of parameters are not realistic. 109 The third problem was that PLAXIS did not allow for allocating excess pore pressures for certain areas in the finite element model. The immediate effect of pile driving -generating excess pore pressures due to vibrations -could not be simulated in this way. In PLAXIS the Pore pressures σ w are calculated with ! = !"#$%& + !"#!$$ (4.6) where the steady state pore pressures are considered to be input data, generated by groundwater flow calculations. Excess pore pressures are calculated during plastic calculations and are not input data. The effect of disturbance due to pile driving could only be simulated by decreasing the effective stresses (e.g. reduce the soil strength and stiffness). Consequently, simulated deflections in this study did not represent the real soil behavior in the field, but an approximation based on the assumptions made in section 4.1.5.

EXCAVATION SIMULATION
As shown in section 4.2 the first excavation step for each design section could be simulated quite well. No strength and stiffness reduction for the silt was needed to get a similar deflection curve like measured at the site. Only the fill layer was excavated into at this time, therefore the influence on the silt layer had to be negligible small. In contrast to this, there was a large strength and stiffness reduction necessary for the simulation of silt layer in excavation stage 2 and especially for the 3rd and final stage.
The question arose if the measured deflections were unusually high compared to common excavation sites. In general, deflections of excavation walls are influenced by soil and groundwater conditions, changes in groundwater level, depth and shape of excavations, type and stiffness of the wall and its supports, methods of construction of the wall and adjacent facilities, surcharge loads (Ergun, 2008). Long (2001) and Clough et al. (1990) developed a database for instrumented walls and categorized mainly according to type of soil and type of supporting system. To compare the results they normalized the maximum lateral wall movements by the total excavation height.  The normalized deflections of the first excavation stage indicate stiff soils whereas with further progress of excavating the soil "classification" changes to soft soils. This indicates that the soil at the existing construction site is softening due to excavation. It has to be assumed that the excavation process itself caused significant soil disturbance (almost liquefaction).
In comparison, normalized deflections for design section A and C are almost the same for all excavation stages, while those for design section B increased unproportional in the 3rd stage and final stage. This can also be visualized in Figure 4-35.  Bradshaw et al. (2007) there is one factor that could have played a role in the excessive wall movements observed at the site. The sump pumps that were used to dewater the excavation eroded the silt from beneath the slab (concrete mud) about 30 cm. Russell (2011) confirmed that unusual amounts of silt sediment were found in the tanks used to collect sediment from the pump effluent. This might have caused a reduced vertical overburden stress on the underlying soils. It is the same effect like overexcavation. Additionally, this gap could have provided a space for the surrounding soil to deform into. Both effects would cause less passive resistance and higher displacements. Evidence of additional cracks observed at the top of the west side embankment also supports the idea that the larger wall deformations actually occurred.

Parameter Design Section A Design Section B Design Section C
Those observations could describe the unusual high deflections after the 3. stage (section A and C) and final excavation stage (section B). Simulating Therefore, including overexcavation in the finite element model did not lead to satisfactory results. In contrast, reducing the silt strength and stiffness in the finite element simulation led to similar deflections curves like the measured ones and has to be treated as the solution of the problem in this study. Nevertheless, in the authors opinion the problem of overexcavation is not negligible and presents an issue that has to be dealt with in future research.
Another explanation for the unusual high measured deflections is the soil surrounding the inclinometer tubes behind the wall moved or became disturbed and the measured movements are not representative of the actual wall movements. The fact that inclinometers 5 and 10 became unreadable during the later pile driving shows the sensibility of those measuring devices.

PILE DRIVING SIMULATION
Reasonable wall deflection curves were generated to simulate the effect of pile driving by reducing the strength and stiffness of the underlying silts. This suggests that the assumptions made in section 4.1.5 may be acceptable. Pile-driving activities caused pore pressure generations by cyclical loading of the surrounding soil. This can lead to a temporary reduction in effective stress and consequently to a decreased soil strength and stiffness. Similar behavior under cyclic loading of non-plastic silts was also reported by Boulanger and Idriss (2004) and Baxter et al. (2008).
For the simulation process it was assumed that the strength reduction remains constant during the whole simulation step. Since there was no time dependency in the "staged construction" simulation, pore pressure dissipation was not included in the model (this ignores the fact that the actual process is at least partially undrained).
However, it was assumed that deflections calculated with this method are the same like a model that would include pore pressure dissipation.
It is still not clear, however, whether the magnitude of strength reduction necessary to match observed deflections are reasonable or exaggerated. Kraft et al. (1981) proposed a way to include the effect of soil disturbance into the concept of pile load transfer curves (t-z curves). The idea is to calculate an average shear modulus at the pile surface that is smaller than the shear modulus of the undisturbed soil. Based on the assumption that the shear modulus is proportional to the undrained shear strength, the modulus is considered to increase linearly with radial distance from the pile until the undisturbed modulus is reached (Figure 4-36).
Figure 4-36: Idealized radial distribution of soil modulus ratio (Kraft et al., 1981) 115 It can be seen that the shear modulus is reduced to 0.20 % of the initial value close to the pile. Based on this, soil strength reductions to 10% in the finite element simulation therefore can be regarded as acceptable results. However, Kraft et al. (1981) intention was to describe the soil-pile interaction for pile bearing capacity analyses. The surrounding soil was not a real issue of their paper, but it is a good first explanation of the problem encountered in this study.
Taylor (2011) developed a method to assess the liquefaction potential and hazard due to pile driving. He found out that the main governing parameters for liquefaction potential were in-situ silt density and shear-wave velocity. Furthermore, the overconsolidation ratio (OCR) of the silt was important, with the hazard decreasing with increasing OCR. Also the sequence of pile driving played a significant role in liquefaction potential. Unfortunately, the model used in this study did not incorporate the parameters that Taylor (2011) found out to be important. Therefore, it is suggested for future research to develop finite element models that also include parameters mentioned above and not only soil strength and stiffness.

SUMMARY AND CONCLUSIONS
The objective of this study was to perform a finite element analysis of a case study involving significant sheetpile wall movements from an excavation and pile driving activities in Rhode Island silts. The case study was the installation of a pilesupported gate and screening structure as part of a combined sewer overflow project for the Narragansett Bay Commission in Providence. As part of the installation, sheetpiles were driven around the site and excavation occurred in four stages prior to pile driving. Inclinometers were installed at three locations, and three design sections A, B and C were modeled. A commercial finite element package, PLAXIS (2-D, version 7.0) was used for the analyses.
First, a literature review of possible results and shortcomings of finite element simulations was presented. The main findings of this review were: • More complex constitutive soil models like the Hardening-soil model of PLAXIS lead to more reliable finite element results compared to simple models like the linear Mohr-Coulomb model.
• Soil disturbance due to sheet pile wall installation cannot be incorporated well in FE-simulations.
• Boundary conditions are especially important for flow calculations.
• Incorporating building sequences as single simulation phases can enhance the finite element results.
• Stiffness effects of corners of excavations can occur and can lead to different results between 2-D (plane strain) and 3-D simulations.

117
In Chapter 3, the case study was described in detail, including the geotechnical site conditions, construction sequence, geotechnical instrumentation, and measured wall deflections. It was shown that the deformation patterns of the sheetpile walls were consistent with engineering practice, but the magnitude of the deflection was considered to be unusually high at the later excavation stages. Additional horizontal movements were measured during pile driving activities, accompanied by increased pore pressures in the underlying silts.
Chapter 4 presents a description of the finite element model used to simulate soil behavior during excavation and pile driving activities. The model incorporated three soil layers representing fill, sand and silt layer, respectively. The fill and sand layer were simulated by means of a Mohr-Coulomb soil constitutive model, whereas the advanced Hardening-Soil model (a non-linear hyperbolic model) was used for the silt layer.
In-situ deflection measurements were used to optimize soil parameters of the finite element model. Parameters that were changed to adjust the deflection curves were stiffness parameters E, !"# !"# , !" !"# and !" !"# and the strength parameter φ'. Since it was not sure if the in-situ inclinometer location represented the true deflection of the sheet pile wall or the surrounding soils, two sets of optimizations -for the wall and for the real inclinometer location (1m away from the sheet pile wall), respectively -were executed.
In summary, the first two stages of excavation and wall displacement were modeled well with reasonable values of strength and stiffness. These parameters would 118 be a good place to start in future modeling efforts involving the Rhode Island silts. This is probably the most important conclusion in going forward with future work.
The only way to simulate the last stages of excavation and displacement was to use unreasonably low values of strength (e.g. φ'=14 degrees) and stiffness. Possible explanations for this poor agreement include: • The loss of ground during pumping reduced the stability in the excavation and led to larger movements.
• The excavation process itself caused significant disturbance (almost liquefaction) to the soil at the base of the excavation.
• The soil surrounding the inclinometer tubes behind the wall moved or became disturbed and the measured movements are not representative of the actual wall movements.
The effect of pile driving on the wall movements was simulated by reducing the drained strength and stiffness significantly. Although this ignores the fact that the actual process is at least partially undrained, the approach used in this thesis is a first step in understanding movement of adjacent structures in Rhode Island silts due to pile driving.