Permanent Sheet Pile Wall in Soft Sensitive Clay

During 2013 to 2017, two railway tracks were constructed just north of Central Uppsala, a city located approximately 60 km N-NW of Stockholm, in Sweden. The elevation of the planned tracks was such that a retaining structure was needed to avoid damage to residential buildings west of the tracks. A tied-back steel sheet pile wall was utilized to handle the height difference during the construction period, as well as in the serviceability stage. The original design consisted of a cast-in-place anchored concrete retaining wall. However, a SPW was considered to be the best alternative from both construction and economical points of view, and it would also reduce the carbon footprint. Monitoring of the SPW performance was carried out using conventional surveying, inclinometers, and anchor force measurements (three anchors at five cross sections). The measurement data from Section 3+615, see Fig. 1, is presented in this paper. Fig. 2 presents the cross section and Table 1 the general schedule of construction activities.

The sheet pile wall consists of AZ24-700 profiles installed to elevation $+3\mathrm{m}$, resulting in a total length of approximately 16 m. At the location of each anchor, single sheet piles were driven into the bearing stratum consisting of coarse-grained material. Anchors consisted of MAI T76S (Minova, Wales, UK) rods grouted into the bedrock, with a center-to-center (c.t.c.) distance of every second 2.8 and 3.5 m. However, adjacent to the studied section the c.t.c., distances varied from 1.3 to 3.9 m due to the presence of some existing and new pipes. The retained height was approximately 6 m in the construction phase and 4.5 m in the long-term. After the final excavation, 0.1 m of insulation and gabions were placed in front of the wall.

The geology of Uppsala is dominated by soft clay deposits with the Uppsala esker ridge running approximately N-S through the city. The clay layers started to form during the last deglaciation as the ice front retreated from the Uppsala area approximately 10,000 years ago (Lundin 1991; Fréden 2002). Postglacial deposits, formed during subsequent isostatic uplift, overlay the varved glacial deposits. The extent and depth of the postglacial deposits varies within the city. At the studied site, varved clay is in general found all the way up to the dry crust. Due to the isostatic uplift the ground surface at the site became exposed approximately 2,500–3,000 years ago (Eriksson 1999).

Pumping of drinking water from various locations along the Uppsala esker started in 1875 in Central Uppsala. As the city grew, the system was expanded. The groundwater well galleries and recharge plant located nearest the studied site were put into operation in the late 1960s to early 1970s (Hummel 2014). Allowable upper and lower groundwater levels for the pumping-recharge system were described by Sidenvall (1981) and are in line with measurements of pore pressures in the lower part of the clay layer at the studied site. The pumping has caused lowering of the groundwater in the aquifer below the clay layer. This contributes to increased effective stresses in the soft clay, and consequently ongoing background settlements of up to $8\mathrm{mm}/\mathrm{year}$ have been monitored within the city center (Fryksten and Nilfouroushan 2019).

The studied cross section of the railway project is located approximately three kilometers north of Central Uppsala. The ground surface at site is located approximately at elevation $+19\mathrm{m}$ (Swedish National reference system RH2000). The soil stratigraphy consists of dry crust down to an approximate depth of 2.5 m below ground surface. Soft sensitive varved clay is found down to an approximate depth of 15 to 16 m, corresponding to elevation $+3\mathrm{m}$ to $+4\mathrm{m}$ in the location of the sheet pile wall. Layers of coarse-grained soils underlay the clay down to approximately $-\text{3\hspace{0.17em}\hspace{0.17em}}\mathrm{m}$ followed by bedrock.

The index properties of the clay, as well as the undrained shear strength and hydraulic conductivity (from here on referred to as permeability) are summarized in Fig. 3. Fig. 3 also contains generalized trends (denoted “FE” in Fig. 3) as input for FE analyses. Soil samples were extracted with a standard Swedish 50mm STII piston sampler. Samples denoted with “CTH” were analyzed and tested in the geotechnical laboratory at Chalmers University of Technology. This supplementary testing was carried out in late 2020–early 2021 to obtain data on the stress-strain response upon shearing (triaxial tests), as well as to investigate the unloading-reloading behavior and the intrinsic properties in oedometer tests.

As seen in Fig. 3 the unit weight of the clay ranges from 15.5 to $18.5\mathrm{kN}/{\mathrm{m}}^3$. The liquid limit is in general 0%–10% lower than the natural water content, and the plasticity index ranges from 13% to 47%. The sensitivity varies from approximately 10–35 and the organic content from 1.7% to 3.2% [Fig. 3(b)]. Sedimentation analysis on a sample from 5 m depth indicates a clay and silt content of 54% and 46% respectively. Fine silt (2–6.3 μm) dominates the silt fraction. According to Casagrandes plasticity chart, the clay is classified as medium plasticity, except the sample from 3 m depth, which classifies as high plasticity clay.

Cone penetration (CPTU) and direct simple shear (DSS) tests indicate an undrained shear strength of 15–20 kPa to elevation $+15\mathrm{m}$ and an increase of $2.2\mathrm{kPa}/\mathrm{m}$ below. Results from CPTU, evaluated according to Larsson (2015), and DSS tests are in general in good agreement with empirical estimates [“Emp.” in Fig. 3(e)] based on Larsson et al. (2007). The low undrained shear strength measured in the two lowermost anisotropically ($K_0$) consolidated undrained triaxial compression (CAUC) tests is likely to be attributed to sample disturbance.

The vertical permeability, $k_v$, was evaluated from the constant rate of strain (CRS) oedometer tests according to Swedish practice (Larsson and Sallfors 1986). At stress levels corresponding to the vertical effective stress in situ, $k_{v0}$ varies from 2 to $6\times {10}^{-10}\mathrm{m}/\mathrm{s}$ [Fig. 3(f)].

The pore pressure in the clay layer and the coarse-grained material below was measured by consulting company Tyréns, as well as by Chalmers with one CPTU test. Pressure levels in the upper part of the clay layer corresponded to a groundwater level located at $+18.2\mathrm{m}$. Due to the history of the pumping of groundwater within Uppsala in the lower aquifer, the pore pressure in the clay is lowered compared to the hydrostatic pore pressure distribution, as seen in Fig. 4. The groundwater level measured in 10T024, at elevation $+5\mathrm{m}$ in Fig. 4, deviates due to a higher elevation of the coarse-grained bottom material to that of the studied section. Previously described allowable upper and lower groundwater levels for the pumping-recharge system are in line with the present pore pressure levels measured in the lower part of the clay layer. There is, however, an uncertainty if the measured pore pressures also include excess pore pressures (due to ongoing settlements). Thus, the measured profile does not necessarily correspond to a steady state.

The vertical preconsolidation pressure, ${\sigma }_{vc}^{\prime }$, of the clay layer has been determined by means of CRS and incremental loading (IL) oedometer tests, as well as triaxial (TX) CAUC and $K_0$-tests (zero radial deformation). The CRS-tests were carried out with different strain rates (0.17%–0.71%/h), since some initial tests with the Swedish standard rate (0.72%/h) resulted in high pore pressures ($>10\%$ of the measured total stress).

Based on the unit weight of the soil, the estimated pore pressure distribution, and the preconsolidation pressure, a trend of the overconsolidation ratio (OCR) is presented in Fig. 5. OCR varies from 2.5 in the upper part of the clay layer to approximately 1.1–1.2 in the bottom. If the pore pressure had been hydrostatic (i.e., no underdrainage), OCR would be in the range 1.6–1.8 in the bottom of the clay layer. However, such a range (1.6–1.8) of a possible historic OCR is likely an overestimate, since measured values of ${\sigma }_{vc}^{\prime }$ most likely have evolved during and after the pore pressure drawdown and the associated effective stress increase. An OCR unaffected by anthropogenic loading, would due to aging (Bjerrum 1967) be expected in the range of 1.2–1.3 based on experience from other Swedish clays; 1.15–1.2 for East Coast and 1.25–1.3 for West Coast (Larsson 2007; Sallfors and Larsson 2016).

As previously mentioned, the background settlement rate in Central Uppsala is up to $8\mathrm{mm}/\mathrm{year}$. However, no detailed data of background settlement rates before construction were available for the studied area. The publicly available InSAR data (WSP 2021) indicates an ongoing, present day, settlement rate of $1.5–3.1\mathrm{mm}/\mathrm{year}$ at approximately 10 m distance behind the sheet pile wall in the studied section. The distribution of settlements versus depth is unknown.

To model the response of the clay layers, the Creep-SClay1S model (Sivasithamparam et al. 2015; Gras et al. 2018) was adopted. The model originates from the modified Cam-Clay model and critical state soil mechanics. The advantage of the Creep-SClay1S model is the ability to incorporate typical soft sensitive clay features such as initial and evolving anisotropy, destructuration, and rate-dependency. A main advantage of including these features and rate-dependency in particular is that one parameter set can be used for predictions of the short- and long-term response in areas with soft, sensitive clay layers and background creep settlements. Rate-dependency also allows for automatic mapping between strain rates adopted in laboratory tests and element level simulations and those predicted in the boundary level modeling. For a brief summary of model details and formulations see Tornborg et al. (2021), and for the history and successive development of the model see Wheeler et al. (2003), Karstunen et al. (2005), Sivasithamparam et al. (2015), and Gras et al. (2018).

The clay layer at the site was divided into five layers according to Table 2. For estimation of initial void ratio, $e_0$, the clay layers were assumed to be fully saturated and with a specific gravity of $27\mathrm{kN}/{\mathrm{m}}^3$ (Larsson 1981). The vertical permeability of the clay was calculated from CRS-tests, and for the dry crust $k_{v0}$ was estimated to be $5\times {10}^{-9}\mathrm{m}/\mathrm{s}$ based on Ringesten (1988). The horizontal permeability of the clay layers was estimated to $1.3k_{v0}$ based on Tavenas et al. (1983) and Müller and Larsson (2012), with the exception of the dry crust, where $k_h=k_{v0}/5$ was assumed based on Ringesten (1988).

The model parameters of Creep-SClay1S are presented in Table 3. Parameter values in Table 3 were estimated based on index, oedometer, and triaxial tests. See Table 3 for symbols relating to the Creep-SClay1S model. The intrinsic modified compression, ${\lambda }_i^{*}$, and creep, ${\mu }_i^{*}$, indices were derived from IL tests on remolded clay, see Fig. 6. The value of ${\lambda }_i^{*}$ is rather low compared to other studies on similar clays, e.g., Karstunen and Koskinen (2008) range 0.08–0.10. However, Karstunen et al. (2005) reported ${\lambda }_i^{*}$ in range 0.03–0.09.

Model parameters $a$, $b$, and ${\chi }_0$ were initially calibrated based on element level simulations of laboratory tests. Parameters $a$ and $b$ would ideally be based on drained triaxial tests probing an isotropic stress path for subsequent numerical optimization of $a$, and respectively, a highly deviatoric stress path for $b$ (Koskinen et al. 2002). Koskinen (2014) recommended values of $a=10$ and $b=0.2$ based on extensive testing of Finnish soft sensitive clays, whereas $a=8$ and $b=0.5$ were used in simulations of soft sensitive Swedish West Coast (Gothenburg) clay (Petalas et al. 2019; Tornborg et al. 2021). Upper and lower bounds for $a$ and $b$ are given by Gras et al. (2018). The value of ${\chi }_0$ can be estimated initially from the sensitivity of the clay (Koskinen et al. 2002). However, some calibration of ${\chi }_0$ is typically needed to fit laboratory data.

As previously mentioned, a groundwater drawdown is present at the site due to historic pumping in the aquifer below the clay layer. This stress history was modeled in order to initialize the stress situation and state parameters prior to construction. However, an inherent challenge in such modeling is that the laboratory tests indicate the in situ state at present day. In other words, the initial state (before the man-made increase of effective stresses due to groundwater pumping) is unknown. Therefore, in modeling of the stress history, “unknown” initial values of the state variables were estimated and assigned. The state then evolves during the boundary value simulation of the stress history. This means that the values of the state variables are not prescribed as input at the start of the construction (phase 01 in Table 5). Rather, they are checked so that they, during the simulation of the groundwater drawdown and up until start of construction, evolve to be within reasonable limits, i.e., in line with the available laboratory test data.

In all, this required an iterative procedure adjusting the initial values of the state variables. Foremost, the initial value of ${\chi }_0$ required some iterations to have it evolve to values in line with laboratory values of sensitivity. The initial values of the state parameters are given in Table 2. Table 2 includes the initial values of the isotropic overconsolidation ratio, $OC{R}^{*}=p_{eq}^{\prime }/p_m^{\prime }$ where $p_{eq}^{\prime }$ is the equivalent isotropic mean effective stress level and $p_m^{\prime }$ the corresponding preconsolidation pressure, for details see Tornborg et al. (2021). Evolved values of $\chi$, $K$, and $OC{R}^{*}$ after modeling of the historic groundwater drawdown are presented in Fig. 7.

Figs. 8 and 9 present data from incremental loading oedometer and anisotropically consolidated undrained triaxial compression (CAUC) and extension (CAUE) tests, respectively. The figures include element level simulations of some of the tests. The element level simulations were carried out with the evolved values of $\chi$, but with consolidation stresses and $OCR$ as imposed, respectively, derived from the individual tests. As previously pointed out [considering Fig. 3(e)] the measured peak strengths in the triaxial CAUC tests were lower than empirical estimates. The element level simulations resulted in emerging peak strengths that were more in line with the empirical estimates. The difference in laboratory data and element level simulations emerge, due to sample disturbance effects and/or consolidation to stress levels approaching the in situ preconsolidation pressure, causing some gradual destructuration of the sample (whereas element level simulations correspond to nonexisting sample disturbance). For instance, the CAUC tests on the samples from 9 and 11 m depth experienced $\mathrm{\Delta }e/e_0=0.060$ and 0.069, respectively, during reconsolidation and thus, according to Lunne et al. (1997), classified as “good to fair” (the 11 m test on the border to “Poor”). It can also be noted in Fig. 9(b) that since ${\kappa }^{*}$ (derived from unloading in IL tests) is rather low, the stiffness emerging in the CAUC and CAUE simulations is overestimated compared to the triaxial test data. However, the value of ${\kappa }^{*}$ was kept unadjusted, since sampling with a block sampler would most likely result in a higher sample quality and elastic stiffness, see Karlsson et al. (2016).

The response of the dry crust, the coarse-grained materials (below the clay layer), the compacted fill and the lime-cement stabilized part of the soil, were simulated using the Mohr-Coulomb model with parameter values according to Table 4.

A two-dimensional finite element (2D FE) model of the studied cross section, 3+615, was constructed in the commercial FE code Plaxis 2D (version 2021). The model geometry is presented in Fig. 10 and consists of 5,763 triangular 6-noded elements.

The analyses were carried out as consolidation analyses, representing the construction activities and times as-built, see Table 5. The analyses starts with modeling of the historic drawdown, which is assumed to have been rapid, followed by 50 years of consolidation. The properties of the structural elements are summarized in Table 6. The analysis is classified as a “Class C” prediction according to the definition of Lambe (1973). The modeling involves the following limitations and assumptions: