Flexible Temporary Shield in Soft and Sensitive Clay: 3D FE Modelling of Experimental Field Test

A ﬁ nite-element (FE) numerical study using PLAXIS-3D software was carried out to reproduce and validate a full-scale experimental in situ test and to investigate the earth pressure on a ﬂ exible temporary trench box shield in soft and sensitive clay soil. The excavation trench model was 6m (20 ft) deep and was considered as nonlinear and anisotropic clay. A 45kPa (0.94 ksf) surface overload on top of the soil near the trench box was also simulated to produce a maximum load case on the ﬂ exible wall of the shield. Both Mohr-Coulomb (MC) and hardening soil (HS) constitutive soil models were considered for FE analysis. Di ﬀ erent values of the modulus reduction factor (MRF) and the coe ﬃ cient of earth pressure at rest ( K 0 ) were considered to validate the model. For a speci ﬁ c shear strength pro ﬁ le, FE analysis with a linear elastoplastic soil model showed relatively small di ﬀ erences in soil pressure with the ﬁ eld test results along the depth of the trench. Results were also compared with the predictions of well-established analytical formulae.


Introduction
Over the past decades, various analytical studies have been carried out to improve our understanding of the behavior of braced excavation protection systems [1]. As a protection system, the trench box shield is different from other braced systems because, instead of shoring up or otherwise supporting the trench face, it primarily aims to protect workers from cave-ins or similar incidents. Shields shall not be subjected to loads exceeding those that the system can withstand [2]. The earth pressure distribution on a shield depends on the type of soil, the shoring, and the method of installation. Generally, no satisfactory consensual theoretical solutions are available to estimate soil pressure for this type of supporting structure with partitions facing land pressures in sensitive clay [3]. Many researchers have suggested theoretical solutions to estimate earth pressure on a flexible temporary support ( [4][5][6]). Consequently, for an excavation shield, the Canadian Foundation Engineering Manual [4] recommends the use of pressure envelopes from empirical formulae.
Our understanding of the behavior of excavations and trenches with flexible retaining walls has evolved significantly in recent years with the help of numerical FE and analytical methods. Using FE analyses, Goldberg-Zoino, and Associates, Inc [5] found that under a given set of soil conditions, the higher the wall rigidity, the greater was the apparent earth pressure. A study by Hashash and Whittle [7] on shoring excavations in clay has shown that the evolution of lateral thrust on a retaining structure (or wall) is a complex function of the flexibility of the retaining structure and the magnitude of shear deformations at depth. Their analyses also revealed the development of an arching effect in the ground in contact with the shoring. Karlsrud and Andresen [1] concluded that the development of earth pressure on supporting structures set up in sensitive clays is a complex function that depends on the flexibility of the support, the anisotropy property, the thickness of the clay layer in the trench bottom, and deformations in the clay layer. Lam [8] showed that a mobilized strength design database can be used to investigate the relationship between structural response ratio and soil-structure stiffness ratio and to capture the range of wall stiffnesses between sheet piles and thick diaphragm walls. Bryson and Zapata-Medina [9] FE work clearly showed the influence of horizontal and vertical strut spacing, wall stiffness, and relative stiffness ratio on lateral wall deformation in an excavation support system (ESS) in three types of clays. However, their work focused on 12 m deep trenches, and a research gap has been observed for trench box shoring at shallower depths of less than 6 m and for soil-structure interaction (SSI) considerations [10]. It may be worth noting that trenches of less than 6 m are very common in practice and particularly in soft and sensitive clay. Therefore, there is a need to study the interaction between the soft and sensitive soil mass and the support, the flexibility in the development of lateral loads, and the movement of structural elements for shallow trench box shoring. This paper presents the details of an FE model and of simulations using the PLAXIS-3D software [11] to simulate a flexible temporary shield in soft and sensitive clay, with particular emphasis on the Mohr-Coulomb (MC) versus hardening soil (HS) constitutive laws used for the soil layers, the structure and the soil-structure interaction, the sequence of excavation, and the installation of the temporary flexible shield walls. The impact of the shear strength of a specific type of soft and sensitive clay on earth pressures will be studied. The results will also be compared to theoretical and experimental field test results.

Finite-Element Analyses
Numerical analyses of the performance of an excavation support system for most recent deep excavation case histories    Modelling and Simulation in Engineering have required three-dimensional FE analyses [12]. In addition, Ou et al. [13] have shown that the complex soilstructure interactions of excavation support systems and excavation-induced ground movements are threedimensional (3D) in nature. To perform this 3D FE analysis (FEA) and obtain a better understanding of these complex soil-structure interactions, the PLAXIS-3D software was used. Analysis output (soil pressure) was com-pared with field test results obtained for Louiseville, Quebec, Canada [14].

Parameters for FE
To simulate the trench with the excavation protection shield, three types of parameters were used in PLAXIS-3D: (i) soil model parameters for the excavation and surrounding soil,  3.1. Soil Modelling. The boundaries of the finite-element models were extended beyond the settlement zone of influence induced by the excavation, as determined in accordance with procedures recommended by Hsieh and Ou [15]. To simulate the trench, a soil model geometry such as soil contour ½7:5 m ð25 ftÞ × 12 m ð40 ftÞ × 15 m ð50 ftÞ was assumed, which was more than twice the excavation contour ½3 m ð10 ftÞ × 1:5 m ð5 ftÞ × 6 m ð20 ftÞ. The Louiseville soil layers were modelled using three depths and properties: (i) 0 m to 0.6 m (2 ft) of depth of soil as fissured brown clay, (ii) 0.6 m (2 ft) to 2 m (6.56 ft) depth of soil as plastic brown clay, and (iii) 2 m (6.56 ft) to 15 m (50 ft) depth of soil as sensitive blue clay in accordance with the stratigraphic profile of the Louiseville soil. Soil properties, especially strength, required careful attention because they are a key factor in the overall performance of the excavation support system (ESS) [16]. Supporting this statement, the in situ value of soil shear strength in Louiseville shown in Figure 1(a) was used in this FEA. The soil contour with the trench model is shown in Figure 1(b).

Structural Modelling.
Bryson and Zapata-Medina [9] indicated that the stiffness of an excavation support system (ESS) is a complex function of the flexural rigidity of the wall element, the structural stiffness of the support elements, the type of connections between the wall and the supports, and the vertical and horizontal spacing of the support system. Therefore, the two trench steel shields "stacked upon each other" to cover the total depth (6 m (20 ft)) of excavation were simulated according to the geometrical dimensions shown in Figure 2 and Table 1. The positions and locations of the struts used for simulation are shown in Figure 3.
Other parameters such as plate and strut mechanical properties are presented in Table 1. The Young's modulus (E), shear modulus (G), and Poisson's ratio (ν) of 4.76 mm (3/16 in) thick A-572 grade 50 steel plate were assumed. Plate unit weight (γ) was calculated from the total weight of the shield, and an equivalent 100 mm (4 in) thick sandwich plate was considered as per PLAXIS-3D input. For the struts (or spreader tube), Young's modulus (E) and unit weight (γ) were taken from the 200 mm strut SCH80 chart. Crosssectional area (A) and moment of inertia (I) were calculated from the original strut diameter. The vertical positions of the struts were made different on both sides to allow the excavator to access the soil to be excavated between the two walls of the shield.
In the PLAXIS-3D simulation, the box shield steel builtin plate walls (sandwich plate as per PLAXIS-3D) are modelled as "plate elements" and the struts as "beam elements." Four-cornered "hinge joints" were used between the two box shields (stacked upon each other) to represent the experimental setup shown in Figures 4 and 5. Similarly, the joints between the struts and the plates were simulated as "hinge joints" and were representative of the experimental setup illustrated in Figures 4 and 6. Note that the bottom end part of the shield (around 300 mm) was embedded into the soil and that the total gravity load of the upper steel box was Hinge joint between plate and strut (see Figure 6 in the experimental setup) Hinge joint between two plates (see Figure  5 in the experimental setup) pushing the lower box shield into the ground during installation of the experiment. Therefore, the bottom part (around 300 mm) of the lower box acted more likely as a "fixed end support" in the experiment and was represented by a "fixed end anchored element," as illustrated in Figure 4.
To analyze the nonlinear stress-strain behavior of the soil model in the trench and the soil surrounding the excavation, two constitutive material models, (a) Mohr-Coulomb (MC) and (b) hardening soil (HS), were used in this study.

Generating the Mohr-Coulomb (MC)
Model. The MC model is a simple and widely used linear elastic perfectly plastic model. The linear elastic part of the Mohr-Coulomb model is based on Hooke's law of isotropic elasticity, and the perfectly plastic part is based on the MC failure criterion [11]. For a first approximation to see the behavior in general, the MC model was chosen. Table 2 shows the soil parameters for the Mohr-Coulomb (MC) model used for finite-element modelling of the Louiseville sensitive clay. The soil stiffness moduli (E) at different depths were calculated from the shear strength (C u ) in the Louiseville soil test results using the equation proposed by Peck [17]: Table 3 presents the average values of E (E avg: ) for PLAXIS-3D input. In the soil model, the stress-strain relationship depends on the soil skeleton. The soil response is influenced by pore pressure. This water-skeleton interaction was considered as a plastic calculation using a PLAXIS-3D drainage-type parameter. For the 0.6 m layer of fissured brown clay, "drained" behavior was assumed, and therefore, in this layer, no excess pore pressure was generated, and full drainage was assumed due to the low rate of loading. On the Hinge joint between plate and strut Struts S h ie ld p la t e S h ie ld p la te Figure 6: Experimental hinge joint between plate and strut of box shield.  Table 3 See Table 3 See Table 3 Cohesion Frictional angle Ǿ (°(degree)) 28 28

Modelling and Simulation in Engineering
other hand, in the saturated soil layer, pore water cannot freely flow through the soil skeleton (due to low permeability) [11]. This phenomenon is described by PLAXIS-3D as an undrained behavior for brown clay and sensitive blue clay. To make sure that the soil skeleton is much more compressible than the pore water, the effective Poisson's ratio should be less than 0.35 for the undrained (B) condition [11]. For practical reasons, the undrained (B) option was chosen because this method allows the Louiseville shear strengths (S u ) to be used as input parameters in PLAXIS-3D. This does not hold true in the undrained (A) condition, where shear strength (S u ) is rather a consequence of the model, not an input parameter. On the other hand, the undrained (C) condition was not considered because, although the shear strength parameter (S u ) is an input parameter, it cannot provide a prediction of pore pressure. The undrained (C) method is not suitable for consolidation analysis [11].

Interface Model.
Interfaces were added as a joint element to the plates for proper modelling of soil-structure interaction. They represent a thin zone of intensely shearing material at the contact between a plate and the surrounding soil. Positive and negative interfaces were added (local z-direction) on either side of a plate surface (Figure 7). The interface properties included material mode, permeability condition, and virtual thickness factor. The interaction between the steel plate wall and the soil was expressed by a suitable strength reduction factor (R inter ). This factor relates the interface strength (wall friction and adhesion) to the soil strength (friction angle and cohesion). Recommended values for R inter are as follows: 2/3 for fissured brown clay and <2/3 for plastic brown and sensitive blue soft clay [11] ( Table 2). The interface was assigned an imaginary dimension called the virtual thickness. In the MC and HS models, the virtual thickness of the interface element varied with mesh type and ranged between 103 × 10 −3 m and 154 × 10 −3 m. The interface element consisted of pairs of nodes compatible with a sixnode triangular side of a soil element or a plate element [11].
3.5. Water Head Variations. Water pressure has a direct effect on strength of soils, on pressure against the wall, and on uplift of soil in the bottom of the excavation. Many situations are not hydrostatic before the work starts but change during the work. These conditions can be modelled in FEA [16]. For the variation in water head, the piezometer readings obtained for different months and presented in Table 4 were used separately for the water table height to obtain the maximum soil stress on the protection shield wall.   Modelling and Simulation in Engineering 3.6. Mesh Generation. A medium-coarse 10-node element was used for each of the simulation and connectivity plot elements shown in Figure 8. This mesh generation process considers the soil, all the structural components, loads, and boundary conditions. As a result of meshing, a total number of elements of 24,271, i.e., 23,221 soil elements and 1,050 structural elements, was reached.

Construction Steps and Phases in PLAXIS-3D Simulation
Poulos et al. [18] showed that construction details and sequence, as well as soil-structure interaction, have a significant impact on the movements and lateral loads acting on a flexible retaining structure. Therefore, the construction steps constituted a major and critical part of this FE simulation. The model assigned a step-by-step excavation sequence including the structural elements inserted into the excavation. All the phases of the construction sequence are summarized in Table 5.

Construction
Step 0: Initial Phase. In the initial phase, only the natural (undisturbed) soil was considered. No excavation was made in this step, and only K 0 (the parameter to produce initial stress) was considered in the calculations. In general, K 0 values can be specified, K 0,x = σ xx ′ /σ zz ′ in the x -direction and K 0,y = σ yy ′ /σ zz ′ in the y-direction. The default K 0 values are defined by the Jaky [19] coefficient as follows: where φ is the frictional angle. A staged construction loading type was selected to generate the initial stresses. The initial stresses in a soil body are influenced by the weight of the soil, the water conditions, and the history of its formation. This stress state can be generated using either the K 0 procedure or gravity loading. The K 0 procedure should preferably be used in cases with a horizontal surface and with all soil and phreatic levels parallel to the surface [11], as in the case under consideration.

Construction
Step 1: Phase 1. In construction step 1, the first layer (0 m-0.6 m depth) of fissured brown clay was excavated, representing an excavation contour of ½3 m ð10 ftÞ × 1:5 m ð5 ftÞ × 0:6 m ð2 ftÞ. For this phase, the plastic calculation and the "drained" soil drainage type were selected, as shown in Figure 9(b). Therefore, the soil will behave as in a drained condition, unlike the clay below, which will behave as an undrained medium for shortterm analyses.

Construction
Step 2: Phase 2. In construction step 2, the second layer (0.6 m-2 m depth) of plastic brown clay was excavated, representing an excavation contour of ½3 m ð10 ft Þ × 1:5 m ð5 ftÞ × 2 m ð6:56 ftÞ, as shown in Figure 9(c). The    undrained B soil drainage type and the plastic calculation were assumed for this layer. In this undrained condition, assuming that no water was moving, long-and shortterm loading behavior was assessed [11], including built-up excess pore pressures. In the undrained (B) drainage type, modelling of undrained behavior using effective parameters for stiffness and undrained shear-strength parameters was allowed.   Modelling and Simulation in Engineering

Construction
Step 3: Phase 3. In this step, a structure consisting of two box-shield excavation protectors "stacked upon each other" ½3 m ð10 ftÞ × 1:5 m ð5 ftÞ × 6 m ð20 ftÞ (Figure 4) was inserted into the simulated excavation, as shown in Figure 9(d). The undrained B soil drainage type and the plastic calculation were assumed for this phase.

Construction
Step 4: Phase 4. In this construction step, 2 m to 6 m of sensitive blue clay soil was excavated, as shown in Figure 9(e). In addition, a 45 kPa (0.94 ksf) surface overload was applied on one side of the excavation in the PLAXIS-3D model to create an extreme load case, as shown in Figure 10. The undrained B soil drainage type and the plastic calculation were also selected for this phase.

Analysis Using Mohr-Coulomb (MC) Models and Results
The MC model represents a "first-order" approximation of soil and rock behavior [11]. For that reason, the MC constitutive model with soil parameters given in Table 2 was considered as a first simulation analysis. The obtained soil stresses are presented in Table 6 for different depths with and without overloading. These depths are representative of the experimental location of the pressure cells because the objective was to find the soil stress in the PLAXIS-3D simulation at the same locations as in the experimental setup. In Table 6, it is very clear that the effect of an overload applied close to the trench was more pronounced on the upper part of the protective shield than on the deeper part [20]. It follows that the pressures on the plate at 0.9 m and 2.4 m depths of the trench were more influenced by the 45 kPa (0.94 ksf) overload both in the MC simulation and in the experimental results. In contrast, it had a negligible effect on the deeper part of the plate.

MC Model with Modulus Reduction Factor (MRF).
Soft to medium clays may exhibit strength anisotropy, or in other words, their strength varies with the orientation of the failure surface [16]. Therefore, the results from the MC model must be verified using another approach. Relative shear stresses were considered, which yield an indication of the stress point to the failure envelope. The relative shear stresses ðrelative shear stress τ rel = ½mobilized shear stress ðτ mob Þ/maximum shear stress ðτ max ÞÞ at the end of phases 2 and 4 of the PLAXIS-3D MC model output are shown in Table 7. Based on the maximum value of relative shear stress, the mobilized shear strength ðτ mob Þ was then adopted from the modulus reduction vs. mobilized strength curve of undrained Thanet   [21] to estimate the modulus reduction factor (MRF). The MRF is the ratio of elastic modulus (E/E max ) or shear modulus (G/G max ). Thanet clay was considered because it is a soft undrained clay, much like the Louiseville clay. New E and G values were computed from the Kramer [22] equations (3) and (4) with the corresponding MRF values of the Mayne [21] curve for each soil layer up to 14 m depth, as shown in Table 7: Then, these values were used as a PLAXIS-3D input to run the model again and obtain the maximum soil pressures MC with MRF (with E (option C 1 ) and with G (option C 2 )).

Mohr-Coulomb Reduction Factor with Shear Strain.
In this method, the shear strains from the PLAXIS-3D output results of the MC model for each depth shown in Table 8 were assumed. The Vucetic and Dobry [23] curve (G/G max vs. cyclic shear strain (γ)) was used to find the corresponding modulus reduction factor (G/G max ). Note that the PI = 50 curve was used because the plasticity index (PI) of the Louiseville soil is 42 [24]. With the value of the modulus reduction factor, Equation (5) was used to calculate the shear modulus for Louiseville clay: Then, these values were input to the analysis to obtain the maximum soil pressures MC with MRF (for IP = 50 (option C 3 )).

Validation of the MC Model.
To validate the MC model, parameters such as K 0 and the pore pressure must be checked. In practice, K 0 for a normally consolidated soil is often assumed to be related to the friction angle by Jaky's empirical expression (Equation (2)). In an overconsolidated soil, K 0 would be expected to be larger than the value given by this expression. However, for the Mohr-Coulomb model, the default K 0 value is based on Jaky's formula. Hamouche et al. [25] evaluated the in situ coefficient of earth pressure at rest for Louiseville sensitive clay. Three values of K 0 (0.55, 1, and 1.5) from the profile were chosen to validate the MC model to take account of fluctuations in soil pressure with depth: (i) K 0 = 0:55 is the value computed from Jaky's formula with ϕ = 27°, which is a common friction angle for clays or gravity loading; (ii) K 0 = 1 represents the case for clay in undrained conditions only (when ϕ = 0); and (iii) K 0 = 1:5 represents the experimental profile at 6 m depth. Table 9 and Figure 11 show the soil pressures with different K 0 values after analysis using the M-C model.

Simulation Analysis Using the Hardening Soil (HS) Material Model
Using the same structural properties and soil layers, the HS model [26] was used to predict the constitutive behavior of the soils. Table 10 presents the soil properties used for HS simulation. Allen Marr and Hawkes [16] stated that for soft clay, the E 50 modulus varies between 2,500 kPa (52 ksf) and 15,000 kPa (313 ksf). For Chicago soft and undrained clay, E 50 was reported to be 2,350 kPa (49 ksf) [9]. Considering that Louiseville soft and sensitive clay is softer than Chicago clay, its E 50 modulus was therefore assumed equal to 2,000 kPa (42 ksf). For the undrained B in the HS model, the stiffness moduli in the model are no longer stress-dependent, and the model exhibits no compression hardening. Again, the undrained shear strength (S u ) for the Louiseville soil was an input parameter to the HS model. Soil pressures from the HS model (option A) along the trench depth are presented in Table 11.

Overall Results and Comparisons
The FEA results were compared to available theoretical predictions and results from the Louiseville experimental in situ test. Apparent earth pressure according to the Terzaghi and Peck [27] methods (TPM) and active earth pressure as developed by Rankine [28] and Yokel et al. [6] were also used to calculate theoretical soil pressures for Louiseville soft and sensitive clay. The results are summarized in Table 11 and Figure 12. Note that the experimental values are based on experimental field results for the period from 14 May to 10 August 2018. From Table 11 and Figure 12, the following comparative observations can be made: (

Modelling and Simulation in Engineering
in situ experimental test value. The reason for this may be that the elastic modulus (E 50 ) assumed in the HS model at 3.9 m depth was extremely close to the measured site value of 2,000 kPa (42 ksf). This brings out that the HS model may be a good option to compare soil pressure with experimental values in a trench box shield when the in situ shear strength of the soil must be assumed   12 Modelling and Simulation in Engineering The MC model offers some advantages because fewer input geotechnical parameters are required, yet the model yields acceptable results (compared to experimental values, except at 3.9 m depth) for the engineer when using common in situ geotechnical parameters such as shear strength. MRF methods explored in this study (options ½C 1 , ½C 2 , and ½C 3 ) failed to offer more accurate results than the direct use of in situ shear strength parameters and Peck's formula (1975) to estimate the elastic properties of the MC model (option ½B). Clearly, precise modelling of the sensitive clay excavation would require more advanced behavioral laws, such as HS, and the input parameters of those constitutive models should be finetuned and adjusted based on extensive experimental laboratory soil testing.
In this study, FE model results were compared with the in situ experimental earth pressure data for soft and sensitive clay only. Further work is needed to gather experimental soil pressure data in various types of soils and then compare it to FE simulations.

Conclusions
The FE simulations using the PLAXIS-3D software presented in this paper confirm the measurements of earth pressures on the steel cage-type temporary shield protection at shallow depth in a soft and sensitive clay trench. The study included simulation of two steel box shields stacked upon each other, using "hinge connections" to cover the total trench depth of 6 m (20 ft) in sensitive clay soil. Surface loads (representing a 45 kPa overload) located close to one side of the trench were simulated to produce a critical load case on the flexible wall of the shield. Two constitutive material models were used for the simulation analyses: (a) Mohr-Coulomb (MC) and (b) hardening soil (HS). Based on the FEA, the following conclusions can be drawn: 13 Modelling and Simulation in Engineering 5.4 m from the top of the trench for the option ½A and option ½C 3 models, respectively (ii) Option ½A of the HS model at 3.9 m trench depth yielded a pressure closer to the in situ experimental test value than options ½B, ½C 1 , ½C 2 , and ½C 3 of the MC model. This occurred because the elastic modulus (E 50 = 2,000 kPa) assumed in the HS model at that depth was extremely close to that on site (iii) Options ½C 1 , ½C 2 , and ½C 3 of the MC model with MRF results were comparable to those of option ½B of the MC model without MRF, showing thereby the key role played by the precise shear strength parameters (iv) Comparisons of theoretical predictions by Rankine [28], Terzaghi and Peck [27], and Yokel et al. [6] for this type of soft and sensitive clay with FEA results revealed that the pressures obtained using Rankine and Yokel analytical formulae were closer to the simulated and experimental values than those of Terzaghi and Peck. Along the depth of the trench, the analytical formulae underestimated soil pressure around 4 m depth for this type of sensitive clay

Data Availability
The data that support the findings of this study are available from the corresponding author upon reasonable request.

Conflicts of Interest
The authors declare that they have no conflicts of interest.