Lateral displacement of soft ground under vacuum pressure and surcharge load

Abstract

Surcharge load (e.g. embankment fill) will induce settlement and outward lateral displacement, while vacuum pressure will induce settlement and inward lateral displacement of a ground. Ideally, combination of surcharge load and vacuum pressure can reduce or minimize the lateral displacement. Laboratory large scale model (length: 1.50 m, width: ~0.62 m, height: 0.85 m) tests and finite element analyses (FEA) were conducted to investigate the main influencing factors on lateral displacement of a soft clayey ground under the combination of vacuum pressure and surcharge load. For the conditions investigated, the results indicate that the outward lateral displacement increases with the increase of the ratio of surcharge load to vacuum pressure (RL) and the loading rate of the surcharge load (LR). Also, it is shown that for a given RL and LR condition, lateral displacement reduces with the increase of the initial undrained shear strength (S_u) of the ground. To predict the lateral displacement of a ground under the combination of surcharge load and vacuum pressure, the loading conditions in terms of RL and LR, and S_u value of the ground have to be considered.

Keywords

vacuum consolidation / lateral displacement / PVD / finite element analysis / surcharge load

Introduction

Preloading soft clayey deposit by surcharge load (e.g. embankment fill), vacuum pressure or combination of the both with prefabricated vertical drain (PVD) is a commonly utilized soft ground improvement method. Vacuum pressure results in settlement and inward (toward the center of the loading area) lateral displacement of a ground and causes cracks adjacent to the treated area, while surcharge load results in settlement and outward (away from the loading area) lateral displacement of a ground [1-4]. In an urban environment, controlling or minimizing the geotechnical engineering activity induced lateral displacement of a ground is important, sometimes may be a crucial design consideration. Conceptually, it is possible to minimize the lateral ground displacement by combining surcharge load with vacuum pressure. However, there is no theoretical solution or laboratory and/ or field test results to quantify the effect of the load ratio of surcharge load to vacuum pressure and the rate of the surcharge load on the amount of lateral displacement of a ground.

In this study, laboratory large scale model (length: 1.50 m, width: ~0.62 m, height: 0.85 m) tests and finite element analyses (FEA) were conducted to investigate the characteristics of lateral displacement of soft ground under the combination of vacuum pressure and surcharge load. The laboratory test results are presented first, followed by the FEA results of simulating the model tests as well as parametric study. From the test and FEA results, the main factors influencing the lateral displacement were identified.

Laboratory model tests

Equipment and the materials used

The model test set-up is illustrated in Fig. 1. The inner dimensions of the model box are: 1.50 m in length, about 0.62 m in width and 0.85 m in height. The model box is made of steel except the front and the back face walls which are made of transparent acrylic glass. A 15 mm thick acrylic glass plate was fixed in the middle of the box (along the longitudinal direction of the model) to create 2 independent model grounds each with a width of about 0.30 m.

The surcharge loading system consists of 3 Bellofram cylinders and 3 steel loading plates (length: 0.29 m, width: 0.166 m, thickness: 0.02 m). To simulate the embankment load, the load applied on the two side loading plates was half of the value on the center one. The technique adopted for applying vacuum pressure is called vacuum-drain method [5,6], which applies vacuum pressure to each prefabricated vertical drain (PVD) and using a surface clayey soil layer as the air-sealing layer. During the test, 3 settlement gauges were set on the steel loading plates to measure the settlements and 2 piezometers, P₁ and P₂ (Fig. 1(a)), were installed in the model ground to monitor the excess pore water pressure variations. In addition, a filter paper grid with spacing of 0.02 m × 0.02 m (openings of 0.01 m × 0.01 m) was attached to the inner face of the transparent acrylic glass side wall by grease to monitor the lateral deformation of the model ground.

Mini-PVDs were installed into the model ground to accelerate the rate of consolidation. The mini-PVD used in the test was made of non-woven geotextile with a cross section of 0.03 m × 0.015 m. The mini-PVD with a rubber cap and 6 mm diameter geosynthetic tube on the top of the rubber cap is designated as mini capped prefabricated vertical drain (mini-CPVD). The geosynthetic tubes of mini-CPVDs were connected together by plastic T-couplings, and then to a vacuum generation system. The soil used was the remolded Ariake clay with liquid limit, w_l = 112.4%, plastic limit, w_p = 56.7%, compression index, C_c = 0.762, and the coefficient of consolidation, c_v = 0.003 m²/day (corresponding to the load increment of 80 – 160 kPa).

Test procedures

Pre-consolidation

To set-up the model test, first 3 layers of non-woven geotextiles (thickness: 3 mm; weight: 130 g/m²) were placed at the bottom of the model as a drainage layer. Next, filter paper grids for measuring the lateral displacement were attached to the transparent acrylic glass walls. Then, the remolded Ariake clay with a water content of about 150% was placed into the model layer by layer. The piezometers, P₁ and P₂ were installed at 0.50 m and 0.25 m from the bottom of the model ground, respectively. After the thickness of the model ground reached about 0.80 m, 3 layers of geotextiles were placed on the top of the model ground as the top drainage layer. The model ground was pre-consolidated under 10 kPa pressure from dead load under two-way drainage condition for about 60 days. Then, the load was removed and 2 independent model grounds (width: 0.30 m, thickness: ~0.65 m) were created. Before installing the mini-CPVD, vane shear test was conducted to determine the initial undrained shear strength (S_u) of the model ground. A custom-made vane shear apparatus was utilized to measure the S_u value of the model ground. The vane shear apparatus consists of manual-drive rotary handle, 1 m length steel rod, 20 mm in diameter and 40 mm in height steel vane. The apparatus was connected to a data logger for monitoring the torque throughout the tests. The apparatus was made in such a way that when rotating in anti-clockwise direction, only the rod is rotating and when rotating in clockwise direction, both the rod and the vane are rotating. Therefore, during the test, the effect of the friction resistance between the rod and the soil can be eliminated.

Installation of mini-CPVD

The mini-CPVD was pushed into the model ground by a stainless steel rod. After the mini-CPVD reached the desired depth, the steel rod was withdrawn and the mini-CPVD was left in the model ground. The mini-CPVD was installed in such a way that there was a layer of about 0.1 m in thickness at the bottom and at the surface of the model ground, respectively, without mini-CPVD. Six (6) mini-CPVDs were installed in a rectangular pattern with 0.16 m × 0.10 m spacings as shown in Fig. 1 (b). To avoid air leakage through the holes at near the surface of the model ground created during the installation, the holes were sealed with the slurry of Ariake clay and bentonite mixture. This mixture was put into the hole around the drainage tube above the cap of the mini-CPVD, which may reduce the permeability of the soil around the tube but not influence the permeability of the soil around permeable part of the mini-CPVD. Therefore, we consider that the effect of the mixture to the rate of the consolidation of the system should be very limited.

Cases tested

The tested cases and the loading conditions adopted are listed in Table 1. In the table, RL means the designed ratio of surcharge load to applied vacuum pressure. Due to the partial leakage of the vacuum pressure during the tests, the measured vacuum pressures were less than the designed ones, and RL_m means the ratio of the applied surcharge load to the final measured vacuum pressure.

For all cases, -40 kPa to -60 kPa vacuum pressure was applied within 2 h. For the surcharge load, basically the loading rates of 6 kPa/day (central loading plate) for case-1 to 4 and 12 kPa/day (central loading plate) for case-5 were adopted. However, for case-1, 3 and 5, 4 kPa of surcharge load was applied on the center loading plate (2 kPa on the both side loading plates) in the first day.

Typical model test results

Initial S_u values of the model ground

Figure 2 presents the variations of initial S_u values with depth for case-3, 4 and 5 (S_u values for case-1 and 2 were not measured). Most of the S_u values are within the range of about 3.5 to about 6.0 kPa. The simulated S_u values in FEA are also indicated in the figure.

Settlements

The surface settlement curves at the center of case-1 and case-2 are shown in Figs. 3(a) and 3(b), respectively. For case-1, the surface settlement was almost constant from about 7 to 15 days of the elapsed time. The reason is that the stroke of the loading piston reached the limit and failed to notice it in an early time. For both cases, with identical surcharge loading rate (LR), the rate of settlement is similar. However, case-2 had a larger final surface settlement because of larger value of the applied surcharge load.

Variations of excess pore water pressure (u)

The variations of excess pore water pressures (u) for case-1 and case-2 are presented in Figs. 4(a) and (b), respectively. The final measured average u value of P₁ and P₂ were about -32 kPa and -28 kPa for case-1 and case-2, respectively. For case-2, vacuum pressure leakage occurred at about 7 days of elapsed time (Fig. 4(b)).

Lateral displacement

Figures 5(a) and 5(b) present the measured final lateral displacement profiles under the edge of the side loading plates for case-1 and case-2, respectively. The values of RL_m are indicated in the figures also. Although the measurements were not symmetric (especially for case-1), generally the lateral displacement increases with the increase of RL_m value. For all tested cases, Case-2 had the largest RL_m (surcharge load/measured vacuum pressure) value and resulted in largest maximum outward lateral displacement of about 17 mm.

Finite element analyses (FEA)

Model and parameters

Since the model test can only be conducted for limited cases, two-dimensional (2D) plane strain finite element analyses (FEA) were adopted for further investigation of the main influencing factors on the lateral displacement. First, the laboratory model tests were simulated to validate the numerical technique and then parametric study was carried out under the model test condition. The program used is a modified form of the original CRISP program [7]. The finite element mesh and the boundary conditions are shown in Fig. 6. At the bottom of the model, the displacements were fixed in both the vertical and the horizontal directions; while at the left and right boundaries of the model, the horizontal displacement was fixed and the vertical movement was allowed. For the drainage boundary conditions, both the top and the bottom of the model were permeable while the left and the right boundaries were impermeable. The effect of the mini-CPVD was modeled by the one-dimensional (1D) plane strain drainage elements [8]. In simulating the model test, the measured variations of the vacuum pressure were simulated closely.

The behavior of the model ground was simulated by modified Cam clay model [9] and the steel loading plates were treated as elastic material. The adopted model parameters are listed in Table 2. The hydraulic conductivities listed in Table 2 were initial values, and during the consolidation, they were allowed to vary with void ratio (e) according to Taylor’s equation [10]:

k=k_0{10}^{\left(e-e_0\right)/C_k}, (1)

where k₀ = initial hydraulic conductivity, e₀ = initial void ratio, and the value of the constant C_k was adopted as 0.4 e₀. The adopted values of the parameters related to the mini-CPVD performance were: unit cell diameter D_e = 0.143 m, diameter of drain d_w = 0.024 m, and discharge capacity q_w = 1 m³/year. The q_w value was determined by referring the back-calculated value of a similar mini-CPVD as reported by Chai et al. [11]. No smear effect was considered.

The initial stress state and the size of the initial yield locus adopted are listed in Table 3. To set up the initial stresses, 4 kPa isotropic effective stresses (balanced by distributed surface load) were added to the gravity stresses. By doing so, a proper initial stiffness and undrained shear strength of the model ground can be simulated. For the constitutive model used, the stiffness is linearly proportional to the mean effective stress (p′) and if only using the gravity stresses, the initial stiffness of the model ground, especially the surface layer will be too low. Physically, this 4 kPa stress can be considered as physical-chemical forces between clay particles. Since the applied maximum consolidation pressure was 10 kPa, and also by comparing the simulated S_u values with the measured ones. In FEA, a maximum consolidation pressure in the vertical direction of 14 kPa was adopted, which can be interpreted as 10 kPa+ 4 kPa (initial stress). With an initial coefficient of earth pressure of 0.5, the resulting size of yield loci are listed in Table 3, and the comparison of simulated S_u and the measured values of the model ground are shown in Fig. 2.

Simulating the laboratory model test

The simulated surface settlement curves at the center of the model ground for case-1 and case-2 are shown in Figs. 3(a) and (b), respectively. Although the simulated rates of settlement during the loading period are slightly lower than the measured values, generally it is considered that FEA yielded acceptable surface settlement curves. For both cases, the variations of excess pore water pressure were simulated closely as compared in Figs. 4(a) and (b).

As for the lateral displacement, for case-1 (Fig. 5(a)), the FEA yielded a good agreement with the measured values at the left side of the model, but there are differences with the measured results at the right side. For case-2 (Fig. 5(b)), the simulation under-predicted the lateral displacement of the surface layer (about 100 mm thick) and over-predicted the values for the depth below it. Quantitatively, the agreement between the measured and simulated lateral displacement is poor, but both of the test and FEA results indicate that the lateral displacement increases with the increase of RL_m value. Also considering the difficulties involved in measuring the lateral displacement in the model tests (by paper grids), it is considered that FEA can be used to investigate the main influencing factors on the lateral displacement.

Numerical investigation

Effect of RL

Since the conditions investigated by the laboratory tests are limited, further investigations were carried out numerically. In this series FEA, vacuum pressure of -40 kPa and surcharge loading rate of 6 kPa/day were fixed and the magnitude of the surcharge load was varied from 20 kPa to 80 kPa (RL = 0.5 – 2.0). In this series of FEA, the model ground has an initial S_u of about 4.6 kPa. The simulated surface settlement curves at the center of the model ground are presented in Fig. 7. Since the vacuum pressure was fixed, increasing RL means increasing the total load, and as a result the final surface settlement increases with the increase of RL. The simulated final lateral displacement profiles are compared in Fig. 8. The vacuum pressure was applied at 0.1 m depth from the surface, and an obvious reduction of the lateral displacement occurred at that depth. The maximum lateral displacement varied from about 1.8 mm inward for RL = 0.5 to about 5.2 mm outward for RL = 2.0. Using the ratio between the maximum lateral displacement and the final surface settlement, for RL = 0.5, this ratio is about -4.0% and for RL = 2.0, the ratio is about 5.6%.

Effect of LR

In this series of numerical simulation, vacuum pressure of -40 kPa, surcharge load of 53.2 kPa (resulting RL value of about 1.33) and initial S_u value of 4.6 kPa of the model ground were adopted. However, the surcharge loading rate (LR) was varied from 3 kPa/day to 12 kPa/day on the center loading plate. Figure 9 presents the simulated surface settlement curves at the center of the ground. With the increase of LR, there is a slight increment of final surface settlement which is considered due to the increase of lateral displacement of the ground as shown in Fig. 10. It can be observed that the inward lateral displacement occurred when LR = 3 kPa/day, while outward lateral displacement occurred when LR≥6 kPa/day. Larger LR value means the model ground behaves closer to undrained condition and subsequently, larger shear stress induced lateral displacement will occur. The ratio between the maximum lateral displacement and the final surface settlement increased from about -2.2% to about 4.5% for LR from 3 kPa/day to 12 kPa/day.

Effect of the initial undrained shear strength (S_u) of the ground

In these simulations, vacuum pressure of -40 kPa, surcharge load of 53.2 kPa (RL = 1.33), and surcharge loading rate of 6 kPa/day were adopted. The initial undrained shear strength (S_u) of the ground was varied from about 1.3 kPa to about 8.6 kPa by varying the initial yield locus (p′_y) of the ground from about 4 kPa to about 32 kPa. Figure 11 presents the simulated surface settlement curves at the center of the ground. With the increase of S_u of the ground, the settlement rate and the final surface settlement are decreased. The simulated lateral displacement profiles are shown in Fig. 12. The maximum lateral displacement varied from about 1.3 mm outward for S_u of about 8.6 kPa to about 7.4 mm outward for S_u of about 1.3 kPa. The ratio between the maximum lateral displacement and the final surface settlement increased from about 3.0% to about 6.1%. These results clearly show that for given RL and LR values, the ratio between the lateral displacement and the final surface settlement are also influenced by the initial S_u value of the ground.

Main influencing factors on lateral displacement

Preloading soft clayey ground by the combination of surcharge load and vacuum pressure may result in three possible lateral displacement patterns. 1) Outward, 2) inward and 3) inward near the ground surface and outward below it. Obviously, adopting either maximum outward or maximum inward lateral displacement cannot give a complete picture of the situation 3). Therefore, a parameter of average lateral displacement, δ_av is introduced and defined as follows:

{\delta }_{av}=\frac{A_1+A_2}{H_L}. (2)

The meaning of A₁, A₂ and H_L are illustrated in Fig. 13. A₁ and A₂ are defined as the area enclosed by the horizontal and vertical axes through the toe of an embankment and the curve of the lateral displacement under the toe. Negative values shall be adopted for inward lateral displacement. H_L is the thickness of improved zone from the ground surface to the end of PVD improvement.

The amount of lateral displacement of a soil deposit depends not only on the loading condition, but also the compressibility of the deposit. To obtain a general trend, it is proposed to use a dimensionless parameter, normalized lateral displacement, DR to investigate the main influencing factors on lateral displacement. DR is defined as:

(3)DR=\frac{{\delta }_{av}}{S_{\text{f}}},

where S_f is the final surface settlement of the ground under the center of the loading area.

Figure 14 presents the results of model test and FEA in form of RL (RL_m) versus DR under the conditions of LR = 6 kPa/day and initial S_u = 4.6 kPa. Although the data from the model tests are scattered, both the test and FEA results indicate a general trend that the DR increases with the increase of RL (RL_m). For the conditions investigated, DR is close to zero for RL (RL_m) of about 0.8. Except two scattered points of the model test, DR is almost linearly increased with the increase of RL (RL_m) as indicated by a dash line in the figure.

Figure 15 presents the relationship of LR versus DR under the conditions of RL (RL_m) = 1.33 and S_u = 4.6 kPa. Both the results of laboratory test and FEA indicate that DR increases with the increase of LR. For the model test case-4, the result of FEA agrees well with the measured value at the left side of the model. However, the difference between the results of the laboratory test and FEA increased with LR. It is considered that for case-5 with LR of 12 kPa/day, the model ground might close to failure condition and may be the FEA failed to simulate the ground deformations at close to the failure state. It is considered that further investigation is needed for this aspect.

It is known that the ratio between the lateral displacement and the surface settlement of a ground is a function of the factor of safety (FS) of the system [12]. For a given RL and LR values, FS is directly proportional to the undrained shear strength (S_u) of a ground. The relationship of initial S_u versus DR under the conditions of RL (RL_m) = 1.33 and LR = 6 kPa/day is presented in Fig. 16. The results of FEA show that the DR nonlinearly decreases with the increase of S_u. This can be explained as increasing S_u reduces the undrained shear deformation of the ground due to the surcharge load.

From the above discussions, it can be seen that for given ground conditions, the dimensionless parameter, DR, which is defined as the average lateral displacement divided by the final surface settlement, is a function of the ratio of surcharge load to vacuum pressure (RL), the rate of surcharge loading (LR), and the initial undrained shear strength (S_u) of the ground. Therefore, to predict the lateral displacement of a ground induced by the combination of vacuum pressure and surcharge load, all these factors should be considered.

Conclusions

Considering the deformation characteristics of vacuum consolidation and surcharge load (e.g. embankment fill) induced consolidation of a ground, conceptually, it is possible to reduce or minimize the lateral displacement of a ground by the combination of vacuum pressure and surcharge load. Five large scale model (1.50 m × 0.62 m × 0.85 m) tests and finite element analyses (FEA) were conducted to investigate the characteristics of lateral displacement of a soft clayey ground under the combination of vacuum pressure and surcharge load. Based on the test and numerical results, it has been identified that the main factors influencing the lateral displacement of a ground are: a) ratio between surcharge load and vacuum pressure (RL); b) rate of surcharge loading (LR); and c) initial undrained shear strength (S_u) of the ground. Denote the average lateral displacement (within the depth of prefabricated vertical drain (PVD) improvement) divided by the surface settlement at the center of the loading area as DR, the detailed conclusions regarding the effect of RL, LR, and S_u are as follows:

1) Effect of RL: For the conditions considered, DR almost linearly increases with the increase of RL and DR is close to zero for RL of about 0.8.

2) Effect of LR: DR increases with the increase of LR. However, since the data are scattered, further investigation is required for this factor.

3) Effect of S_u: For given RL and LR values, DR nonlinearly decreases with the increase of S_u.

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