Time-dependent deviation of bridge pile foundations caused by adjacent large-area surcharge loads in soft soils and its preventive measures

Abstract

Time-dependent characteristics (TDCs) have been neglected in most previous studies investigating the deviation mechanisms of bridge pile foundations and evaluating the effectiveness of preventive measures. In this study, the stress-strain-time characteristics of soft soils were illustrated by consolidation-creep tests based on a typical engineering case. An extended Koppejan model was developed and then embedded in a finite element (FE) model via a user-material subroutine (UMAT). Based on the validated FE model, the time-dependent deformation mechanism of the pile foundation was revealed, and the preventive effect of applying micropiles and stress-release holes to control the deviation was investigated. The results show that the calculated maximum lateral displacement of the cap differs from the measured one by 6.5%, indicating that the derived extended Koppejan model reproduced the deviation process of the bridge cap-pile foundation with time. The additional load acting on the pile side caused by soil lateral deformation was mainly concentrated within the soft soil layer and increased with the increase in load duration. Compared with t = 3 d (where t is surcharge time), the maximum lateral additional pressure acting on Pile 2# increased by approximately 47.0% at t = 224 d. For bridge pile foundation deviation in deep soft soils, stress-release holes can provide better prevention compared to micropiles and are therefore recommended.

Graphical abstract

Keywords

bridge pile foundation / surcharge load / soft soil / time-dependent deformation / interaction mechanism / preventive measure

1 Introduction

To limit the post-construction settlements of high-speed railway (HSR) tracks, many HSR lines were built using the construction strategy of “bridge instead of embankment” when passing through special foundation soils, e.g., deep soft soils [1,2] or wet sink loess [3]. However, with the gradual densification of HSR lines, an increasing number of accidents involving lateral deviations of HSR bridge pile foundations occurred due to irregularities in construction, e.g., surcharges and excavations, especially in deep soft soil areas [4,5]. Numerous studies including theoretical analysis [6], laboratory tests [4,7,8], field tests [9,10], and numerical simulation [11–14] have shown that the adjacent surcharge (or lateral loading) induces considerable lateral movements of the soft soil, increasing the lateral additional load acting on the pile shaft. As a result, the pile foundation and bridge pier are laterally deflected together, resulting in frequent damage to the bridge pier superstructure, e.g., pier support damage caused by shear deformation (Fig.1(a)) or deviation of railway lines (Fig.1(b)), which significantly affects the safety of train operations.

The lateral deformation of soft soils induced by surcharge loads exhibits time-dependent characteristics (TDCs) dominated by primary consolidation [15] and secondary consolidation (i.e., creep deformation) [16–18]. To reveal the influence of soft soil lateral deformation on adjacent piles, many scholars have conducted studies from different points of interest. Hara et al. [19] proposed a two-dimensional finite element (FE) program incorporating the Cam-Clay model and Biot’s theory to study the time-dependent deformation of bridge abutments constructed on pile foundations, based on field prototype tests. Karim et al. [20] investigated the deformation behavior of adjacent piles over time using a numerical model embedded with the Modified Cam-Clay (MCC) model based on the Leneghans embankment project in Sydney. Similarly, Bian et al. [4] focused on the time-dependent response of monopiles and pile groups with variable pile lengths by using a numerical model, embedded with the MCC model, in combination with centrifugal tests. Considering the effects of the loading schedule and consolidation situation, Yang et al. [21] studied the effect of soft soil consolidation behavior on the pile response using a numerical model with the MCC model. Moreover, Wang et al. [8] investigated the time-dependent behavior of monopiles under surcharge loads using a hypoplastic clay model based on a series of centrifugal tests with different drainage conditions and pile lengths. Notably, however, the above studies considered only the effect of primary consolidation deformation on the pile response while ignoring the effect of creep deformation. For long-term surcharge loads, analysis of the effect of creep deformation better reflects the time-dependent behavior of piles in actual situations [20]. In addition, the mechanism of time-dependent interaction between the soft soil and pile was not revealed in detail, especially in terms of characterizing the time-dependent variation of lateral additional loads acting on the pile side.

Micropiles [22,23] and stress-release holes [24] are widely applied to prevent additional loads acting on the ground from disturbing buildings and pile foundations [25]. However, for the evaluation of the prevention effect of both types of measure, most previous studies [22–25] neglected the TDC of soil deformation under long-term loads (e.g., considering the soil as a time-independent elastic or elasto-plastic material), as emphasized above, resulting in a large discrepancy between the evaluation results and the actual application, especially in soft soils.

In this study, a typical engineering case of bridge pile foundation deviation induced by adjacent large-area surcharge loads in soft soils was introduced. A series of consolidation-creep tests were conducted to illustrate the stress–strain–time characteristics of the soft soil, and three typical consolidation-creep models were selected to fit the test results. By comparing two fit indices, i.e., the correlation index and the residual sum of squares, the one-dimensional Koppejan model was selected to characterize the time-dependent deformation of the soft soil, and then extended to a 3D FE model using a user-material subroutine (UMAT). Based on the validated FE model, the time-dependent behavior of the pile response and the interaction mechanism between the soft soil and pile were revealed. In addition, the preventive effect of applying micropiles and stress-release holes to prevent the time-dependent deflection of the pile was investigated.

2 Description of the case study of pile foundation deviation

The bridge studied in this paper belongs to a HSR in a soft soil area along the coast of China. After the completion of the construction of the bridge, large surcharges of soil accumulated in the adjacent area due to the industrial building construction (Fig.2). The maximum and minimum widths of the surcharge area were approximately 100.0 m and 50.0 m, respectively, and the thickness ranged from 2.0 to 4.0 m, with a trapezoidal distribution from Cap 651# to Cap 655#. The duration of the surcharge was approximately 224 d. Such a large-area surcharge triggered a considerable lateral deviation from Cap 651# to 655#, as shown in Fig.2. Through the field measurement, the maximum lateral displacement of Cap 653# reached 27.8 mm, the value of the pier top reached 14.6 mm, and the deviation development of Cap 653# is shown in Fig.3. (Here, some data were missing due to monitoring instruments not being installed on the pier-cap before the pile foundation deviation.) The lateral displacement increased gradually with increasing load duration, showing a significant TDC. It is worth noting that the pier top deviations of Piers 653# and 654# exceeded the deviation limit of 8.0 mm specified in the codes of China [26], EU [27], and Japan [28], and the pier-cap-pile foundation deviation posed a major threat to the safe operation of high-speed trains.

Taking Pier 653# as an example, the support structure of the girder consisted of a pier, a cap and a pile foundation, and their structural parameters are shown in Fig.4. The height of the pier was 16.5 m, and the length, width and thickness of the cap were 11.1, 7.9, and 3.0 m, respectively. The pile foundation was composed of 12 bored piles with a diameter of 1.0 m and a length of 60.5 m. To overcome the post-construction settlement of the bridge piers, the pile ends were located in the medium sand layer with greater strength and stiffness than the soft soil layer (Fig.4(b)). According to the geological survey, the foundation soil consisted of a silt layer, a muddy−silty clay layer, a silty clay layer, a fine round gravel layer and a medium sand layer. Mechanical properties of each soil layer obtained from laboratory tests including wet density tests, lateral limit compression tests, triaxial consolidation-drainage tests, and falling head permeability tests, etc. are shown in Tab.1. The authors tentatively concluded that the reason for the pier deviation was that the lateral movement of the soft soil caused by the surcharge load induced the pile foundation lateral deviation.

3 Material model for the time-dependent deformation of soft soils

Understanding the stress–strain–time properties of the soft soil is necessary to fully reveal the mechanism underlying the time-dependent lateral deviation of the pile foundation. In this study, a series of consolidation-creep tests were conducted to select a material model that fits the time-dependent deformation behavior of the soft soil.

3.1 One-dimensional consolidation-creep tests

According to the geotechnical test standard for soil sample dimensions [29], in situ soil samples of silt, muddy−silty clay and silty clay with thicknesses of 2 and 4 cm (Fig.5(a)) were selected for axial compression tests. Axial loads of 100, 200, 300, and 400 kPa were applied to each sample step by step, and the duration of each level of loading was 14 d. In these tests, when the height change of the samples was less than 0.01 mm in 24 h, the soil sample was considered to be in a stable creep stage [30]. After the sample was in this stage under a specific level of loading, the next level of loading was added. To minimize the effect of external disturbances on the in situ soil samples, e.g., human test operations or sample transport, each sample was pretreated with low-level loads of 25, 50, and 75 kPa for a short time before the consolidation-creep test.

Fig.5(b) shows the consolidation-creep test results for a typical silt sample. The sample deformed significantly within 1 d after loading, and then from Day 1 to Day 3, the strain rate gradually decreased; the strain rate stabilized after Day 4. The soft soil deformation showed significant time-dependent properties under different loading levels.

3.2 Comparison of consolidation-creep models

After a preliminary comparison, the Mesri model, Time-hardening model and one-dimensional Koppejan model were selected to describe the time-dependent deformation of the soft soil at the case site. The Mesri model is suitable for describing the creep properties of soils at arbitrary stress levels, and its expressions are given in Ref. [31]. The Time-hardening model is applicable to describe the time-dependent growth of strain in a constant stress state, and its expression is given in Ref. [32]. The one-dimensional Koppejan model [33] comprehensively considers the primary consolidation and secondary consolidation (i.e., creep stage), and is appropriate for describing the long-term deformation behavior of soft soils with large compressibility and sensitivity properties. The strain expression is:

(1){\epsilon }_{\mathrm{p}\mathrm{s}}=\left(\frac{1}{C_{\mathrm{p}}}+\frac{1}{C_{\mathrm{s}}}\lg t\right)\ln \frac{\sigma }{{\sigma }_0},

where C_{\mathrm{p}} is the primary consolidation coefficient, which can be obtained with the formula C_{\mathrm{p}}=\left(1+e_0\right)/C_{\mathrm{c}} (where e_0 is the initial void ratio and C_{\mathrm{c}} is the compression index); C_{\mathrm{s}} is the secondary consolidation coefficient, which can be obtained with the formula C_{\mathrm{s}}=\left(1+e_0\right)/C_{\mathrm{a}} (where C_{\mathrm{a}} is the secondary-consolidation index from the curve of e-\lg t); \sigma is the additional stress; and {\sigma }_0 is the initial stress.

To minimize the influence of disturbing factors (e.g., test operation error or sample randomization) on the determination of creep parameters and to maximize the use of consolidation-creep test results, the fitting method [34] was adopted to fit the creep models and the fitted curves of each model are shown in Fig.6(a). The comparison of the fit indices R² and R_s (where R² is the correlation coefficient, and R_s is the residual sum of squares) is shown in Fig.6(b). In the short-term after loading (i.e., t ≤ 2 d), the fitted curves of the three models differed from the test results to some extent, while in the long-term after loading (i.e., t > 2 d), the fitted curves of the three models were in good agreement with the test results.

More importantly, the R² values for the fitted curves of the one-dimensional Koppejan model were larger than those of the other two models, and the R_s values were less than those of the other two models, indicating that the one-dimensional Koppejan model fit the test results better. Furthermore, according to the expression (Eq. (1)), the one-dimensional Koppejan model comprehensively considers the primary consolidation effect and secondary consolidation effect and has high accuracy in describing the short-term and long-term deformation of soft soils. Therefore, the one-dimensional Koppejan model was selected to characterize the time-dependent deformation of the soft soil at this case site.

3.3 Extension of the one-dimensional Koppejan model

However, the one-dimensional Koppejan model adopted above is only applicable to describe axial deformation under axial loads and cannot reflect the time-dependent lateral deformation of soft soils under vertical surcharge loads. Therefore, it was necessary to extend it to the three-dimensional stress space. The authors extended the one-dimensional Koppejan model in the three-dimensional incremental form in their published study [10] and validated the extended Koppejan model using prototype test results. The detailed derivation of the extended Koppejan model can be found in Ref. [10]. The key steps in the derivation process are briefly described below.

First, the consolidation-creep strain increment \mathrm{\Delta }{\epsilon }_{\mathrm{p}\mathrm{s}} of the one-dimensional Koppejan model obtained from Eq. (1) is expressed as:

(2)\mathrm{\Delta }{\epsilon }_{\mathrm{p}\mathrm{s}}=\frac{1}{C_{\mathrm{p}}}\left(1+\frac{{\epsilon }_{\mathrm{s}\mathrm{e}}}{{\epsilon }_{\mathrm{p}\mathrm{r}}}\right)\frac{\mathrm{\Delta }\sigma }{\sigma }+{\epsilon }_{\mathrm{p}\mathrm{r}}\mathrm{\Delta }t\frac{C_{\mathrm{p}}}{C_{\mathrm{s}}\mathrm{l}\mathrm{n}10}\exp \left(-\frac{{\epsilon }_{\mathrm{s}\mathrm{e}}}{{\epsilon }_{\mathrm{p}\mathrm{r}}}\frac{C_{\mathrm{s}}}{C_{\mathrm{p}}}\mathrm{l}\mathrm{n}10\right),

where {\epsilon }_{\mathrm{p}\mathrm{r}} is the primary consolidation strain; {\epsilon }_{\mathrm{s}\mathrm{e}} is the secondary consolidation strain; \mathrm{\Delta }\sigma is the additional stress increment; and \mathrm{\Delta }t is the time increment.

Then, the one-dimensional strain increment \mathrm{\Delta }{\epsilon }_{\mathrm{p}\mathrm{s}} was transformed into the three-dimensional deviatoric strain increment, whose tensor form is:

(3)\mathrm{\Delta }{e}_{ij}^{\mathrm{p}\mathrm{s}}=\frac{1}{C_{\mathrm{p}}}\left(1+\frac{{\epsilon }_{ij}^{\mathrm{s}\mathrm{e}}}{{\epsilon }_{ij}^{\mathrm{p}\mathrm{r}}}\right)\frac{\mathrm{\Delta }{S}_{ij}}{S_{ij}}+{\epsilon }_{ij}^{\mathrm{p}\mathrm{r}}\mathrm{\Delta }t\frac{C_{\mathrm{p}}}{C_{\mathrm{s}}\mathrm{l}\mathrm{n}10}\exp \left(-\frac{{\epsilon }_{ij}^{\mathrm{s}\mathrm{e}}}{{\epsilon }_{ij}^{\mathrm{p}\mathrm{r}}}\frac{C_{\mathrm{s}}}{C_{\mathrm{p}}}\mathrm{l}\mathrm{n}10\right),

where i,j = 1,2,3; \mathrm{\Delta }{e}_{ij}^{\mathrm{p}\mathrm{s}} is the consolidation-creep deviatoric strain increment tensor; {\epsilon }_{ij}^{\mathrm{p}\mathrm{r}} and {\epsilon }_{ij}^{\mathrm{s}\mathrm{e}} represent the primary and secondary consolidation deviatoric strain tensors, respectively; \mathrm{\Delta }{S}_{ij} is the deviatoric stress increment tensor; and S_{ij} is the deviatoric stress tensor.

Finally, the three-dimensional expression for the consolidation-creep strain increment derived from the one-dimensional Koppejan model was obtained based on the principles of elastic-plastic mechanics:

(4)\begin{array}{rl}\mathrm{\Delta }{\epsilon }_{ij}=& \frac{1}{C_{\mathrm{p}}}\left(1+\frac{{\epsilon }_{ij}^{\mathrm{s}\mathrm{e}}}{{\epsilon }_{ij}^{\mathrm{p}\mathrm{r}}}\right)\frac{\mathrm{\Delta }{S}_{ij}}{S_{ij}}+{\epsilon }_{ij}^{\mathrm{p}\mathrm{r}}\mathrm{\Delta }t\frac{C_{\mathrm{p}}}{C_{\mathrm{s}}\mathrm{l}\mathrm{n}10}\exp \left(-\frac{{\epsilon }_{ij}^{\mathrm{s}\mathrm{e}}}{{\epsilon }_{ij}^{\mathrm{p}\mathrm{r}}}\frac{C_{\mathrm{s}}}{C_{\mathrm{p}}}\mathrm{l}\mathrm{n}10\right)\\ & +\frac{\left(1-2\mu \right)\mathrm{\Delta }{\sigma }_{\mathrm{A}}}{E}{\delta }_{ij},\end{array}

where \mathrm{\Delta }{\sigma }_{\mathrm{A}}={\displaystyle \frac{1}{3}}\left(\mathrm{\Delta }{\sigma }_{11}+\mathrm{\Delta }{\sigma }_{22}+\mathrm{\Delta }{\sigma }_{33}\right) which represents the average stress; E is the elastic modulus; μ is Poisson’s ratio; and {\delta }_{ij}=\{\begin{array}{ll}1,& i=j\\ 0,& i\ne j\end{array}.

4 Time-dependent mechanism of pile foundation deviation

4.1 Finite element modeling

To reveal the time-dependent mechanism of pile foundation deviation, a simplified FE model embedded with the extended Koppejan model was developed to fully characterize the time-dependent pile−soil interaction.

The geometric model was established using Abaqus software based on the structural dimensions and geological conditions in the above engineering case. Considering the most significant deviation of Pier 653# in this case, the FE model was established with Pier 653# as the research object. The full model is shown in Fig.7. The surcharge load was reduced to a surface load, applied at once to the adjacent ground surface with a distance of 4.5 m between the load and the cap. The FE mesh near Pier 653# was refined to obtain calculation results that were as accurate as possible, with a minimum grid width of approximately 0.09 m.

A series of contact elements with the pile surface as the master surface and the soil surface as the slave surface was established and attached to the interface between the pile foundation and soil. The “hard” contact model and the “penalty” model were selected to describe the normal and tangential behavior of the interface, respectively. The interaction behaviors between different structural surfaces and the soil under surcharge loads were different; thus, the tangential friction coefficients of the interfaces were also different. Here, the results of model tests and numerical back-analysis [8,35] were used to determine the tangential friction coefficient of the cap-soil interface, pile shaft-soil interface and pile bottom-soil interface with values of 0.19, 0.25, and 0.30, respectively.

A UMAT based on the extended Koppejan model developed above was written and embedded in the FE model to adequately reflect the time-dependent lateral deformation behavior of soft soils. In the UMAT, an array of six material properties, elastic modulus E, Poisson’s ratio \mu, primary consolidation coefficient C_p, secondary consolidation coefficient C_s, cohesion c and internal friction angle φ, were defined. In addition, the Drucker–Prager (D–P) yield criterion was employed to determine whether the soil element was in a plastic state. To simplify the calculation, the flow law associated with the D–P yield criterion was applied to calculate the plastic strain increment, i.e., the plastic potential function was equal to the yield function. The operation process of the UMAT is shown in Fig.8.

The upper soft soil layer (i.e., the silt layer, muddy−silty clay layer and silty clay layer) was considered the time-dependent deformation material and simulated with the extended Koppejan model and given consolidation properties described by C_p and C_s, and these were determined by a combination of the consolidation-creep tests described above and numerical back-analyses. The deep soil layer was considered an elasto-plastic material and simulated with the Mohr–Coulomb (M–C) yield criterion. The pier-cap-pile foundation structure was simulated as a linear elastic material. The material properties of each structural component (pier, cap, pile) and soil layer are shown in Tab.2.

4.2 Validation of the finite element model

The FE model was submitted to a process of validation with field measurements that were of major importance to assure the subsequent correct evaluation of pile responses under surcharge loads. Fig.9(a) shows a comparison of the calculated lateral displacement of the cap with the measured results. The calculated displacement increased with increasing load duration, and the development process was in good agreement with the field measurement. By 224 d, the calculated cap displacement was 29.6 mm, which was 6.5% different from the field measurement. To verify the short-term deformation behavior of the cap-pile foundation, the trend curve of the measured displacement was fitted and compared with the calculated results of the short-term displacement, as shown in Fig.9(a). The data point for the trend curve was obtained from the measured data and the data at the initial moment t = 0. The trend curve fitted the measured data quite well with a correlation coefficient of 0.989.

When t = 3 d, the difference between the calculated results and measured values was 31.5%, while when t = 30 d, the difference was 16.6%, indicating that the calculated displacement of the cap was overall close to the field measurement. It is worth noting that the numerical model simulated the surcharge load under rapid construction conditions and simplified the surcharge load to a uniformly distributed ground surface load (where the surface load intensity was equal to the actual final surcharge load intensity). Therefore, the model did not take into account the effects of certain construction operations during the previous stage of the surcharge process, such as the disturbance by construction equipment, the difference in the surcharge sequence, and the non-uniformity of the surcharge height, resulting in some differences between the calculated and measured displacement in the previous stage of the surcharge process (e.g., before Day 55). However, with the increases of loading time, the calculated displacement and the measured displacement gradually stabilized and were similar, indicating that the FE model established in this study has a high accuracy in reflecting the lateral deviation of the cap.

In addition, based on the displacement and turning angle of the cap top surface and the distance between the cap top surface and the pile top, the horizontal displacement at the pile top could be derived [4]. Fig.9(b) shows a comparison of the derived and calculated pile top displacement for Pile 2#. The derived displacement matched the calculated result, with a difference of only 8.6%, further indicating that the numerical model is reliable.

Fig.9(c) shows the variation in the lateral displacement of the pile foundation with time. When t = 3 d, transient transfer of the surcharge load occurred in the ground, resulting in lateral deformation of the soft soil, which triggered significant lateral deviation of the pile foundation. The pile segment with the largest lateral displacement was located at a depth of 12.0–16.0 m. With increasing load duration, the lateral consolidation-creep deformation occurred in the upper soft soil, resulting in a gradual increase in the lateral deformation of the upper pile segment (i.e., the depth was 0–12.0 m). When t = 224 d, the lateral displacement of the upper pile segment and the cap were significantly larger than that of the deep pile segment, and the lateral displacement of the cap and the pier became the maximum displacement of the overall structure.

4.3 Time-dependent deformation behavior of the pile foundation

The time-dependent deformation behavior of the pile and its interaction mechanism with the soft soil was revealed based on the validated FE model. Fig.10 shows the variation in the soil deformation, pile displacement, and bending moment with time.

As revealed by Fig.10(a), the soft soil lateral deformation showed a significant TDC, which was consistent with the law presented in Fig.6(a). With increasing load duration, the soil deformation increased until it tended to stabilize. The deformation of the silt layer and muddy−silty clay layer was significantly larger than that of the silty clay layer.

Since the responses of the side piles (e.g., Piles 1#, 3#, 4#, and 6#) and the middle piles (e.g., Piles 2# and 5#) were basically the same, the following calculation results of extracting the pile-shaft nodes were analyzed by taking Piles 2#, 5#, 8#, and 11# as the only study objects. The closer a pile was to the surcharge load, the more severe the pile deflection (Fig.10(b)). The depth at which the maximum pile displacement occurred increased with decreasing distance between the pile and the surcharge load for a short time (e.g., t = 3 d) after the surcharge load was applied. For example, the maximum displacement of Pile 11# occurred at the pile top, and the maximum displacement of Pile 2# occurred at a depth of 15.0 m. With increasing load duration, the lateral deformation of the upper soft soil triggered by consolidation behavior gradually increased, leading to a gradual increase in the lateral deformation of the upper pile segment and a rise in the depth where the maximum pile displacement was located. For example, when t = 224 d, the maximum displacement of Pile #2 occurred at a depth of 10.0 m. This indicated that the extension of the load duration gradually changed the distribution of the pile response in deep-thick soft soils.

For the bending moment, the maximum value (absolute value, similarly hereinafter) increased significantly with decreasing distance between the pile and the surcharge load (Fig.10(c)). When t = 3 d, for Pile 2#, the maximum bending moment occurred at the pile segment connected to the cap (depth 1.0 m), which was prone to tensile cracking damage. For other piles, there was no clear pattern of maximum bending moment influenced by the compatible deformation between the cap and pile foundation. For proximity piles (e.g., Piles 2# and 5#), with increasing load duration, the lateral displacement of the upper pile segment induced by the soil lateral deformation increased, resulting in a decrease in the bending moment of the upper pile segment and an increase in the bending moment of the deep pile segment. For example, when t = 224 d, the maximum bending moments of Piles 2#, and 5# occurred at a depth of 32.0 m, which was the interface between the soft-weak soil layer and the hard soil layer. This indicated that the mechanical behavior of the pile gradually changed as the loading time increased, i.e., there was change in the part of the pile where the damage was most likely.

To further reveal the essential cause for the time-dependent deflection of the pile foundation, the lateral load acting on the pile side was analyzed. Fig.11 shows the normal soil pressure (NSP) distribution on the front side (i.e., the pile side near the surcharge load) of Piles 2#, 5#, 8#, and 11#. The NSP showed a distribution of increase and then decrease along the depth and reached a maximum at a depth of 32.0 m. This depth position was the interface between the silt layer and the muddy−silty clay layer. With increasing load duration, the NSP triggered by the time-dependent lateral displacement of the soft soil gradually increased, but the distribution range of the NSP along the depth remained basically the same and was mainly concentrated in the soft-weak soil layer.

Combined with Fig.11, the lateral additional soil pressure (LAP) acting on the front side of the pile was extracted, as shown in Fig.12. For the LAP acting on the front side, a positive value represents that the soil displacement is larger than the pile displacement, while a negative value represents the opposite. The LAP distributions of piles (e.g., Piles 2# and 5#) close to the surcharge were significantly different from those of piles (e.g., Piles 8# and 11#) far from the surcharge. For piles close to the surcharge, the LAPs of the pile segments at depths from 4.0 to 32.0 m significantly increased, showing the mechanical model of “piles pressed by soil,” which was the essential reason for the maximum positive bending moments in this depth range (Fig.10(b)). In addition, the LAPs of the pile segments with depths from 0 to 4.0 m and from 32.0 to 41.0 m decreased, showing the mechanical model of “soil pressed by piles”. For piles far from the surcharge, the LAPs along the entire pile length increased due to compatible deformation between the cap and pile foundation.

With increasing load duration, the LAPs acting on the front side of the pile segment within soft soils increased significantly. Compared with t = 3 d, the maximum LAP of Pile 2# increased by approximately 47.0% at t = 224 d, corresponding to an increase of approximately 48.6% for Pile 11#. It is worth noting that the depth range of the pile segment with increasing LAP remained unchanged, mainly distributed from 4.0 to 32.0 m in depth, indicating that the distribution range along the depth of the LAP triggered by lateral displacement of the soft soil remained unchanged with time, which was consistent with the findings in Fig.11.

5 Preventive measures for pile foundation deviation

It is very desirable to proactively control the adverse effects of surcharge loads on pier-cap-pile foundations through preventive measures before surcharges occur. Based on numerous actual engineering projects [22–25], micropiles and stress-release holes were considered in this study as potential preventive measures to isolate soil lateral movements induced by adjacent surcharge loads. The preventive effects of both measures were investigated by considering the TDCs of soil movements.

5.1 Micropiles for isolation

5.1.1 Arrangement of micropiles

Micropiles are widely applied in foundation-strengthening projects, and mainly consist of steel pipes and cement slurry (Fig.13(a)). Because of the large number and small diameter of micropiles, modeling each pile would cause a sharp increase in the numbers of FE elements and nodes, resulting in greater calculation costs. Therefore, referring to the simplified method adopted by Jiang et al. [22], the micropile area was simplified into a micropile wall with the same length (Fig.13(b)). Different numerical calculation schemes were determined by adjusting the height h_w and elastic modulus E_sp of the micropile wall using the above validated FE model.

Referring to the determination method of the deformation modulus for a composite foundation [36], the calculation formula of the elastic modulus E_sp for a micropile wall is:

(5)E_{\mathrm{s}\mathrm{p}}={\omega }_{\mathrm{A}}{E}_{\mathrm{p}}+\left(1-{\omega }_{\mathrm{A}}\right)E_{\mathrm{s}},

where E_sp is the elastic modulus of the micropile wall, ω_A is the lateral area replacement rate, E_p is the elastic modulus of the micropile, and E_s is the elastic modulus of the soil. Referring to the specification [36], ω_A = A_p/A_s, where A_p is the lateral pile area of a single pile, and A_s is the lateral soil area shared by a single pile to form the reinforcement effect.

Based on the actual condition of the case site, the micropile wall was proposed to be 4.5 m wide and 130.8 m long (Fig.13(b)). Two pile lengths, 34.0 and 51.6 m, were determined according to the stratigraphic distribution. The elastic modulus E_p of the micropile was taken according to those of C25 and C70 cement grades [37]. Considering the contribution of steel pipes inside the micropile, the values of E_p corresponding to C25 and C70 cement are 29.0 and 38.0 GPa, respectively. The elastic modulus E_s of the corresponding soil layers were determined according to Tab.2, and were 6.0 MPa for the silt layer, 8.0 MPa for the muddy−silty clay layer, and 40.0 MPa for the silty clay layer. The diameter and clear spacing of the micropiles were set to 0.15 and 0.5 m, respectively, and the lateral area replacement rate ω_A was determined as 0.3 [36]. Therefore, calculation schemes for the micropile wall representing six different lengths and stiffnesses were established, as shown in Tab.3, where schemes h_w34-no and h_w516-no represent that the elastic modulus E_sp of the micropile wall is equal to the pile elastic modulus E_p under ideal conditions.

5.1.2 Prevention effect of micropiles

The lateral displacement development of the cap under different micropile schemes was obtained, as shown in Fig.14. When the micropile length was 34.0 m, the displacement of the cap under each scheme was slightly smaller than that under the scheme without micropiles in the short term (t ≤ 100 d), while when t > 100 d, the displacement gradually increased and exceeded that under the scheme without micropiles. Even with the h_w34-no scheme, the cap displacement was the same as that under the scheme without micropiles, indicating that the micropile scheme with a length of 34.0 m failed to have a preventive effect. The reason was that in cases with deep soft soils, when the micropile length was the same as the thickness of the soft-weak soil layer, the micropile wall underwent time-dependent lateral movement together with the soft soil.

When the micropile length increased to 51.6 m, the pile segment with a depth greater than 34.0 m was embedded in the deeper silty clay layer, and the micropile relied on the stiffness to resist the lateral soil movement, thus having an isolating effect on the bridge pile foundation. Under schemes h_w516-C25, h_w516-C70, and h_w516-no, the cap displacements were 22.51, 21.34, and 17.14 mm at 224 d of loading, respectively, which were approximately 24.0%, 28.0%, and 42.2% less than those under the no-pile scheme, respectively. This indicated that although the micropile wall with a length of 51.6 m had a certain isolation effect, it could still not meet the deviation limit of the cap within 8.0 mm [26–28] for this engineering case.

Taking Pile 2# as an example, the variations in the pile displacement and bending moment under different schemes were revealed, as shown in Fig.15 and Fig.16. Although micropiles could not effectively reduce the lateral displacement of the cap to within the limit, they could still effectively improve the stress state of bridge pile foundations and reduce their deflection and bending moment due to their role as a “partition board” in the soil. For example, under schemes h_w516-C25, h_w516-C70, and h_w516-no after 224 d, the maximum displacements of Pile 2# were reduced by 30.6%, 34.3%, and 47.4%, respectively, and the maximum bending moments were reduced by 53.4%, 57.2%, and 71.3%, respectively, compared with the scheme without micropiles.

5.2 Stress-release hole

Stress-release holes (SRHs) protect bridge pile foundations by blocking the transfer of stress and deformation in the adjacent foundation soil. The following evaluation focused on the preventive effect of SRHs with the consideration of soil time-dependent movement.

5.2.1 Arrangement of stress-release holes

In actual engineering, the diameter, spacing, and depth of SRHs are generally in the range of 0.2–0.6, 0.8–2.0, and 10.0–30.0 m [38], respectively. For the engineering case of this study, considering that the stratum contained a thick, soft soil layer, two hole diameters of 0.3 and 0.6 m and two hole depths of 12.0 and 34.0 m were selected to establish the numerical calculation scheme using the above validated FE model, as shown in Tab.4. The SRHs were arranged in two rows at a spacing of 1.5 m in quincunx (Fig.17(a)) between the bridge pier and the surcharge. To minimize the disturbance of the soil around the pile foundation by the borehole, the minimum distances of the SRH from the cap and the surcharge boundary were 2.0 and 1.0 m, respectively, and the plan layout and FE simulation are shown in Fig.17.

5.2.2 Prevention effect of stress-release holes

The lateral displacement development of the cap under different SRH schemes was obtained, as shown in Fig.18. When the depth of the SRHs was 12.0 m, the reduction in the lateral displacement of the cap was not significant compared with the calculated results under the scheme without SRHs, which indicated that the application of SRHs with a depth of 12.0 m failed to achieve the expected prevention effect. From Fig.12, the LAP induced by the surcharge load was mainly concentrated in the depth range of 4.0–32.0 m. The SRHs with a depth of 12.0 m could not completely separate the transfer of the LAP and thus could not effectively reduce the lateral deviation of the cap-pile foundation.

In contrast, when the depth of the SRHs was 34.0 m, the LAP acting on the pile was effectively separated; thus, the lateral deviation of the cap-pile foundation was effectively reduced. The final lateral displacements of the cap were 10.6 and 7.5 mm for the 0.3 and 0.6 m diameter schemes, respectively, which were approximately 64.2% and 74.8% less than the results under the scheme without SRHs. This showed that the application of SRHs with a 0.6 m diameter and a 34.0 m length could achieve the expected prevention effect of keeping the lateral displacement of the cap within the 8.0 mm limit [26–28].

It is worth noting that the stress-release effect occurred in the soil around the bridge pile foundation after the construction of SRHs with a length of 34.0 m. Under the vertical constant load from the superstructure, the pile foundation underwent reverse deformation, i.e., the pile foundation is offset toward the side of surcharge loads. The reverse displacements of the cap, i.e., the initial negative displacement in Fig.18, were 6.3 and 11.3 mm for the schemes of 0.3 and 0.6 m diameter, respectively.

Fig.19 and Fig.20 show the variation in the displacement and bending moment of Pile 2# under different SRH schemes. When the depth of the SRHs was 12.0 m, the distribution of the pile displacement and bending moment along the depth was unchanged compared with the results under the scheme without SRHs, and the maximum displacement and maximum bending moment were slightly reduced. However, when the depth of the SRHs was 34.0 m, the distribution of the pile displacement and bending moment along the depth changed significantly. The main differences were that: 1) reverse deflection occurred in the pile foundation, and the larger the diameter of the SRH was, the more significant the reverse deflection. In addition, the pile foundation gradually deflected away from the surcharge load with increasing load duration. 2) The depth where the maximum bending moment occurred was reduced from 17.0 to 26.0 m, and the front side of the pile at this depth was converted from a compressive to a tensile state. With increasing load duration, the reverse deflection caused by the SRH was offset by the forward deflection caused by the time-dependent lateral deformation of the soil, resulting in a decrease in the maximum bending moment (Fig.20).

5.3 Design recommendations for preventive measures

Based on the above numerical results, some design recommendations for preventive measures can be drawn.

1) For pile foundations in deep soft soil areas, the preventive effect of micropiles can be categorized into two isolation mechanisms depending on the pile length, i.e., short-micropile isolation and long-micropile isolation, see Fig.21. For short-micropile isolation (Fig.21(a)), the micropiles were located within the depth of the soft soil layer. Although the stress state of the pile foundation improved to some extent (both the maximum pile displacement and maximum bending moment were reduced), the lateral deviation of the cap remained large at large load duration, indicating that it was less effective in prevention. For the long-micropile isolation (Fig.21(b)), the depth of the micropile end was greater than the thickness of the soft soil layer and part of the pile segment was embedded in the hard soil layer below the soft soil layer. The long micropile, by virtue of its stiffness, acted as a barrier to the lateral soil deformation and improved the stress state of the pile foundation while significantly reducing the overall deviation of the pier-cap-pile foundation. However, for the engineering case studied in this paper, even when the length and stiffness of the micropiles were increased to large values, the cap deviation could not be reduced to within the code limits. The essential reason for this was that the time-dependent lateral deformation of the soft soil under surcharge loads caused the micropiles to move along with soft soil movement. Therefore, isolation micropiles are not recommended as a preventive measure for pier-cap-pile foundation deviation in deep soft soils.

2) When SRHs were adopted to prevent pile foundation deflection, the preventive effect was mainly determined by the length of the SRH. When the length was less than the thickness of the soft soil layer, the SRH could not block the lateral additional load and provide protection to the adjacent bridge pile foundations. When the length of the SRH was larger than the thickness of the soft soil layer, the SRH could separate the lateral deformation of the soft soil and significantly reduce the lateral deviation of the cap-pile foundation. However, it is worth noting that when SRHs were applied, the pile foundation was prone to deflection close to the surcharge due to the stress release around the pile and the vertical load from the superstructure, resulting in a tendency for the cap to deflect close to the surcharge in the short-term. Therefore, the borehole should be backfilled in time after the construction of the SRH is completed.

6 Conclusions

The time-dependent mechanism of bridge pier-pile foundation deviation in deep soft soils and the corresponding preventive measures was investigated using a FE model embedded with an extended Koppejan model. The main research conclusions are as follows.

1) The one-dimensional Koppejan model was more suitable for describing the time-dependent deformation of soft soils than the Mesri model and the Time-hardening model. The extended Koppejan model well reflected the pile−soil time-dependent interaction behavior and reproduced the deviation process of the bridge cap with time in the engineering case, and the calculated maximum lateral displacement of the cap differs from the measured one by 6.5%.

2) The additional load on the pile side caused by the soft soil lateral deformation induced the time-dependent deviation of the pier-cap-pile foundation. The soft soil lateral deformation increased with time under adjacent surcharge loads, resulting in an increase in the lateral additional load. Compared with t = 3 d, the maximum lateral additional pressure acting on Pile 2# increased by approximately 47.0% at t = 224 d. But the load distribution along the depth remained unchanged and was mainly concentrated in the soft soil layer.

3) For bridge pile foundations with large deviations in deep soft soils, although micropile measures can improve the stress state of the pile foundation, it is difficult to limit the displacement of the caps (or piers) to less than 8 mm, either by using short micropiles or long micropiles.

4) The application of stress-release holes of the same length as the thickness of the soft soil layer can effectively reduce the pile deformation caused by the additional load, but the pile foundation in this study was prone to deflection close to the surcharge due to the stress release and the vertical load from the superstructure, resulting in a tendency for the pier structure to deflect close to the surcharge in the short-term.

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