Stability analysis of a high loess slope reinforced by the combination system of soil nails and stabilization piles

Abstract

While the soil nails and the corresponding compound technology are widely used as the support techniques for deep foundation pit and normal slopes, few related engineering cases are found for high loess slopes. By utilizing the finite element software of PLAXIS 8.5, the behavior of a high loess slope reinforced by the combination of soil nails and stabilization piles (hereinafter for CSNSP) is studied in this paper. It can be found that the potential slide surface of the slope moves to deeper locations during the process of the multi-staged excavations. The measure of reducing the weight of the top of the slope is a positive factor to the stability of the loess slope, while the rainfall is a negative factor. The slope can’t be stable if it’s reinforced only by stabilization piles or soil nails during the process of the multi-staged excavations. The soil nail contributes greater to the overall system stability when the excavation depth is relatively shallow, while the stabilization pile takes it over when the excavation depth reaches a large value. Compared to the results from the Sweden circular slip surface, the data derived from the method of phi/c reduction is relatively large when the slope is unreinforced or reinforced only by stabilization pile, and the data turns to be small when the slope is strengthened by soil nails or the combination system of soil nails and stabilization piles.

Keywords

high loess slope / CSNSP / PLAXIS / phi/c strength reduction method / Sweden circular slip surface

Introduction

Compared to the traditional support technology, the soil nails with the features of low cost, high reliability, great construction efficiency [1], have been widely used in the geotechnical engineering [2,3]. Meanwhile, the compound support technology developed from soil nails is also applied extensively in deep foundation pits and normal slopes [4]. The evaluation of the stability of high slopes is of vital importance to ensure the safe operation of the geotechnical engineering. Zheng et al. [5] develop an equivalent pseudo-static force analysis based on the finite element method to evaluate the seismic stability of reinforced rock slopes. Rabczuk et al. [6] present a methodology to model slip lines as strong displacement discontinuities within a continuum mechanics context. Cai et al. [7] propose a novel continuous/discontinuous deformation analysis method for modeling crack problems which is useful to the safety assessment and life prediction of cracked engineering structures. Zhang et al. [8] analyze the effects of complex geometries on three-dimensional (3D) slope stability using an elastoplastic finite difference method (FDM) with a strength reduction technique which can be used directly to offer suggestions for landslide hazard preparedness or safe and economical design of infrastructures. Zhu et al. [9] analyze a substantial high rock slope by the dam shoulder of Jinping Hydropower Station by a developed MSLS method for modeling jointed rock mass and the joint is modeled as discontinuity governing the near field stress.

Due to the orthostatic property of loess, the slope of the natural loess slope is commonly gentle which will result in an overly high steep slope after an excavation [10]. Therefore, slope failure and landslide will be potentially triggered for a high loess slope under the condition of rainfall and excavation unloading [11]. Although some research works about the treatment of loess slopes have been launched and lots of related achievements are obtained [12,13], these related works are basically focused on slopes whose height is less than 30 m and whose gradient is relatively slow. The research of high steep loess slope, especially, the multi-staged excavations are rare.

In this paper, a loess slope with multi-staged excavation procedures is studied, and the project site is an open cut tunnel of a high-speed railway located in Shaanxi province of China. The eventual height of the slope after excavation reaches up to 42.5 m, and the slope is reinforced by the combination system of soil nails and stabilization piles. To investigate the behavior and stability of the slope during the process of excavations, the finite element software of PLAXIS 8.5 and the traditional Sweden circular slip surface are used in this study.

Description of the project site

To ensure the long-term stability of the temporary slope result from the open cut tunnel, a row of stabilization piles, with 2.75 m × 3.5 m cross section, 33 m length, 6 m horizontal spacing are installed at the toe of the temporary slope. Meanwhile, soil nails and the affiliated shell bolting spray layer are set from the top of the stabilization piles to the head of the slope, as shown in Fig. 1.

The soil nails (adopted φ25HRB335 steel wire with lengths of 8 m and 9.5 m) appear to be equal interval arrangement, and the vertical spacing of nearby soil nails is 1.4 m and the horizontal spacing is 1.2 m. The shell bolting spray layer with a thickness of 10 cm is made up of concrete of C25 degree and steel wires. The strata of the slope are mainly composed of two layers: the overlying layer is loess (Q₂) of Middle Pleislocene series and the underlying layer is Lower Sinian Nantuo sandstone (Z_1^m) of Majiahe group. The detail of the multi-staged excavation of the slope is listed in Table 1.

Finite element numerical simulation

Numerical model

PLAXIS is a finite element program for the two-dimensional analysis of deformation and stability in geotechnical engineering. It has advanced constitutive models for the simulation of the nonlinear, time-dependent and anisotropic behavior of soils and/or rock. High-order elements, such as quadratic 6-node and 4th order 15-node triangular element are available to model the deformations and stresses in the soil [14]. In addition, special structural elements like plates, anchors, geogrids, interfaces and others can be used in practice for the construction of practical engineering.

In this paper, the behavior of the loess slope in the whole process of excavation is simulated by PLAXIS 8.5. The geological environment is simplified due to the reason that the strata layer is almost flat. The numerical model (70 m length and 90 m height) is composed of 757 elements and 6207 grid points which are illustrated in Fig. 2.

The function of staged construction which can simulate the behavior of the slope in different stage is designed in PLAXIS 8.5. The parameters of the structure including shell bolting spray layer, stabilization pile and soil nail are based on the data from the in situ field and similar construction engineering [15]. Among them, the shell bolting spray layer and the stabilization pile adopt the plate element, and the soil nail utilizes geogrid element. The parameters of the structural element are listed in Table 2. The soil and the rock obey the yield criterion of Mohr-Coulomb, and the corresponding parameters are shown in Table 3. Since there was a strong rainfall lasted for about 10 days in stage 4, the soil strength in stage 4 is reduced for calculation. The permeability of loess is quite different from other soils whose velocity of permeability is larger in the vertical direction than in the horizontal direction. Based on the long-term field data from Dingxi of Gansu province in China [14], the vertical seepage velocity of loess is potentially large which can get to 35 m depth of soil in 20 days, and the horizontal velocity is less than 7 m in 30 days. It can be seen that the permeability of loess is closely related to its structure and ages. In this paper, in order to facilitate the modeling and avoid small mesh grid which can be a puzzle for PLAXIS program to realize the large deformation, the strength of the whole loess layer in stage 4 is reduced to simplify the influence of rainfall on soil strength.

The soil-structure contact is also considered in this simulation and the contact formula can be described as follows.

(1)S_{\mathrm{c}}=S_{\mathrm{s}}\cdot R_{\mathrm{i}\mathrm{n}\mathrm{t}\mathrm{e}\mathrm{r}},

where, S_c is the strength of the contact surface for soil and structures, S_s is the soil strength around the structures, and R_inter is the frictional contact coefficient, when R_inter = 1 means that there is no relative displacement between soil and structure and when R_inter<1 which suggests that the relative displacement can be generated.

Mechanical analysis of the support system

After the parameters and the element types are assigned to the model, the calculation will be carried out considering the duration of each construction stage. Additionally, the parameters of loess will be changed in stage 4, as shown in Table 3 due to the fact that the rainfall weakens the strength of the overlying soil layer. The shearing force and the moment of stabilization pile varying with the construction stages are illustrated in Figs. 3 and 4, respectively.

It can be inferred from Figs. 3 and 4 that:

1) When the excavation depth does not exceed 13.5 m, the biggest shearing force of stabilization pile increases with the construction stages and the location of the maximum shearing force moves continuously downward with the increment of excavation of depth. When the excavation depth is beyond 13.5 m, the distribution pattern of the shearing force basically remains unchanged. The force of the pile body above 18.0 m is positive, and the force below 18.0 m is negative. The maximum shearing force which appears at the pile body position of 8.0 m is 876.6 kN.

2) When the excavation depth is less than 13.5 m, the bending moment gradually increases with the depth of excavation deepened, and the location of the maximum bending moment of the pile moves downward with the increment of excavation depth. When the excavation depth is more than 13.5 m, the maximum bending moment appears at the pile body position of 20.0 m, basically with no trend of downward movement.

3) The values of shearing force and bending moment are relatively small when the excavation depth is shallow and less than 9.5 m. However, when the depth reaches 9.5 m, these values are changed greatly, thus indicating that the stability of slope is particularly influenced by the rainfall in stage 4 when the excavation depth is 9.5 m during rainy days. The potential slide surface generally appears near the maximum shearing force of the pile body 9. It can be seen from Fig. 3 that the location of the maximum shearing force keeps moving downward with the increasing excavation which indicates that the potential slide surface has a trend of continued downward expansion. When the excavation depth is over 13.5 m, the potential slide surface position remains unchanged, basically at the position of 15.0 m depth of the pile body.

According to the recorded maximum axial force of soil nails, the local slide surface of the upper part of the slope under different stages can be drawn as shown in Fig. 5.

As can be seen from Fig. 5, when the excavation develops to 2 m, a relatively deep local slide surface which terminates approximately in the middle of the second level slope is generated. After the top part of the whole slope is removed, the local slide surface moves forward greatly which indicates that the measure of reducing the top weight of the slope can effectively improve the local stability of the slope and is of great benefit to the subsequent stages. With the excavation to continue, the local slide surface develops downward constantly and runs through the entire upper slope when the excavation reaches 9.5 m.

Overall stability analysis

The Plaxis program can be used as an effectively way for the stability analysis of slopes by the FEM analysis of strength reduction, namely phi/c reduction method [16], and the stability analysis can be carried out after each construction stage. According to the module of phi/c strength reduction, the safety coefficient of the slope in every stage can be obtained as shown in Table 4.

In which, K_S0 represents the safety coefficient of the system with no reinforcement structure, K_S1 is the coefficient only considering the reinforcement of soil nails, K_S2 means only considering the reinforcement of stabilizing piles, and K_S is the safety coefficient, considering both the soil nails and piles. Due to the phi/c reduction method in PLAXIS can’t plot the detailed value when the safety coefficient is less than 1; the loss of data in Table 4 is the reflection of this situation.

Meanwhile, according to the program module of phi/c reduction method, the failure situation of slope without any support measures in each stage, namely the distribution of potential sliding surface, can be drawn as shown in Fig. 6.

To validate the results of the numerical simulation theoretically, based on the traditional Sweden circular slip surface, a simplified stability analysis model considering the interaction of structure and geologic layers is established as shown in Fig. 7. The potential slide surface in this model is based on the result from FEM simulation which shown in Fig. 6.

In Fig. 7, W_k is the weight of slice k; N_k is the normal counterforce at the bottom of slice k; N_ktanφ_k + l_kc_k is the shearing force at the bottom of slice k, l_k means the arc length of slice k in it, and φ_k, c_k represent the internal friction angle and the cohesion of slice k, respectively; for the soil nails in the i row, its effective anchoring force T_i which is taken into account is against sliding in the overall stability, and the role of stabilization pile is considered on the basis of the counter torque M_p which can be derived from the load P_p working on the pile through the upper slope. The safety coefficient K_s can be calculated from the Eqs. (2) and (3) below.

(2)K_{\mathrm{s}}={\displaystyle \frac{{\displaystyle \sum _{k=\mathrm{1}}^m\left(c_k{l}_k+w_k\cos {\beta }_k\tan {\varphi }_k\right)+M_{\mathrm{p}}/\left(BR\right)+{\displaystyle \sum _{i=\mathrm{1}}^m\left(T_i\cos {\beta }_i+T_i\sin {\beta }_i\tan {\varphi }_i\right)/S_i}}}{{\displaystyle \sum _{k=\mathrm{1}}^m{W}_k\sin {\beta }_k}}},

(3)M_{\mathrm{p}}=P_{\mathrm{p}}\cos \left({\beta }_{\mathrm{p}}-\delta \right)R_{\mathrm{p}},

where, m is the total number of the sliding slices; n is the total row number of the soil nails; d_k is for the horizontal width of slice k; β_k is the angle between the tangent line of the slide surface and the horizontal line; β_i is the angle between tangent line of the slide surface and the axial direction of the i row soil nail; α_i is angle between the axial direction of the i row soil nail and the horizontal line; S_i is the horizontal spacing between two nearby soil nails; B is the spacing between two nearby stabilization piles; R is the radius of the slide arc; δ is the angle between P_p and the horizontal line.

According to the analysis model described above, the safety coefficient of each stage with different ways of support structures can be obtained as listed in Table 5.

From the results in Tables 3 and 4 can be seen:

1) The values of K_S0 and K_S2 derived from the phi/c reduction method are larger than ones obtained from the Sweden circular slip surface because the strength reduction of structures is not considered in PLAXIS and the distribution of geological layers is ignored in the traditional method of Sweden circular slip surface.

2) The values of K_S1 and K_S derived from the phi/c reduction method are less than ones from the Sweden circular slip surface. This is because the anchoring force of soil is treated as in full exertion for the Sweden circular slip surface which does not actually conform to the practical situation.

3) Without reinforcement measures, the slopes are unstable, except in stages 1 and 2, and need to be reinforced. The slope cannot be stable if only supported by one of the soil nails and stabilization piles.

4) Before stage 5 (excavation to 13.5 m), the contribution of soil nail to overall stability is greater than the stabilization pile’s, the reversal situation happens only in stages 5 and 6. Therefore, the 10-m-deep excavation can be treated as the boundary between soil nails and stabilization piles for which is superior to the whole stability.

5) Among the coefficients, the data of stage 2 is the largest and the data from stage 4 is the least which indicates that the measure of reducing the top weight of the slope is a positive factor to the stability of the slope while the rainfall has a great influence on the safety coefficient of the system.

Overall, the results derived from the two methods are basically similar. By using only one support measure of the soil nails and stabilization piles cannot meet the requirements of the overall stability of the slope. When the depth of excavation is relatively shallow, the contribution to the overall stability of soil nails is larger than piles’, and with the increment of the excavation depth, the effect of stabilization piles began to dominate.

Conclusion

By using the finite element software of Plaxis 8.5, a high loess slope reinforced by the combination of soil nails and stabilization piles is discussed in this paper, and the following conclusions are obtained:

1) The values of shearing force and bending moment are relatively small when the excavation depth is less than 9.5 m. However, when the depth reaches 9.5 m, these values are changed greatly because the stability of slope is particularly influenced by the rainfall in stage 4 when the excavation depth is 9.5 m during rainy days.

2) When the excavation develops to 2 m, a relatively deep local slide surface which terminates approximately in the middle of the second level slope is generated. After the top part of the whole slope is removed, the local slide surface moves forward greatly which indicates that the measure of reducing the top weight of the slope can effectively improve the local stability of the slope and is of great benefit to the subsequent stages. With the excavation continuing, the local slide surface develops downward constantly and runs through the entire upper slope.

3) By using only one support measure of the soil nails and stabilization piles cannot meet the requirements of the overall stability of the slope. When the depth of excavation is relatively shallow, the contribution to the overall stability of soil nails is larger than piles’; and with the increment of the excavation depth, the effect of stabilization piles began to dominate.

4) The results derived from the two methods used for the stability analysis of the slope in this paper are basically similar. Compared to the results from the Sweden circular slip surface, the data derived from the method of phi/c reduction is relatively large when the slope is unreinforced or reinforced only by stabilization pile, and the data turns to be small when the slope is strengthened by soil nails or the combination system of soil nails and stabilization piles.

References

[1] Da Costa A, Sagaseta C. Analysis of shallow instabilities in soil slopes reinforced with nailed steel wire meshes. Engineering Geology, 2010, 113(1–4): 53–61

[2] Zhang M, Song E, Chen Z. Ground movement analysis of soil nailing construction by three-dimensional (3-D) finite element modeling (FEM). Computers and Geotechnics, 1999, 25(4): 191–204

[3] Dong C, Zheng Y R, Chen X Y, Tang X S. Research on composite support pattern of soil nails and prestressed anchors in deep foundation pits. Rock and Soil Mechanics, 2009, 30(12): 3793–3796, 3802 (in Chinese)

[4] Feng-bin Z, Lin-chang M, Huan-da G. A case study on behaviors of composite soil nailed wall with bored piles in a deep excavation. Journal of Central South University, 2013, 7(20): 2017–2024

[5] Zheng W, Zhuang X, Cai Y. On the seismic stability analysis of reinforced rock slope and optimization of prestressed cables. Frontiers of Structural and Civil Engineering, 2012, 6(2): 111–120

[6] Rabczuk T, Areias P M A. A new approach for modelling slip lines in geological materials with cohesive models. International Journal for Numerical and Analytical Methods in Geomechanics, 2006, 30(11): 1159–1172

[7] Cai Y, Zhu H, Zhuang X. A continuous/discontinuous deformation analysis (CDDA) method based on deformable blocks for fracture modelling. Frontiers of Structural and Civil Engineering, 2013, 7(4): 369–378

[8] Zhang Y, Chen G, Zheng L, Li Y, Zhuang X. Effects of geometries on three dimensional slope stability. Canadian Geotechnical Journal, 2013, 50(3): 233–249

[9] Zhu H, Zhuang X, Cai Y, Ma G W. High rock slope stability analysis using the enriched meshless Shepard and least squares method. International Journal of Computational Methods, 2011, 8(2): 209–228

[10] Zhao D A, Wang T J, Hui Y P, Chen Z M, Ma Z Q. Summarization on control of subgrade landslide in Baoji-Zhongwei Railway. Chinese Journal of Geotechnical Engineering, 2008, 30(8): 1248–1255 (in Chinese)

[11] Shang H, Ni W.K, Niu F J.Development characteristics and causes of seismic loess landslides in north-west China. Disaster Advances, 2013, (6): 24–38

[12] Wang G X, Xu J L, Liu G D. Landslidology and technique of landslide control. Beijing: China Railway Publishing House, 2004 (in Chinese)

[13] Li J, Tham L G, Junaideen S M, Yue Z Q, Lee C F. Loose fill slope stabilization with soil nails: Full-scale test. Journal of Geotechnical and Geoenvironmental Engineering, 2008, 134(3): 277–288

[14] Liang Y, Xing X L, Li T L, Xu P, Liu S L. Study of the anisotropic permeability and mechanism of Q₃ loess. Rock and Soil Mechanics, 2012, 33(5): 1313–1318 (in Chinese)

[15] Otani J, Miyata Y, Mukunoki T. Study of a 15 in vertical soil nailed wall at Capella@Sentosa. In: Proceedings of the 5th International Symposium on Earth Reinforcement (IS Kyushu 07). November, Fukuoka, Japan, 2007

[16] Brinkgreve R B J, Broere W, Waterman D. Plaxis2D Manual Books, 2006

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