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Undrained seismic bearing capacity of strip footings lying on two-layered slopes

https://doi.org/10.1016/j.compgeo.2020.103539Get rights and content

Abstract

In this study, finite element limit analysis (FELA) is employed to investigate the undrained seismic bearing capacity of strip footings placed on two-layered slopes. Upper bound theorem (UB), lower bound theorem (LB) and adaptive meshing technique were used in parametric studies to investigate the effects of various factors on seismic bearing capacity Ncs and failure mechanism, especially the seismic coefficient kh and the shear strength ratio of top layer and bottom layer cu1/cu2. The angle of the slope β, the absolute strength of top layer cuB, horizontal offset distance b and the thickness of top layer D are also taken into consideration. Furthermore, the comparisons between present study and previous studies are provided. Detailed design tables are presented to distinguish the failure patterns and estimate the seismic bearing capacity of slopes under different conditions.

Introduction

Strip footings are frequently encountered near or on the slope in engineering practices, especially for bridge abutments, roads and pylons in mountainous areas [1], and the presence of slopes can inevitably bring about significant effects on bearing capacity of strip footings. Over the years, many researchers investigated the issue on strip footings resting near slopes by various approaches, including the semi-empirical solutions [2], limit-equilibrium methods [3], [4], [5], slip-line methods [6], [7], and upper-bound and lower-bound solutions [8], [9]. Most of these methods, however, need to presume a precise failure curve in procedures. Depending on many factors, the failure patterns exhibit various and difficult to identify a priori. In view of this, Georgiadis [9] employed the finite element method (FEM) to investigate the static stability of strip footings on slopes, and took the inclination of load into consideration [10]. Subsequently, Shiau et al. [11] inquired the undrained bearing capacity of strip footings located on slopes by finite element limit analysis (FELA), and developed a program for predicting the bearing capacity. Discontinuity layout optimization (DLO) was also adopted to investigate the bearing stability of strip footings resting on c-φ slopes [12] and the failure patterns lying on level ground of slopes [13], respectively.

In addition to the effects of slopes, more attentions are drawn in the seismic bearing capacity in recent years. The limit equilibrium approach is an admitted method to predict the seismic bearing capacity (e.g. Sarma and Iossifelis [14], Budhu and Al-Karni [15], and Choudhury and Subba Rao [16]). The stress characteristics approach is adopted by Kumar and Mohan [17] to study the seismic stability of footings setting on slopes, and the results indicate that the larger the seismic coefficient is, the lower the bearing capacity becomes. Besides, the UB solution [18], [19], [20], [21] and LB solution [22] are also efficient methods. Without presuming a precise failure curve, Kumar and Chakraborty [23] investigated the seismic stability of a rough footing lying on the cohesionless slope by LB solution-FELA, and the research was further extended to the case of strip footings on slope grounds and embankments [24]. In recent, Zhou et al. [25] studied the seismic bearing capacity of strip footings by DLO approach, and a detailed design chart to calculate the seismic bearing capacity of footings near slopes was presented [26]. Taking the inhomogeneity of soils into consideration, Keshavarz et al. [27] investigated the seismic stability of strip footings on top of slopes by FELA.

These researches mentioned above all took uniform soil into consideration, however, the soil tends to be layered in sedimentation processes in reality. The bearing capacity of two-layered slope was studied by kinematic analysis [28], [29]. More recently, Jahani et al. [30] investigated the seismic stability of shallow foundations on layered level ground, and the effects of building height were taken into account. Xiao et al. [31] developed an adaptive finite element limit analysis (AFELA) program to make an overall parametric study about undrained stability of strip footings resting adjacent to two-layered slopes. It is noteworthy that the bearing mechanisms and failure modes of layered slopes are quite different to the single-layered slopes. To the authors’ knowledge, only few researchers investigate the seismic bearing capacity with layered slopes. This cases can be commonly encountered in hilly regions and the failure mechanisms and bearing capacity of these cases can be affected by many complex factors in engineering practice.

For that reasons, this study adopts FELA to investigate the undrained seismic bearing capacity of strip footings located on two-layered slope. Parametric studies for a set of parameters including the seismic coefficient, the undrained shear strength, the shear strength ratio of top layer and bottom layer, the thickness of the top layer D, the angle of the slope β and the horizontal offset distance of the footing b will be presented in detailed design charts to reveal their effects on the seismic bearing capacity. Three typical failure patterns (overall slope failure; failure only occurs in the top layer of slopes; failure occurs in both top and bottom layer of slopes) are revealed, which cover most cases in this study. Relevant failure mechanisms are discussed in this study and detailed design tables are presented to distinguish the failure pattern and predict the seismic bearing capacity.

Section snippets

Problem definition

Fig. 1 shows a sketch of the footing-slope system and the definition of constants. A strip footing of width B under distributed load resting adjacent to a two-layered slope under seismic loads. A series of normalized parameters are introduced for convenience. The slope angle, β, the horizontal offset distance of the footing, b/B, the normalized thickness of the top layer, D/B, the normalized height of the slope, H/B, the normalized strength of top and bottom soil, cu1/γB and cu2/γB, are

FELA model

FELA combines the finite element discretization with the limit theory of classical plasticity. There are two bound solutions in this method, lower bound solution and upper bound solution. The lower bound solution aims to a lower bound of the collapse load from a statically admissible stress field, whereas the upper bound solution deems that there exists an upper bound of the true bearing capacity based on the kinematically admissible velocity field. A precise solution for ultimate bearing

Comparisons with Previous Researches

Cases of footings resting at the crest of the 30° and cu1/γB = 2.5 with different kh are compared with the results from previous studies [27], [28] to inquire the seismic behavior of the strip footing adjacent to the slope, as shown in Table 1. Results obtained from FEM [27] and FELA [28] are enclosed in the interval of UB and LB solutions, and approximate the average value of UB and LB solutions, and the average value can be accepted as the prediction of the performance of the strip footing.

Results and Discussions

The effects of main parameters presented in Eq. (2) on the undrained seismic bearing capacity factor Ncs are studied in this section. Detailed design tables are presented in Table 4, Table 5, Table 6.

Design Tables

Table 4, Table 5, Table 6 show predictions of undrained seismic bearing capacity factor of footings lying adjacent to the slope from FELA, and the failure modes can be classified into roughly three types according to these data.

One general failure corresponds to the whole domain that the slope cannot sustain a self-stability under overlarge seismic actions. All dashes in these tables can distinguish this kind of failure pattern.

The other pattern is footing failure confined in top layer. In this

Conclusions

This paper concentrates on the undrained seismic bearing capacity of strip footings placed on two-layered slopes by FELA. Various factors have been investigated, including the seismic coefficient kh, normalized thickness of the top layer D/B, undrained shear strength ratio cu1/cu2, normalized strength ratio cu1/γB, normalized horizontal offset distance of the footing b/B and slope angle β. Detailed design tables and charts were provided to facilitate engineering practice, and the failure

CRediT authorship contribution statement

Gaoqiao Wu: Conceptualization, Methodology, Software, Writing - original draft. Heng Zhao: Writing - review & editing, Funding acquisition. Minghua Zhao: Supervision, Project administration. Yao Xiao: Resources, Software.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements

This research is a part of the work carried out by grants from the National Natural Science Foundation of China (No. 51978255).

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