Seismic bearing capacity of strip footings placed near c-φ soil slopes
Introduction
Footings constructed on top of slopes are often encountered in engineering practice, such as those for transmission towers, bridge abutments or buildings in hilly regions. In such cases, the slope can have significant impacts on the bearing capacity of a footing, which if not being properly accounted for may lead to dangerous designs. Early studies on this subject have been focused on the static bearing capacity of strip footings placed near slopes, e.g., analytical solutions [[1], [2], [3], [4], [5], [6], [7], [8], [9]] and numerical simulations [[10], [11], [12], [13], [14], [15], [16]]. However, a usually stable structure may still fail when significant seismic effects arise during an earthquake. Therefore, in earthquake zones, seismic effects on the footing-slope bearing system cannot be ignored in view of its devastating consequences.
The so-called pseudo-static approach has been commonly used in the design of earth structures under seismic conditions. In this method, the standard static problem is augmented by the inertia forces representing the effects of seismicity [17]. The popularity of this approach mainly owes to its simplicity in design practice [18]. By incorporating the pseudo-static seismic forces, various analytical methods have been used to determine the ultimate seismic bearing capacity of strip footings near slopes, such as: the limit equilibrium approach [[19], [20], [21]], analytical upper bound (UB) and lower bound (LB) methods [[22], [23], [24], [25], [26]] and the slip-line field method [27].
As mentioned above, analytical solutions proposed by these former researchers are useful for providing meaningful physical insights into the studied problem, however, they usually require skillful construction of the failure mechanism. For the footing-slope system, either a bearing capacity failure or an overall slope failure, or even a mixed failure mood may occur, which makes it hard to determine the actual failure mechanism a priori. To avoid this, many researchers have turned to the employment of numerical methods, such as: Shiau et al. [18], Kumar and Chakraborty [28], Chakraborty and Kumar [29] and Chakraborty and Mahesh [30] via finite element limit analysis (FELA); or Cinicioglu and Erkli [31] via displacement finite element method (D-FEM). However, these early studies only considered the static bearing capacity of footings placed near slopes.
More recently, seismic bearing capacity of strip footings placed adjacent to c-φ soil slopes has been investigated by Zhou et al. [32] based on discontinuity layout optimization (DLO) and Raj et al. [[33], [34], [35]] based on FELA. In addition, considering the important role of soil dilatancy in evaluating the bearing capacity of soil structures, Halder et al. [36] studied the seismic bearing capacity of strip footings placed near slopes using LB-FELA with a non-associated flow rule. However, in the aforementioned studies, the impact of the distance of footing to slope crest has not yet been considered in the analysis, which constitutes one of the main objectives of this study.
In this work, a FELA program with automatic mesh adapdation feature is employed to investigate the seismic bearing capacity of strip footings placed near c-φ soil slopes. To quantitatively describe the seismic effects, the so-called pseudo-static approach is used in the analysis. Based on the method, both the UB and LB solutions of the normalized seismic bearing capacity factor are calculated and summarized in design tables/charts for practitioner's use. The effects of all problem variables (to be introduced in the next section) on the footing-slope bearing system are investigated through detailed parametric studies. Finally, typical failure mechanisms of the footing-slope bearing system are depicted using graphical results from the UB analyses.
Section snippets
Problem description
Fig. 1 illustrates the graphical representation of the studied problem under plane-strain condition. In this problem, a rigid strip footing of width B is placed on top of a soil slope of height H and with slope angle β. The distance from the inner edge (relative to the slope) of the footing to the slope crest equals L. The soil mass of unit weight γ is modelled as a homogeneous and isotropic material obeying the Mohr-Coulomb (MC) yield criterion, that is, the soil strength can be described by
Adaptive finite element limit analysis
FELA combines the powerful capabilities of finite element method (FEM) with classical limit theorems in plasticity to evaluate the collapse loads of structures directly [42,43]. By formulating the UB and LB problems as standard mathematical programming models, the method can handle complex geotechnical stability problems involving heterogeneity, complicated geometry and complex loading, etc., on an ordinary computer, without a priori assumption on the potential failure mechanism. Therefore, it
Static bearing capacity of strip footings on slopes
In this section, the results obtained in this study for static bearing capacity of strip footings on slopes are compared with those from existing solutions, including: the limit equilibrium solutions by Bishop [56] and Narita and Yamaguchi [5], the analytical UB solution by Kusakabe et al. [6], and the FELA solution by Shiau et al. [18]. Fig. 3 shows the variation of the normalized static bearing capacity factor p/γB with respect to c/γB for the cases with L/B = 0, β = 30° and φ = 30°. It can
Results and discussion
In this section, the normalized seismic bearing capacity factors p/γB are calculated for all the problem variables introduced in section 2. Note that, a fixed value of H/B = 5 is assumed for all the studied cases. For practitioner's use, the calculated results have been summarized in Tables 1–3 and graphically depicted in Fig. 7–12. Since the REs measured by Eq. (5) are found to be within ±10% in all these simulations, only the average values of the UB/LB solutions have been used for
Failure mechanisms
In Fig. 13, power dissipations are plotted to illustrate the impacts of the parameters H/B and c/γB on the failure mechanism of the footing-slope system. For comparison purpose, different combinations of H/B and c/γB have been considered, while the other problem variables (kh, β, φ and L/B) have been specified as constants, of which the adopted values are depicted in the caption of the figure. From Fig. 13, it can be easily seen that the shape of the failure mood remains almost unchanged for
Conclusions
Seismic bearing capacity of strip footings placed near c-φ soli slopes has been investigated in this work based on FELA with mesh adapdation technique. By conducting a series of UB- and LB-FELA simulations, the normalized seismic bearing capacity factors p/γB have been calculated and summarized in tables/charts for practitioner’ use. Also, detailed parametric studies have been performed to investigate the effects of all the defined problem variables on the normalized seismic bearing capacity
CRediT authorship contribution statement
Rui Zhang: Software, Writing - original draft. Yao Xiao: Methodology, Writing - review & editing. Minghua Zhao: Conceptualization. Jianqing Jiang: Visualization, Investigation.
Declaration of competing interest
The authors declare no conflicts of interest.
Acknowledgments
The authors would like to acknowledge the financial support of Science and Technology Project of Hunan Provincial Department of Education (Grant No. 158068), which made the work presented in this paper possible.
References (56)
- et al.
Bearing capacity analysis of foundations on slopes by use of log-spiral sliding surfaces
Soils Found
(1990) - et al.
Bearing capacity of slopes under strip loads on the top surfaces
Soils Found
(1981) The influence of load inclination on the undrained bearing capacity of strip footings on slopes
Comput Geotech
(2010)- et al.
The bearing capacity and failure mechanism of a vertically loaded strip footing placed on the top of slopes
Comput Geotech
(2018) Static and seismic earth pressure coefficients for vertical walls with horizontal backfill
Soil Dynam Earthq Eng
(2018)- et al.
Seismic bearing capacity of surficial foundations on sloping cohesive ground
Soil Dynam Earthq Eng
(2018) - et al.
Smoothed finite element approach for kinematic limit analysis of cohesive frictional materials
Eur J Mech Solid
(2019) - et al.
Stability of dual circular tunnels in a rock mass subjected to surcharge loading
Comput Geotech
(2019) - et al.
Stability of two circular tunnels at different depths in cohesive-frictional soils subjected to surcharge loading
Comput Geotech
(2019) - et al.
Mathematical programming models and algorithms for engineering design optimization
Comput Methods Appl Mech Eng
(2005)
A smooth hyperbolic approximation to the Mohr-Coulomb yield criterion
Comput Struct
The ultimate bearing capacity of foundations on slopes
A general formula for bearing capacity
Danish Geotech Inst Bull
Loaded areas on cohesive slopes
J Geotech Eng
Stress characteristics for shallow footings in cohesionless slopes
Can Geotech J
Bearing capacity of strip footings near slopes
Geotech Geol Eng
An upper-bound solution for the undrained bearing capacity of strip footings at the top of a slope
Geotechnique
Undrained bearing capacity of strip footings on slopes
J Geotech Geoenviron Eng
Undrained stability of footings on slopes[J]
Int J GeoMech
Bearing capacity of footings placed adjacent to c′-φ′ slopes
J Geotech Geoenviron Eng
Bearing capacity for spread footings placed near c′-φ′ slopes
J Geotech Geoenviron Eng
Undrained bearing capacity of strip footings placed adjacent to two-layered slopes
Int J GeoMech
Application of pseudo-static limit analysis in geotechnical earthquake design
Proc., 6th European conf. On numerical methods in geotechnical engineering
Seismic bearing capacity of soils
Geotechnique
Seismic bearing capacity for embedded footings on sloping ground
Geotechnique
Seismic bearing capacity of shallow strip footings embedded in slope
Int J GeoMech
Seismic bearing capacity of foundation on cohesionless soil
J Geotech Eng
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