Bearing Capacity of Strip Footing on Clay Slope Reinforced with Stone Columns

Bearing capacity of strip footings on sand slopes reinforced with geogrid and grid-anchor

Ultimate bearing capacity of strip footings on Hoek-Brown rock slopes – A stress characteristics solution

The effect of slope-stabilizing stone columns on the bearing capacity of a rigid strip footing placed on a sand slope has experimentally and numerically investigated in this paper. A broad series of conditions has been tested by varying parameters such as the rigidity of stone columns and their spacing in a row. Different types of stone columns were studied including ordinary stone columns, encased stone columns, and concrete piles. Soil displacement fields were obtained via particle image velocimetry method. The results were analyzed to find qualitative and quantitative relationships among bearing capacity and various parameters. A series of finite-element analyses was additionally carried out on a prototype slope and the findings were compared with the results from the laboratory model tests. They were also used to complement the results of the model tests. The agreement between observed and computed results is found to be reasonably good in terms of load–settlement behavior and optimum parameters. Findings of the study showed that increasing rigidity and decreasing the stone columns spaces result in increasing bearing capacity of footing. This enhancement in bearing capacity is attributed to arching effect of soil between stone columns. The rigidity and spacing of stone columns had a significant effect on soil arching. Moreover, the load–settlement behavior of rigid footing is improved.

The paper deals with evaluation of bearing capacity of strip foundation on random purely cohesive soil. The approach proposed combines random field theory in the form of random layers with classical limit analysis and Monte Carlo simulation. For given realization of random the bearing capacity of strip footing is evaluated by employing the kinematic approach of yield design theory. The results in the form of histograms for both bearing capacity of footing as well as optimal depth of failure mechanism are obtained for different thickness of random layers. For zero and infinite thickness of random layer the values of depth of failure mechanism as well as bearing capacity assessment are derived in a closed form. Finally based on a sequence of Monte Carlo simulations the bearing capacity of strip footing corresponding to a certain probability of failure is estimated. While the mean value of the foundation bearing capacity increases with the thickness of the random layers, the ultimate load corresponding to a certain probability of failure appears to be a decreasing function of random layers thickness.

Rock masses are non-homogenous, discontinuous media composed of rock material and naturally occurring discontinuities such as joints, fractures and bedding planes. Due to the presence of the geological discontinuities such as joints, faults and bedding planes, the compressive strength and modulus of elasticity of jointed rock mass are significantly reduced and the measurement of the strength behaviour of these jointed rock masses below the foundation becomes a challenging task. Previous researches have dealt with the bearing capacity of strip footings on the jointed rock mass for concentric, eccentric, inclined loading, separately. But, very limited work has been carried out for determining the bearing capacity of footings on jointed rock mass under eccentric-inclined loading together. In this study, the behaviour of rock masses under the pressure of strip footing has been investigated. To make the problem, more realistic, eccentric-inclined load was applied on the strip footing resting on horizontal jointed rock mass. A parametric study has also been carried out to develop some non-dimensional correlation between different parameters including GSI, e/B ratio, inclination, bearing capacity, etc. Three-dimensional analysis has been carried out by the finite element method using PLAXIS 3D software. Modified Hoek–Brown criteria was used to simulate the behaviour of rock mass and elastic behaviour of foundation was taken into the consideration for analysis. From the results, it can be concluded that the bearing capacity values drop as the eccentricity of the load increases. This indicates that as the eccentricity of the load increases, the bearing capacity of jointed rock mass diminishes. The bearing capacity value decreases with increasing loading inclination with respect to vertical. In the current study, non-dimensional correlations have been developed using data from non-linear elasto-plastic FEA to forecast footing’ bearing capacity, settlement and tilt of shallow foundation. These connections rely on the inclination of the load as well as the eccentricity to breadth ratio. The results obtained from the non-dimensional correlations holds goods on comparing the results obtained from the FEM analysis.

Footings placed on or near a slope, the slope face act as a finite boundary that leads to an inappropriate and inadequate development of the plastic region of failure as the foundation approaches the limit state under the applied loading. Depending upon the position of the footing and steepness of the slope, the above-mentioned phenomena might lead to considerable decrease in the bearing capacity of the foundation. A sequence of finite element analysis has been carried out using Plaxis 2D v2015.02 to inspect the ultimate bearing capacity of strip footings placed at the crest of the c–φ soil slope. The effect of various geo-parameters namely internal angle of friction (φ), cohesion (c), setback distance (b), width of footing (B), slope angle (β) and embedment depth of footing (Df) on the ultimate bearing capacity of the footing have been investigated and the outputs obtained are appropriately elucidated. In addition, large database of numerically simulated ultimate bearing capacity has been considered to develop and verify the ANN model to establish the relative importance of the input parameters.

Construction of shallow footing near the sloping ground is a common practice in the hilly region. However, bearing capacity estimation of such footings requires special attention due to the interference of slope geometry with the failure zone of the footing. It has been observed that the bearing capacity of footing reduces substantially for such cases as compared to the plain ground due to the lesser passive resistance offered by the disturbed failure zone of the footing. In this regard, the conventional limit analysis-based bearing capacity theories are noticed to provide conservative results which lead to uneconomical design of the sub-structure. A finite element-based numerical study has been carried out in the present study to investigate the bearing capacity of strip footings resting on the sandy sloping ground. The influence of setback ratio and the effect of inclined loading on the load-carrying capacity of the footing has been investigated, and the results are discussed in details.

Effect of inclined and eccentric loading on the bearing capacity of strip footing placed on the reinforced slope

This paper develops an analytical method to calculate seismic bearing capacity of a strip footing, which is located on a slope reinforced with rows of pile. The resistance of passive pile is determined based on normal and shear stress of the soil around the pile, which is then compared to other analytical methods. This comparison indicates an acceptable agreement. The variants of the study include location of pile rows, location of footing with respect to the slope crest, foundation depth, and horizontal seismic coefficient. The footing seismic bearing capacity is calculated based on seismic slope stability with limit analysis method (yield acceleration coefficient of reinforced slope with pile row) as well as soil stability beneath the footing by means of virtual retaining wall method. The main objective is to determine and establish the relation between various parameters and seismic bearing capacities of the footing, and to find the best location of the pile row that gives the best improvement in the footing seismic bearing capacity. Results indicate that stabilizing the earth slope with rows of piles has a significant effect on the improvement of seismic bearing capacity of the footing. In addition, the results of the present method are compared with those, reported by others, to demonstrate a reasonable agreement.

The finite element method is used to compute the ultimate bearing capacity of a fictitious strip footing resting on the surface of c-φ weightless soils and a real strip footing buried in the c-φ soils with weight. In order to compare the numerical solutions with analytical solutions, the mainly existing analytical methods are briefly introduced and analyzed. To ensure the precision, most of analytical solutions are obtained by the corresponding formulas rather than table look-up. The first example shows that for c-φ weightless soil, the ABAQUS finite element solution is almost identical to the Prandtls closed solutions. Up to date, though no closed analytical solution is obtained for strip footings buried in c-φ soils with weight, the numerical approximate solutions obtained by the finite element method should be the closest to the real solutions. Apparently, the slip surface disclosed by the finite element method looks like Meyerhofs slip surface, but there are still some differences between the two. For example, the former having an upwarping curve may be another log spiral line, which begins from the water level of footing base to ground surface rather than a straight line like the latter. And the latter is more contractive than the former. Just because these reasons, Meyerhofs ultimate bearing capacity is lower than that of the numerical solution. Comparison between analytical and numerical solutions indicates that they have relatively large gaps. Therefore, finite element method can be a feasible and reliable method for computations of ultimate bearing capacity of practical strip footings.

All available solutions for the problem of bearing capacity on clays of anisotropic and nonhomogeneous strength are based on the assumption of either circular or Prandtl-type failure mechanisms. Although these solutions are rigorous within the concept of limit analysis or limit equilibrium methods, the formulations are too mathematical and exceedingly cumbersome and the bearing capacity value can only be determined through numerical optimization for each given combination of soil and failure mechanism parameters. By means of the upper bound approach of limit analysis, and adopting translational failure mechanisms, this paper presents analytical solutions for the bearing capacity of surface strip footings on clays of strength anisotropic and linearly increasing with depth. Closed-form expressions for bearing capacity factors in the case of smooth and rough footings, have been derived by considering two newly introduced kinematically admissible translational failure mechanisms with varying wedge angles. It was remarkable to find that the two mechanisms would render closed-form expressions for the bearing capacity factor if and only if the deformed region underneath the footing is set to be bounded by two vertical discontinuity surfaces. The derived formulas are expressed in terms of degree of strength anisotropy and a nondimensional parameter that reflects strength nonhomogeneity. Besides being the only closed-form solutions yet available for the bearing capacity of strip footings on clays with anisotropic and nonhomogeneous strength, the derived expressions have been found to not only provide upper bound values for the bearing capacity factor that compared favorably with available solutions, but also yield the best upper bound values when strength increase with depth becomes predominant.

Seismic bearing capacity of strip footings is a challenging task for geotechnical engineers due to its stochastic framework instigated by the natural uncertainties incorporated into geotechnical properties and earthquake parameters. Consequently, the introduction of the random field theory into reliability analysis may provide power tools to succor designers check how reliable their designs. This paper aims to assess the seismic bearing capacity of shallow strip footings resting on soils with randomly varying parameters. Bearing capacity formulas for purely cohesive and cohesive-frictional soils are considered. The influence of the type of the autocorrelation functions (ACFs), the scale of fluctuations (SOFs) and the coefficient of variation (COV) of the random parameters are investigated. Statistical moments, probability density function (PDF) and failure probability (Pf) of the seismic bearing capacity are computed. It is shown that the Single Exponential (SNE) ACF is the most appropriate function to characterize the spatial variability of the soil properties since it provides conservative results. On other hand, the results indicate that the increase in the coefficients of variation (COV) of the cohesion or the friction angle increases the variability of the seismic bearing capacity while this variability remains unaffected when the COV of the seismic coefficient increases. The results also highlight that the effect of the vertical SOF on the PDF and the failure probability is much more significant than that of the horizontal SOF. In addition, the mean seismic bearing capacity fluctuates slightly as the horizontal or vertical SOF increases so that the increment of variation is between 0.4% and 2% for the both two soil types.

Studies of the bearing capacity of footings usually do not take into account the effect of the intermediate principal stress. In practice, the intermediate principal stress has certain influences on the strength of geomaterials (e.g., rock and soil) or concrete. This paper focuses on a numerical study using the finite-difference code Fast Lagrangian Analysis of Continua (FLAC) and the united strength theory (UST) to investigate the influence of the intermediate principal stress on the bearing capacity of strip and circular footings. A series of numerical solutions are presented to determine the vertical bearing capacity of strip and circular footings using an elastic–perfectly plastic constitutive model following UST and the associative flow rule. First, the bearing capacity of flexible and strip footings according to UST and other criteria are compared. Second, three bearing capacity factors (Nc, Nq, and Nγ) are evaluated for strip and circular footings subjected to centered vertical loads with rough interfaces. A certain influence of the intermediate principal stress on the bearing capacity of strip and circular footings was detected based on UST and the associative flow rule. It was found that the intermediate principal stress has more influence on the bearing capacity of a strip footing than the bearing capacity of a circular footing. It was also found that the bearing capacity factor Nγ is more significantly influenced by the intermediate principal stress than are the factors Nc and Nq. The influence of the intermediate principal stress on three bearing capacity factors for strip and circular footings analyzed in this paper has been obtained using the elastic–perfectly plastic constitutive model based on UST.

FELA-DNN framework to predict the seismic bearing capacity of skirted strip footing built on a non-cohesive slope

The presence of underground voids within a failure zone usually results in a reduction in the bearing capacity of footings. This paper presents results for the ultimate bearing capacity ratio, qu/γB, of a strip footing on top of a sand layer overlying a clay layer with voids, with and without the placing of geotextile reinforcement at the interface between the sand and clay layers. Using the finite difference software FLAC 2D, the bearing capacity ratio of the strip footing was calculated for voids with different depths and horizontal distance for two configurations: parallel and symmetrical. The effect of parameters on the ultimate bearing capacity ratio was also investigated, including the undrained shear stress ratio of the soil, the thickness of the top layer and the size, location, height, width and spacing of the voids, with and without placing of geotextile layers at the interface between the sand and clay layers. It was found that the influence of a void on the ultimate bearing capacity ratio of the strip footing vanished when the void was located outside the failure zone beneath the footing and increased further with reinforcement until it reached a constant limit value.