Capacity Of Strip Footings Research Articles

Ultimate bearing capacity of strip footings above rectangular voids in Hoek-Brown rock masses

The bearing capacity of a rigid strip footing placed on a rock mass with a rectangular void is determined using the upper bound finite element limit analysis in conjunction with the adaptive mesh refinement technique. The rock mass is assumed to obey the generalized Hoek-Brown (GHB) yield criterion. The optimization model is solved by using the second order cone and power cone programming, which enables the GHB yield criterion to be used in its native form, without the need for smoothing. Based on the method, the reduction factor is calculated and presented in a series of dimensionless charts for design purpose. The influence of material parameters (such as the geological strength index GSI, material constant mi and intact rock strength σci) and geometric parameters (including the height and width of the void, as well as the horizontal and vertical distance between the void and the strip footing) on the reduction factor is considered. Typical failure patterns are discussed in detail to offer a deeper explanation of how the voids affect the bearing capacity of strip footing.

Bearing Capacity of Strip Footings Seated on Unreinforced and Geosynthetic-Reinforced Granular Layers over Spatially Variable Soft Clay Deposits

Bearing Capacity of Strip Footings Seated on Unreinforced and Geosynthetic-Reinforced Granular Layers over Spatially Variable Soft Clay Deposits

Machine Learning Prediction Tool for Seismic Bearing Capacity of Strip Footings in Rock Mass

Machine Learning Prediction Tool for Seismic Bearing Capacity of Strip Footings in Rock Mass

Soft-Computing Techniques for Predicting Seismic Bearing Capacity of Strip Footings in Slopes

In this study, various machine learning algorithms, including the minimax probability machine regression (MPMR), functional network (FN), convolutional neural network (CNN), recurrent neural network (RNN), and group method of data handling (GMDH) models, are proposed for the estimation of the seismic bearing capacity factor (Nc) of strip footings on sloping ground under seismic events. To train and test the proposed machine learning model, a total of 1296 samples were numerically obtained by performing a lower-bound (LB) and upper-bound (UB) finite element limit analysis (FELA) to evaluate the seismic bearing capacity factor (Nc) of strip footings. Sensitivity analysis was performed on all dimensionless input parameters (i.e., slope inclination (β); normalized depth (D/B); normalized distance (L/B); normalized slope height (H/B); the strength ratio (cu/γB); and the horizontal seismic acceleration (kh)) to determine the influence on the dimensionless output parameters (i.e., the seismic bearing capacity factor (Nc)). To assess the performance of the proposed models, various performance parameters—namely the coefficient of determination (R2), variance account factor (VAF), performance index (PI), Willmott’s index of agreement (WI), the mean absolute error (MAE), the weighted mean absolute percentage error (WMAPE), the mean bias error (MBE), and the root-mean-square error (RMSE)—were calculated. The predictive performance of all proposed models for a bearing capacity factor (Nc) prediction was compared by using the testing dataset, and it was found that the MPMR model achieved the highest R2 values of 1.000 and 0.957 and the lowest RMSE values of 0.000 and 0.038 in both the training and testing phases, respectively. The parametric analyses, rank analyses, REC curves, and the AIC showed that the proposed models were quite effective and reliable for the estimation of the bearing capacity factor (Nc).

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

Miscellaneous conditions reduce the bearing capacity of strip footings, including the location of the strip footings near the slopes. Earthquakes can also affect existing infrastructure and reduce the bearing capacity of the footing. Non-cohesive slopes are affected more by this factor. Various methods have been considered to increase the bearing capacity of the footing under these conditions. Using vertical skirt elements in strip footings is one of the most effective solutions. In this study, the seismic bearing capacity of skirted strip footings near a non-cohesive slope was investigated by soft computing. Complex and time-consuming calculations in this field have drawn attention to soft computing methods. Thus, the SBC-SSF dataset (containing 8000 samples) was used to predict the seismic bearing capacity of a skirted strip footing. Accordingly, a comprehensive comparison was made between various regression and Deep Neural Network (DNN) models. Also, three different methods based on soft computing were proposed to predict the seismic bearing capacity of a skirted strip footing adjacent to a non-cohesive slope.

Seismic combined bearing capacity of strip footings on partially saturated soils using lower bound theorem of finite element limit analysis and second-order cone programming

The seismic bearing capacity of strip footings resting on unsaturated soils subjected to combined loading is investigated in this study using a combination of lower bound limit analysis and finite element discretization. Second-order cone programming (SOCP) is used in this instance to simulate the nonlinear form of the universal perfectly-plastic Mohr-Coulomb yield criterion during the stress field optimization process. Under no-flow and steady-state infiltration/evaporation flow conditions, the significant influence of matric suction induced below the surface footing is accounted for using the suction stress concept. The load eccentricity and inclination applied to the footing and pseudo-static forces exerted simultaneously to the footing (superstructure) and underlying soil are all incorporated into the equilibrium equations, resulting in combinations of limit moment (M), and vertical (V), and shear (H) forces, under the influence of seismic loading. The results demonstrate that the matric suction induced within the porous structure of the underlying soil stratum increases the capacity of the surface footing to withstand various combinations of eccentric and inclined loadings under seismic excitation. Moreover, at a given hydraulic condition, the failure envelopes of obliquely/eccentrically loaded shallow foundations shrink significantly with the increase in the seismic intensity; the process which is more highlighted in sand (no-suction and all flow conditions). As the flow state in the unsaturated clay changes from infiltration to evaporation, the failure envelopes are observed to enlarge. In addition, as the load inclination angle reaches the soil-footing interface friction angle, the ultimate horizontal bearing capacity of the foundation resting on sand (no-suction) drops to zero; however, there still exists a residual shear resistance in the underlying clay layer or unsaturated sand, posing non-zero horizontal bearing capacity even at extremely high angles of inclination. Last but not least, the influence of earthquake horizontal loading on the bearing capacity envelopes of a shallow footing resting on a sand deposit was corroborated to be more pronounced than on a cohesive soil deposit. Indeed, the intrinsic (residual) cohesion, normally found in cohesive soils, was realized to contribute significantly to suppress the detrimental effect of earthquake horizontal loading.

Impact of Transient Infiltration on the Ultimate Bearing Capacity of Obliquely and Eccentrically Loaded Strip Footings on Partially Saturated Soils

Soils above the groundwater table and near the ground surface are often partially saturated, and the changes in the degree of saturation and matric suction caused by infiltration may have substantial effects on the stability of geotechnical systems. This work evaluates the significant effect of transient flow on the ultimate bearing capacity of strip footings founded on unsaturated soils under the simultaneous actions of vertical and horizontal loads and moment using the lower-bound theorems of the finite-element limit analysis and the incorporation of second-order cone programming. The unified effective stress theory is incorporated into the soil yield function to model the partially saturated state, and the closed-form solution for one-dimensional transient flow is adopted so as to evaluate the tempo-spatial variations of suction stress. For both sand and clay underlying soils, it is found that the increase of infiltration time leads to a notable decrease of the size of the normalized failure envelopes for either obliquely or eccentrically loaded shallow foundations. The impact of transient flow on the ultimate bearing capacity of surface footings is also observed to be greater for clay soils as compared with sand deposits due to the significant contribution of higher induced suction stress.

Effect of twin underground Voids on Bearing Capacity of Strip footings

Effect of twin underground Voids on Bearing Capacity of Strip footings

Inclination Factors for Bearing Capacity of Strip Footings on Sheet Pile Reinforced Slopes

Inclination Factors for Bearing Capacity of Strip Footings on Sheet Pile Reinforced Slopes

Performance of reliability-based design formats in geotechnical applications

Geotechnical design codes and guidelines are all switching from traditional factor of safety design to modern load and resistance factor design (LRFD) or partial factor design (PFD), in the belief that the latter two bring more flexibility and reliability consistency across various design scenarios, thus produce safe and cost-effective design outcomes. This paper first reviews the LRFD and PFD developed for geotechnical applications. A total of seven methods to calibrate the load and resistance factors are also introduced. The ability of the LRFD and PFD to produce designs with consistent reliability is examined and compared to that of a traditional factor of safety method using two examples of the bearing capacity of strip footings and the global stability of soil nail walls. Results showed that the framework of LRFD offers no apparent advantages over working stress design (WSD) in achieving more consistent reliability for geotechnical structures; the dispersion in design probabilities of failure could be five to seven orders of magnitude difference. The variation will be reduced to three orders if using the PFD. Neither reducing the variability in soil shear strength parameters nor allocating partial resistance factors with respect to soil types would efficiently harmonize the reliability levels when dealing with multiple soil layer conditions. In addition, the uniformity of reliability levels is insensitive to calibrations with or without presetting the load factors. This study provides insights into the LRFD and PFD frameworks currently developed for geotechnical applications.

Numerical Modeling of the Ultimate Bearing Capacity of Strip Footings on Reinforced Sand Layer Overlying Clay with Voids

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.

Influence of geosynthetic stiffness on bearing capacity of strip footings seated on thin reinforced granular layers over undrained soft clay

Thin granular fill layers are routinely used to aid the construction of shallow footings seated over undrained soft clay foundations and to increase their load capacity. The influence of time- and strain-dependent reduction in reinforcement stiffness on the bearing capacity and load-settlement response of a footing seated on a thin reinforced granular fill layer over undrained soft clay foundations is examined in this paper using finite-difference method (FDM) numerical models. The time- and strain-dependent stiffness of the reinforcement described by a two-component hyperbolic isochronous tensile load-strain model is shown to influence the bearing capacity and load-settlement response of the reinforced granular base scenario. The additional benefit of a reinforced granular layer diminishes as the time-dependent stiffness of the geosynthetic reinforcement increases. An analytical solution for the ultimate bearing capacity of strip footings seated on thin unreinforced and reinforced granular layers over undrained clay is proposed in this study. The main practical outcome from this study are tables of bearing capacity factors to be used with the analytical solution. The bearing capacity factors were back-calculated from the numerical analyses and account for the influence of rate-dependent properties of geogrid reinforcement materials and clay foundations with soft to very soft undrained shear strength.

Method of Rigorous Characteristics for Seismic Bearing Capacity of Strip Footings Placed Adjacent to Homogeneous Soil Slopes

Method of Rigorous Characteristics for Seismic Bearing Capacity of Strip Footings Placed Adjacent to Homogeneous Soil Slopes

Bearing capacity of strip footings on jointed rock mass

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.

Estimation of the Seismic Bearing Capacity of Shallow Strip Footings Based on a Pseudodynamic Approach

The bearing capacity of a shallow strip footing is investigated by a pseudodynamic method under earthquake conditions. A nonsymmetrical multiblock mechanism is herein adopted to describe the uplift failure of the foundations based on the kinematic theorem of limit analysis. This nonsymmetrical mechanism comprises a series of rigid triangular blocks that translate into the failure area. The seismic load, varying with time and space, is represented by a pseudodynamic method that considers the dynamic properties of earthquake waves. A slice method is proposed to adapt the variation in inertial force with time and depth for the convenience of calculating the earthquake-induced work rate. Then, equating the external work rate and the internal dissipation rate, the rigorous upper-bound solution of the seismic bearing capacity factors, which will be optimized by the sequential quadratic programming (SQP) in the MATLAB toolbox for searching for the optimal value, is explicitly derived. Comparisons between the present solution and previous works are made to validate the rationality and accuracy of the proposed methodology. A specific parametric analysis is conducted to reveal the influence of dynamic parameters on the bearing capacity of the strip footing. Numerical results are provided graphically as well as in the tabular form for reference in footing design.

Lower Bound Capacity of Strip Footings on Rock Masses with Two Discontinuity Sets

This paper presents a lower bound model for predicting the rock strip footing bearing capacity. The model is based on strip footings on rock masses with two sets of ubiquitous, closed discontinuities. The model considers explicitly the strength of the intact rock and the discontinuities, as well as the number and orientation of the discontinuities. The validation of the model is presented. The parametric study of footings on rock masses with two discontinuity sets having the same strength is performed, and the results are reported graphically in detail. The bearing capacity is controlled primarily by the rock structures (number of discontinuity sets and orientation) and the discontinuity strength, and it is controlled by the intact rock strength for a very limited number of cases. The minimum bearing capacity factor is independent of the intact rock friction angle, but it is a linear function of discontinuity cohesion. The bearing capacity factor is also presented in terms of its ratio to UCS; the ratio for the maximum bearing capacity is rather insignificantly affected by intact rock friction angle, and not linearly correlated to discontinuity cohesion. The bearing capacity factor for rock masses with low discontinuity strengths tends to be more sensitive to any variation in discontinuity orientation. There are some exceptions to the above points, suggesting that there would always be some rock mass conditions leading to unexpected rock footing bearing capacities and therefore good characterization processes of rock masses would always be essential. The practical significant of this study is briefly discussed.

Numerical Evaluation of Bearing Capacity of Strip Footing on Rockmass Slope

Numerical Evaluation of Bearing Capacity of Strip Footing on Rockmass Slope

Determining Seismic Bearing Capacity of Footings Embedded in Cohesive Soil Slopes Using Multivariate Adaptive Regression Splines

Seismic bearing capacity of strip footings in cohesive soil slopes considering various embedded depths is investigated in this study. Novel solutions using pseudo-static method and finite element limit analysis (FELA) with upper bound (LB) and lower bound (LB) theorems are presented. The influences of footing depth, slope angle, slope height, undrained shear strength and pseudo-static acceleration on bearing capacity and failure mechanisms are examined using dimensionless parameters. With the comprehensive numerical results, the multivariate adaptive regression splines (MARS) model is then utilized to simulate the sensitivity of all dimensionless input parameters (i.e., the normalized depth of footing D/B, the normalized slope height H/B, the normalized distance from top slope to edge of the footing L/B, slope angle β, the strength ratio cu/γB, and the pseudo-static acceleration factor, kh). The degree of influence of each design parameter is produced, and an empirical equation for the dimensionless output parameter (i.e., bearing capacity factor Nc) is proposed. The study results are accessible in the design charts, tables, empirical equation for design practitioners.

Effect of Embedment Depth on the Seismic Bearing Capacity of Strip Footing in Rock Mass

Effect of Embedment Depth on the Seismic Bearing Capacity of Strip Footing in Rock Mass

Bearing Capacity of Eccentrically Loaded Strip Footing on Geogrid Reinforced Sand

This study aims to demonstrate the effects of geogrid reinforcement on the bearing capacity of strip footing under eccentric loading. Numerical analysis using finite element program called (PLAXIS 2D Professional v.8.2) are presented. The effect of each of the depth ratio of the topmost layer of geogrid (u/B), the vertical distance ratio between consecutive layers (h/B), number of geogrid layers (N), and the effective depth ratio of reinforcement (d/B) on the bearing capacity were studied, where (B) is the footing width. Also, the combined effect of load eccentricity ratio (e/B), depth of embedment ratio of footing ( f D /B) and the angle of internal friction ( ) on the ultimate bearing capacity were investigated.