Bearing Capacity Of Strip Footings Research Articles

A numerical investigation into the equivalent parameters of a compressible soil treated by stone columns

A series of triaxial test simulations are adopted to estimate the equivalent strength parameters for compressible soil samples reinforced with stone columns. The simulations utilize the finite difference code, Fast Lagrangian Analysis of Continua in three dimensions FLAC3D. An elasto-plastic model is applied to utilize a Mohr-Coulomb yield criterion. The equivalent strength parameters are estimated using newly proposed formulas for geo-composite materials. The researchers compare the obtained results to the analytical formulas proposed in the literature. Additionally, the equivalent parameters are used in equivalent area models. This study investigates the effect of the replacement area ratio. This study offers two applications. Firstly, it evaluates the safety factor of embankments constructed on compressible soil improved with stone columns. Secondly, it estimates the bearing capacity of strip footings on compressible soil treated with stone columns. In all applications, both individual column and equivalent area models are considered. The proposed equations for the equivalent elastic parameters (E, ν) and the mechanical properties, equivalent cohesion, and internal frictional angle (c and φ) give results that agree with the solutions reported in the existing literature.

Appraisal of numerous machine learning techniques for the prediction of bearing capacity of strip footings subjected to inclined loading

Appraisal of numerous machine learning techniques for the prediction of bearing capacity of strip footings subjected to inclined loading

Seismic bearing capacity of strip footings placed on reinforced soil slopes using slip line method

This study investigates the seismic vertical bearing capacity of strip footings positioned on reinforced soil structures employing a two-phase approach and the slip line method. The investigation aims to establish a slip line field and determine the critical slip surface without any assumptions of predefined surfaces. The obtained results are compared with previous studies, demonstrating a good agreement and validating the accuracy of the proposed approach. The variation of the bearing capacity factor with the horizontal seismic coefficient, soil internal friction angle, setback distance normalized by footing width, and slope incline angle. An increase in the horizontal seismic coefficient leads to a decrease in bearing capacity factor, while an increase in the soil internal friction angle has the opposite effect. The influence of the setback distance on the bearing capacity is also examined, highlighting significant improvements with increased setback distances. Additionally, the study investigates the impact of the tensile strength ratio and setback distance on the ultimate bearing capacity factor and the bearing capacity ratio. The distribution of reinforcement forces beneath the footing is analyzed and presented through contour plots, providing valuable insights into the seismic behavior of footings on reinforced soil slopes.

Seismic Bearing Capacity of Strip Footings with Modified Pseudo-dynamic Method

Seismic Bearing Capacity of Strip Footings with Modified Pseudo-dynamic Method

Optimized neural network-based state-of-the-art soft computing models for the bearing capacity of strip footings subjected to inclined loading

Determining the bearing capacity of a strip footing under inclined loading is crucial in designing foundations. Due to the complex correlations, the subject area remains predominantly unexplored, or it has been simulated using only limited datasets. This paper presents the development of a prediction model based on machine learning (ML), leveraging advanced hybrid artificial neural network (ANN) models for estimating the bearing capacity of strip footings under inclined loading. The ANN models are hybridized with four different optimization algorithms, ant colony optimization (ACO), artificial lion optimization (ALO), the imperialist competitive algorithm (ICA), and shuffled complex evolution (SCE), which enhance the accuracy and efficiency of the predictive capabilities of ANN. The models are trained on a dataset of 920 records, and their performance is evaluated using a range of significant performance metrics. The ANN-ICA model achieved the highest rank in the score analysis (R2 =0.912, RMSE=0.165 in testing), followed by ANN-ALO and ANN-ACO. To reinforce the trustworthiness of the predictions, external validation is employed, and visual analysis is conducted using the Taylor diagram. The findings suggest that the proposed models are robust, and the incorporation of optimization techniques has improved the performance of traditional ANNs. The research findings have significant implications for the field of geotechnical engineering, providing engineers and researchers with valuable insights into the applicability of hybrid artificial neural network (ANN) models and alternative machine learning (ML)-based prediction models in assessing the bearing capacity of strip footings.

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

The present study addresses the ultimate bearing capacity of strip footings on rock slopes under seismic conditions. The stress characteristics method (SCM) is combined with the modified pseudo-dynamic (MPD) approach for the intended purpose. Unlike the solutions available in the literature, the generation of the stress characteristics network within the framework of the SCM automates the potential failure mechanism of the slope medium at the limiting state of collapse. The MPD approach enables the analysis to capture realistic earthquake inertia forces induced in the slope, considering the material damping properties of the slope. The non-linear nature of the rock mass strength is captured using the generalized Hoek-Brown failure criterion. The seismic ultimate bearing capacity of strip footings is reported as non-dimensional charts. Additionally, the impact of relevant dynamic characteristics of seismic waves and rock mass properties is thoroughly assessed by conducting a detailed parametric investigation. The results reveal a substantial reduction in the ultimate bearing capacity of footings resting on rock slopes under earthquake conditions. The efficacy of the proposed methodology is validated with the existing solutions reported by various researchers.

On the Potential of Using Random Forest Models to Estimate the Seismic Bearing Capacity of Strip Footings Positioned on the Crest of Geosynthetic-Reinforced Soil Structures

Geosynthetic-reinforced soil structures are often used to support shallow foundations of various infrastructure systems including bridges, railways, and highways. When such infrastructures are located in seismic areas, their performance is linked to the seismic bearing capacity of the foundation. Various approaches can be used to calculate this quantity such as analytical solutions and advanced numerical models. Building upon a robust upper bound limit analysis, we created a database comprising 732 samples. The database was then used to train and test a model based on a random forest machine learning algorithm. The trained random forest model was used to develop a publicly available web application that can be readily used by researchers and practitioners. The model considers the following input factors: (1) the ratio of the distance of the foundation from the edge and the width of the foundation (D/B), (2) the slope angle (β), (3) the horizontal seismic intensity coefficient (kh), and (4) the dimensionless geosynthetic factor, which accounts for the tensile strength of the geosynthetic. Leveraging the model developed in this study, we show that the most important features to predict the seismic bearing capacity of strip footings positioned on the crest of geosynthetic-reinforced soil structures are D/B and kh.

Reliability-based analysis of seismic bearing capacity of shallow strip footings resting on soils with randomly varying geotechnical and earthquake parameters

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.

Bearing capacity and failure mechanism of strip footings lying on slopes subjected to various rainfall patterns and intensities

Footing on slope is a prevalent construction encountered in geotechnical engineering, and its safety is receiving increased attention. A natural rainfall event will inevitably have adverse influences on the stability and bearing capacity of strip footings lying on slopes; however, the conventional practice to simulate the rainfall is realized by varying the soil moisture content and the actual rainfall characteristics cannot be fully reflected. As a result, the finite element (FE) software ABAQUS is employed in this study to model the temporally varying rainfall, and the bearing capacity, as well as failure mode of the strip footing placed at the top of slopes, is estimated accordingly. A series of FE analyses are carried out to quantify the influences of rainfall pattern, rainfall intensity, soil strength properties (i.e., effective cohesion c′ and effective friction angle φ′) and several geometric parameters associated with the location of embedded footing with B in width, such as the edge distance ratio L/B and the embedded depth ratio D/B. Results show that the bearing capacity will be decreased and the failure mode evidently changes under rainfall condition. Moreover, it is noted that the rainfall pattern produces less substantial impact on the bearing capacity and failure mode, compared with the rainfall intensity.

An Analytical Framework for Assessing the Unsaturated Bearing Capacity of Strip Footings under Transient Infiltration

The evaluation of the bearing capacity of strip footings generally assumes that the soil is either dry or fully saturated, which contradicts the actual condition in nature where the soil is often in a partially saturated state. Furthermore, infiltration has a significant impact on the shear strength of the soil. Following the upper bound theory of the limit analysis, this article provides a theoretical framework for assessing the bearing capacity under transient flow with linear variation in infiltration intensity for the first time. Firstly, the closed form of suction stress under linear transient infiltration is derived using Laplace transform and introduced into the Mohr–Coulomb criterion. A discrete failure mechanism with fewer variables and higher accuracy is provided to ensure kinematic admissibility. The upper bound solution for bearing capacity is obtained by solving the power balance equation. The present results are compared with results from the published literature and the finite element, confirming the validity and superiority of the theoretical framework provided. A parametric analysis is also conducted on three hypothetical soil types (fine sand, silt, and clay), and the results show that unsaturated transient infiltration has a positive influence on increasing the foundation bearing capacity. The magnitude of the influence is comprehensively controlled by factors such as soil type, saturated hydraulic conductivity, infiltration intensity, infiltration time, and water table depth. The increase in bearing capacity due to unsaturated transient infiltration can be incorporated into Terzaghi’s equation as a separate component presented in tabular form for engineering design purposes.

Ultimate bearing capacity of rigid strip footings on c-ϕ soil subjected to combined eccentric and inclined loading

The present study calculated the maximum bearing capacity of a strip footing against eccentrically inclined coupled loading on c-ϕ soil, by means of the plane strain rigid plastic finite element method (RPFEM). The influence of soil strengths and footing width on the V-H and H-M failure envelopes (presenting the vertical load V, horizontal load H, and moment M) was thoroughly surveyed to assess the uniqueness of the V-H-M failure envelope. Based on the obtained results, the V-H-M failure envelope was found to be distinct for each value of normalized cohesion c/γB and internal friction angle ϕ. A novel equation, which is a function of c/γB and ϕ, was achieved to predict the failure envelope of the V-H-M limit load space.

Seismic Bearing Capacity of Strip Footings Placed Adjacent to Rock Slopes

ABSTRACT The bearing capacity of strip footings placed adjacent to the rock slopes subjected to pseudo-static horizontal earthquake body forces has been investigated by using the upper bound (UB) finite element limit analysis (FELA) in combination with a mesh adaptive strategy. The generalized Hoek–Brown (GHB) failure criterion is applied to describe the strength properties of rock masses, which can be treated as its native form without the smoothing of the yield surface while employing the second-order cone and power cone programming to solve the optimization models. Based on the UB FELA method, the seismic bearing capacity factor is determined considering the effect of different governing parameters, namely the horizontal earthquake acceleration coefficient k h , the normalized slope height H/B, the rock strength ratio σ ci /γB, the geological strength index GSI and the material constant m i . For design purpose, a series of non-dimensional charts are provided, and typical failure mechanisms are also discussed in detail.

Numerical Modeling of the Effect of a Weak Zone on the Bearing Capacity of Strip Footings

Numerical Modeling of the Effect of a Weak Zone on the Bearing Capacity of Strip Footings

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.

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.

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.