Bearing Capacity Of Shallow Foundations Research Articles

Seismic Bearing Capacity of Shallow Foundations Under Large Earthquakes Using an Extended Pseudo-Dynamic Method

Seismic Bearing Capacity of Shallow Foundations Under Large Earthquakes Using an Extended Pseudo-Dynamic Method

Bearing capacity evaluation of embedded circular footing considering presence of an overload adjacent

The bearing capacity of axially loaded embedded foundations has been widely studied using analytical and numerical methods. However, there are many discrepancies in the literature results regarding the bearing capacity factors and depth factors of circular embedded footings proposed by different authors. Terzaghi's hypothesis has been used to assess the bearing capacity of shallow foundations and several analytical solutions have been proposed for computing bearing capacity factors, even though a superposition of individual contributions may lead to some error in the computed bearing capacity. This assumption has sometimes been criticized as being more conservative. This article aims to study two problems; The first part is focuses on the numerical evaluation of the superposition hypothesis in the calculation of the bearing capacity for rough circular foundations embedded in sand. In this section, the bearing capacity factors contributing to the conventional solution have been evaluated and superposition errors are indicated and compared with those found by different authors. The latter part of the work is devoted to studying the depth effect on the estimation of the bearing capacity of a rough circular footing embedded in the sand considering presence of an overload adjacent. For both analyses, the finite-difference code Flac2d (FLAC 2007) was used to reach the bearing capacity for embedded circular footings, the ground friction angles are between 25° and 40° and a depth ratio Df/D varies from 0.1 to 2. The calculation results are presented in tables and graphs and compared to previously published results available in the literature.

Integrated machine learning for modeling bearing capacity of shallow foundations

Analyzing the stability of footings is a significant step in civil/geotechnical engineering projects. In this work, two novel predictive tools are suggested based on an artificial neural network (ANN) to analyze the bearing capacity of a footing installed on a two-layered soil mass. To this end, backtracking search algorithm (BSA) and equilibrium optimizer (EO) are employed to train the ANN for approximating the stability value (SV) of the system. After executing a set of finite element analyses, the settlement values lower/higher than 5 cm are considered to indicate the stability/failure of the system. The results demonstrated the efficiency of these algorithms in fulfilling the assigned task. In detail, the training error of the ANN (in terms of root mean square error—RMSE)) dropped from 0.3585 to 0.3165 (11.72%) and 0.2959 (17.46%) by applying the BSA and EO, respectively. Moreover, the prediction accuracy of the ANN climbed from 93.7 to 94.3% and 94.1% (in terms of area under the receiving operating characteristics curve—AUROC). A comparison between the elite complexities of these algorithms showed that the EO enjoys a larger accuracy, while BSA is a more time-effective optimizer. Lastly, an explicit mathematical formula is derived from the EO-ANN model to be conveniently used in predicting the SV.

Behavior of soil reinforced with micropiles

Abstract Soil investigation is very important to check the bearing capacity before constructing any structure. There are different types of soils that cause many problems for the structure in short and long term, which are known as problematic soils. A lot of researchers dealt with improvement and reinforcement of the problematic soils by physical and chemical treatments. The objective of this study is reinforcing the problematic soil with micropiles with different depths and different configurations. In this study, two types of soils, soft clay and loose sand, were used to study the effect of adding micropiles of different depths and different configurations to investigate the best improvement of bearing capacity for shallow foundations on these soils. The results showed that reinforcing the natural soil with micropiles could improve the pressure carrying capacity of the problematic soils. When the design width is changed from under foundation alone to under foundation and 2B width, the soil reinforced with 2B depth of micropiles can raise the soil’s load carrying capacity by 45 to 65% when compared to untreated soil. Just 7% more bearing capacity may be achieved by increasing the depth of the micropiles from 2B to 3B (where B is the footing width); as a result, going deeper than 2B is not advantageous. Additionally, the bearing capacity of the micropiles increases by only 3% when the breadth of the configuration is increased from 1B to 2B; so, wider configurations than 1B are invalid.

Fast Lagrangian analysis of the short-term bearing capacity of shallow foundations in clays on the basis of the cone penetration test

Based on a numerical modelling of the cone penetration test CPT as well as the vertical response of shallow foundation in saturated clays, derivation of the cone factor Nk led to propose a CPT-based method of computation of the bearing capacity. This study was carried out by launching a detailed parametric study using the software FLAC-2D (Fast Lagrangian Analyses of Continua) based on the finite difference method. The soil material was modeled as a homogeneous elastic-perfectly plastic medium obeying the Mohr-Coulomb criterion, and the effects of the soil rigidity index Ir, the cone-soil interface, and the initial depth of the penetration on the cone factor Nk were investigated leading to an analytical formulation of Nk. After a comparative study with those proposed in the literature, the cone factor Nk was used to derive the bearing capacity factor Kc of a shallow foundation. Compared to current CPT-based methods proposed in the literature, this method reasonably predicts the short-term bearing capacity of shallow foundations in saturated clayey soil.

The Effect of Lateral Confinement on The Ultimate Bearing Capacity of Shallow Foundations on Sand

The Effect of Lateral Confinement on The Ultimate Bearing Capacity of Shallow Foundations on Sand

Prediction of ultimate bearing capacity of shallow foundations on cohesionless soil using hybrid LSTM and RVM approaches: An extended investigation of multicollinearity

This research presents the optimum performance model for predicting the shallow foundation ultimate bearing capacity (UBC). Twenty-one models are employed, trained, tested, and compared to find the best architecture computational model. Thirteen performance metrics, including three new index metrics, are used to calculate and analyze the model's performance. Five kernels, linear, polynomial, gaussian, laplacian, and exponential, have been implemented in RVM (mentioned by SRVM). These RVM models have been optimized by each particle swarm optimization (PSO) and genetic (GA) algorithm. Moreover, the kernel function of the higher-performance SRVM model has been used as kernel 1 to develop dual (parallel) kernel function-based RVM (mentioned by HRVM) models. Thus, four combinations have developed four HRVM models optimized by each GA and PSO algorithm. The Adam, root mean square propagation, and stochastic gradient descent with momentum algorithms have optimized long short-term memory (LSTM) models. The analysis of performance metrics reveals that (i) the GA-optimized laplacian SRVM model UBC3 has performed better than the PSO-optimized exponential SRVM model UBC10, (ii) PSO-optimized dual kernel-based HRVM model UBC18 has attained higher performance than GA-optimized dual kernel-based HRVM model UBC14, i.e., 0.9985. Adam-optimized model UBC19 based on the LSTM approach has gained higher performance (R = 0.9999) and the least residuals (RMSE = 5.9132 kPa, MAE = 3.7037 kPa, MAPE = 2.5314 kPa, and WMAPE = 0.0118 kPa). Also, model UBC19 has outperformed models UBC3, UBC10, UBC14, and UBC18 and published models available in the literature with higher index metrics. This study reveals that the HRVM models are less affected by multicollinearity.

Comparative study of homogenization techniques for evaluating the bearing capacity of bimsoils under shallow foundations

Bimsoils, characterized by discrete blocks within a finer-grained matrix, pose challenges in evaluating the bearing capacity of shallow foundations due to their spatial variability. To address this, a binary random field coupled with a Finite-Element model is used to simulate the variability of bimsoils. This study focuses on investigating the effect of the blocks spatial fraction (γ), the isotropic and anisotropic spatial correlations, and the undrained shear strength (cu) ratio between the matrix and the blocks. The results reveal that the coefficients of variation (CV) for the bearing capacity (qu), at a given γ, reach nearly 20% due to the diverse spatial configurations. This dispersion is attributed to the development of distinct failure mechanisms. However, optimizing the local average area used to evaluate γ can help reduce these CV values. The average qu for a given γ can be accurately determined using the Bruggeman symmetric effective medium (BEM) equation, ensuring safe design compared to traditional homogenization techniques. The BEM equation considers γ and the cu ratio, providing an accurate estimation of bearing capacity for an equivalent homogeneous model suitable for probabilistic analyses.

Working platforms and bearing capacity assessments of sand overlying clay using finite element limit analysis

The bearing capacity of shallow foundations on layered soils is typically based on empirical models assuming a strip footing. Shape factors are then applied to the strip footing solution to account for the specific geometry of the foundation being considered. A common practical application of this methodology is when the ultimate bearing capacity of a granular working platform constructed over a clay subgrade is estimated using the Working Platforms for Tracked Plant BRE-470 guideline. Previous studies using finite element limit analysis have been undertaken to examine a strip footing on a layered soil and how the resulting bearing capacity compares to that derived from BRE-470. This paper presents an extension of previous work by the authors using finite element limit analysis to investigate the three-dimensional influence on the bearing capacity of square and rectangular footings on sand over clay. The finite element limit analysis solutions are used to produce charts to assist designers with estimating the ultimate bearing capacity of granular working platforms overlying clay. The paper also aims to highlight some important considerations when adopting the BRE-470 guideline to design granular working platforms overlying clay.

Bearing capacity of shallow foundations on Florida limestone: A study of single layer and rock-over-sand subsurface

This study investigated the bearing capacity of shallow foundations on Florida limestone using 3D finite element modeling (FEM) with a bilinear strength envelope based on rock formations and bulk dry unit weights. Most Florida limestones at shallow depths are highly porous and have a low density and strength, thereby resulting in a ductile stress–strain response and contractive volumetric behavior under service loads, both of which are not well characterized by conventional bearing capacity methodologies.In this study, a bilinear Mohr–Coulomb elastoplastic model with a non-associated flow rule (negative dilation angle) was integrated into a 3D FEM code from a series of laboratory triaxial strength test results. Numerical simulations were performed for different footing sizes, shapes, and embedment depths using homogeneous rock and rock-over-sand subsurface. Beginning with the numerical results from a strip footing on a homogeneous rock deposit, a bearing capacity equation was developed for bilinear strength conditions. Further, the width, shape, and embedment factors were developed, and a reduction factor was developed based on the rock layer thickness and moduli of rock and sand for the rock-over-sand condition often encountered in South Florida. The study concludes with a comparison between developed equations and conventional bearing capacity methodologies.

Effect of Aspect Ratio on Bearing Capacity of Footings in Structured Clay

This research analyzed the role of footing aspect ratio in influencing the limit bearing capacity and associated failure mechanism in saturated, structured clays. The effects of footing aspect ratio and footing–soil interface conditions on the extent of soil destructuration, during mobilization of limit load, were investigated using advanced finite-element analyses. These analyses employed a clay constitutive model that accounted for continuous load-induced evolutions of soil destructuration and stress-induced anisotropy. The soil destructuration process caused 30%–35% reduction in the limit bearing capacity of shallow foundations. Moreover, the proposed analysis-based shape factor for footings in structured clay suggests that the use of shape factors available in the literature would overpredict the limit bearing capacity for footings in clays prone to destructuration.

Increasing the Bearing Capacity of Shallow Foundations on Soft Soil After the Installation of Micro-Piles

The bearing capacity of shallow foundations on soft soils can generally be estimated based on Local Shear Failure (Terzaghi theory). Several researchers previously stated that the installation of micro-piles on the failure area (slide) can increase the shear strength of the soil. This can be followed up by providing micro-pile reinforcement to prevent lateral soil movement. Therefore, this research was conducted to increase the bearing capacity of shallow foundations on medium-consistency soft clay soils that have been reinforced with micro piles. The research was conducted using modeling in the laboratory with a scale of 1:30. The soil sample used was kaolin clay made from slurry made from kaolin powder with a water content (wc = 1.77 LL), liquid limit (LL = 62.35%) and sample diameter (d = 33 cm). The slurry was formed by compacting at a medium consistency level with an undrained cohesion value (cu = 0.397 kg cm-2). The micro-pile material in the form of apus bamboo was installed, varying in diameter (d) 0.2 cm (0.027 B), 0.3 cm (0.04 B), and 0.5 cm (0.07 B); sum (n) 4, 9, 16, and 25; and length (L) 10 cm (1.33B), 13 cm (1.73B), and 16 cm (2.13B) micro-piles. While the foundation model uses a squarefoundation B x B with B = 7.5 cm. The tests were carried out before and after the micro-piles were reinforced with a soil shear failure test. The results showed that a decrease of 0.1B caused an increase in the ultimate bearing capacity of the micro-pile (qult-empirical, 0.1B) from the ultimate bearing capacity before installing the micro-pile. This value is then used to determine the ultimate bearing capacity ratio so that Rq,0.1B = qult-empirical,0.1B/qult-Terzaghi with the optimum bearing capacity ratio occurring at Rq,0.1B with n3 = 16, d2 = 0.04B, L2 = 1.73B.

Bearing capacity of shallow foundations accounting for seismic excess pore pressures

The method of characteristics has been used to develop a rigorous solution for the evaluation of seismic bearing capacity of shallow foundations resting on homogenous fully submerged soil accounting for the effect of earthquake-induced pore water pressures. The solution, derived with reference to both the Hill and Prandtl plastic mechanisms, is essentially referred to the bearing capacity factor Nγ, is of general validity and has been checked against finite element analysis results. An original empirical expression providing the corrective coefficient to be introduced in the usual trinomial bearing capacity formula has been proposed, accounting for the reduction in bearing capacity due to combined effect of soil inertia and earthquake-induced pore water pressures. It has also been demonstrated that, even considering earthquake-induced excess pore pressures, the soil and superstructure inertial effects are still decoupled. This allowed introducing an overall corrective coefficient accounting for both the inertial (soil and superstructure) and excess pore pressure effects, computed as the product of the corresponding corrective coefficients. Finally, original simple equations were derived giving a threshold value of the excess pore pressure ratio required to trigger a bearing capacity failure in the static post-seismic conditions because of the soil shear strength reduction.

Seismic Bearing Capacity of Eccentrically and Obliquely Loaded Strip Footings on Geosynthetic-Reinforced Soil

The paper aims to evaluate the pseudostatic seismic bearing capacity of shallow foundations on geosynthetic-reinforced granular soil subjected to inclined/eccentric combined loading. This is achieved through a comprehensive set of lower-bound finite-element limit analysis (LB FELA) simulations adopting the second-order cone programming. The pseudostatic seismic loading is incorporated into the element equilibrium equations as body forces. Both sliding and structural modes of geosynthetic failure are simulated within the FELA framework. The influences of pseudostatic acceleration, embedment depth (u), and the ultimate tensile strength (Tu) of the reinforcement layer on the failure mechanism, bearing capacity ratio, and failure envelope of the overlying obliquely/eccentrically loaded shallow foundation are thoroughly investigated and discussed. It is generally concluded that at a given reinforcement embedment depth, failure envelopes shrink substantially with the increase of the seismic horizontal acceleration and the reduction of the geosynthetic ultimate tensile strength.

Evaluation of equations for the determination of the ultimate bearing capacity of shallow foundation in cohesionless soils

Evaluation of equations for the determination of the ultimate bearing capacity of shallow foundation in cohesionless soils

Behavior of Partially Saturated Cohesive Soil under Strip Footing

In this paper, a shallow foundation (strip footing), 1 m in width is assumed to be constructed on fully saturated and partially saturated Iraqi soils, and analyzed by finite element method. A procedure is proposed to define the H – modulus function from the soil water characteristic curve which is measured by the filter paper method. Fitting methods are applied through the program (SoilVision). Then, the soil water characteristic curve is converted to relation correlating the void ratio and matric suction. The slope of the latter relation can be used to define the H – modulus function. The finite element programs SIGMA/W and SEEP/W are then used in the analysis. Eight nodded isoparametric quadrilateral elements are used for modeling both the soil skeleton and pore water pressure. A parametric study was carried out and different parameters were changed to study their effects on the behavior of partially saturated soil. These parameters include the degree of saturation of the soil (S) and depth of water table. The study reveals that when the soil becomes partially saturated by dropping water table at different depths with different degrees of saturation, the bearing capacity of shallow foundation increases about (4 – 7) times higher than the bearing capacity of the same soil under saturated conditions. This result is attributed to matric suction value (i.e negative pore water pressure). The behavior of soil in partially saturated condition is likethat of fully saturated condition but with smaller values of displacement. It is found that the settlement is reduced when the water table drops to a depth of 2 m (i.e. twice the foundation width) by about (92 %).

The effect of cohesion heterogeneity and anisotropy in c–φ soils on the static and seismic bearing capacity of shallow foundations

The effect of cohesion heterogeneity and anisotropy in c–φ soils on the static and seismic bearing capacity of shallow foundations

Seismic bearing capacity of shallow foundations subjected to inclined and eccentric loading using modified pseudo-dynamic method

In this paper, a comprehensive parametric study is conducted to evaluate the seismic bearing capacity of shallow strip foundations overlying dry and cohesionless granular soil under the actions of inclined and eccentric loadings. For this purpose, a systematic combination of the lower-bound theorems of the limit analysis, the finite element method, and the nonlinear programming is implemented. The seismic loading condition is simulated by the well-established modified pseudo-dynamic (MPD) approach by accounting for the significant influence of phase difference as well as the primary and shear waves propagation through applying non-uniform inertia forces along the vertical and horizontal directions, respectively. Unlike the pseudo-static approach, in the so-called modified pseudo-dynamic loading, a more realistic dynamic nature of the seismic excitation is taken into account using various soil dynamic properties and spectral parameters of the problem under study. In this way, a more viable response of the shallow foundation subjected to seismic loading could be captured by simulating a visco-elastic material through the well-defined Kelvin-Voigt model. The modified pseudo-dynamic (MPD) method considers the influences of shear and primary wave velocities, amplification of earthquake loading, and period of lateral shaking. The current MPD approach is capable of considering the local site effects and damping characteristics of the soil deposit underneath shallow footing by adopting a non-uniform and nonlinear acceleration field inside the soil medium. The results of the seismic bearing capacity are presented in the forms of spectral responses and failure envelopes for the eccentric and inclined loadings. The results show that the failure envelopes of the shallow foundation subjected to either inclined or eccentric loading significantly shrink with the increase in the earthquake accelerations and decrease in the material damping of the underlying soil mass. The amount of changes in the size of failure envelopes in the normalized V-H and V-M spaces due to the variation of seismic intensity and material damping depends directly on the non-dimensional frequency of the earthquake excitation.

Development of mathematically motivated hybrid soft computing models for improved predictions of ultimate bearing capacity of shallow foundations

Ultimate bearing capacity (UBC) is a key subject in geotechnical/foundation engineering as it determines the limit of loads imposed on the foundation. The most reliable means of determining UBC is through experiment, but it is costly and time-consuming which has led to the development of various models based on the simplified assumptions. The outcomes of the models are usually validated with the experimental results, but a big gap usually exists between them. Therefore, a model that can give a close prediction of the experimental results is imperative. This study proposes a grasshopper optimization algorithm (GOA) and salp swarm algorithm (SSA) to optimize artificial neural networks (ANNs) using the existing UBC experimental database. The performances of the proposed models are evaluated using various statistical indices. The obtained results are compared with the existing models. The proposed models outperformed the existing models. The proposed hybrid GOA-ANN and SSA-ANN models are then transformed into mathematical forms that can be incorporated into geotechnical/foundation engineering design codes for accurate UBC measurements.

Bearing capacity of foundations resting on rock masses subjected to Rayleigh waves

This study investigates the ultimate bearing capacity of shallow foundations resting on rock masses under earthquakes using upper-bound limit analysis. A modified pseudodynamic method (MPD) that considers the influence of Rayleigh waves is initially used to characterize the spatiotemporal variation in earthquake acceleration. The strength of rock masses is governed by the generalized Hoek‒Brown criterion and the plastic flow at failure is assumed to respect the associated flow rule. The generalized tangential technique is introduced to provide a linear approximation of the strength envelope for capturing the equivalent Mohr‒Coulomb strength parameters. The classic nonsymmetrical multi-block translational mechanism, which is capable of assessing a rock-foundation system under asymmetrical load, is reconstructed to portray the velocity discontinuity of the plastic failure region. Based upon the energy equilibrium theorem of the limit analysis, an analytical solution of seismic bearing capacity is derived and then formulated as a multivariate optimization problem. Comparisons show good agreement with the literature and validate the correctness and rationality of this work. Parametric study indicates that the seismic foundation capacity obtained by MPD tends to be conservative compared to the pseudostatic method with the same seismic coefficients, and that the period of a Rayleigh wave has only a slight effect on the bearing capacity. The failure region is more sensitive to the disturbance coefficient than it is to the other rock strength parameters.