Search

Analytical approaches to determine the long-term settlement of shallow foundations subjected to dynamic cyclic loading with a large number of cycles (millions) are presented. The approaches use the high-cycle accumulation (HCA) model to calculate the permanent strain caused by the cyclic loading and are conceptionally similar to conventional settlement analyses. The incorporation of a threshold strain amplitude, below which no accumulation of deformations occurs, in the HCA model is discussed. It is demonstrated that the simple analytical approach, which does not require numerical calculations, gives results very similar to more complex finite-element simulations. [ABSTRACT FROM AUTHOR]

The strength anisotropy and strain softening of natural soil can significantly impact the bearing capacity of shallow foundations on clay. In this article, we present a nonlocal numerical method to study the coupled rotation of the maximum normal stress axis and strain softening on the bearing capacity of shallow foundations on clay through a Cosserat strain softening constitutive model. The strength anisotropy and strain softening characteristics were numerically implemented into a finite-element (FE) program by dynamically updating the anisotropic cohesion in global Newton–Raphson iterations. Due to its nonlocal feature, the proposed nonlocal numerical method can overcome the mesh dependence in simulating the progressive failure of clay through the classical FE method. We first validated the efficacy of this method against the results of the plane strain test and numerical results in the literature. We then study the bearing capacity of a strip footing over anisotropic and strain-softening clay through the implemented numerical method. The results indicated that the deposition angle has an important effect on the bearing capacity and failure mode. The effects of the degree of anisotropy and strain softening on the ultimate bearing capacity are quantified through the numerical method. It is found that (1) the proposed method can effectively reflect the characteristics of the maximum normal stress axis rotation on the failure surface of the footing; (2) the ultimate bearing capacity of a footing (Pu) on anisotropic clay could increase linearly with an increase in the anisotropy ratio k (i.e., k is the ratio between C1 and C2) and decreases with an increase in the softening modulus; and (3) the strength anisotropy and strain softening are strongly coupling factors impacting the bearing capacity of anisotropic clay. [ABSTRACT FROM AUTHOR]

Water table elevation leads to saturation of the soil surrounding the foundation. Saturated soil loses its load-bearing capacity due to suction reduction, becoming less stable and more prone to settling. This phenomenon can result in differential settlement, leading to uneven stress distribution on the structure. Over the last few years, substantial research efforts have been dedicated to analyzing the bearing capacity of saturated reinforced sand when subjected to loading at the foundation center, with limited attention given to unsaturated reinforced sand under eccentric loading. Eccentric loading can also result in additional stresses and moments that need to be considered in the design of the foundation to ensure its long-term integrity and functionality, especially when subjected to wetting conditions. Hence, this study investigated this aspect experimentally and numerically using the discrete element method (DEM) to uncover the intricate interactions between soil-reinforcement conditions, applied stress, and wetting-induced settlement. The results reveal that the geosynthetic reinforcement influences the extent of collapse settlement. While the reinforcement reduces collapse settlement, the enhancement is particularly notable when subjected to eccentric loadings. For both semisaturated and fully saturated conditions, the bearing capacity ratio (BCR) not only increases with the number of geosynthetic layers but also exhibits a higher rate for fully saturated sand than for the dry and semisaturated states. Unlike unreinforced sand where load eccentricity increases collapse settlement and differential settlement, reinforced sand experiences reduced settlement as load eccentricity increases. Finally, an empirical relationship by assessing the effect of the interface between the soil and the reinforcement layer was derived from regression analyses to predict the eccentric bearing capacity of strip footing under conditions of upward seepage. Practical Applications: Alterations in pore-water pressure can influence the bearing capacity of shallow foundations. When the ground beneath a foundation reaches complete saturation, the in situ stresses that usually act as confining pressure experience an abrupt decrease. This phenomenon can induce additional settlements, which is very critical in foundation design applications, especially for foundations with eccentric loading, e.g., foundations subjected to wind load. Many shallow foundations are rested on deposits in coastal regions and along riverbanks. The failure due to the accumulation of pore-water pressure occurs when the shear stress applied by the superstructure surpasses the shear strength of the compromised soil. However, in cases where failure does not emerge, there remain issues related to serviceability and the potential for excessive settlement. This research demonstrates that the geosynthetic layers not only enhance the bearing capacity of strip footing but also show a greater improvement for eccentrically loadings in fully saturated sand compared to dry and semisaturated states. [ABSTRACT FROM AUTHOR]

Over the last few decades, reliability-based design methods have been widely implemented into the foundation design practice. However, several design codes for transmission tower foundations are still based on the allowable stress design (ASD) approach and are yet to adopt the reliability-based approach for design. This paper developed a load and resistance factor design (LRFD) method based on an existing ASD code to design spread foundations of transmission towers under uplift loading in cohesionless soils. In the LRFD development procedures, additional analysis was carried out to check the statistically significant dependency of the model factors (i.e., the ratio between the measured and calculated foundation capacities) on the foundation design parameters. The analysis results showed that there were statistical dependencies between the model factors and the foundation width, which are known as scale effects. By incorporating the identified dependencies, reliability analysis was carried out via Monte Carlo simulations (MCS) by considering the context of transmission tower foundations. From the reliability analysis outputs, it was found that the foundation width had notable effects on the foundation reliability and the calibrated resistance factors. The LRFD format of the existing code was proposed, along with the resistance factors for varying foundation widths and target reliability indices. Finally, a design example was illustrated to compare the design uplift capacities from the existing ASD format and the proposed LRFD format of the design code. Compared to the existing code, the developed LRFD method showed significant improvements in the consistency of the design capacities and the associated reliability levels for a given foundation design. [ABSTRACT FROM AUTHOR]

This paper utilized an advanced surrogate modeling technique known as adaptive kriging (AK) for the probabilistic design of foundations. The quantile-based approach accounted for the variability in soil and foundation dimensions with an adequate level of safety, and the AK algorithm replaced the theoretical or numerical models with surrogate models to improve the computational efficiency. The AK model had the advantage of considering the design dimensions and their variability in its optimization algorithm. For the design of shallow foundations, the variability in the design dimensions and its optimization was carried out by introducing the width-to-length ratio as the design parameter. This meant that a surrogate model for different foundation dimensions did not need to be developed separately. This paper showed that the computational time for the AK model was much less compared with the probabilistic analysis that used numerical models. A quantile-based design and optimization procedure that used the AK model was illustrated through a shallow foundation example and provided economical design parameters. [ABSTRACT FROM AUTHOR]

Hydraulic hysteresis and mechanical behavior [i.e., void ratio (e) dependency] are fundamental in unsaturated soil behaviors. Applications of the upper bound theorem to account for these aspects in unsaturated soil mechanics have never been reported in geotechnical problems, such as bearing capacity, to the best of the author's knowledge. Therefore, this paper presented modifications to and the development of a computational limit analysis method [discontinuity layout optimization (DLO)], which considered the influence of hydraulic hysteresis, mechanical behavior, and changes in soil fabric on strength. The modified approach unsaturated DLO (UNSAT-DLO) was utilized to carry out a parametric study for a bearing capacity problem, where the numerical results were compared with 1g physical modeling tests that were conducted for a surface strip footing that was placed on sandy soil. The comparison demonstrated that the UNSAT-DLO approach could capture the nonlinearity of the experimental results within a small range of suction (s) profiles. In addition, the bearing capacity scatter-induced hydraulic hysteresis, mechanical behavior, and soil fabric changes, even at approximately the same applied s, were reasonably well defined by the UNSAT-DLO approach, because the parameters were carefully assigned. In addition, differences in the failure mechanisms due to the hysteresis were investigated to provide insights into distinct changes in the failure modes due to the hydraulic hysteresis and mechanical behaviors. The conventional design of shallow foundations was based on dry or saturated states, according to the saturation conditions, which led to a conservative design. Due to the drying and wetting cycles, soils are frequently found in unsaturated conditions. The additional strength that was imparted to soils, which was attributed to the effect of partial saturation, led to more stable geotechnical structures. The literature confirmed that suction (s) had a significant effect, and a ≤10-fold increase in bearing capacity was obtained when unsaturated cases were compared with the fully saturated conditions. Further evidence of this was the stability of vertical cuts (trenches), embankments, retaining walls, and railways. With a better understanding of the mechanics of unsaturated soils, the design of the geotechnical structures could impart additional strength due to partial saturation. The utilized (UNSAT-DLO) approach, which accounted for the effect of s and saturation, exhibited good agreement with the experimental data. In addition, it considered hydraulic and mechanical hysteresis. Therefore, the approach was a robust tool that could help with safe structures and more economical designs. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The effect of soil density on the soil–water characteristic curve (SWCC) is becoming a topic of universal interest due to the heterogeneity of soils and environmental variables. In this study, a simple and effective model based on the idea of translating the particle-size distribution curve to the SWCC is proposed for predicting SWCC change with initial density. There is only one new parameter introduced, and it is easily calibrated using two SWCCs obtained from test data. The SWCCs for the same soil at different initial void ratios can be estimated using the developed model. Several existing models are also thoroughly examined, with an emphasis on the advantages and disadvantages of each model. The validity of the proposed model was then verified by comparing it to three other models and experimental data for eight different types of soils. The proposed model also outperforms other existing models in this extensive study, providing good and consistent prediction performance across various soils. The proposed model is then applied to different engineering challenges involving the estimation of bearing resistance of unsaturated soils. Three typical examples chosen for illustration in this paper are the effect of soil density variation on unsaturated shear strength, bearing capacity of a shallow foundation, and ultimate bearing resistance of an energy pile. The findings of the investigation reveal that the proposed model can be utilized to solve a variety of problems involving soil–structure interaction in unsaturated soils. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Finite-element limit analysis (FELA) is an effective numerical method to evaluate the stability of reinforced geostructures. Such an analysis has been commonly performed in the literature by assuming the earthen material to follow the well-defined associated plastic flow rule. In this study, the effect of adopting the nonassociated plastic flow rule on the ultimate bearing capacity of eccentrically-obliquely loaded shallow footings placed over geosynthetic-reinforced granular soil is rigorously examined through a comprehensive set of lower-bound FELA simulations along with second-order cone programming. The nonassociativity of the plastic flow rule is incorporated into the formulation of the Mohr–Coulomb yield criterion by considering a wide range of dilation angles (ψ) varying between 0 and the soil internal friction angle (φ). Unlike the previous FELA studies, both pull-out (sliding) and tensile (structural) modes of geosynthetic failure are taken into account. Accordingly, the impact of considering the nonassociated flow rule for the sand deposit on the bearing capacity ratio, failure envelopes, and the failure mechanism of overlying shallow foundation is investigated and discussed. The results show that failing to consider the significant influence of nonassociativity in the FELA simulations leads to overestimations of the tensile forces mobilized in the reinforcement layer as well as the ultimate bearing capacity of the overlying shallow foundation, thus yielding nonconservative and insecure designs. [ABSTRACT FROM AUTHOR]

Shallow foundations are commonly resting on partially saturated soil and are very likely to be exposed to severe variations of temperature. The degree of saturation and matric suction will be changed at the elevated temperatures, thus resulting in different hydromechanical behavior and a considerable variation in the imposed suction stress. In this study, the effect of temperature increase on the ultimate bearing capacity of strip shallow foundations resting on partially saturated clay layer subjected to vertical (V)–horizontal (H)–moment (M) combined loading is examined through a set of finite-element limit analyses (FELA) adopting lower bound theorems and second-order cone programming (SOCP). The unified effective stress for partially saturated soils is first incorporated into the soil yield function, considering the significant effect of temperature variations on suction stress by means of the well-established previously developed nonisothermal soil–water retention curve (SWRC) model. The equilibrium equations corresponding to the combined loading are also incorporated into the FELA formulations to account for the effects of inclined and eccentric loadings. Accordingly, the failure loci of obliquely and eccentrically loaded shallow foundations are presented for a wide range of temperatures. It is shown that with an increase of the temperature in the underlying unsaturated clay, the suction stress within the soil medium significantly rises, and thus, the failure wedges as well as the failure loci for both eccentric and inclined loadings substantially expand at elevated temperatures, revealing the considerably greater bearing capacity of the strip footing. The contact pressure beneath the foundation in all loading scenarios increases with an increase in the temperature of the underlying clay. This trend is much less pronounced at higher angles of load inclination, while it is barely affected by the load eccentricity. In addition, with an increase in the induced temperature and consequently the suction stress within the partially saturated clay beneath the foundation, the failure wedge expands, thereby resulting in an overall increase in the bearing capacity of the shallow foundation against vertical–horizontal–moment combined loading. [ABSTRACT FROM AUTHOR]

Interaction of two back-to-back mechanically stabilized earth (MSE) walls in bridges has been the subject of many studies in road engineering. But regarding the other formations of this system with other types of retaining walls in excavation cuts stabilization, structure retrofitting, and other factors, the analysis of the interactive behavior of two back-to-back anchored walls (BBAW) by plate anchors and subjected to the vertical loading of a shallow foundation has not been the subject of comprehensive studies. This study experimentally investigated the effect of compound system architectural parameters [horizontal distance of two walls (W) and breadth of loading plate (B)] on its mechanical behavior. The loading plate yield and shear failure stresses, and also displacements and deformations of BBAW were measured and the results are presented. In order to evaluate the shape and form and how the critical failure surfaces behind the walls and beneath the foundation intersect with one another, the particle image velocimetry (PIV) technique was applied. The experimental tests results showed that in this compound system, the effective distance of walls is about W = 2.5*H (H: height of walls) and foundation effective breadth is about B = H, concerning foundation yield and shear failure stresses, walls displacement, and their deformations. In larger values of W and B, foundation and walls have no interaction that can be considered as an alternative solution to the limitations of the architectural parameters in practical cases. In addition, in this study, the failure modes and their mechanisms of this compound system were studied as well as its mechanical behavior. [ABSTRACT FROM AUTHOR]

The bearing capacity of foundations constructed on unsaturated soils depends on the soil saturation degree and thus the soil suction. This paper presents a simple limit equilibrium approach to compute the foundation bearing capacity on unsaturated soil using lateral earth pressure theory. An imaginary retaining wall is assumed to pass the edge of the foundation and active and passive lateral pressures on both sides of the wall are computed using the distribution introduced in an earlier study. Equating total active and passive thrusts on two sides of the wall gives the footing bearing capacity. The soil–water characteristic curve is used to obtain soil suction corresponding to different moisture contents and drained shear–strength parameters are used to determine the foundation bearing capacity. The developed method is applicable to sands and c-φ unsaturated soils with varying saturation degrees. The predicted results have been compared with data from seven case studies reported in the literature and found a satisfactory agreement. Parametric studies have been conducted to investigate effects of foundation embedded depths, two-layer soils, various suction stresses, and ground slope changes on the footing ultimate bearing capacity. The results show that with increasing the soil suction, the footing bearing capacity increases significantly. [ABSTRACT FROM AUTHOR]

Many published studies on seismic conditions have focused on a pseudostatic method with a linear Mohr–Coulomb failure criterion. However, the pseudostatic method ignores the influence of time and spatial variables on seismic accelerations, and almost all soils have nonlinear strength properties rather than linear properties. Herein, a new approach was established for calculating the seismic bearing capacity that considers a linear distribution of the seismic coefficients. A nonsymmetrical failure mechanism and the nonlinear Mohr–Coulomb failure criterion were used to describe the collapse process and soil properties. A layerwise summation method was developed to calculate the work rates because the pseudodynamic method depicts the variation in seismic acceleration as well as the time and spatial variables. In this work, a first application for calculating the seismic bearing capacity of soil foundations with nonlinear strength properties was conducted using the kinematic approach of limit analysis. Based on the numerical results and discussions, the key conclusions were as follows: (1) the reliability of this approach was verified by making exact comparisons with theoretical results and lab data; (2) in general, nonlinear solutions were more conservative than linear solutions; and (3) a high value of initial cohesion c0 resulted in an increase in the seismic bearing capacity qlim, and qlim decreased when the ratio of tensile strength σt to initial cohesion c0 or the value of nonlinear parameter m increased for a given value of initial cohesion c0. [ABSTRACT FROM AUTHOR]

Shear strength (τ) analysis has received considerable attention, because of its importance when designing various geotechnical structures, such as tunnels, retaining walls, shallow foundations, and slopes. Predicting the unsaturated τ from water retention curves (WRCs) is an existing method. The validity of this method for the prediction of unsaturated τ over a wide suction (ψ) range has been discussed by several researchers. However, the existing method ignores the influence of void ratio (e), which plays a strong part in the water holding capacity and the τ analysis of unsaturated soils. Therefore, according to an existing WRC equation that distinguishes capillary water and adsorbed water, a new WRC equation was proposed to consider the effect of e on the water holding capacity. In addition, using the e dependent WRC, a new method that predicted the τ of unsaturated silts or silty clays at various e over a wide ψ range (that included the residual zone) was proposed. The prediction of τ by the proposed method produced better predictions for experimental data than that of the existing method. [ABSTRACT FROM AUTHOR]

Deep mixed (DM) columns are being increasingly used in regions that host thick saturated soft clays. Under such geotechnical conditions, partially penetrated DM columns are predominantly designed to improve shallow foundations. Ground settlement can develop gradually over decades, however, due to the consolidation and rheological behavior of the subsoil. This work developed an analytical solution for calculating the rheological consolidation of partially penetrated DM-column-reinforced ground under a rigid foundation following the rheological Burger's model. Based on the equal strain assumption, the consolidation problem was converted into a simple problem of one-dimensional consolidation with a double-layered system. The derived solution revealed that the reduction in column permeability to less than 10% of the soil permeability had a minor influence on the consolidation rate. The consolidation rate increased slowly with increasing penetration depth. [ABSTRACT FROM AUTHOR]

Guidelines on the response analysis of rocking shallow foundations considering material uncertainties under earthquake loading are not available in any great detail. In this study, a reliability analysis of a bridge pier with a rocking shallow foundation (RSF) was performed, using the Monte Carlo simulation technique, applied on the performance functions of the bridge pier, approximated using the response surface method. The soil–structure interaction was modeled using a beam on the nonlinear Winkler foundation approach. Two ground motions, corresponding to moderate and strong seismic intensities, were used in the study. Four model configurations of the bridge pier–RSF system were considered, and the probabilities of failure were evaluated, corresponding to three performance levels. It was concluded that the probabilities of failure changed drastically with the performance level of the bridge pier. The results showed that the bridge pier–RSF system suffered minimal damage during the moderate earthquake and was effective in enhancing seismic performance during the strong earthquake. [ABSTRACT FROM AUTHOR]

This paper develops an approach that utilizes kriging surrogate models for the reliability-based design of geotechnical structures. Surrogate models improve the computational efficiency and reduce the complexity of implementation to model the deterministic numerical models. This procedure involves the calibration of a kriging model, using samples generated by any deterministic geotechnical numerical model, which can be used in geotechnical design and optimization. Reliability-based design and optimization using a numerical model involve multiple calls of the numerical model, which is made possible with the kriging surrogate model. The procedure is illustrated through a simple shallow foundation example. The results demonstrate that reliability-based design and optimization based on surrogate modeling are efficient tools that can be used to design geotechnical structures. [ABSTRACT FROM AUTHOR]

In practical engineering projects, bedrock is often encountered under a compressible soil layer. Compared with the soil layer, the hard bedrock has negligible deformation, so the displacement at the bottom of the soil layer is considered to be zero. In this case, it is difficult to use the Boussinesq solution to accurately calculate the stress and displacement of the soil layer under the action of shallow foundations. In the past, the solution has mostly been approximated by the layer-wise summation method or the finite-element method. So far, there is no analytic method to accurately calculate the stress and displacement of the elastic compressible soil layer. In this paper, an analytic method is proposed to solve the plane strain problem under the action of strip foundations. By using a mapping function to convert a soil layer with a finite thickness into the unit circle in the image plane, the stress boundary conditions at the ground surface and the displacement boundary conditions at the bottom of the soil layer are represented by a combined expression for the boundary values of the two analytic functions. A system of linear equations to find the coefficients of the analytic functions is established using a new power series method, and it is solved using the least-squares method. The stress and displacement at any point in the soil layer can be calculated quickly and efficiently using the derived analytic function. The effects of soil layer thickness on soil layer stress and ground surface settlement are discussed, and the results are compared with those obtained by the finite-element method. [ABSTRACT FROM AUTHOR]

In this study, the Taguchi design of experiments (TDOE) is employed to enhance the bearing capacity of geotechnical structures. To this end, two different case studies, including tapered helical piles as a novel kind of deep foundation (Case 1) and a shallow foundation resting on braid-reinforced soil as a new type of soil reinforcing technique for shallow foundation beds (Case 2), are studied. A series of large-scale tests, including pile loading tests in frustum confining vessel (Case 1) and standard plate load tests in test pit (Case 2), have been conducted in conjunction with numerical analyses. To the best of the authors' knowledge, this study is the first of this kind that uses the capability of the TDOE method to evaluate and improve the bearing capacity using large-scale tests. After conducting the tests, analysis of signal-to-noise, analysis of means, and analysis of variance were used to interpret the experimental results, to obtain the optimum condition, and to determine the percentage of each factor's participation in bearing capacity. Moreover, the Taguchi method output predictions are compared with the test observations and numerical modeling results. The comparison between test results and TDOE method predictions confirms that the Taguchi method can predict the bearing capacity well (R2 > 0.95). Additionally, verification tests on optimum models show a low level of relative error (RE < 5%) between the TDOE predictions and test results for both the case studies. Therefore, the results prove the ability of the TDOE method to predict and determine the optimum condition in geotechnical bearing capacity problems. [ABSTRACT FROM AUTHOR]

The soil stratum is heterogeneous and may be tilted with significant influence on the footing bearing capacity (BC). In this paper, a combination of influence of the anisotropy orientation and thickness of soil layer and rock stratum inclination on the BC of strip footings was evaluated using a random finite-difference method (RFDM). The Monte Carlo simulation (MCS) approach was used to elucidate the effect of spatial variability, and soil strength characteristics were assumed as log-normal and bounded random fields. The failure mechanism and produced shear strain in probabilistic method were compared to those obtained from deterministic analysis. The results showed that the soil stratum inclination has a significant effect on the footing BC magnitude, which reaches a minimum value when the deposition orientation is 45°−ϕ/2 with the horizontal direction (ϕ = soil friction angle). Parametric studies were performed on the variability level of strength parameters, the correlation coefficient of strength characteristics, correlation length, soil layer thickness, and stratification orientation. [ABSTRACT FROM AUTHOR]

Issue 1 The authors employed three-dimensional (3D) finite-element software Plaxis 3D ([1]) to model a ring foundation in a cohesive soil, where a quarter of the problem domain (i.e., a 90° sector of the domain) was discretized. The authors employed the commercial finite-element software, namely, Plaxis 3D, to determine the ultimate bearing capacity of ring foundations in cohesive soils. In particular, for both cases of rough and smooth foundations, Eq. (10) of the original paper cannot make a realistic prediction in terms of the change of undrained bearing capacity when the I k i value varies from 1 to 10. Rather, Eq. (10) of the original paper generates almost constant undrained bearing capacity with all I k i values for each interface condition (i.e., rough I q SB ult sb i 363 kPa and smooth case I q SB ult sb i 93 kPa). [Extracted from the article]

A lower bound finite element analysis in conjunction with linear programming technique was used to evaluate the effect of soil–foundation interface roughness on the seismic limit load of shallow foundations placed in the vicinity of slopes. The approach followed in this study to take into account seismic forces is pseudostatic. The roughness factor (δ/φ) at soil–foundation interface was considered in a complete range of 0 (perfectly smooth) to 1 (fully rough) stepwise with an increment of 1/3. Furthermore, the effects of superstructure seismic inertia forces, and nonlinear programming, which is called second-order cone programming, are also addressed. The formulation of the finite element lower solution was extended for the case of pseudostatic conditions. The findings of this study have been compared with solutions reported in the literature, and the consistency of the results confirmed the formulation of the extended finite element lower bound in the presence of seismic forces. Results of the current study clearly endorse the fact that the soil–foundation interface roughness exhibits more highlighted contributions when a footing is underlain by an adjacent slope and subject to seismic loading. The results of the current study are presented in the form of table design charts. [ABSTRACT FROM AUTHOR]

In this study, the ultimate bearing capacity and settlement of square and strip foundations in the presence of upward seepage were assessed using physical modeling. The experiments were conducted in two series with different loading values of excess pore-water-pressure paths. The experimental results demonstrate significant degradation of bearing capacity resulting from excess pore-pressure development; however, a remarkable amount of soil strength was observed when the excess pore-pressure ratio was unity in the free-field ground. A correction coefficient (fγ) for the bearing-capacity factor Ng was estimated based on the results. This factor is a function of upward-seepage magnitude. Based on the experimental results, dimensionless charts are presented to predict the settlement of square and strip footings rested on saturated sand with varied amounts of excess pore-water pressure. Results show strong dependency of settlement on the bearing-capacity safety factor presumed for the foundation design. [ABSTRACT FROM AUTHOR]

The stability of a footing may be destabilized near a retaining wall because of increased lateral displacement and decreased soil confining pressure. The stability of footing within this footing-soil-wall system is complex and not predicted using the classical solutions utilized for a semi-infinite footing-soil system. In this study, the bearing capacity of a concrete footing placed near a wall of spaced driven concrete piles using three-dimensional finite-element (FE) analysis with ANSYS 13.0 is investigated. All system materials are idealized as nonlinear, elastic-perfectly plastic, and rate independent using the upper bound function of the Drucker-Prager yield criterion. Three different soil deposits are studied: kaolin, silty clay, and kaolin-sand. A total of 144 unique FE analysis runs are executed. The footing bearing capacity is computed from the output footing pressure-settlement curve using several well-known postprocessing linearization criteria from which the lowest value is chosen. Soil yielding patterns and failure mechanisms are also studied and presented. Empirical equations capable of predicting the footing bearing capacity and the footing-pile distance without the effect of destabilizing factors are developed. [ABSTRACT FROM AUTHOR]

Shallow foundations are designed to limit settlements within tolerable limits. Additional settlements produced by the rise of the water table due to rain or floods can jeopardize the integrity of the foundation. This paper proposes a rational method, based on strain influence factors, to predict the additional settlement produced by the rise of the water table on a footing resting on sands. The proposed method was validated using extensive laboratory test data, where model footings of five different shapes were loaded in sand placed at two relative densities, and the water level was raised from the bottom while the additional settlements were measured. The clean sands used in the tests were such that there were negligible capillary effects. Separate tests were carried out to demonstrate that the capillary effects were insignificant. The proposed method can be used as the basis for further studies that incorporate the effect of grain size distribution or the effects of water table fluctuations on additional settlement. [ABSTRACT FROM AUTHOR]

By using the lower-bound theorem of the limit analysis in conjunction with finite elements and nonlinear optimization, bearing-capacity factors, and , with an inclusion of pseudostatic horizontal seismic body forces, have been determined for a shallow embedded horizontal strip footing placed on sloping ground surface. The variation of and with changes in slope angle () for different values of seismic acceleration coefficient () has been obtained. The analysis reveals that irrespective of ground inclination and the embedment depth of the footing, the factors and decrease quite considerably with an increase in . As compared with , the factor is affected more extensively with changes in and . Unlike most of the results reported in literature for the seismic case, the present computational results take into account the shear resistance of soil mass above the footing level. An increase in the depth of the embedment leads to an increase in the magnitudes of both and . [ABSTRACT FROM AUTHOR]

The load deformation and failure behavior of shallow footings can be described in a macroelement formulation. This paper deals with the study of the failure surface and the definition and validation of plastic load deformation by single surface hardening models. The straightforward application of the plasticity theory to the soil-foundation system makes it possible to extend the given expression for the case of unsaturated soils. This paper studies a small-scale footing test on unsaturated sand for the formulation of the elastoplastic macroelement of shallow footings under a centrally applied vertical load. The influence of soil suction on different parameters associated with the macroelement is studied and calibrated against experimental results. The presented model shows good agreement with the experimental results. Finally, the limitations and still open questions of the approach are discussed in detail. [ABSTRACT FROM AUTHOR]

The behavior of axially loaded skirted shallow foundations resting on sand was studied using an extensive numerical analysis. Surface, pier, and skirted square foundations resting on sand with different shear strength properties were utilized in the analysis. A physical model testing, although on much smaller scale, was also carried out to support the numerical analysis results. The effects of foundation size, shear strength of sand, and skirt depth on bearing capacity and settlement of skirted foundations were assessed. The results of this study revealed that skirted foundations exhibit bearing capacity and settlement values that are close, but not equal, to those of pier foundations of the same width and depth. The enhancement in bearing capacity of shallow foundation increases with increasing skirt depth and decreasing relative density of sand. Settlement reduction may exceed a value of 70% in the case of having skirt-depth/foundation-width of 2.0. Charts and equations are presented to estimate bearing capacity and settlement of skirted shallow foundations in terms of those of surface foundation and skirt-depth/foundation-width. [ABSTRACT FROM AUTHOR]

The concept of an open pipe pile with a gravel plug is used to develop a new short rigid composite caisson foundation for floodplains and lowlands. It consists of a shallow pipe or caisson, sunk to the desired depth by conventional sinking techniques; the soil within the caisson shaft is removed; and granular material is filled in and compacted to enhance the stability and load-carrying capacity. The caisson shaft is considered to be rigid, undergoes rigid body translation, and hence is analyzed as an incompressible cylinder, whereas the core inside is treated as a compressible pile. The soil displacements are calculated at the midpoints of the outer surfaces of each element and at the centers of the bases of the caisson shaft and the granular core by numerically integrating Mindlin's solution for a vertical point load inside a semiinfinite medium. A parametric study is carried out to bring out the effects of various parameters on the load sharing, the shear stress distribution, and the settlement of the proposed foundation. [ABSTRACT FROM AUTHOR]

In this study, a three-dimensional microscale framework utilizing the discrete-element method (DEM) is presented to analyze the seismic response of soil-foundation-structure systems subjected to three-directional base motion. The proposed approach is employed to investigate the response of a single lumped mass on a square spread footing founded on a dry granular deposit. The soil is idealized as a collection of spherical particles using DEM. The spread footing is modeled as a rigid block composed of clumped particles, and its motion is described by the resultant forces and moments acting upon it. The structure is modeled as a column made of clumped particles with a concentrated mass specified for the particle at the top. Analysis is done in a fully coupled scheme in time domain while taking into account the effects of soil nonlinear behavior, possible separation between the foundation base and soil because of rocking, possible sliding of the footing, and dynamic soil-foundation interactions. A technique to idealize several base boundary conditions to mimic rigid and elastic rock as well as an infinite medium is also presented. Microscale energy dissipation in the soil deposit in the free field and in the presence of the structure is quantified. Simulations were conducted to investigate the response of the deposit with and without the structure to various scenarios of multidirectional shaking patterns. Vertical motion amplification in the free field was similar to that of shear wave propagation. However, there was less nonlinearity for vertical motion than there was for horizontal motion. Lateral motion had a small impact on the amplification of the vertical input motion. The inclusion of vertical motion did not influence the amplification of horizontal motion at frequencies far from the resonance frequency of vertical motion. [ABSTRACT FROM AUTHOR]

A set of analytical formulas for the estimation of foundation model parameters is presented by synthesizing mechanical models at three different levels with corresponding variants of a generalized continuum model presented recently. The generalized continuum model was derived using a unified approach on the basis of a subgrade idealized as an elastic layer of finite thickness overlying a rigid base without making prior simplifying assumptions. The spring stiffness in all variants is inversely proportional to the layer thickness, rendering the model sensitive to this parameter with the potential to yield excessively large deflections for thick formations. This problem is alleviated by eliminating the layer thickness through introduction of a calibration factor in the form of a ratio of the layer thickness to the foundation width. It has been demonstrated that the calibration factor for each model type can be established from comparative analytical-numerical studies. Values obtained in this manner are suggested for practical use. The proposed calibrated formulas have potential applications in routine analysis of beam-like and plate-like shallow foundations and rigid pavements. [ABSTRACT FROM AUTHOR]

Obtaining the bearing capacity of shallow foundations in a nonhomogeneous soil profile has been a challenging task in geotechnical engineering. In this paper, a new geometric average for the equivalent soil friction angle () of various layers beneath shallow strip foundations is used to determine the ultimate bearing capacity. This approach is based on the concept of geometric mean value; however, the method involves applying a power to each variable, which is here the internal friction angle of each soil layer. Numerical methods based on finite elements and also experimental data have been used to verify the presented average method. It will be shown that data obtained from the developed method are well in agreement with those obtained from finite-element analysis and with those obtained from full-scale loading. This agreement is closer when the difference between the shear strength parameters of layers is small, which is the case for sedimentary soil profiles and also for artificially compacted soils. A computer program has been developed to investigate the influence of various parameters and to compute equivalent for different cases. [ABSTRACT FROM AUTHOR]

A simplified analytical method that determines the axial load and biaxial moment capacities of a rigid spread footing of regular or arbitrary shape resting on soil is presented. Three different types of pressure distribution at the soil-footing interface are considered: uniform, linear, and parabolic. The proposed algorithm can be used to determine (1) the maximum soil-bearing stress under rigid spread footings subjected to vertical load and biaxial bending moments; (2) the vulnerability of exceeding the maximum soil-bearing stress by comparing the biaxial moment-axial load interaction diagrams of the footing with those of the attached wall or column; and (3) the development of nomograms for the analysis and design of spread rigid footings of different shapes. Three comprehensive examples are included that show the first two applications. The third application is shown in a companion paper that deals with development of design aids for the analysis and design of rectangular and trapezoidal spread footings. [ABSTRACT FROM AUTHOR]

Design aids (nomograms) for rectangular and symmetrical trapezoidal rigid spread footings are developed using a method previously developed by the writers in a companion paper. The nomograms can be used by designers to directly determine their maximum axial load and biaxial moment capacities without exceeding the bearing capacity of the supporting soil. Three different types of pressure distribution at the soil-footing interface are considered: uniform, linear, and parabolic. The results obtained can then be compared with the biaxial moment-axial load interaction diagrams of the attached concrete walls or columns. This allows the structural designer to determine the vulnerability and likelihood of exceeding the bearing capacity of the supporting soil. Four examples are presented that show the effectiveness and simplicity of the proposed nomograms in the analysis of isolated rectangular and trapezoidal rigid spread footings resting on soil. [ABSTRACT FROM AUTHOR]

A foundation system may involve more than a single footing with an arrangement such that the footings are sufficiently closely spaced that adjacent footings interact. Vertical, horizontal, and moment capacity of multifooting foundation systems are potentially dependent on footing interaction, and in particular overturning capacity can be significantly enhanced by the structural rigidity of a multifooting foundation system. There is no established procedure for the calculation of bearing capacity of a shallow foundation system comprising cojoined footings and ad hoc approaches may simply involve summing the ultimate limit states of the individual footings as if they acted independently; neglecting additional capacity of the system available from the kinematic constraint provided by the structural connection between the footings. Plane strain finite-element analyses have been carried out to investigate the undrained ultimate limit states under general loading of skirted two-footing foundation systems at various normalized spacing compared to a single skirted footing of equal bearing area and embedment ratio. [ABSTRACT FROM AUTHOR]

Immediate and long-term settlement checks are an integral part of foundation design. Therefore, reasonably accurate estimates of the immediate settlement of shallow foundations bearing on clay are necessary, particularly for highly plastic clays or organic soils, for which the immediate settlement may be significant. This immediate settlement is due entirely to the distortion of the clay underneath the shallow foundations because, in the short term, there is no opportunity for change in the clay volume. Since soil stress-strain response is nonlinear even at small strains, design procedures based on linear elasticity cannot accurately predict soil deformations. Hence, an immediate settlement analysis that takes soil nonlinearity into account is needed. In this paper, finite-element analysis is used to develop design charts that can be used to estimate the immediate settlement of axially loaded square, rectangular, and strip footings bearing on clay. The clay is modeled with a simple nonlinear constitutive relationship. A design example is included to illustrate how the proposed procedure can be readily applied in practice with the knowledge of the undrained shear strength and the initial shear modulus of the clay. [ABSTRACT FROM AUTHOR]

A reliability-based analysis of a strip foundation subjected to a central vertical load is presented. Both the ultimate and the serviceability limit states are considered. Two deterministic models based on numerical simulations are used. The first one computes the ultimate bearing capacity of the foundation and the second one calculates the footing displacement due to an applied load. The response surface methodology is utilized for the assessment of the Hasofer–Lind reliability indexes. Only the soil shear strength parameters are considered as random variables while studying the ultimate limit state. Also, the randomness of only the soil elastic properties is taken into account in the serviceability limit state. The assumption of uncorrelated variables was found to be conservative in comparison to the one of negatively correlated variables. The failure probability of the ultimate limit state was highly influenced by the variability of the angle of internal friction. However, for the serviceability limit state, the accurate determination of the uncertainties of the Young's modulus was found to be very important in obtaining reliable probabilistic results. Finally, the computation of the system failure probability involving both ultimate and serviceability limit states was presented and discussed. [ABSTRACT FROM AUTHOR]

There is no established procedure for the calculation of bearing capacity of a shallow foundation system comprising cojoined footings. Ad hoc approaches are relied on and may simply involve summing the ultimate limit states of the individual footings as if they acted independently; neglecting additional capacity of the system available from the kinematic constraint provided by the structural connection between the footings. In this study, the undrained capacity under general loading of rigidly connected two-footing systems at various separations has been investigated with finite-element analyses. Results are presented in terms of ultimate limit states under pure vertical (V), horizontal (H), and moment (M) loading, and failure envelopes defining limiting load states under combined VH, VM, HM, and VHM loads. Kinematic failure mechanisms observed in the finite-element analyses are presented and in cases used to provide the basis for upper bound solutions. [ABSTRACT FROM AUTHOR]

The uniaxial vertical bearing capacity of square and rectangular footings resting on homogeneous undrained clay is investigated with finite element analyses, using both Tresca and von Mises soil models. Results are compared with predictions from conventional bearing capacity theory and available analytical and numerical solutions. By calibrating the finite element results against known exact solutions, best estimates of bearing capacity for rough-based rectangular footings are derived, with the shape factor fitted by a simple quadratic function of the footing aspect ratio. For a square footing, the bearing capacity is approximately 5% lower than that based on Skempton’s shape factor of 1.2. [ABSTRACT FROM AUTHOR]

The ultimate bearing capacity of shallow foundations on unsaturated soils is investigated through the concept of suction-dependent effective stress. The first approach is a new analytical solution considering the influence of matric suction on ultimate bearing capacity by extending Vesic's solution for saturated soils. Accordingly, a modification factor has been introduced as a nonlinear function of matric suction for tuning the cohesion-dependent component in the bearing capacity equation. The second approach is incorporating the unsaturated effective stress state in conjunction with the suction-dependent cohesion into a three-dimensional (3D) finite-difference code. In developing the 3D simulations, the variation in matric suction versus the depth of the soil was considered as well as the dependency of the degree of saturation on the soil suction. In addition, in three-dimensional numerical analyses, the input material parameters were modified to take into account the suction-stress concept in unsaturated soils. To assess the validity of the analytical and numerical approaches, four series of experimental data from physical plate load tests conducted under different matric suctions and embedment depths of the footing were selected. Accordingly, water retention curves of different test materials were considered as key input parameters used in both approaches to improve model predictions. Results from the analytical approach show the dependency of the presented correction factor on the soil properties, geometrical aspects of the foundation, and its embedding depth. In addition, the 3D numerical simulation revealed the suitable functionality of the effective stress approach on predicting the load-displacement behavior of shallow foundations on unsaturated soils. Moreover, the comparison between analytical, numerical, and experimental data shows a good conformance between the experimental test results, analytical solutions, and numerical predictions, especially for sandy soils. [ABSTRACT FROM AUTHOR]