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The bearing capacity of shallow foundation is significantly affected by stratum uncertainty, mainly including geological uncertainty and spatial variability of soil properties. This paper aims to develop a general framework of shallow foundation to characterize the influence of two types of uncertainties on bearing capacity quantitatively. The geological uncertainty is simulated by Markov random field with different borehole schemes. The spatial variability is characterized using random field theory considering variations of the vertical scale of fluctuation. The bearing capacity of shallow foundation analysis is then conducted based on the proposed calculation framework. Borehole data and soil properties collected from Shenzhen Mawan are adopted as an example to illustrate the proposed framework. A reduction factor is developed to reveal the relationship of two category uncertainties on bearing capacity. A contribution rate indicator is defined to quantitatively evaluate the impact of two category uncertainties. Results show that the geological uncertainty greatly influences the calculation results when boreholes are sparse. However, spatial variability dominates in two kinds of uncertainties when having relatively more boreholes. [ABSTRACT FROM AUTHOR]

The static stiffness of suction caisson foundations is an important engineering factor for offshore wind foundation design. However, existing simplified design models are mainly developed for nonlayered soil conditions, and their accuracy for layered soil conditions is uncertain. This creates a challenge for designing these foundations in offshore wind farm sites, where layered soil conditions are commonplace. To address this, this paper proposes a multifidelity data fusion approach that combines information from different physics-based models of varying accuracy, data sparsity, and computational costs in order to improve the accuracy of stiffness estimations for layered soil conditions. The results indicate that the proposed approach is more accurate than both the simplified design model and a single-fidelity machine learning model, even with limited training data. The proposed method offers a promising data-efficient solution for fast and robust stiffness estimations, which could lead to more cost-effective offshore foundation designs. [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]

This paper investigates probabilistic failure envelopes of strip foundations on spatially variable soils with profiles of undrained shear strength, su, linearly increasing with depth using lower-bound random finite-element limit analysis. The spatially variable su is characterised by a non-stationary random field with linearly increasing mean and constant coefficient of variation (COV) with depth. The deterministic uniaxial capacities and failure envelopes are first derived to validate the numerical models and provide a reference for the subsequent probabilistic analysis. Results indicate that the random field parameters COVsu (the COV of su) and Δ (dimensionless autocorrelation distance) have a considerable effect on the probabilistic normalised uniaxial capacities, which alters the size of the probabilistic failure envelopes. However, an insignificant effect of COVsu and Δ on the shape of probabilistic failure envelopes is observed in the V–H, V–M and H–M loading spaces, such that failure envelopes for different soil variabilities can be simply scaled by the uniaxial capacities. In contrast to COVsu and Δ, the soil strength heterogeneity index κ = μkB/μsu0 has the lowest effect on the probabilistic normalised uniaxial capacity factors, but the highest effect on the shape of the probabilistic failure envelopes. A series of expressions is proposed to describe the shape of deterministic and probabilistic failure envelopes for strip foundations under combined vertical, horizontal and moment (V–H–M) loading. [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]

Characterization and analysis of foundation material are basic concerns of geotechnical activities to have safety for the structure and users as well. Particularly, it is quite important for the areas of lagging experiences with a lack of equipment and accessibility to investigate the subsurface conditions sufficiently. This study was designed for comprehensive soil investigations through analytical and Plaxis 2D simulation by considering square footing in Bule Hora town, Southern Ethiopia. Considering the investigation depth up to 5.0 m, fourteen soil samples at 1.5 m and 3.0 m depths (two samples from seven pits) were collected, and physical and engineering properties were investigated. Grain and consistency results indicated that soils lying between low to high plastic silt regions. Undrained shear strength (Cu) ranges from 49.5-–64.30 and 52.40–103.10 kN/m2 at 1.5 m and 3.0 m depth, respectively. An average allowable bearing capacity of 145.35 kN/m2 with a settlement of 40.77 mm at 1.5 m depth and 191.41 kN/m2 with a settlement of 47.84 mm at a depth of 3.0 m using the analytical method whereas 122.72 kN/m2 was obtained with the settlement of 30.57 mm at a depth of 1.5 m and 155.11 kN/m2 with 29.08 mm at depth of 3.0 m using Plaxis 2D analysis. The results of bearing capacity and settlement analyzed by the numerical method are lower than the analytical method, which confirms that comparatively, Plaxis 2D analysis gives a better output in selected square footing of shallow foundations. In conclusion, Plaxis was a preferable analysis tool for a shallow foundation, square footing, using inputs of the exhaustively investigated actual condition of soils specifically in Bule Hora town. [ABSTRACT FROM AUTHOR]

The limit analysis approach is used in this paper to analyse the problem of a strip foundation on cohesive-frictional soil under seismic conditions, based on the pseudo-static approach, considering different inclination factors. In particular, for a weightless c–ϕ soil, the upper-bound (UB) and the lower-bound solutions are found to be coincident, and then the exact solutions for the bearing capacity factors Nqe and Nce under seismic conditions are obtained. The effect of soil weight is considered with the UB method. A discussion is presented on seismic reduction factors and their superposition. [ABSTRACT FROM AUTHOR]

Gypsum is regarded as an environmentally friendly binding material and is widely used to enhance the engineering properties of soft fine-grained soils. However, the time-dependent strength and deformation characteristics of fine-grained soils stabilised with gypsum have not yet been thoroughly investigated and rational evaluation of these characteristics will assist in the formulation of cost-effective and reliable design approaches. In this study, the time-dependent mechanical behaviours of gypsum-mixed fine-grained soil (GMFS) specimens were investigated under unconfined monotonic loading conditions, considering ageing periods of 3–90 days and five different loading rates (LR = 0.0005–1.0%/min). The results revealed that the unconfined compressive strength and stiffness of the GMFS specimens initially decreased with ageing and finally became stable after 14 days and 28 days of ageing for water/gypsum ratios of 1.30 and 1.60, respectively. Furthermore, the strength and stiffness of the GMFS specimens increased with an increase in LR. [ABSTRACT FROM AUTHOR]

In this paper, the finite element method (FEM) is applied to calculate the bearing capacity of two footings having the aspect ratio L/B (where L and B are the length and width of the footing, respectively) equal to 1, 2 resting on one-layer and two-layer soil. Soil profile contains two soil types including sand and clay. The soil strip is 500mm × 500mm × 350mm; however, only a quarter of the model (250mm × 250mm × 350mm) is examined in the study. Two primary situations are investigated in this study. In the first situation, the one-layer system is supposed to be sandy soil with footing overlays on medium-dense sand. The soft clay/stabilized clayey layer is supposed to be on top of the sandy soil in the second condition, with the footing resting on top of the soft clay/stabilized clay. The influence of layer thickness, aspect ratio, and material property on the bearing capacity value and footing failure mechanism is studied for eight different combinations of layered soil. The bearing capacity for a one-layer case is also estimated, and it agrees well with Vesic (1973), Hansen (1970), and Terzaghi's (1943) equations. The bearing capacity of footings is observed to decline when the height of unstabilized clayey soil increases, and it increases when clayey soil is stabilized with molasses, waste foundry sand, and lime alone and in combination with each other. [ABSTRACT FROM AUTHOR]

The reduction of soil strength and stiffness caused by soil liquefaction is an important issue in designing pile or shallow foundations on liquefiable soils. In practice, strength and stiffness reduction is considered via a reduction factor ( D E ) approach in seismic design. Different sets of values of D E are available according to the factor of safety against liquefaction ( F L ) of the liquefiable soil; these ( F L ) values are usually calculated using simplified liquefaction analysis procedures. Each set of D E is calibrated and constructed for specific simplified liquefaction analysis procedures or soil conditions. Thus, engineers have difficulty in selecting D E when using a simplified liquefaction analysis procedure without a corresponding set of D E . In this study, values of D E for simplified liquefaction analysis procedures commonly used in Taiwan are obtained using a single element test via FLAC program and UBCSAND model. In addition, a novel application of D E is introduced to improve the usability of the simplified numerical procedure used to predict the liquefaction-induced settlement of a shallow foundation. Simulation results show that the simplified numerical procedure with D E approach yields a convincing and conservative result. [ABSTRACT FROM AUTHOR]

The extensive injury caused to buildings by liquefaction during past earthquakes, with the uneven spatial distribution of damage, raises the need for rapid predictive tools, applicable at a large scale, that comprehensively account for the properties of earthquake, subsoil and structure. A method is herein proposed to quantify the angular distortion of framed low-rise buildings based on a simple characterization of the above factors. The analysis moves from past literature criteria introduced to quantify the vulnerability of buildings under static conditions and extends their applicability to liquefaction assessment integrating parametric two-dimensional numerical analyses with recent literature predictive formulas and machine learning inference. The numerical calculation, performed for variable stratigraphic and mechanical characteristics of the subsoil, ground motion and equivalent flexural stiffness of the foundation, quantifies the role of each factor on the absolute settlement and angular distortion. Then the dependency on the different factors of the angular distortion is inferred with an artificial neural network, grouping parameters to limit the number of input variables and express results with charts that make prediction more accessible. [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]

Foundation in construction is part of a structural system that supports and anchors the superstructure of a building. Settlement and bearing capacity are crucial factors in the foundation design of a building or structure. The two main components of foundation settlement are consolidation settlement and instantaneous (or elastic) settlement. The ultimate bearing capacity is the greatest load that the soil beneath the foundation can support before failing due to shear. The applied loads, soil stiffness, and geometrical characteristics of the foundation have an impact on shallow foundation settlement. Settlement calculations are based on soil properties which are obtained from field and laboratory investigations. In this study, laboratory tests are performed on samples gathered from the site, and settlement calculations are computed using conventional methods; also, software analysis and settlements were recorded. [ABSTRACT FROM AUTHOR]

The addition of a soil–cement reinforcement layer is an alternative to improve the bearing capacity of shallow foundations on weak soils. Recent research with small-scale tests highlighted the influence of the soil–cement layer's geometry and tensile strength in bearing capacity prediction of footings resting on treated layers. This work presents the evaluation of field static load tests of circular steel footings resting on soil–cement layers above a weak residual soil. Results showed on the one hand that traditional methods for predicting bearing capacity in homogeneous soils could be applied when the foundation and reinforcement layer are expected to punch together into the weakly bonded residual soil, without the failure of the reinforcement layer until some prescribed load. On the other hand, methods for continuous double-layer systems could be used where the reinforcement layer is expected to fail before reaching the prescribed load. The failure mode could be predicted by calculating the maximum tensile stress at the bottom of the reinforcement layer at the prescribed foundation load. An equation for this purpose was suggested and successfully tested against real-size field test results. Finally, analytical solutions for determining the bearing capacity were effective in foreseeing the field values. [ABSTRACT FROM AUTHOR]

Fine-grained sedimentary deposits can bear an increased risk for building settlements due to their moderate stiffness and strength properties, as well as high groundwater tables. However, some buildings, e.g., situated on shallow foundations in Alpine basins, show only relatively small settlements because the formation of carbonate cement can create bridging bonds between the detrital soil particles, leading to increased stiffness. These weak bonds can be damaged through dynamic loads and high static loads, causing a weakening of the soil's microstructure and resulting in large settlements in several cases. However, the environmental controls and mechanistic processes underlying the formation versus damaging of microstructure in fine-grained, postglacial sediments are, to date, poorly understood. In the present study, fine-grained sediments are artificially cemented by calcium carbonates (CaCO3) to investigate (i) the influence of a mild and sustainable cementation process on the stress–strain behavior of silicate- and carbonate-rich soils and (ii) the possibilities and limitations of artificial microstructure development for soil stabilization. Incremental load oedometer testing (IL), bender element testing (BE), X-ray diffraction (XRD), scanning electron microscopy (SEM) and Brunauer–Emmett–Teller (BET) specific surface area (SSA) measurements are used to characterize the development of cementation and to elucidate the improvements in the soil mechanical properties. It is shown that cementation induced by CaCO3 mineralization (by 5–15% replacement) leads to an increased stiffness (factor ≈ 5–7) and shear wave velocity (factor ≈ 1.1), caused by the formation of nanocrystalline, particle-binding CaCO3 cements. The improvement of soil stiffness is dependent on the CaCO3 replacement level, reaction time and primary soil mineralogical composition. [ABSTRACT FROM AUTHOR]

Soil mixing is considered to be effective for a range of applications and the required design specifications can be achieved by varying the percentage of additives, commonly cement and lime. This paper describes the results of a comprehensive laboratory investigation involving the assessment of cement/lime treatments for improving the geotechnical characteristics of three different soft clays: kaolin, sleech and Belfast clay. The investigation is coupled with an assessment of the durability of the treated soil and the effects of water ingress after treatment. Observations showed that the large-strain Young's modulus increased significantly with curing period after 28 days. The evolution of the small-strain shear stiffness was progressive, and all soils exhibited a steady increase in stiffness, the rate of which reduced as the curing period approached 7 days. The relative increase in strength of the different soils was highly variable. It is postulated that suction was one of the contributors to undrained shear strength gain. When allowed access to water, strength and stiffness increased, although at a much reduced rate. The stress–strain behaviour of kaolin also changed from ductile when untreated to highly brittle as the curing period approached 90 days. [ABSTRACT FROM AUTHOR]

Design of shallow foundations subjected to dynamic loading is an important topic in the geotechnical engineering practice. In this study, an attempt has been made to evaluate the seismic bearing capacity of a strip footing founded on a soil deposit using the lower bound limit analysis method merged with the finite element formulation adopting the second-order conic programming (SOCP) approach. To this end, a well-established pseudo-dynamic loading scheme has been employed to apply the seismic loading on the surface footing. Accounting for the various conditions of the underlying soil layer, the results of the so-called 'conventional pseudo-dynamic (CPD)', 'spectral pseudo-dynamic (SPD)' and 'modified pseudo-dynamic (MPD)' bearing capacity analyses are compared with one another and their pseudo-static counterparts in terms of the value of N γ parameter. The results show the notable influence of the amplification factor, the impedance factor and the site characteristics on the seismic bearing capacity of shallow foundations. In addition, the results obtained from the MPD, CPD and SPD methods are observed to bear a good agreement with each other. Moreover, the MPD approach was observed to render the most conservative seismic bearing capacity values. [ABSTRACT FROM AUTHOR]

This paper is a continuation of the research on the influence of different modeling of the subgrade reaction coefficient on the selected static system. This paper analyzes the behavior of a two-story reinforced concrete frame for different foundation dimensions and different values of the subgrade reaction coefficient. It presents an overview of values of these coefficients, which represent the stiffness of Winkler springs with respect to the specific geometry of shallow foundations. The values are different depending on the author, and the average value was used as relevant for comparison. Results of the numerical analysis for an individual reinforced concrete two-story frame were obtained using the SE_Calc and Tower 8 programs. After obtaining the results for each individual frame, they were combined and analyzed [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]

A computationally efficient semianalytical framework for obtaining the consolidation settlement of flexible foundations such as beams and strip footings resting on nonlinear, saturated, poroelastic, and multilayered continua (soil) is developed. Two-dimensional (2D) plane strain is assumed, and Biot's consolidation theory is used in the analysis. The differential equations governing the displacements and excess pore pressure dissipation of the beam-soil system are developed using the variational principles of mechanics in which the soil is modeled as a simplified continuum and the foundation is modeled as an Euler-Bernoulli beam. The developed differential equations are coupled and are solved following a unique iterative algorithm using one-dimensional (1D) finite-element analysis. The numerical solution is less expensive than conventional 2D numerical methods. A distinct feature of the developed framework is that the effect of soil stress-strain nonlinearity is considered in the calculation of the consolidation settlement, which is usually not considered in Terzaghi's and Biot's consolidation theories. It is observed that soil nonlinearity and foundation flexibility can significantly impact the foundation settlement and consolidation rate. The developed framework provides a fast, easy-to-use, and accurate method for estimating the consolidation settlement of flexible shallow foundations. [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]

The calculation of vertical bearing capacity plays a crucial role in the design of suction caissons, particularly under more complex loading conditions. In this paper, a series of three-dimensional axisymmetric finite element limit analyses were carried out to measure vertical bearing capacities of circular footings and suction caissons in cohesionless soils. The empirical shape and depth factors were derived by analyzing bearing behavior of cohesionless soil. Considering the presence of friction on imaginary cylindrical retaining wall for the active–passive Coulomb wedge mechanism, the theoretical bearing capacity equation of suction caissons was established based on limit equilibrium of sliding bodies to provided new predictive solutions. The results showed that for a shallow foundation, the empirical equations obtained by regression methods can better depict the mathematical relationship between the factors (s γ , d γ and s q d q) and the affected parameters (ϕ' and L/D) as a result of that the error is less than 5%. The friction angles along virtual cylindrical retaining wall were given by combining the above empirical equations. Due to a corresponding change in surcharge load caused by the friction force acting on outer wall, the theoretical equation is relatively conservative for predicting the bearing capacity of suction caissons. [ABSTRACT FROM AUTHOR]

Loess soil presents a collapsible behavior and suffers significant settlements due to wetting that can seriously affect the structures supported on it. The increase in water content produces a permanent change in loess soil microstructure and sudden volume reductions. In this work, a hydro-mechanical (H-M) model is presented to analyze the soil response and the behavior of strip foundations on loess soil using a 2D finite element model. Numerical models were calibrated, on one hand, from experimental data of double oedometer tests and soil water retention curve; and on the second hand, by retrofit analysis from the measurement of settlements in full-scale foundation prototypes over collapsible loess during controlled water pipe leakage. The settlements were studied by performing statistics, sensibility, and inverse analyses. Final settlements after 2 years of infiltration of water were computed using Monte Carlo simulations. The results show that the compression index at saturation is the most significant parameter controlling the behavior of collapsible loess. Optimum sets of parameters were achieved with inverse analysis, demonstrating the accuracy of the H-M model to predict collapse-induced settlements of shallow foundations. [ABSTRACT FROM AUTHOR]

Shallow foundations are widely employed in offshore engineering. However, there is a limited number of studies that investigate the probabilistic undrained bearing capacity of shallow foundations in three-dimensional space. This study utilize random finite element method to explore the probabilistic undrained bearing capacity of skirted circular foundations in three-dimensional spatially variable soils. Results show that the failure mechanism under vertical loads can vary dramatically in the presence of spatial variability, while its effect on the failure mechanism under horizontal loads or moments is minimal. The variation of stochastic uniaxial capacities becomes larger with increasing coefficient of variation of soil strength and scale of fluctuation or decreasing embedment ratio. The probabilistic failure envelopes are affected by embedment ratio and soil heterogeneity index in terms of the shape and size, while the probability level and random field parameters mainly have an impact on the size rather than the shape of the failure envelopes. The application of the expressions describing the failure envelopes in different normalised loading planes was demonstrated through an example. • The three-dimensional geometry of spatially variable soils and foundations is considered in probabilistic analysis. • Probabilistic uniaxial capacities and failure envelopes are obtained for skirted circular foundations in different types of spatially variable soils. • The influence of foundation geometry, soil profile and random field parameters on the probabilistic bearing capacities and failure envelopes are investigated. [ABSTRACT FROM AUTHOR]

A number of simple models containing frequency‐independent elements have been presented to simulate unbounded soil in dynamic soil‐structure interaction problems. Most of the existing models were established through a traditional top‐down strategy with significant computational complexities. This study develops an alternative method based on a bottom‐up strategy, in which the optimal element layout is determined by an adaptive refinement procedure considering finite modularized units. This innovation eliminates the need for lengthy procedures to establish simple models. The proposed three‐parameter model is used to simulate the layered soil for rigid foundations undergoing vertical vibration. The accuracy of the model is validated by comparing the magnified responses obtained when a foundation is subjected to harmonic forces with those obtained via theoretical solutions and advanced numerical simulations. The proposed model is found to effectively simulate a layered half‐space and a soil layer on rock. Compared to two existing models, the proposed model performs better and has fewer parameters and a higher degree of adaptivity. Therefore, the adaptivity of simple models obtained using the proposed method may allow simulation of a variety of layered soil systems. [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 paper, the limit equilibrium method with the pseudo-static approach is developed in the evaluation of the influence of slope on the bearing capacity of a shallow foundation. Particle swarm optimisation (PSO) technique is applied to optimise the solution. Minimum bearing capacity coefficients of shallow foundation near slopes are presented in the form of a design table for practical use in geotechnical engineering. It has been shown that the seismic bearing capacity coefficients reduce considerably with an increase in seismic coefficient. Be sides, the magnitude of bearing capacity coefficients decreases further with an increase in slope inclination. [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 robust and integrated interpretation of soil data from field investigations can provide valuable insights into the important role of soil deterioration following the installation of suction caissons. Therefore, a field experiment was conducted at a site in Frederikshavn to simulate laterally loaded suction caisson in a layered soil profile. The experiment was performed to validate our modeling approach and to systematically analyze the predictive capabilities of three classes of numerical predictions (Classes A, A1, and C). The Class A1 prediction focused primarily on the trajectory of the rotation center and the capacity of existing failure criteria to predict the bearing strength of shallow foundations under combined loading, despite differences in stress conditions, foundation geometries, and soil weakening due to the installation effect. On the other hand, the Class A prediction was carried out based on wished-in-place conditions. Failure envelopes within the Class C predictions were adopted to be scaled by the pure bearing capacities (given by intersections with the axes). Subsequently, the appropriateness of identical envelopes was examined here by employing three-dimensional finite-element analyses in the presence of the parabolic variations in soil stiffness with depth. An alternative macroelement model of varying failure surface parameters was also represented, which enables the bearing capacity of skirted foundations to be predicted for a wide range of embedment ratios and sand strength inhomogeneities. [ABSTRACT FROM AUTHOR]

Foundations may be constructed at close spacings. Prior investigations have presented insights into the interference effect of two nearby shallow foundations on homogenous soils. However, soils are often deposited in layers, such as a sand layer overlying clay. Hence, the interference effect of two adjacent foundations on their ultimate bearing capacity for sand overlying clay has been a relevant topic, which is complex because it is tied to a coupling effect of the geometric configurations and the soil properties. In this paper, the ultimate bearing capacity of two interfering strip footings on sand overlying clay is determined using an upper-bound limit state plasticity method known as discontinuity layout optimization (DLO). The solution is illustrated as design charts constructed through the use of dimensionless parameters. Parametric studies are performed to explore the influence of geometric and strength parameters on the bearing capacity and the failure mechanism. A simplified model is developed based on the data obtained from DLO. Validations are carried out to demonstrate the accuracy of the developed model using various statistical criteria, including coefficient of determination (R2), arithmetic mean and coefficient of variation. [ABSTRACT FROM AUTHOR]

This paper presents a field study of obliquely loaded rocking shallow foundations resting on cohesive soil. Lateral snap-back and cyclic loading tests at an oblique angle of 45° with respect to the footing axes were carried out. During the snap-back tests, an initial drift ratio was applied to the deck and then the system was released to enable the free vibration. The cyclic loading consisted of five packets containing three to four cycles of similar displacement amplitude. The rocking system consisted of a 1·5 m by 1·0 m concrete footing, steel column and deck. The factors of safety against bearing failure were varied from 4 to 20. It was observed that the system primarily rocked in plane. The moment capacities about footing axes deviated from the calculated values at the orthogonal loading conditions. A method of estimating the rocking moment capacity of a footing subjected to oblique loading was developed and validated by the tests. Natural periods, damping ratio, re-centring ratio, settlement and stiffness degradation during the tests are discussed and compared with the results from previous studies with orthogonal loading. The soil–footing contact area was approximately triangular. A method of calculating the critical contact area was developed based on the bearing capacity theory with two-way eccentricity and then confirmed by observation. [ABSTRACT FROM AUTHOR]

In the tropical area, most shallow foundations and embankments are involved in dealing with unsaturated soils. Any collapse or settlement in unsaturated soils is determined by two independent stress variables: the applied stress and suction. The massive collapse related to suction changes may lead to unrecoverable damages to compacted earth fills both economic and human loss while this collapse has not been seen in the design. The aim of this study was to investigate the influence of stress states and matric suction on collapse behavior of an unsaturated Malaysian granitic residual soil grade V. A suction-controlled double wall triaxial test was carried out to obtain the axial strain of the compacted specimen during loading and wetting collapse. In addition, there has been an attempt to predict the collapse behavior of the soil by using Rotational Multiple Yield Surface Framework (RMYSF). During loading in imposed suction, the axial strain increased as deviator stress increased. When the soil was inundated and the imposed suction was decreased step by step down to zero, the axial strain was very small at suction close to residual suction. It gradually increased as suction decreased. A massive settlement around 1.92% of the initial height was observed while the soil was nearly saturated. The findings also proved that the RMYSF model is able to predict the collapse behavior of the tested soil sufficiently. [ABSTRACT FROM AUTHOR]

Based on the characteristics of moso bamboo including high short-term strength, stable performance, and ability to provide temporary support for shallow foundation pits in soft soil, the stress characteristics and supporting effects of the ecological composite supporting system have been explored through model tests and numerical calculation analysis of the moso bamboo micropile-composite soil nailing structure. The results showed that the bamboo pile can effectively control the horizontal deformation of the side wall of the foundation pit and the ground surface settlement, achieving a relatively satisfactory supporting effect. Furthermore, the bamboo pile has visibly bent in middle and lower parts, where the regional shear point is most likely to appear, the axial force of the soil nail is distributed in an oval pattern with a smaller force on both sides and a larger force in the middle part, the maximum axial strain is 447.3 με, and the axial force of the soil nails in each row follows a similar trend. The synergy of piles and soil nails can delay the formation of the slip surface, therefore enhancing the overall bearing capacity of the foundation pit. These results can shed light on the support mechanism and engineering design of bamboo piles in shallow soft soil foundation pits. [ABSTRACT FROM AUTHOR]

A numerical and an empirical method for calculating nonlinear load-settlement curves for shallow foundations on sand are examined and used in a new methodology. Both methods have merits and drawbacks. The drawbacks are overcome by the methodology proposed and verified in the paper. This methodology combines the merits of each method. For this purpose, a modification of the empirical method is proposed that accounts for the finite initial soil stiffness at very small strains. Computer programs with sophisticated nonlinear stress-strain relationships, such as Hardening Soil Small in Plaxis 2D, which are versatile in solving complex foundation problems, can cover strains from very small to large. When the foundation soil is layered, it is proposed to fit such a numerical load-settlement curve against the modified empirical relationship for each sand layer separately. This requires cone penetration tests, measurements of the shear wave velocity, and basic laboratory tests. The methodology is described and applied at two locations where load tests on footings were carried out. At one location there was a top layer of clay, which was also taken into account. The results of the application of the proposed methodology are very good. [ABSTRACT FROM AUTHOR]

In this study, a probabilistic approach for evaluating the bearing capacity of surface footings is discussed. The evaluation is based on a kinematic approach. The considered substrate consists of two different layers of soil: a top layer formed of medium or dense sand followed by a layer of soft clay. The sand layer is assumed to be homogenous, whereas the undrained shear strength of the soft clay layer is assumed to be spatially variable, described by a lognormal random field. The random field is discretized according to Vanmarcke's spatial averaging along dissipation regions in the considered failure mechanism. The mechanism utilizes plane strain conditions; however, due to consideration of the soil spatial variability in three dimensions, the impact of the length of the foundation on the random bearing capacity evaluation is considered in this study. As a result of the discretization procedure, a set of correlated random variables is obtained (each associated with an individual dissipation region in the failure mechanism). A series of numerical analyses are performed for two thicknesses of the first layer and a set of anisotropic correlation structures for the spatial variability of the undrained shear strength. The proposed method is computationally efficient and allows consideration of three-dimensional spatial variability in soil strength properties. The results are discussed and compared with those obtained by other methods. [ABSTRACT FROM AUTHOR]

The numerical modeling of soil–structure interaction systems for cracked foundations laying on nonlinear clay soils is performed by solving line spring model, using the method of exact series solutions. This semi-analytical approach is well known in fracture mechanics practice for the computation of structural responses near the crack tips, as well as for the calculation of normalized stress intensity factors (SIF). The effects of the crack topologies and soil material nonlinearity are analyzed especially on SIF and biaxiality rates (SBR) tendencies. A parametric study based on the variations of equivalent (SIF) for cracked foundations is discussed to investigate the prediction of failure occurrences for several cases of crack extensions and positions along shallow spread footing span. The numerical finding of this study can be potentially employed to direct engineers and researchers to optimal solutions for revamping design works, as well as in the improvement of mechanical reliability of cracked foundations mainly the ones of strategic industrial parts of petrochemical and nuclear infrastructures. [ABSTRACT FROM AUTHOR]

Abstract There are limited information on how an artificially non-liquefiable soil layer created by ground improvement beneath shallow foundations can help the reduction of liquefaction induced foundation settlements and the deterrence of bearing capacity failure effectively. This is addressed herein, numerically through a three-dimensional finite difference model using FLAC3D. The validity of the developed model was evaluated by comparing the results obtained from the model with the results of numerical studies and experimental centrifuge tests available in the literature. Using the validated model, the seismic response of a shallow foundation including bearing capacity and settlement was evaluated parametrically over a single DSM column in terms of its diameter and depth and also DSM group columns in terms of the diameter of columns and their center-to-center distance. Afterward, the influence of shallow foundation characteristic parameters was evaluated including thickness, width and embedded depth on the seismic response of shallow foundations over liquefiable soils improved by DSM columns. The obtained results can be used in practical engineering applications and provide new insight into the seismic performance of shallow foundations with DSM columns located over liquefiable soils. [ABSTRACT FROM AUTHOR]

Nonlinear methods for calculation of shallow foundation settlements in sand are addressed in the paper. One of them relies on the Hardening Soil Small constitutive relationship incorporated in the computer program Plaxis 2D. It has a significant drawback in the need to model the unknown strain history of the foundation soil prior to simulating the load test on a shallow foundation. This can be overcome by preloading the soil with a pressure which gives good matching between calculated and measured settlements. However, predictions of soil settlements cannot be made in such a way, because the soil strain history is not a priori known. It is shown in the paper how predictions of soil settlements can be made by Plaxis 2D by calibrating calculations against a simple direct method. A new direct method is developed along the lines of this simple method, on the basis of results of 16 load tests performed at 4 locations. The important advantage of the new method is that it properly takes into account the soil behavior at very small strains. [ABSTRACT FROM AUTHOR]

Abstract The major objective of this paper is to quantify the effects of uncertainties in soil properties and loading conditions on the performance of rocking foundations during seismic loading. Probabilistic numerical simulations were carried out using a validated soil-foundation Contact Interface Model in OpenSees finite element framework. Results indicate that for relatively larger static vertical factor of safety systems, the moment capacity of rocking foundations mainly depends on the applied vertical load on the foundation as opposed to the bearing capacity, while the energy dissipation and settlement are more sensitive to initial vertical stiffness of soil-foundation system and applied vertical load. Highlights • The research methodology presented in this paper includes systematic propagation of uncertainties in soil properties and loading conditions through soil-foundation interface to the rocking behavior of shear walls supported by shallow foundations during seismic loading. • Probabilistic numerical simulations were carried out using OpenSees finite element framework, where the structural behavior is represented by an elastic-beam-column element and the soil-foundation system behavior is simulated by a validated Contact Interface Model (CIM). [ABSTRACT FROM AUTHOR]

Skirted foundations are widely used in offshore engineering. The soils that skirted foundations are sited in commonly exhibit inherent spatial variability due to complex formation processes and stress history. In this study, probabilistic undrained capacities are investigated for skirted foundations with varying embedment ratios in spatially variable soils characterised by both stationary and non-stationary random fields using lower bound random finite element limit analysis combined with Monte Carlo simulation. Results show that the spatial variability of soil tends to decrease the uniaxial capacities. The coefficient of variation of soil strength, among the investigated parameters, could significantly affect stochastic uniaxial bearing capacities. Both embedment ratio and soil heterogeneity index affect the size and the shape of probabilistic failure envelopes, while statistical characteristics of soil strength including coefficient of variation and autocorrelation distance affect the size of probabilistic failure envelopes but have a minor influence on the shape. A larger embedment ratio is recommended to be adopted for skirted foundations sited in spatially variable soils from the perspective of load-carrying capacity. A series of expressions are proposed to describe the deterministic and probabilistic normalised failure envelopes for skirted foundations under combined vertical, horizontal and moment loadings. • Probabilistic undrained capacities are investigated for skirted foundations in both stationary and non-stationary random fields. • The effect of soil heterogeneity index, embedment ratio and random field parameters on probabilistic uniaxial capacities and failure envelopes were explored. • A series of expressions are proposed to describe the deterministic and probabilistic normalised failure envelopes. [ABSTRACT FROM AUTHOR]

Soil-shallow foundation interaction models that are incorporated into most structural analysis programs generally lack accuracy and efficiency or neglect some aspects of foundation behavior. For instance, soil-shallow foundation systems have been observed to show both small and large loops under increasing amplitude load reversals. This paper presents a practical macroelement model for soil-shallow foundation system and its stability under simultaneous horizontal and vertical loads. The model comprises three spring elements: nonlinear horizontal, nonlinear rotational, and linear vertical springs. The proposed macroelement model was verified using experimental test results from large-scale model foundations subjected to small and large cyclic loading cases. [ABSTRACT FROM AUTHOR]

No method or approach was provided in the paper to identify, determine, or investigate whether a soil is collapsible because at times the collapsible soil was referred to in the text as unsaturated natural soil. While this may be practically viable, the depth of compaction of unsaturated soil requires the determination of whether this can be done in situ or would require the soil to be excavated and replaced so that compaction can be afforded in lifts. Soil improvement by compaction has been touted by several researchers over the years as an effective measure in treating unsaturated soils to mitigate collapsibility under small- to medium-sized foundations. [Extracted from the article]

In this study, artificial neural networks (ANNs) were used to predict the settlement of pad footings on cohesionless soils based on standard penetration test. To achieve this, a computer programme was developed to calculate the settlement of pad footings from five traditional methods. The footing geometry (length and width), the footing embedment depth, Df, the bulk unit weight, γ, of the cohesionless soil, the footing applied pressure, Q, and corrected standard penetration test, Ncor, varied during the settlement analyses and the settlement value of each footing was calculated for each method. Then, an ANN model was developed for each traditional method to predict the settlement by using the results of the analyses. The settlement values predicted from the ANN model were compared with the settlement values calculated from the traditional method for each method. The predicted values were found to be quite close to the calculated values. It has been demonstrated that the ANN models developed can be used as an accurate and quick tool at the preliminary designing stage of pad footings on cohesionless soils without a need to perform any manual work such as using tables or charts. Sensitivity analyses were also performed to examine the relative importance of the factors affecting settlement prediction. According to the analyses, for each traditional method, Ncoris found to be the most important parameter while γ is found to be the least important parameter. [ABSTRACT FROM AUTHOR]