Rigid Footing Research Articles

Large deformation assessment of the bearing capacity factor for rigid footing: effect of soil heterogeneity

Large deformation assessment of the bearing capacity factor for rigid footing: effect of soil heterogeneity

Bearing capacity of shallow foundations: a focus on the depth factors in combination with the respective N-factors

The ongoing refinement of bearing capacity equations remains pivotal in soil mechanics and foundation engineering, reflecting its critical role in ensuring design efficacy and construction safety. This study conducts a thorough evaluation of classical bearing capacity methods—Terzaghi, Meyerhof, Vesic, and Hansen—and methods included in various design standards, such as EN1997:2004, prEN1997:2023, GEO, AASHTO, FHWA, and API. It explores the performance and applicability of these approaches, identifying areas for potential improvement. In response to identified challenges, the paper proposes the integration of a unified depth factor. This new factor is designed to be applicable across all N-terms, providing a more versatile and accurate tool for bearing capacity predictions. Unlike the original depth factors unique to each method, which may not fully address complex soil and footing conditions, the unified depth factor is developed to enhance prediction accuracy for a wide range of conditions, including both flexible and rigid footings under varying flow rules (ψ = 0 and ψ = φ). This depth factor corrects for modeling errors, emphasizing the importance of pairing the correct set of N-factors with their corresponding depth factor. By offering a singular depth factor that aligns with the outcomes of finite element analysis, this paper not only simplifies the computational process but also enhances the accuracy of bearing capacity predictions across a diverse range of soil conditions and footing types. The comparative analysis, based on finite element analysis, validates the proposed method’s effectiveness, showcasing its potential to significantly refine foundation design practices by comparing it with both traditional and newly developed depth factors.

Multiphysics simulation of freezing and thawing granular media using material point method

In this paper, a fully coupled thermo-hydro-mechanical material point method, applicable to liquid-saturated porous systems undergoing large deformations and phase transitions, is presented. A mathematical framework was established based on multiphasic mixture theory and fundamental physical conservation laws, rather than using phenomenological or semi-empirical equations. A fractional-step-based semi-implicit solution scheme was proposed to solve the coupled formulations within the framework of the generalized interpolation material point method. The proposed method was validated using several benchmark examples, including the talik closure and thaw consolidation. Its performance in simulating climate-driven large deformation problems was further demonstrated by simulating the settlement of a rigid footing on thawing ground. This paper presents an innovative and rigorous framework for predicting the impact of climate change on engineering practices.

Optimizing ground improvement with encased stone columns: a 3D numerical analysis in very soft clay

Purpose This study aims to investigate the behavior of different types of stone columns, including the short and floating columns, as well as the ordinary and the geosynthetic encased stone columns (OSC and GESC). The effectiveness of the geosynthetic encasement and the impact of the installation using the lateral expansion method on the column performance is evaluated through a three-dimensional (3D) unit cell numerical analysis. Design/methodology/approach A full 3D numerical analysis is carried out using the explicit finite element code PLAXIS 3D to examine the installation influence on settlement reduction (ß), lateral displacement (Ux) and vertical displacement (Uz) relative to different values of lateral expansion of the column (0% to 15%). Findings The findings demonstrate the superior performance of GESC, particularly short columns outperforming floating counterparts. This enhanced performance is attributed to the combined effects of geosynthetic encasement and increased lateral expansion. Notably, these strategies contribute significantly to decreasing lateral displacement (Ux) at the column’s edge and reducing vertical displacement (Uz) under the rigid footing. Originality/value In contrast to previous studies that examined the installation effect of OSC contexts, this paper presents a comprehensive investigation into the effect of geosynthetic encasement and the installation effects using the lateral expansion method in very soft soil, using 3D numerical simulation. The study emphasizes the significance of the consideration of geosynthetic encasement and lateral expansion of the column during the design process to enhance column performance.

Load Carrying Mechanism of Geocell Reinforced Embankment on Soft Soil

This paper investigates the influence of geocell reinforcement on the load carrying mechanism of embankments over soft soil. Using a geocell mattress beneath an embankment on soft soil, the size of the rupture zone in the foundation bed is found to have increased significantly, leading to increase in the mobilized shear resistance, and giving rise to enhanced bearing capacity. While the unreinforced embankment, owing to differential settlements, tends to crack and disintegrate, the geocell reinforced embankment continues to behave as a monolith up to a high surcharge pressure/fill height. The performance improvement tends to increase with increase in height of the geocell mattress. Strain variation in the geocell mattress indicates that its reinforcing efficacy is the largest at the central crest region of the embankment and decreases toward the toe. As the geocell mattress behaves as a semirigid slab, when it is present, the stress dispersion angle tends to increase significantly. Considering the stress dispersion zone as an equivalent rigid footing, the bearing capacity of unreinforced and geocell reinforced embankments are analyzed. The predicted bearing capacities are found to be in close agreement with the experimentally observed ones. Three-dimensional numerical analyses indicate that the pressure–settlement behavior of the embankments observed in the model tests is reproduced at large scale.

Axial stiffness of floating pile foundations and rigid footings with Vlasov-Leont′ev foundation model and expressions for a rigid disk

In the manuscript, a hybrid formulation to evaluate the axial dynamic and static head stiffness of pile foundations and rigid footings floating in a homogeneous half-space is demonstrated. In the formulation, the soil adjacent to the pile is modeled with the Vlasov-Leont′ev foundation model, and the underlying soil beneath the pile is modeled by a spring-dashpot system. The spring-dashpot system is described with expressions obtained from the solution of a vertically vibrating rigid massless disk on the surface of a homogeneous half-space. The expressions are obtained from the literature reported by several authors. The results obtained from the proposed formulation and the expressions are compared with rigorous formulations in the literature for pile foundations and rigid footings. It is found, the formulation demonstrated produces accurate dynamic and static head stiffness for pile foundations and rigid footings. Besides, it captures the essential mechanics of a foundation floating in a homogeneous half-space. Based on an investigative study, it is found, the expression proposed by Veletsos and Verbic accurately models and simulates the homogeneous half-space underneath the pile foundations and rigid footings.

SPH implementation of a critical state-based hypoplastic model for granular materials in large-deformation problems

In this work, an advanced hypoplastic model incorporating the critical state is integrated into smoothed particle hydrodynamics (SPH) for numerical investigation of problems with large deformation. This numerical method performs well in cases of element tests such as oedometer test, simple shear test and plain strain compression test, which usually own regular velocity fields. However, the standard SPH implementation will generate significant stress drift away from the failure surface in more complex geotechnical problems featured with dramatically-varying velocity field. This unrealistic stress state may deteriorate the stress state with a further step. As a result, a vicious circle takes place, which could give rise to a calculation failure. With this regard, a return mapping strategy is proposed to regulate the stress state locating beyond the failure surface. To this end, a closed-form solution to predicting the failure surface implicitly incorporated in the hypoplastic model is derived. Finally, the capability of the proposed numerical method is examined with two classical benchmark problems for granular materials, including the sand column collapse and rigid footing by comparing the numerical results with those from experiments and theoretical solutions.

Effect of strain-softening and strength anisotropy on the undrained bearing capacity of non-associated clay

The bearing capacity of soils is critical in the design and analysis of foundations. The classical solutions derived from methods of characteristics and bound theories are based on the rigid plasticity and associated flow rule, which may not be realistic for natural soils. The undrained shear strength of soft clays exhibits strain-softening and anisotropic behaviour in laboratory tests, which creates complexity when choosing appropriate strength parameters in the conventional design process. In addition, the stress–strain characters are non-associative and path dependent, which also affects the bearing capacity of soils. This paper investigates two classical stability problems (i.e. deeply embedded pile/pipe section and rigid strip footing) using finite-element analysis and the MIT-E3 soil model, and demonstrates the effects of stain-softening and strength anisotropy on the undrained bearing capacity of soils. The computed results are compared with analytical solutions and finite-element limit analyses, as well as those from finite-element analysis using conventional soil models. These findings have strong practical implications in predicting the bearing capacity of foundations and interpreting in situ tests.

Investigation on dynamic performance of soilbag cushion using shaking table tests

Soilbag cushion is one of the promising base isolation methods to reduce seismic energy transfer from ground to building structure. In this study, a series of shaking table tests were conducted comparatively on foundation models with soilbag cushion and sand cushion to evaluate their dynamic performance. The test results indicate that soilbag cushion could significantly reduce acceleration response and accumulated settlement compared to sand cushion. And the relatively smaller amplitude of dynamic lateral earth pressure measured on contact surface of soilbags within soilbag cushion also indicates its stability during oscillation. The advantages of soilbag cushion for energy dissipation and damping are more easily highlighted under the condition of high-acceleration, high-frequency or high uniformly distributed load. The dynamic performance of soilbag cushion is dependent on embedded depth and thickness. It is most effective for soilbag cushion to be arranged near the rigid footing of building structures; it is suggested that the number of layers of soilbag cushion be controlled on the premise of the designed ratio of the thickness to the width of soilbag cushion ranging from 0.125 to 0.4 for low- or middle-rise masonry buildings in practical engineering.

P-y curves from in-situ ROBOCONE tests: a similarity approach for laterally loaded piles in clay

p-y curves from in-situ ROBOCONE tests: a similarity approach for laterally loaded piles in clay

Experimental and numerical study for seismic response of strip footing on slopes

The present study investigates the free-field response of slopes as well as the seismic response of strip footing on slopes. The small-scaled physical model tests (PMT) have been performed under one-directional excitation. The sinusoidal waves of different amplitudes and frequencies are applied at the base of the model. To examine the kinematic interaction between the footing and slope, a rigid strip footing is placed at the center of the slope. The free-field response of the slope as well as the seismic response of the footing on the slope from PMT is determined using digital image correlation (DIC). Two-dimensional finite element analysis (FEA) has been carried out to simulate the PMT results. No study has been reported in the literature considering both experimental and numerical work. Further, the effects of increasing load on the footing on slopes have not been examined yet. Results from PMT and FEA are found in good agreement. The maximum amplification is observed near the crest for free-field response of slope. For both horizontal ground surface and sloping ground, the maximum amplification occurs at the frequency of excitation. However, some small peaks at other frequencies are also observed for the sloping ground due to the reflection of waves from the sloping surface. The seismic settlement of strip footing is increased with the increase of slope angle, amplitude and frequency of the excitation. However, the seismic settlement decreases with the increase in footing width and edge distance of footing from the slope. For footing on slope, the maximum amplification is observed at the center of the slope. A large settlement of footing is observed when the footing is heavily loaded (e.g., 80% of the ultimate bearing capacity of footing).

Failure Mechanism and Bearing Capacity of Rigid Footings Placed on Top of Cohesive Soil Slopes in Spatially Random Soil

Failure Mechanism and Bearing Capacity of Rigid Footings Placed on Top of Cohesive Soil Slopes in Spatially Random Soil

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

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

Rigid circular footing on the surface of a transversely isotropic linear elastic half-space

It is sometimes convenient to treat a relatively rigid footing as a single element subjected to up to six force resultants: vertical load, horizontal load in two directions, overturning moment about two axes and torsion. Applications include calculations of initial, elastic settlement; foundation responses under seismic loading or for machine vibrations; and fixity of an offshore jack-up foundation under cyclic wave loading. Present codes of practice provide formulae that assume fully isotropic and linear elastic soil and in some case assume no friction between the footing and soil. This paper uses recent theoretical advances to develop solutions for stiffnesses of rigid circular footings on transversely isotropic linear elastic soil, including with interface friction. Closed-form solutions are developed for vertical load and overturning moment on a frictionless interface and for vertical load and torsion on a frictional interface. A boundary-element analysis is presented for the cases of lateral load and overturning moment on a frictional interface. By fitting expected forms to the results, new formulae are proposed for stiffnesses for these cases. The effects of interface friction on limiting loads are calculated. Practical applications are outlined, and some limitations are briefly discussed.

Point loads on the surface of a transversely isotropic linear elastic half-space

General solutions for the displacements, strains and changes in stress in a transversely isotropic linear elastic (TILE) half-space subject to a point load were published in 1998. They represent a massive advance on the nineteenth-century solutions by Boussinesq, Cerruti and others, which were for fully isotropic linear elastic half-spaces. The 1998 solutions were for loads at a general depth below the surface and were criticised for being difficult. The present paper deduces more accessible expressions for the special case of loads that are on the surface. This allows one clarification and one potential error in the original equations to be identified and avoided. With support from existing data of geological materials, agreement is found with a previous claim that a limit proposed in 1970 on one of the shear moduli for a TILE material is invalid. Corrected equations derived herein can be the basis of calculating ground stresses and movements due to linear responses to distributed surface loads, behaviours of flexible foundations and stiffnesses for rigid surface footings.

Vertical vibration of rigid strip footings on poroelastic soil layer of finite thickness

This paper presents a numerical solution that describes the response to forced vertical vibrations of rigid strip footings founded on the surface of a poroelastic soil layer of finite thickness. To mathematically describe this mixed boundary value problem, we relax the boundary conditions and cast it as a pair of dual integral equations, which are transformed to a system of linear equations by means of Jacobi orthogonal polynomials. The system is solved numerically to provide the frequency-dependent footing compliance, and the associated nearby soil displacement. Results obtained with the model at hand underline the important contribution of standing waves to the response of the soil-foundation system, and draw the limits of existing solutions that consider the foundation soil as infinite half-space, where standing waves cannot form.

Elastic and Consolidation Settlement Analysis of Rigid Footings Relying on the “Characteristic Point”

Elastic and Consolidation Settlement Analysis of Rigid Footings Relying on the “Characteristic Point”

Bearing capacity and deformation behavior of rigid strip footings on coral sand slopes

Porous coral sands formed by the remains of marine organisms are important foundation-filling materials for artificial island construction and other marine geotechnical projects. A typical situation is that the significantly reduced bearing capacity of a rigid footing adjacent to coral sand slopes threatens the safety and stability of the upper structures. In this study, a series of model-scale tests were conducted to investigate the bearing capacity and deformation behavior of a rigid strip footing resting on the top of coral sand slopes with consideration of the effects of edge distance, slope height, slope angle, number of geogrid layers, burial depth and spacing of the geogrid layer. The measured deformation field based on particle image velocimetry (PIV) technology indicates that the unreinforced coral sand slope is dominated by unilateral sliding patterns, and its bearing area is significantly smaller than that of the geogrid reinforced coral sand slope (GRCSS). The bearing capacity in unreinforced coral sand slopes increases with the increasing edge distance, and the decreasing slope height and angle. Although the geogrid reinforcement significantly improves the bearing capacity, it is also affected by the number of layers, burial depth and spacing between reinforcement layers. Besides, the reduction coefficient of bearing capacity (RCBC), the bearing capacity factor (Nγq) and the normalized bearing capacity (Nγq/NγqR) were further calculated and discussed based on the test results and classical bearing capacity theory.

Limit load space of rigid strip footing on cohesive-frictional soil subjected to eccentrically inclined loads

In geotechnical engineering, the stability of strip footings under eccentrically inclined coupled loads is a major concern. The objective of this paper was to estimate the ultimate bearing capacity of a rigid strip footing, subjected to eccentrically inclined loads resting on cohesive-frictional soil, using the rigid plastic finite element method (RPFEM). In the numerical analysis, an interface element was introduced to properly evaluate the interaction between the footing base and the soil. The footing base was assumed to be rigid and rough, as it most often is in reality. Focus was placed on the effect of the soil properties (cohesive strength c, internal friction angle ϕ, and unit self-weight γ) and footing width B on the loading planes of the V-H-M limit load space (vertical load-horizontal load-moment) in order to consider the uniqueness of this limit load space. In particular, the effect of the two directions of the horizontal load, namely, positive and negative horizontal loads, on the V-H-M limit load space was clarified. The numerical results of the RPFEM showed that the negative horizontal load had a positive effect on supporting a higher bearing capacity than the positive horizontal load in the presence of a small eccentricity length. However, the results also showed a negligible effect on the bearing capacity for both directions of the horizontal load in the presence of a large eccentricity length. New equations were proposed to determine the V-H-M limit load space, predicted as functions of c/γB and ϕ, by taking into account the direction of the horizontal load. The applicability of the V-H-M limit load space was widely examined for several loading paths with different prescribed loads for V, H, and M. Consequently, the limit load space of the strip footing was clearly found to be unique for each value of c/γB and ϕ.

Vertical vibration of a rigid strip footing on a half-space of unsaturated porous soil

This study presents an analytical solution to the compliance coefficient of rigid strip footings lying on an unsaturated porous soil half-space when subjected to vertical vibration. Using the Fourier transform techniques, the complex interaction between unsaturated soils and rigid strip foundations is transformed into a mixed boundary-value problem based on the developed framework of Biot’s model. The wavenumber domain auxiliary function and boundary conditions are used to convert the governing equations to a pair of dual integral equations. To yield the compliance function, the integral equations are transformed into a system of inhomogeneous linear equations by utilizing hypergeometric polynomials and Bessel functions. The proposed analytical solution is verified against existing solutions to interactions between foundations and saturated soil or single-phase soil by adjusting the parameters in the unsaturated soil model. Additionally, the impacts of soil skeleton saturation, intrinsic permeability, and Poisson’s ratio of unsaturated soil on the dynamic compliance coefficient of rigid strip footings are examined. It is shown that the Poisson’s ratio of the soil skeleton and the soil saturation at critical saturation have a significant effect on the dynamic compliance coefficient, but have a negligible effect on the intrinsic permeability.