Strip Footings Research Articles

Complex Variable Solution of Interference Effect of Two Nearby Strip Footings on Layered Soil

Complex Variable Solution of Interference Effect of Two Nearby Strip Footings on Layered Soil

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

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

Circumventing volumetric locking in stabilized smoothed particle finite element method and its application to dynamic large deformation problems

AbstractThe smoothed particle finite element method (SPFEM) is an effective framework for large deformation analysis. The original SPFEM possesses the rank deficiency issue due to the direct nodal integration technique, which can be overcome by incorporating the strain gradient stabilization method. However, an extra volumetric locking due to the strain gradient stabilization term has been found. In this study, we propose a simple and efficient approach, the B‐dev approach, which only considers the deviatoric part of the smoothed strain gradient for stabilization to overcome the volumetric locking issue. First, the correctness of the stabilized SPFEM method is verified by an elastic cantilever beam vibration problem without considering incompressibility. Then, through the example of the strip footing penetration problem, the volumetric locking in the stabilized SPFEM is demonstrated and the capability of the proposed B‐dev approach in terms of overcoming the volumetric locking is verified. Furthermore, the stabilized SPFEM with B‐dev approach is applied to two types of elastoplastic problems in geotechnical engineering. All numerical results illustrate that the proposed approach can improve the performance of the stabilized SPFEM in dealing with incompressible and large deformation problems in geomechanics.

Model Test Study on the Response of Two Different Shallow-Foundation Framed Buildings under Tunnel Volume Loss

In order to study the influence of tunnel volume loss on adjacent framed buildings with different shallow foundations, this paper carried out physical model experiments with two common types of footings (isolated and strip footings) under different working conditions based on the digital image correlation (DIC) technique. The main finding of the present paper is that the increase in formation loss rate will aggravate the deformation and damage of the structure, and the strip foundation shows stronger integrity and stability compared with the isolated foundation in this process. With the increase in the eccentricity of the frames with respect to the tunnel, the overall tilt and damage degree of structural elements increases first and then decreases for both foundations, reaching the maximum value with the eccentric distance of one multiple of the tunnel diameter. Interestingly, when the isolated footings are located directly above the tunnel, the damage in the inner panels is the most severe and gradually decreases with eccentricity, changing from a sagging mode to a hogging mode for the frame form. While the strip footings always maintain slight hogging, and the trend of the damage degree of panels is similar to that of elements, with the eccentric distance reaching two times the tunnel diameter, the strip foundation structure tends to be stable, while the isolated one still needs attention for its potential possibility of damage in panels. The research results have reference value for the impact assessment of adjacent shallow-foundation framed buildings in subway tunnel construction.

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

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

Limit load and failure mechanisms of a vertical Hoek-Brown rock slope

The problem considered in this short note is the limit load determination of a vertical rock slope. The classical limit theorem is employed with the use of adaptive finite elements and nonlinear programming to determine upper and lower bound limit loads of a Hoek-Brown vertical rock slope. The objective function of the mathematical programming problem is such as to optimize a boundary load, which is known as the limit load, resembling the ultimate bearing capacity of a strip footing. While focusing on the vertical slope, parametric studies are carried out for several dimensionless ratios such as the dimensionless footing distance ratio, the dimensionless height ratio, and the dimensionless rock strength ratio. A comprehensive set of design charts is presented, and failure envelopes shown with the results explained in terms of three identified failure mechanisms, i.e. the face, the toe, and the Prandtl-type failures. These novel results can be used with great confidence in design practice, in particularly noting that the current industry-based design procedures for the presented problem are rarely found.

Analytical Solution for Bearing Capacity of Reinforced Strip Footings on Unsaturated Soils under Steady Flow

The study of analytical solutions for the bearing capacity of reinforced soil foundations is a very important topic in engineering mathematics. Existing evaluations of the foundation-bearing capacity on reinforced soils are based on dry conditions, while many foundations are located on unsaturated soils in real engineering. In this paper, a new formula for the bearing capacity of reinforced strip footings on unsaturated soils is presented. Two sliding failure mechanisms are constructed based on the position of the reinforcement layer relative to the sliding surface. The distribution of apparent cohesion in the depth direction is calculated by considering the effect of matrix suction. By additionally considering the work conducted by the reinforcement and the contribution of the apparent cohesion, the bearing capacity formula is obtained using the upper bound theorem of limit analysis. The bearing capacity solution is obtained by adopting the sequential quadratic programming (SQP) algorithm. Comparing the results under two failure mechanisms, the optimal bearing capacity and the optimal embedment depth of reinforcement are obtained. The results of this paper are consistent with those of the existing literature. Finally, the effects of reinforcement embedment depth, effective internal friction angle, uniform load, and unsaturated soil parameters on the optimal bearing capacity are investigated through parametric analysis. This paper provides useful recommendations for the engineering application of reinforced strip footings on unsaturated soils.

Revisiting Active and Passive Earth Pressure Problems using Three Stability Factors

This paper presents rigorous plasticity solutions to the classical active and passive earth pressure problems. The primary method adopted is a conventional equation based on the soil property and three stability factors (Fc, Fs, and Fγ), that are analogous to Terzaghi’s bearing capacity factors (Nc, Ns, and Nγ) of strip footings. The proposed method is considered as a practical yet smart approach to the determination of earth pressures and is one of the main novelties in this study. To achieve this, the finite element limit analysis (FELA) of upper and lower bounds solutions, a powerful tool in studying the behaviour of soil stability, is employed to compute the three stability factors for a wide range of soil internal friction angles, wall roughness, and surcharge pressures. In addition, analytical solutions based on statistically admissible stress fields are adopted to validate the proposed FELA solutions. The validation satisfactorily demonstrated the accuracy and reliability of the proposed solutions. It follows that the numerical results are presented in the form of tables, figures, and several examples provided to demonstrate the practical use of the three factors in estimating active and passive earth pressures with various backfill soils, wall roughness, and surcharge pressure. The study should, therefore, be of value to practitioners.

The Effect of Different Fiber Reinforcement on Bearing Capacity under Strip Foundation on the Sand Soil: An Experimental Investigation

The aim of this study is to investigate the bearing capacity-settlement behavior of strip footing settling on sand soil randomly reinforced with glass fiber, basalt fiber, macromesh fiber, and four different hybrid fiber additives in which these fibers are used together. Model tests were carried out in the laboratory on the strip footing and placed on the unreinforced and reinforced sand with different fibers. In the study, model tests were carried out on seven types of randomly reinforced soils by using glass, basalt, macrame, and mixtures of these fibers as reinforcement. In the model tests, two different fiber contents, 1% and 2%, and two different fiber lengths, 24 mm and 48 mm, were used. Tests were carried out with Dr = 30% and 50% relative density, and reinforcement depths 1B, 2B, and 3B were selected. In addition, the photographs taken during the test were analyzed with the particle image velocimetry (PIV) method and the displacements on the soil were examined. As a result of the reinforced and unreinforced model tests, the highest ultimate bearing capacity was measured as 680 kPa from the tests with Dr = 50% relative density, 48 mm length, 2% contents, and 3B depth macromesh fiber reinforced. In hybrid fibers, the highest ultimate bearing capacity was measured as 495 kPa, with Dr = 50% relative density, 48 mm length, 2% contents, and 2D depth micromesh and basalt fiber-reinforced tests. In the reinforced tests, it was concluded that the most effective fiber on bearing capacity is macromesh fiber. It can be seen that in the PIV analysis, as the fiber additive increased, the settlements made by the foundation decreased under the same pressure. It has also been observed that adding reinforcement to the soil transfers the stresses occurring in the soil to a wider area.

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).

Reliability analysis framework for shallow foundations resting on reinforced cohesionless soils

Improving soil mechanical properties using reinforcement inclusions has become of major interest to many researchers. Accordingly, several numerical, analytical, and experimental studies have been conducted to explore the improvement of soil’s mechanical properties under shallow foundations. However, a comprehensive Reinforced Soil Foundations (RSF) design framework has not been established. This paper introduces a novel design framework for RSF based on the Load and Resistance Factor Design (LRFD) approach. Resistance factors for improved bearing capacity are computed using the First Order Reliability Method (FORM) for strip and square footings resting on loose sandy soil. A spreadsheet-based model is developed to compute the resistance factors at a targeted reliability index (βT) equal to 3 for ASCE-7 2000, AASHTO 1998, and EC7 (DA2) load factors. The resistance factors developed using ASCE-7 load factors ranged from 0.2 to 0.55 and 0.27 to 0.7 for a geogrid tensile strength of 45 kN/m and 160 kN/m, respectively. Load factors of different established design codes had a significant effect on the developed resistance factors. Soils with high frictional angles and embedment ratios resulted in conservative resistance factors. Moreover, the computed resistance factors for square footings were slightly higher in reinforced cases and lower for unreinforced cases than in strip footings.

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

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

Bearing capacity of strip footing on c-ϕ slope under rainfall condition

This paper presents a novel solution for predicting the bearing capacity of a strip footing on a c-ϕ (cohesive-frictional) slope under rainfall conditions. The commercial finite element PLAXIS code was adopted for numerical modelling purposes. The bearing capacity of the strip footing is expressed through a dimensionless bearing capacity factor. The bearing capacity was examined considering the rainfall conditions and variation of design parameters, e.g., soil strength parameters, slope angle, and setback ratio. The results show that the bearing capacity of strip footing on the slope decrease under rainfall compares to its normal condition and the effects of each parameter on the UBC. The paper’s results can be a helpful reference for practical engineering in predicting the bearing capacity of strip footing on the c-ϕ slope under rainfall conditions.

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.

Effect of Relative Density and Particle Morphology on the Bearing Capacity and Collapse Mechanism of Strip Footings in Sand

Effect of Relative Density and Particle Morphology on the Bearing Capacity and Collapse Mechanism of Strip Footings in Sand

Efficient adaptive reliability-based design optimization for geotechnical structures with multiple design parameters

Reliability-based design optimization (RBDO) aims to improve the reliability of geotechnical systems while minimizing the cost of design. However, the conventional RBDO method suffers from a large computational cost and intractable convergence problem due to the double-loop structure involving numerical optimization and repeated reliability analysis. To address this issue, this paper proposes an efficient adaptive RBDO framework for geotechnical structure with multiple design parameters. The proposed framework mainly includes two parts: a novel expanded inverse first-order reliability method (E-IFORM) for dealing with the inverse reliability problem with multiple design parameters, and an adaptive surrogate model to decouple the double-loop structure and improve the efficiency. The proposed methodology is applied to four geotechnical systems (i.e., a soil slope, an excavation pit, a strip footing and a retaining wall), and the results demonstrate the effectiveness and efficiency of the proposed framework.

Seismic Bearing Capacity of Strip Footings Placed Adjacent to Rock Slopes

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

Finite elements limit analysis formulation using the power type yield criterion for plane strain and axisymmetric stability problems

The current research employs a power type yield criterion which accounts for the dependency of the shear strength parameters, namely, cohesion and internal friction, on stress level which becomes quite effective in obtaining very accurately the solutions of different stability problems in geomechanics involving soil and rock media. The present manuscript introduces plane strain and axisymmetric formulations which deal with the power type yield criterion and are based on the lower and upper bound finite elements limit analysis in conjunction with the power cone programming (PCP). To demonstrate the efficacy of the proposed formulations, the problems of the determination of the bearing capacity of strip and circular foundations in a cohesive-frictional soil medium have been addressed. In the case of a strip footing, the earthquake inertial forces in a horizontal direction have also been incorporated. The adaptive mesh pattern has been employed to improve the accuracy of the solution at the expense of minimal computational effort. The results have been thoroughly validated by making the comparison of the obtained solutions with that reported in literature. The proposed formulations are expected to be quite useful in solving different stability problems in geomechanics.

Bearing capacity of footings on geosynthetic-reinforced soils under combined loading

In this study, the ultimate bearing capacity of shallow strip footings resting on a geosynthetic-reinforced soil mass subjected to inclined and eccentric combined loading is rigorously examined through the well-established method of lower bound limit analysis (LA) in conjunction with finite element (FE) and second-order cone programming (SOCP). Lower bound limit analysis formulation is modified to consider the ultimate tensile force of the geosynthetic layer in the soil mass so as to account for both pullout (sliding) and rupture (structural) modes of reinforcement failure. The effects of several parameters, including the embedment depth (u) and the ultimate tensile strength (Tu) of the geosynthetic layer along with load inclination angle (α) and load eccentricity (e), on the bearing capacity ratio (BCR) and failure envelopes of the overlying shallow foundation are examined and discussed. The results generally show a marked increase in the ultimate bearing capacity of the surface footing against combined loading with the inclusion of a single geosynthetic layer. Results also reveal that a second intermediate reinforcement might be required to bear a dual performance against both vertical concentric and combined loading scenarios so as to more effectively support the footing.

Bearing capacity factors of single- and double-strip footings placed over an embankment

The rigid pavements and rigid base supporting rails can be considered as a strip footing resting over an embankment. In addition, there can also be single or double-strip footings resting over an embankment. These strip footings are influenced by the properties of the soil, slope angle of an embankment, setback distance, and spacing between the footings and the height of embankment. In this study, the bearing capacity factors for the single- and double-strip footings resting over an embankment are evaluated using the finite element method (FEM). The bearing capacity factors [Formula: see text] and [Formula: see text] are evaluated for different soil friction angles [Formula: see text], slope angles of embankment [Formula: see text], setback distances [Formula: see text], embankment heights [Formula: see text] and spacing between the footings [Formula: see text]. Considering the practical aspect, i.e., the surcharge is not present for footing on an embankment, the [Formula: see text] is not evaluated in the study. Based on the analysis, it is observed that the bearing capacity factors [Formula: see text] and [Formula: see text] increase with increase in friction angle of the soil and setback distance and reduce with increase in the slope angle of the embankment. The effect of depth of embankment on the [Formula: see text] and [Formula: see text] is negligible for smaller friction angles [Formula: see text], whereas it increases marginally for higher friction angles [Formula: see text]. Furthermore, the [Formula: see text] and [Formula: see text] are influenced by the spacing between the footings. This study’s results are compared with the results available in the literature. This study’s results are presented as design charts, and these could be adopted in the practice in routine designs of shallow foundations.