Shallow Strip Footings Research Articles

Evaluating the N γ Coefficient for Shallow Strip Footings on Sloping Ground by the Method of Stress Characteristics

Evaluating the <i> N _γ </i> Coefficient for Shallow Strip Footings on Sloping Ground by the Method of Stress Characteristics

Influence of the superposition and flow rule assumptions on the bearing capacity of shallow strip footings

Influence of the superposition and flow rule assumptions on the bearing capacity of shallow strip footings

Critical acceleration of shallow strip footings

Critical acceleration of shallow strip footings

Reliability-based analysis of seismic bearing capacity of shallow strip footings resting on soils with randomly varying geotechnical and earthquake parameters

Seismic bearing capacity of strip footings is a challenging task for geotechnical engineers due to its stochastic framework instigated by the natural uncertainties incorporated into geotechnical properties and earthquake parameters. Consequently, the introduction of the random field theory into reliability analysis may provide power tools to succor designers check how reliable their designs. This paper aims to assess the seismic bearing capacity of shallow strip footings resting on soils with randomly varying parameters. Bearing capacity formulas for purely cohesive and cohesive-frictional soils are considered. The influence of the type of the autocorrelation functions (ACFs), the scale of fluctuations (SOFs) and the coefficient of variation (COV) of the random parameters are investigated. Statistical moments, probability density function (PDF) and failure probability (Pf) of the seismic bearing capacity are computed. It is shown that the Single Exponential (SNE) ACF is the most appropriate function to characterize the spatial variability of the soil properties since it provides conservative results. On other hand, the results indicate that the increase in the coefficients of variation (COV) of the cohesion or the friction angle increases the variability of the seismic bearing capacity while this variability remains unaffected when the COV of the seismic coefficient increases. The results also highlight that the effect of the vertical SOF on the PDF and the failure probability is much more significant than that of the horizontal SOF. In addition, the mean seismic bearing capacity fluctuates slightly as the horizontal or vertical SOF increases so that the increment of variation is between 0.4% and 2% for the both two soil types.

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.

Seismic Bearing Capacity Solution for Strip Footings in Unsaturated Soils with Modified Pseudo-Dynamic Approach

In engineering mathematics, the unsaturated nature of soil has a significant impact on the seismic bearing capacity solution. However, it has generally been neglected in the published literature to date. Based on the kinematic approach of limit analysis, the present study proposes a method for calculating the bearing capacity of shallow strip footings located in unsaturated soils, taking four common types of soils as examples. The modified pseudo-dynamic (MPD) approach is used to calculate the seismic forces varying with time and space, and the layerwise summation method is used to derive the power generated by the seismic forces. In the calculation of internal energy dissipation, this paper introduces the effective stress based on the suction stress to derive the cohesion expression at different depths. The analytical formula of bearing capacity is obtained by the principle of virtual work, and its value is optimized by the Sequential Quadratic Programming (SQP) algorithm. In order to verify the validity of the proposed method, the present results are compared with the solutions published so far and a good agreement is obtained. Finally, a parametric study is performed to investigate the influence of different types of parameters on the bearing capacity.

Bearing capacity of shallow strip foundations on reinforced soil subjected to combined loading using upper bound theorem of finite element limit analysis and second-order cone programming

Bearing capacity of shallow strip foundations placed over both unreinforced and reinforced granular soils and subjected to combined loading is calculated by implementation of upper bound finite element limit analysis in conjunction with second-order cone programming technique. The soil mass is considered to be a granular medium reinforced with the inclusion of horizontal single and double layers of geogrid elements. To represent the impact of tensile resistance of reinforcement elements, an axillary variable is utilized to simulate the plastic energy dissipation of reinforcing elements without the application of any stress variables. General loading conditions are considered to profile the expansion of the failure envelopes in the V-H and V-M spaces for shallow strip foundations resting on reinforced soils. Results of this study are compared and validated against three different cases including the bearing capacity of shallow strip foundations subjected to vertical loading in the case of perfectly smooth and fully rough interfaces, limit load of shallow strip foundations subjected to combined loading, and vertical bearing capacity of shallow strip footings over a soil deposit reinforced with a single-layer of geosynthetic. Consistency of the results with those reported in the literature demonstrates the efficiency of proposed extended finite element upper bound formulations. The results are reported in the form of an efficiency factor which can be multiplied by the vertical bearing capacity of the shallow strip footing over unreinforced soil to find the ultimate bearing capacity of the reinforced foundation. The results show that the load inclination angle and eccentricity have significant impacts on the limit load and the optimum embedment depths of the reinforcement layer. It is further noted that the effect of reinforcement layer(s) in the improvement of bearing capacity in the V-M space is more pronounced than in the V-H space. The efficiency of reinforcement elements inclusion in improving the expanse of safe loading domain in the V-H and V-M spaces enhances with an increase in the soil internal friction angle.

Seismic bearing capacity of rock foundations subjected to seepage by a unilateral piece-wise log-spiral failure mechanism

Most of the current studies on the bearing capacity of rock foundations follow the Hoek-Brown (HB) criterion, but all adopt the generalized tangent technique or the multi-tangent approach, which does not reflect the essence of the nonlinear dependence of the Hoek-Brown criterion. Therefore, a modified unilateral failure mechanism is proposed in the paper, using which the bearing capacity of shallow strip footings considering seepage and seismic forces is evaluated. Use of a statics-like approach for seepage condition and a modified pseudo-dynamic method for seismic condition. The comparison with the results of other literature confirms the feasibility and effectiveness of the study in the paper, while the parametric analysis shows that a smaller upper bound solution is yielded based on the failure mechanism proposed in this paper, and the horizontal gradient ratio, the horizontal factor of seismic acceleration, the normalized frequency, the geological strength index, the disturbance coefficient, and the rock type-dependent parameter all have significant effects on the bearing capacity of rock foundations. In addition, the analysis of the working conditions considering both seepage and seismic forces confirmed the dominance of seismic forces. The results of the superposition treatment between different working conditions are inaccurate, which will underestimate the foundation bearing capacity and cause a waste of cost. This paper develops a more accurate method of assessing the bearing capacity of rock foundations and gives a table of coefficients that can be adopted in engineering practice.

Estimation of the Seismic Bearing Capacity of Shallow Strip Footings Based on a Pseudodynamic Approach

The bearing capacity of a shallow strip footing is investigated by a pseudodynamic method under earthquake conditions. A nonsymmetrical multiblock mechanism is herein adopted to describe the uplift failure of the foundations based on the kinematic theorem of limit analysis. This nonsymmetrical mechanism comprises a series of rigid triangular blocks that translate into the failure area. The seismic load, varying with time and space, is represented by a pseudodynamic method that considers the dynamic properties of earthquake waves. A slice method is proposed to adapt the variation in inertial force with time and depth for the convenience of calculating the earthquake-induced work rate. Then, equating the external work rate and the internal dissipation rate, the rigorous upper-bound solution of the seismic bearing capacity factors, which will be optimized by the sequential quadratic programming (SQP) in the MATLAB toolbox for searching for the optimal value, is explicitly derived. Comparisons between the present solution and previous works are made to validate the rationality and accuracy of the proposed methodology. A specific parametric analysis is conducted to reveal the influence of dynamic parameters on the bearing capacity of the strip footing. Numerical results are provided graphically as well as in the tabular form for reference in footing design.

Effect of the circular cavity on the undrained bearing capacity of shallow strip footing

Effect of the circular cavity on the undrained bearing capacity of shallow strip footing

Comparing bearing capacity factor Nγ of finite element method with analytical methods for sandy soils

Shallow strip footings are essential to carry loads from structures. Load bearing capacity factors can be calculated both by the field tests (plate load test) and numerically. Bearing capacity factors are the main parameters that affect the bearing capacity of any foundations. Nγ, one of these factors, have significant impact. Increase in internal frictional angle (ϕ), causes enhance the Nγ value. However, after ϕ value reaches 30°, dramatic increase is observed. This make the bearing capacity values complicated. In this study, strip foundation on surface resting on sandy soils were designed with a Geostudio 2012 software. Various foundation width (1, 1.25, 1.5, 1.75 and 2 m) and internal friction angle (29°, 31°, 33°, 35°, 37°, 39°, and 41°) was selected. Bearing capacity values were calculated with both numerical (software) and analytical methods. After, Nγ values of analytical methods were compared to results obtained from software. Results indicate that, Biarez 1961 has the average Nγ values while Terzaghi (1943) and Michalowski (1997) have the maximum. Nγ value obtained from numerical analysis (finite element method) increased with an increase in foundation width also. Values from finite element method is average of other analytical methods when B = 1.25 m, while Nγ values of numerical methods are the biggest when B = 2 m.

The use of the node-based smoothed finite element method to estimate static and seismic bearing capacities of shallow strip footings

The node-based smoothed finite element method (NS-FEM) is shortly presented for calculations of the static and seismic bearing capacities of shallow strip footings. A series of computations has been performed to assess variations in seismic bearing capacity factors with both horizontal and vertical seismic accelerations. Numerical results obtained agree very well with those using the slip-line method, revealing that the magnitude of the seismic bearing capacity is highly dependent upon the combinations of various directions of both components of the seismic acceleration. An upward vertical seismic acceleration reduces the seismic bearing capacity compared to the downward vertical seismic acceleration in calculations. In addition, particular emphasis is placed on a separate estimation of the effects of soil and superstructure inertia on each seismic bearing capacity component. While the effect of inertia forces arising in the soil on the seismic bearing capacity is non-trivial, and the superstructure inertia is the major contributor to reductions in the seismic bearing capacity. Both tables and charts are given for practical application to the seismic design of the foundations.

Evaluating the [formula omitted] coefficient for rough strip footing located adjacent to the slope using the stress characteristics method

The method of characteristics was used to estimate the coefficients Nγ for shallow strip footings located adjacent to the slopes. The soil-footing interface roughness (δ) was considered from perfectly smooth to fully rough state by 1/3 increments in each step. The effect of roughness factor (δ/φ) on the magnitude of Nγ has been evaluated for different friction angles (φ) and slope inclinations (β°). The arrays of the slip lines have been extracted and the geometric properties of plastic and non-plastic regions have been presented in tabular form. The results of the present research for both smooth and rough footings rested on the horizontal ground and adjacent to the slope showed a favorable consistency with findings reported in the literature by adopting various solution approaches. It was found that the Nγ coefficient increases and diminishes dramatically by increasing φ and β°, respectively. More than almost 95% of the Nγ magnitude in full roughness state is provided by mobilizing about 60% of the footing's roughness. The sizes of the plastic region as well as the elastic wedge beneath the rough footing extend with increasing both φ and δ/φ. An increase in β° leads to increasing and decreasing the plastic domains on the downslope zone and the horizontal ground part behind the crest, respectively. The dimensions of the non-plastic curved wedge slowly reduce and the intersection point of two plastic regions gradually tends toward the left edge of the footing. For β=20° and beyond, the maximum depth of the right plastic region from the right edge shifts toward the sloping ground face.

Groundwater effect on bearing capacity of shallow strip footings

A rigorous and practical solution aimed at accounting for the effect of groundwater in the assessment of bearing capacity of shallow strip footings in plane strain conditions has been developed using the method of characteristics.A steady water table in the foundation soil is considered and a bearing capacity factor Nγw to be used in the classical trinomial bearing capacity equation is introduced. The proposed bearing capacity factor depends on the angle of shear strength, on the footing roughness and on the water table depth and is also influenced by the soil unit weight.Normalizing Nγw with respect to the bearing capacity factor Nγ computed for the case of dry foundation soil, a corrective coefficient has been introduced for which best-fit empirical relationships have been proposed for both smooth and rough foundations. The size of the plastic mechanism under the footing has also been investigated and equations allowing to evaluate its relevant dimensions have been provided.The proposed solutions have been checked against results obtained via finite element analyses, finding a perfect agreement in terms of both corrective coefficients and shape and size of the soil plastic volume. Finally, the actual bearing capacity problem was solved showing that the trinomial formula, even in presence of a steady water table, still yields conservative values of the bearing capacity.

Cracked Equivalent Beam Models for Assessing Tunneling-Induced Damage in Masonry Buildings

This paper proposes simple numerical models that simulate the influence of tunneling-induced ground movements on masonry buildings founded on shallow strip footings. The focus is on developing an improved understanding of the impact of structural discontinuities due to pre-existing cracks and joints between adjacent buildings. The soil–structure system is idealized with equivalent Timoshenko beams connected to a homogenous elastic half-space with rigid links. The flexibility of the equivalent beam at the location of the crack or building interface is determined using linear-elastic fracture mechanics. The proposed models are first applied to a generic numerical example. Then, they are used to interpret the detailed displacement and strain measurements gathered from a masonry church during nearby tunneling. The results show that pre-existing cracks can have variable influence on the soil–structure interaction depending on their extent and position relative to the building and settlement trough. For the investigated case study, the proposed models illustrate how pre-existing large cracks in the hogging zone localized deformations and how the interaction between adjacent buildings drastically altered response mechanisms.

Bearing capacity under increasing undrained shear strength

The undrained shear strength of naturally deposited, consolidated and saturated clay usually increases with depth due to the overburden pressure and the decreasing water content. Nonetheless, calculations of the bearing capacities of foundations under undrained conditions are usually done using the approach of Prandtl, which assumes constant values of the undrained shear strength. Analytical models using the kinematic element method show that the failure mechanism and the bearing capacity are both influenced by the increasing undrained shear strength; therefore, Prandtl's method might overestimate the bearing capacity of a shallow foundation assuming an average value of the undrained shear strength. Centrifuge tests of shallow strip footings on kaolin clay were conducted to validate the analytical model in terms of bearing capacity and failure mechanism. The estimated bearing capacity of the shallow foundation based on analytical models show good agreement with the centrifuge test results. However, the shape of the failure mechanisms is considerably different. In the analytical models, the development of the failure mechanism is estimated based on the assumption of a perfectly plastic behaviour, developing a rigid-body collapse. This behaviour was not observed in the physical models due to the development of the failure mechanism.

Seismic Bearing Capacity of Shallow Strip Footings on Sand Deposits with Weak Inter-layer

The main objective of this study is to evaluate the ultimate seismic bearing capacity of a shallow strip footing resting on a frictional soil stratum containing a weak intervening layer. The majority of the studies throughout the literature pertain to the static loading condition. The previous seismic analyses have also been devoted to the studies on the bearing capacity of shallow strip footings resting on a two-layered soil. The influence of weak middle layer on the pseudo-static seismic bearing capacity of shallow foundations is the main focus of the present study. To determine the seismic bearing capacity, the limit equilibrium method (LEM) was combined with the pseudo-static seismic loading approach. Bearing capacity was defined by a single equivalent coefficient which combines the contributions of cohesion, surcharge and soil weight. A two-wedge failure surface, known as the Coulomb failure mechanism, was adopted to model the slip lines in each layer to calculate the seismic bearing capacity of the overlying shallow strip footing. The Particle Swarm Optimization (PSO) algorithm was invoked to seek the optimal bearing capacity value under different strength and loading conditions. In order to verify the validity of the presented formulations, the results were compared with some Finite Elements Method (FEM) analyses available in literature. Furthermore, the influence of the embedment depth, thickness, and strength of the weak inter-layer on the seismic bearing capacity of the shallow footing is investigated in the presence of different seismic loading arrangements. The results of this study could be very helpful in the seismic analysis and design of shallow foundations overlying a soil medium containing a weak layer of various strengths.

Seismic Bearing Capacity of Strip Footing Resting on Reinforced Layered Soil Using Chaotic Particle Swarm Optimization Technique

In this paper limit equilibrium method under pseudo-static approach is applied to evaluate the ultimate bearing capacity of shallow strip footing resting on geosynthetic reinforced soils. The foundation is resting on two layered c − ϕ soils. Chaotic Particle Swarm Optimization algorithm is used to optimize the solution. Failure mechanism has been assumed as linearly varying with depth with different wedge angle. Bearing capacities evaluated for different reinforcement geometries and soil properties. Bearing capacity of shallow strip footing in two-layered soil conveyed as a single coefficient for a coincident resistance of unit weight, surcharge and cohesion. The effect of different parameters on the seismic bearing capacity coefficients is studied in details. A comparison of the present method with other theories is presented, which shows the merits of the present study. Hence, it was concluded that present method for reinforcement layered soils can be prosperously utilized in calculating the bearing capacities of geosynthetic reinforced soils.

Influence of the unified strength theory parameters on the failure characteristics and bearing capacity of sand foundation acted by a shallow strip footing

The unified strength theory can account for the influence of intermediate principal stress using a specified parameter b, with which the determination of the values and influences of b is significant. In this research, a physical model test was carried out in combination with the numerical simulations to explore the effect of b on a sand foundation loaded by a shallow strip footing. Variation of parameter b would produce significant effect on the deformation characteristics, stress response, failure model, as well as bearing capacity of the sand foundation. In general, a larger b could be adopted to yield smaller magnitudes of stress. The calculated ultimate bearing capacity Pult increases linearly with increase in b, and an increment of 470% can be obtained using b = 1.0 relative to b = 0.0. The comparison of the bearing capacities of physical model test and numerical simulation suggests that b = 0.89–0.99 is the appropriate value for the experimental sand foundation, that ultimately results in a capacity increase in 420%–465% relative to the result of Mohr–Coulomb failure law.

Unified upper bound solution for bearing capacity of shallow rigid strip foundations generally considering soil dilatancy

In light of the upper bound method of a kinematical limit analysis, traditional log-spiral shear zones in the admissible failure mechanism of foundation soil loaded by shallow rigid strip footings are unified by introducing a nonnegative coefficient for the internal friction angle of the soil to generally reflect practical soil dilatancy. While the computed coefficient is generally between 0 and 1 to be compatible with its physical meaning, in many cases it was between 0.5 and 1. The proposed mechanism includes the traditional log-spiral and circular-arc mechanism, and is capable of determining a smaller value of the solution to the bearing capacity than some classic theoretical methods. Based on the proposed mechanism, two bearing capacity factors are refined from the traditional three factors based on the finding that the traditional factors Nq and Nc are not independent of the footing depth and soil cohesion, respectively. A formula including the two items is provided to make the proposed method convenient for use for the practical footings on homogeneous soil.