Strip Footings Research Articles

Estimation of bearing capacity of shallow footings on layered sand using finite elements analysis

PurposeThis paper aims to estimate the bearing capacity of a surface strip and circular footings lying on layered sand using numerical limit analysis.Design/methodology/approachLower and upper bound limit analysis, as well as finite elements and second-order conic programming (SOCP), are used in this analysis. The yield criterion of Mohr-Coulomb is used to model soil behavior. Using this technique, stringent lower and upper bounds on ultimate bearing capacity can be achieved by assuming an associated flow law.FindingsThe obtained results indicate that the exact collapse load is typically being bracketed to within 6% about a mean of both the bounds. The obtained results are compared with the existing literature wherever applicable.Originality/valueTo the best of the authors’ knowledge, no study has used lower and upper bound limit analysis, as well as finite elements and SOCP, to estimate the bearing capacity of a surface strip and circular footings lying on layered sand.

Estimation of Bearing Capacity of Strip Footing Rested on Bilayered Soil Profile Using FEM‐AI‐Coupled Techniques

In this research work, finite element method (FEM) and 2D Plaxis were employed to generate numerical values for bilayered soils bearing a strip footing of width B and depths, h and H, in order to predict the ultimate bearing capacity (UBC) of the strip footing underlain by layered soil profile. Several research works have tried to solve bearing capacity problems using limit equilibrium (LE) techniques. But, the LE techniques have limitations in terms of soil properties and profile arrangement. The need, however, for using constitutive models or numerical methods powered by FEM and discrete element method (DEM) has been on the rise due to the versatility and robustness of these techniques to accommodate erratic soil behaviors. Multiple numerical data were generated for the case under study and artificial intelligence (AI)‐based techniques; generalized reduced gradient (GRG), genetic programming (GP), artificial neural network (ANN), and evolutionary polynomial regression (EPR) were used to predict the UBC. In order to conduct the parametric analysis to investigate the effect of different soil layers, footing width and overburden pressure at foundation level on the ultimate bearing capacity sets of finite element models were prepared. This was executed using the following soil properties: soil type of top layer (from S1 to S6), soil type of bottom layer (from S1 to S6), strip footing width (B) (from 1.0 to 5.0 m), thickness of the top layer (h) (from 0.5 B to 1.0 B), overburden pressure (σ′v) (from 1.0 m to 3.0 m multiplied by the γ′t), and the parameters combination of each finite model in the set is randomly selected. The results of the FEM/Plaxis parametric study produced the 2D‐model, deformed shape, stress distribution, and plastic point (failure point) models. The loading produced appreciable deformation on both x‐ and y‐axes of the soil profile with the y‐axis showing a scattered failure configuration. The AI‐based prediction produced UBC equations which performed at over 90% accuracy with ANN (99.9%; 6.3%) outperforming other techniques followed by GRG, GP, and EPR.

Impact Of Underground Cavity on A Strip Footing at The Edge of a Cohesionless Slope and Subjected to Eccentric Load

Owing to the comeback of small-scale models, this paper presents results of an experimental study based on the effect of underground circular voids on strip footing placed on the edge of a cohesionless slope and subjected to eccentric loads. The bearing capacity-settlement relationship of footing on the slope and impact of diverse variables are expressed using dimensionless parameters such as the top vertical distance of the void from the base of footing, horizontal space linking the void-footing centre, and load eccentricity. The results verified that the stability of strip footing is influenced by the underground void, as well as the critical depth between the soil and top layer of the void. The critical horizontal distancebetween the void and the centre were also affected by the underground void. Furthermore, the results also verified that the influence of the void appeared insignificant when it was positioned at a depth or eccentricity equal to twice the width of footing.

A Method of Strip Footings Design for Light Structures on Expansive Clays

Shallow stiffened footing, in particular the Vierendeel typology, are considered as a design techniques for structures on expansive soils which have proven their success as challenging solutions; combining economy and safety. The current study is investigating an analytical model for preminiraly design of strip footings for light structures on expansive soils, in particular the Vierendeel beam. The developed model is used to calculate, through soil–structure interaction analysis, the algebraic expressions for the bending moment and the footing displacement at any point on the footing. The method is based on a simplification of the clayey ground reaction (Pi) and structure geometry and is derived from an integration of the beam-on-Winkler mound equation. The analytical model is then used to assess the effect of the structure loads on the contact state between the structure and the clayey ground (full or partial contact) as well as the impact of this contact state on the value of the maximum bending moment inside the beam. The results underlines the influence of the construction load on the contact state between the foundation and the swelling soil. The results shows that the bending moment in the footing strongly depends on the contact state between this footing and the clayey ground.

Stability Assessment of Rock Mass System under Multiple Adjacent Structures

Numerical modeling is important for exploring the fundamental processes occurring in rock and for evaluating the real performance of structures built on and in rock mass system, and thus for supporting the design of rock engineering problems. Estimating the stability of rock mass foundation systems entirely based on a theoretical approach is a complicated task if there exists overlapping of their potential collapse modes. This paper applies finite element limit analysis to evaluate the bearing capacity of equally spaced multiple strip footings resting on rock mass obeying the modified non-linear Hoek–Brown failure criterion. Numerical solutions are expressed in terms of the efficiency factor that is dependent on the spacing between footings, as well as the rock mass properties. In addition, the effects of surface surcharge and footing roughness are quantified. The maximum spacing at which the interfering effect of adjacent footings becomes disappeared is evaluated and an algebraic expression for approximating the maximum spacing is proposed. Failure mechanisms for a few cases of rock mass under multiple strip footings are examined.

Bearing Capacity Factors for Rough Conical Footing by Viscoplasticity Finite-Element Analysis

Many researchers have computed the bearing capacity of the strip and circular footings resting on the soil with the low and medium friction angle (ϕ ≤ 35°) by employing the finite-element method (FEM). It is reported that the numerical instability occurs with the high value of ϕ. Thus, based on the suggested values of soil dilation angle (ψ) in this study, the numerical computation can be achieved for all ϕ. Therefore, this paper presents the computation of the vertical bearing capacity factors Nc, Nq, and Nγ of a rough conical footing placed on the soil with friction angle ranging from ϕ = 5° to 45° by using the FE-based viscoplastic strain method under the Mohr–Coulomb (MC) yield criterion. The numerical simulations are solved using in-house MATLAB codes. The effects of the cone apex angle (β) and ϕ on the bearing capacity are examined thoroughly by the computation of factors individually and compared with the available solutions. The current solutions are found to be in good agreement for Nc, Nq, Nγ values; however, the discrepancies are also observed and presented. Therefore, the bearing capacity factor charts are established, and, consequently, the ultimate load of the footing can be determined by using the superposition assumption in Terzaghi’s equation.

Horizontal vibration of rigid strip footings on poroelastic half-space

This paper presents an analytical method to determine the response of rigid strip footings to harmonic horizontal loads, while considering the foundation soil as poroelastic, two-phase medium. The derived solution is the first of its kind that allows considering in a robust manner the coupled effects of soil deformation and flow on the dynamic response of strip footings to horizontal loads. The strategy for treating this complex problem analytically comprises transforming the mixed boundary conditions to a pair of dual integral equations that provide the contact stresses at the soil-footing interface, which are solved by means of Jacobi orthogonal polynomials. Presentation of the solution is followed by a discussion on how soil flow parameters affect the dynamic response of strip footings to horizontal loads, and the importance of considering the foundation soil as two-phase medium.

Theoretical studies and applications of an upper-bound stability analysis method based on the failure mode of inclined slices

This paper provides an in-depth study of the upper-bound slope stability analysis method proposed by Donald and Chen using inclined slices to simulate the sliding mass (Energy Method Upper-bound, abbreviated to EMU). After a brief review of the theoretical background and numerical method of the EMU, the authors present a weightless slope subjected to a vertical ultimate load to demonstrate its theoretical background. It has been proven that the analytical formulation of the EMU is identical to the closed-form solution given by the slip line method (SLM) for this selected example. Conversely, using its computer program, EMU has produced several closed-form solutions selected from Sokolovski. Thus, the potential for applications in practical engineering problems is demonstrated. With its theoretical background and numerical feasibility, EMU is extended to the area of bearing capacity of strip footings whose theoretical background is based on the slip line theory by Prandtl but involves various semi-empirical factors accounting for the effect of the soil weight, inclined and eccentric loading, and multi-layer foundations. This paper presents a preliminary investigation of semi-empirical approaches to the factors accounting for soil weight. Alternatively, the authors present a computer program Bearing-IWHR at the web, which is an Excel/VBA coded spreadsheet to perform numerical bearing analysis without the need for the semi-empirical factors.

Limit Analysis of Lateral Earth Pressure on Geosynthetic-Reinforced Retaining Structures Subjected to Strip Footing Loading Using Finite Element and Second-Order Cone Programming

Limit Analysis of Lateral Earth Pressure on Geosynthetic-Reinforced Retaining Structures Subjected to Strip Footing Loading Using Finite Element and Second-Order Cone Programming

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.

Estimating the Ultimate Bearing Capacity for Strip Footing Near and within Slopes Using AI (GP, ANN, and EPR) Techniques

Numerical and computational analyses surrounding the behavior of the bearing capacity of soils near or adjacent to slopes have been of great importance in earthwork constructions around the globe due to its unique nature. This phenomenon is encountered on pavement vertical curves, drainages, and vertical infrastructure foundations. In this work, multiple data were collected on the soil and footing interface parameters, which included width of footing, depth of foundation, distance of slope from the footing edge, soil bulk density, slope and frictional angles, and bearing capacity factors of cohesion and overburden pressure determined for the case of a foundation on or adjacent to a slope. The genetic programming (GP), evolutionary polynomial regression (EPR), and artificial neural network (ANN) intelligent techniques were employed to predict the ultimate bearing capacity of footing on or adjacent to a slope. The performance of the models was evaluated as well as compared their accuracy and robustness with the findings of Prandtl. The results were observed to show the superiority of GP, EPR, and ANN techniques over the computational works of Prandtl. In addition, the ANN outclassed the other artificial intelligence methods in the exercise.

Effect of size and depth on capacities of strip footings in limiting settlement approach

Structural and geotechnical engineers very often seek different options while deciding foundation sizes for buildings. In this research, the effect of different sizes and depths of strip footings below existing ground are studied based on the load bearing capacity using Geo5 spread footing software. Only vertical loadings were taken into account for this study. Four different strip footing widths (1.0m, 1.5m, 2.0m and 2.5m) were modeled under three different loads, 260kN, 600kN and 1000kN. The ground profile considered in this work was having a 2.0m thick weak layer at 6.0m below the existing ground level. Results showed that as the depth of footing increases, the depth of influence underneath the footing and settlement decreases. Also, it was noticed that as the footing width increases, the influence zone’s depth below the footing that passing the weak layer increases.

Analytical evaluation of the effect of failure mechanisms on the bearing capacity factor Nγ for smooth strip footings

ABSTRACT This paper describes an analytical approach to investigating the role of failure mechanism in the bearing capacity of a smooth strip footing located on a -- soil. The approach combines the plane strain equilibrium condition and Mohr-Coulomb failure criterion to obtain the stress distribution along a translational, rotational and composite failure path. It is shown that the exact solutions for cohesion factor and surcharge factor for a -- soil do not require the superposition assumption and that both these factors are path-independent. A general closed-form path-dependent expression for the soil weight factor is also derived in terms of internal friction angle of the soil and the geometry of the failure path. The application of proposed expression on two-line and three-line failure modes as well as the well-known Hill mechanism are evaluated and discussed. Due to the overestimation of the soil weight factor by two-line and three-line modes, and by Hill mechanism, geometric modifications on the failure paths are proposed. The proposed mechanism and its bearing capacity are verified using the method of the stress characteristics. The effect of a non-associated flow rule on the reduction of the soil weight factor is also investigated quantitatively.

Probabilistic study on the bearing capacity of strip footing subjected to combined effect of inclined and eccentric loads

This paper investigates the importance of inherent variability of soil under strip footing subjected to combined effect of inclined and eccentric loads using probabilistic analysis. Plastic analysis is performed using lower bound formulation of finite element limit analysis. Soil is considered as cohesionless, and modelled as a random field. The random field is discretized using Karhunen-Loéve expansion method. Stochastic results of the collapse load for various conditions of internal friction angle, load inclination angle, eccentricity, vertical correlation distance and coefficient of variation of the tangent of internal friction angle are determined using Monte Carlo Simulation technique. Failure probability results are plotted as contour charts to show the effect of combined loading as well as the spatial variability of soil on the bearing capacity of strip footing. For all the cases of higher vertical correlation distances, the mean bearing capacity factor is found to be higher than the deterministic value. However, the probability of failure of the footing is reported to be more than 50% for the same case, addressing the need for probabilistic analysis. Failure contours are presented for some representative cases to display the behavior of footing due to different loading and spatial variability conditions.

Numerical Investigation of the Bearing Capacity of Strip and Rectangular Shallow Footings on Cohesive Frictional Soils Under Eccentric Loads

Numerical Investigation of the Bearing Capacity of Strip and Rectangular Shallow Footings on Cohesive Frictional Soils Under Eccentric Loads

Physical Modelling of a Strip Footing on a Geosynthetic Reinforced Soil Wall Containing Tire Shred Subjected to Monotonic and Cyclic Loading

In this study, the mechanical behavior of geosynthetic reinforced soil (GRS) walls has been investigated through physical modeling subjected to strip footing monotonic and cyclic loads at various stress paths. The influence of footing location, stress level, post-cyclic behavior and sand-tire shred admixture on the lateral deformations of the wall facing, bearing capacity and the settlement beneath the footing were assessed. To this aim, 12 physical model tests were conducted with a scale of 1: 4. Results indicated that the bearing capacity has increased with the increase in the offset distance of the strip footing to the wall facing and adding tire shred to the backfill material, but the increase is more prominent by adding tire shred to the backfill material. The location of the footing from the wall facing was a crucial parameter on the deformation of facing and the failure mode of the footing. Failure in the facing was the predominant mode of failure in the near facing footing. However, a rupture in the geosynthetic caused failure in the footing far from facing footing. Also result of cyclic loading tests showed both permanent displacement and residual settlement accumulated with load cycles and a majority of them occurred over the first fifteen cycles. Depending on where strip footing was located, it may or may not induce a magnifying effect on subsequent cyclic loading responses.

Bearing capacity analysis of surficial strip footing at sub-watershed of downstream Muara Bangkahulu River, Indonesia

The downstream area of Muara Bangkahulu River has transformed into a developing area and a promotable area. This is because the area is relatively closed to the center of local government and the downtown area. This paper presents a bearing capacity analysis for surficial strip footing considering the variation of the geological condition along the river sub-watershed. Those locations are located at the coastal area, the housing area, and the plantation area along the river sub-watershed. In this area, the socio-economic aspect is also centralized. Laboratory tests were conducted to collect soil properties. A finite element simulation is used to observe the bearing capacity. The effects on the variation of footing width with bearing capacity and the available factor of safety are presented. The results showed that the larger width means the larger bearing capacity and factor of safety. The bearing capacity in the coastal area is lower than in other studied areas. The results could recommend local engineers in choosing the suitable strip footing in the studied area.

Probabilistic failure envelopes of shallow foundations on soils with strength anisotropy under combined loading

ABSTRACT The paper presented probabilistic analyses of the bearing capacity of strip footings in spatially variable undrained soil with a linearly increasing mean shear strength profile. The probabilistic response of strip footings was approached by the random finite element method (RFEM) in conjunction with the Monte Carlo simulation. Probabilistic failure envelopes were constructed to analyze the effect of spatial variability on strip footings subjected to different combinations of horizontal (H) and moment (M) loading. The probability of failure was independent on the strength gradient in the HM plane, but tended to increase with a wide fluctuation. Tabulated values of factor of safety for the probability of failure at 1% in different undrained shear strength random fields were also provided, which could be applied toward a foundation safety assessment.

Coupled three-dimensional analysis of the progressive tunnelling-induced damage to masonry buildings: is it always worth it?

The development of urban mobility implies the construction of tunnels, often interacting with valuable masonry structures. It is thus necessary to develop rational and reliable procedures to estimate the potential excavation-induced damage, which imply the analysis of the related soil-structure interaction problem.Classical approaches to soil-structure interaction are often characterised by relatively simple schematisations for either one or both components of the problem, as, for example, springs for the soil or equivalent plates for the structure. Such simplified assumptions prove to be appropriate for conventional soil-foundation cases, while show all their limitations when tackling more complex problems, as those involving the excavation in the vicinity or beneath masonry structures. In such cases, the need for reliable prediction of the potential damage induced by construction activities on surface structures justifies the adoption of more advanced numerical approaches, based on realistic constitutive assumptions for both soil and masonry, together with an accurate modelling schematisation of the excavation process.This is what proposed in this paper, where a 3D Finite Element approach is adopted to realistically model the multidimensional and progressive nature of the excavation process, the strongly non-linear soil behaviour and the non-linear anisotropic response that characterises masonry structures, here included accounting for their 3D geometrical characteristics. All the analyses are carried out with reference to a sample masonry building founded on strip footings, interacting with a shallow tunnel in a typical London soil profile, already examined in the literature. Different configurations of the structure, considering the sole façade or the whole building, are examined. Also, different relative positions of the tunnel and the structure, in terms of skew angle and eccentricity, are considered. In all the analyses, the excavation is simulated either reproducing the whole three-dimensional advancement of the tunnel or through a simplified single-step analysis.A critical review of the deformation regimes and related plastic points patterns resulting from the different analyses point out in which cases it is necessary to accurately model the 3D tunnel advancement to detect the transient effects governing the onset of structural damage.

A novel implicit coupled hydro-mechanical SPFEM approach for modelling of delayed failure of cut slope in soft sensitive clay

Modelling of delayed failure of cut slopes in soft sensitive clays is a significant challenge because of three major features taking place simultaneously: large deformation of the slope up to failure, pore water pressure generation and dissipation in the slope, and complicated time-dependent deformation of sensitive clay. This paper proposes a novel fully hydro-mechanical coupled edge-based strain smoothed particle finite element (ES-PFEM) modelling approach for delayed failure of cut slope with three outstanding features: (1) the particle finite element method with low-order edge-based strain-smoothed element for large deformation analysis, (2) an efficient stabilization method for pore water pressure to circumvent the Babuška-Brezzi stability restriction and (3) the elasto-viscoplastic model considering time-dependency, anisotropy and destructuration of soft sensitive clays. The accuracy and efficiency of the proposed approach are first examined by simulating consolidation test and strip footing. Furthermore, an adaptive substepping algorithm is proposed for the elasto-viscoplastic model. Finally, a typical case of delayed failures of cut slopes with different angles in soft sensitive clays is simulated and analysed, demonstrating the predictive ability of the proposed approach. The relationship between slope angle, sensitivity of clay and time of failure occurring is obtained for predicting the slope failure time in practice.