Bearing capacity of interfering multiple strip footings by using lower bound finite elements limit analysis

The ultimate bearing capacity of a number of multiple strip footings, identically spaced and equally loaded to failure at the same time, is computed by using the lower bound limit analysis in combination with finite elements. The efficiency factor (ξ_γ), due to the component of soil unit weight, is computed with respect to changes in the clear spacing (S) between the footings. It is noted that the failure load for a footing in the group becomes always greater than that of a single isolated footing. The values of ξ_γ for the smooth footings are found to be always lower than the rough footings. The values of ξ_γ are found to increase continuously with a decrease in the spacing between footings. As compared to the available theoretical and experimental results reported in literature, the present analysis provides generally a little lower values of ξ_γ.     

Horizontal Pullout Resistance for a Group of Two Vertical Plate Anchors in Clays

The horizontal pullout capacity of a group of two rigid strip plate anchors embedded along the same vertical plane in clays, under undrained condition, has been determined. An increase of cohesion with depth has also been incorporated. The analysis has been performed by using an upper bound finite element limit analysis in combination with linear optimization. For different clear spacing (S) between the anchors, the efficiency factor (η_cγ) has been determined to evaluate the group failure load for different values of (1) embedment ratio (H/B), (2) the normalized rate (m) which accounts for a linear increase of cohesion with depth, and (3) normalized unit weight (γH/c_o). The magnitude of the group failure load (1) becomes maximum corresponding to a certain spacing (S_cr) between the anchors, and (2) increases with an increase in the γH/c_o up to a certain value before attaining a certain maximum magnitude. The value of S_cr/B has been found to vary generally between 0.7 and 1.2. The maximum magnitude of η_cγ, associated with the critical spacing, (1) increases generally with increases in H/B, and (2) decreases with an increase in m. For a greater spacing between the anchors, the analysis reveals the development of a local shear zone around the lower anchor plate. The numerical results developed are expected to be useful for purpose of design.     

Seismic interference of two nearby horizontal strip anchors in layered soil

In the present analysis, an attempt is made to explore the seismic response of two nearby horizontal strip anchors embedded in non-homogenous c-? soil deposit at different depths. The analysis is performed by using two-dimensional finite-element software PLAXIS 2D. Each anchor carries equal static safe-working load without violating the ultimate uplift capacity under static condition. The soil is assumed to obey the Mohr?CCoulomb failure criterion. The behavior of single isolated anchor subjected to an earthquake loading is determined first to study the interference effect between two anchors. The horizontal acceleration response obtained from the Loma Prieta Gilroy Earthquake (1989) is considered as the input excitation in the analysis. A parametric study is performed by varying the clear spacing (S) between the anchors at different embedment ratios (??). The magnitude of vertical displacement, shear stress, and shear strain developed at different locations of the failure domain is determined for different clear spacings between the anchors.     

Ultimate bearing capacity of equally spaced multiple strip footings on cohesionless soils without surcharge

The ultimate bearing capacity of a group of equally spaced multiple rough strip footings was determined due to the contribution of soil unit weight. The analysis was performed by using an upper bound theorem of limit analysis in combination with finite elements and linear programming. Along the interfaces of all the triangular elements, velocity discontinuities were considered. The value of ξ_γ was found to increase continuously with a decrease in S/B, where (i) ξ_γ is the ratio of the failure load of an interfering strip footing of a given width (B) to that of a single isolated strip footing having the same width and (ii) S is the clear spacing between any two adjacent footings. The effect of the variation of spacing on ξ_γ was found to be very extensive for small values of S/B; ξ_γ approaches infinity at S/B=0. In all the cases, the velocity discontinuities were found to exist generally in a zone only around the footing edge. Copyright © 2008 John Wiley & Sons, Ltd.     

The influence of horizontal confinement on the bearing capacity factor Nγ of smooth strip footing

We studied the upper-bound ultimate bearing capacity of smooth strip shallow footings with symmetrical and asymmetrical horizontal confinements on purely frictional sand within the framework of upper-bound limit analysis. The subsoil follows the associated flow rule, and no surcharge on the soil surface is assumed. The contact between the soil and the horizontal confinement walls is assumed to be perfectly rough. The upper-bound solutions for the objective functions are obtained using nonlinear sequential quadratic programming. The results for the different internal friction angles φ are provided in terms of the variation of two parameters, namely, the bearing capacity factor N_γ and the correction factor of bearing capacity K_γ, with respect to the change in the clear spacing between the edge of smooth footing and the rigid vertical walls. The values of N_γ and K_γ increase with φ and decrease with the clear spacing between the edge of the smooth footing and the rigid vertical walls. N_γ and K_γ are more sensitive to this confining effect as φ increases. The numerical results, a comparative analysis with the results from previous studies, and design charts are also included.     

Vertical Uplift Capacity of Equally Spaced Multiple Strip Anchors in Sand

The ultimate uplift resistance of a group of multiple strip anchors placed in sand and subjected to equal magnitudes of vertical upward pullout loads has been determined by means of model experiments. Instead of using a number of anchor plates in the experiments, a single anchor plate was used by simulating the boundary conditions along the planes of symmetry on both the sides of the anchor plate. The effect of clear spacing (s) between the anchors, for different combinations of embedment ratio (λ) of anchors and friction angle (ϕ) of soil mass, was examined in detail. The results were presented in terms of a non-dimensional efficiency factor (ξ_γ), which was defined as the ratio of the failure load for an intervening strip anchor of a given width (B) to that of a single strip anchor plate having the same width. It was clearly noted that the magnitude of ξ_γ reduces quite extensively with a decrease in the spacing between the anchors. The magnitude of ξ_γ for a given s/B was found to vary only marginally with respect to changes in λ and ϕ. The experimental results presented in this study compare reasonably well with the theoretical and experimental data available in literature.     

Bearing capacity of two interfering footings

By using an upper bound limit analysis in conjunction with finite elements and linear programming, the ultimate bearing capacity of two interfering rough strip footings, resting on a cohesionless medium, was computed. Along all the interfaces of the chosen triangular elements, velocity discontinuities were employed. The plastic strains were incorporated using an associated flow rule. For different clear spacing (S) between the two footings, the efficiency factor (ξ_γ) was determined, where ξ_γ is defined as the ratio of the failure load for a strip footing of given width in the presence of the other footing to that of a single isolated strip footing having the same width. The value of ξ_γ at S/B = 0 becomes equal to 2.0, and the maximum ξ_γ occurs at S/B = S_cr/B. For S/B?S_cr/B, the ultimate failure load for a footing becomes almost half that of an isolated footing having width (2B + S), and the soil mass below and in between the two footings deforms mainly in the downward direction. In contrast, for S/B>S_cr/B, ground heave was noticed along both the sides of the footing. As compared to the available theories, the analysis provides generally lower values of ξ_γ for S/B>S_cr/B. Copyright © 2007 John Wiley & Sons, Ltd.     

Estimation of Pullout Capacity of Vertical Plate Anchors in Cohesionless Soil Using MARS

Vertical plate anchors provide an economical solution to safely resist the large horizontal forces experienced by the foundation of different structures such as bulkheads, sheet piles, retaining walls and so forth. This paper develops a multivariate adaptive regression spline (MARS) model-based approach for the determination of horizontal pullout capacity (P _u ) of vertical plate anchors buried in cohesionless soil by utilizing experimental results reported by different researchers. Based on the collection of forty different pullout experimental test results reported in the literature for anchors buried in loose to dense cohesionless soil with an embedment ratio ranges from 1 to 5, a predictive approach for P _u of vertical plate anchors has been developed in terms of non-dimensional pullout coefficient (M _γq ). The capability of the proposed MARS model for estimating the values of M _γq is examined by comparing the results obtained in the present study with those methods available in the literature. Using different statistical error measure criteria, this study indicates that the present approach is efficient in estimating the horizontal pullout capacity of vertical plate anchors as compared to other methods. The sensitivity analysis indicates that the embedment ratio (H/h, where H = embedment depth of anchor, and h = height of anchor) and internal friction angle (?) of soil mass are the two most important parameters for the evaluation of non-dimensional pullout coefficient (M _γq ) using the proposed MARS model.     

Upper bound limit analysis for finding interference effect of two nearby strip footings on sand

The ultimate bearing capacity of two closely spaced strip footings, placed on a cohesionless medium and loaded simultaneously to failure at the same magnitude of failure load, was determined by using an upper bound limit analysis. A logarithmic spiral radial shear zone, comprising of a number of triangular rigid blocks, was assumed to exist around each footing edge. The equations of the logarithmic spiral arcs were based on angles φ_L and φ_R rather than soil friction angle φ; the values of φ_L and φ_R were gradually varied in between 0 and φ. The ultimate bearing capacity was found to become maximum corresponding to a certain critical spacing between the footings. For spacing greater than the critical, the bearing capacity was found to decrease continuously with increase in the spacing. The extent of the spacing corresponding to which the ultimate bearing capacity becomes either maximum or equal to that of a single isolated footing increases with increase in φ. The results compare reasonably well with the available theoretical and experimental data.     

Seismic uplift capacity of inclined strip anchors in sand using upper bound limit analysis

Pseudo-static approach is adopted in this paper to determine the seismic uplift capacity of an inclined strip anchor using upper bound limit analysis. Two different failure mechanisms are considered to obtain the magnitudes of unit weight component of uplift factor f_γE for different values of soil friction angle, interface friction of anchor plate, anchor inclination, embedment ratio and horizontal seismic acceleration coefficient. The failure mechanism 1 consists of a triangular and quadrilateral rigid blocks; whereas the failure mechanism 2 comprises a logarithmic spiral failure zone with varied focus, sandwiched between a triangular and quadrilateral rigid blocks. It is observed that the magnitude of uplift factor f_γE decreases significantly with the increase in seismic acceleration but increases with the increase in embedment ratio and roughness of the anchor surface. However, a mixed trend in the values of f_γE can be observed for different inclination of the anchor, which is clearly discussed in this paper. The results are compared with the existing values in the literature and the significance of the present methodology for designing the inclined strip anchor is discussed.     

Horizontal Pullout Capacity of a Group of Two Vertical Strip Anchors Plates Embedded in Sand

The horizontal pullout capacity of a group of two vertical strip anchor plates placed along the same vertical plane in sand, has been determined by using the lower bound finite element limit analysis. The effect of vertical spacing (S) between the anchor plates on the magnitude of the total group horizontal failure load (P_uT) has been determined for different combinations of H/B, δ/ϕ and ϕ. The magnitude of P_uT has been obtained in terms of a group efficiency factor, η_γ, with respect to the failure load for a single vertical plate with the same H/B. The magnitude of η_γ becomes maximum corresponding to a certain critical S/B, which has been found to lie between 0.5 and 0.8. The value of η_γ for a given S/B has been found to become larger for greater values of H/B, ϕ, and δ.     

The variation of Nγ with footing roughness using the method of characteristics

By using the method of characteristics, the effect of footing–soil interface friction angle (δ) on the bearing capacity factor N_γ was computed for a strip footing. The analysis was performed by employing a curved trapped wedge under the footing base; this wedge joins the footing base at a distance B_t from the footing edge. For a given footing width (B), the value of B_t increases continuously with a decrease in δ. For δ=0, no trapped wedge exists below the footing base, that is, B_t/B=0.5. On the contrary, with δ=?, the point of emergence of the trapped wedge approaches toward the footing edge with an increase in ?. The magnitude of N_γ increases substantially with an increase in δ/?. The maximum depth of the plastic zone becomes higher for greater values of δ/?. The results from the present analysis were found to compare well with those reported in the literature. Copyright © 2008 John Wiley & Sons, Ltd.     

Influence of overburden pressure and soil rigidity on uplift behavior of square plate anchor in uniform clay

A numerical study incorporating three-dimensional Eulerian large deformation finite element analyses is performed to investigate the pullout process of horizontal square plate anchors in both hypothetical weightless soil and soil with self-weight. The validity of the numerical model is established through verification against published experimental and numerical results. The failure mechanisms during the pullout process under different conditions are then investigated. Three types of failure mechanism are observed; of which only two have been reported in the literature. The third mechanism identified in this study, which is a partially localized flow mechanism, is operative when the soil overburden ratio is not high enough to mobilize the full flow mechanism. The influence of soil self-weight is directly investigated by incorporating the density of the soil in the finite element model and maintaining the gravitational acceleration field throughout the analysis. The critical overburden ratio corresponding to the full transition to a localized plastic flow mechanism is identified in this study. The effect of the soil rigidity index (E/s_u) on the anchor uplift capability has not been systematically investigated in earlier studies. Contrary to the general failure mechanism and the full flow mechanism described in the literature, the capacity factor corresponding to this new mechanism increases with increasing E/s_u. The capacity factors for square plate anchors corresponding to different anchor embedment ratios, overburden ratios and E/s_u are provided in the form of design charts.     

Ultimate Bearing Capacity of a Footing Considering the Interference of an Existing Footing on Sand

The ultimate bearing capacity of a new strip footing placed on a cohesionless soil medium, in the presence of an existing strip footing, the load on which is assumed to be known, has been determined. Both the footings are assumed to be perfectly rigid and rough. The analysis is carried out by using an upper bound finite element limit analysis. For different clear spacing (S) between the footings, the values of the efficiency factor (ξ_γ) were determined; where ξ_γ is defined as the ratio of the failure load for an interfering new footing of a given width (B) to that for a single isolated footing having the same width. For ϕ < 30°, it is generally noted that the magnitude of ξ_γ increases continuously with a decrease in S/B. For ϕ > 30°, on the other hand if the applied load on the existing footing is approximately greater than half the failure load for a single isolated footing having the same width, the peak magnitude of ξ_γ was found to occur at around S/B ≈ 0.1 rather than at S/B = 0. The increase in ξ_γ becomes further significant with an increase in the magnitude of the load on the existing footing.     

Risk de-aggregation and system reliability analysis of slope stability using representative slip surfaces

This paper develops a risk de-aggregation and system reliability approach to evaluate the slope failure probability, p_f, using representative slip surfaces together with MCS. An efficient procedure is developed to strategically select the candidate representative slip surfaces, and a risk de-aggregation approach is proposed to quantify contribution of each candidate representative slip surface to the p_f, identify the representative slip surfaces, and determine how many representative slip surfaces are needed for estimating the p_f with reasonable accuracy. Risk de-aggregation is performed by collecting the failure samples generated in MCS and analyzing them statistically. The proposed methodology is illustrated through a cohesive soil slope example and validated against results from previous studies. When compared with the previous studies, the proposed approach substantially improves the computational efficiency in probabilistic slope stability analysis. The proposed approach is used to explore the effect of spatial variability on the p_f. It is found that, when spatial variability is ignored or perfect correlation assumed, the p_f of the whole slope system can be solely attributed to a single representative slip surface. In this case, it is theoretically appropriate to use only one slip surface in the reliability analysis. As the spatial variability becomes growingly significant, the number of representative slip surfaces increases, and all representative slip surfaces (i.e., failure modes) contribute more equally to the overall system risk. The variation of failure modes has substantial effect on the p_f, and all representative surfaces have to be incorporated properly in the reliability analysis. The risk de-aggregation and system reliability approach developed in this paper provides a practical and efficient means to incorporate such a variation of failure modes in probabilistic slope stability analysis.     

Efficient stochastic analysis of unsaturated slopes subjected to various rainfall intensities and patterns

Rainfall infiltration poses a disastrous threat to the slope stability in many regions around the world. This paper proposes an extreme gradient boosting (XGBoost)-based stochastic analysis framework to estimate the rainfall-induced slope failure probability. An unsaturated slope under rainfall infiltration in spatially varying soils is selected in this study to investigate the influences of the spatial variability of soil properties (including effective cohesion c′, effective friction angle φ′ and saturated hydraulic conductivity k_s), as well as rainfall intensity and rainfall pattern on the slope failure probability. Results show that the proposed framework in this study is capable of computing the failure probability with accuracy and high efficiency. The spatial variability of k_s cannot be overlooked in the reliability analysis. Otherwise, the rainfall-induced slope failure probability will be underestimated. It is found that the rainfall intensity and rainfall pattern have significant effect on the probability of failure. Moreover, the failure probabilities under various rainfall intensities and patterns can be easily obtained with the aid of the proposed framework, which can provide timely guidance for the landslide emergency management departments.     

Bearing capacity of strip foundations reinforced with geogrid sheets by using upper bound finite‐element limit analysis

By using the upper bound finite‐elements limit analysis, with an inclusion of single and two horizontal layers of reinforcements, the ultimate bearing capacity has been computed for a rigid strip footing placed over (i) fully granular, (ii) cohesive‐frictional, and (iii) fully cohesive soils. It is assumed that (i) the reinforcements are structurally strong so that no axial tension failure can occur, (ii) the reinforcement sheets have negligible resistance to bending, and (iii) the shear failure can take place between the reinforcement and soil mass. It is expected that the different approximations on which the analysis has been based would generally remain applicable for reinforcements in the form of geogrid sheets. A method has been proposed to incorporate the effect of the reinforcement in the analysis. The efficiency factors, η_c and η_γ, to be multiplied with N_c and N_γ , for finding the bearing capacity of reinforced foundations, have been established. The results have been obtained (i) for different values of ? in case of fully granular and cohesive‐frictional soils, and (ii) for different rates at which the cohesion increases with depth for a fully cohesive soil. The optimum positions of the reinforcements' layers have also been determined. The effect of the reinforcements' length on the results has also been analyzed. As compared to cohesive soils, the granular soils, especially with higher values of ?, cause a much greater increase in the bearing capacity. The results compare reasonably well with the available theoretical and experimental data from literature. Copyright © 2013 John Wiley & Sons, Ltd.     

Uplift capacity of pile group anchors

Experimental investigations on model single pile anchor and pile group anchors of configuration 2 × 2 subjected to uplift loads were conducted on dry Ennore sand, obtained from Madras, India. The embedment length to shaft width ratios, L/d = 20 and L/d = 30, and enlarged base width to shaft width ratios, B/d = 1,2,3, center to center spacing of pile anchors in the groups, 3d, 4d, 6d and 8d were used. The load displacement response, ultimate resistance and variation of group efficiency with L/d, B/d and spacing have been studied quantitatively and qualitatively. For short pile group anchors (L/d = 20), the isolation spacing appears to be at a spacing of about 4d to 6d and 8d for B/d = 1 and B/d = 2 and 3, respectively. For long pile group anchors (L/d = 30), the isolation spacing appears to be at a spacing of about 4d, 6d and 8d for B/d = 1, 2 and 3, respectively. The analytical model of limit equilibrium method has been proposed to predict the net uplift capacity of pile group anchors. The predicted results compare reasonably well with the experimental results.     

Risk Factor Based Design of Cantilever Retaining Walls

Sensitivity analysis of geotechnical random variables on potential failure modes (overturning, sliding, bearing capacity and eccentricity) of a cantilever retaining wall reveals that high sensitivity of a particular variable on a particular mode of failure does not necessarily imply a remarkable contribution to the overall failure probability. The present paper aims to combine probability of failure (P _f ) of each failure mode and sensitivity of the random variables to these failure modes and introduces a new factor, called Probabilistic Risk Factor (R _f ) for each random variable. P _f is calculated by Monte Carlo Simulation and sensitivity analysis of each random variable is calculated based on normalized F-Statistics value. R _f is a reduction factor which takes into account the variations of random variables and hence can be directly implemented in design by the designers. The random variables (friction angle and unit weight of backfill soil; and friction angle, unit weight and cohesion of foundation soil), when divided by R _f and applied in design, yield a structure which is safe against variations of the random variables. It is observed that R _f of friction angle (φ ₁ ) of backfill increases and cohesion (c ₂ ) of foundation soil decreases with an increase in variation of φ ₁ , while R _f for unit weights (γ ₁ and γ ₂ ) of both the soil and friction angle of foundation soil (φ ₂ ) remains almost constant. Finally, design guidelines for different variations of φ ₁ are provided based on the proposed methodology, which proves to be cost effective.     

Semi-empirical Model for Estimating the Small-Strain Shear Modulus of Unsaturated Non-plastic Sandy Soils

The shear modulus at small-strain, G _max is a maximum value of shear modulus for a given stress state and void ratio, and is a key parameter to evaluate the dynamic response of geotechnical structures. However, the laboratory testing procedures for determining G _max are time-consuming, cumbersome and require elaborate equipment especially for unsaturated soil samples. A semi-empirical model is proposed in this paper that can be used to estimate the variation of G _max with respect to matric suction for non-plastic sandy soils (i.e. I _p  = 0 %). The proposed model uses the Soil–Water Characteristic Curve (SWCC) and the shear modulus at saturation condition along with two fitting parameters ζ and ξ. The proposed model permits estimation of the variation of G _max with respect to matric suction over different zones of the SWCC (i.e. boundary effect, transition, and residual zones) for various non-plastic sandy soils. The fitting parameters ζ and ξ required for the proposed semi-empirical model can be estimated from simple relationships derived from the grain size distribution curve.