Bearing capacity of foundations on slopes

By applying the lower bound finite element limit analysis in conjunction with non-linear optimisation, the bearing capacity factors, N_c, N_q and N_γ, due to the components of cohesion, surcharge and unit weight, respectively, have been estimated for a horizontal strip footing placed along a sloping ground surface. The variation of N_c, N_q and N_γ with changes in slope angle (β) for different soil friction angle (φ) have been computed for smooth as well as rough strip footings. The analysis reveals that along a sloping ground surface, in addition to N_γ, the factors N_c and N_q also vary considerably with changes in footing roughness. Compared to the smooth footing, the extent of the plastic zone around the footing becomes greater for the rough footing. The results obtained from the analysis are found to compare well with those previously reported in literature.     

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.     

Application of statistical learning algorithms to ultimate bearing capacity of shallow foundation on cohesionless soil

This study employs two statistical learning algorithms (Support Vector Machine (SVM) and Relevance Vector Machine (RVM)) for the determination of ultimate bearing capacity (q_u) of shallow foundation on cohesionless soil. SVM is firmly based on the theory of statistical learning, uses regression technique by introducing varepsilon‐insensitive loss function. RVM is based on a Bayesian formulation of a linear model with an appropriate prior that results in a sparse representation. It also gives variance of predicted data. The inputs of models are width of footing (B), depth of footing (D), footing geometry (L/B), unit weight of sand (γ) and angle of shearing resistance (?). Equations have been developed for the determination of q_u of shallow foundation on cohesionless soil based on the SVM and RVM models. Sensitivity analysis has also been carried out to determine the effect of each input parameter. This study shows that the developed SVM and RVM are robust models for the prediction of q_u of shallow foundation on cohesionless soil. Copyright © 2010 John Wiley & Sons, Ltd.     

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.     

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.     

Bearing capacity of strip and circular footings in sand using finite elements

Design of shallow foundations relies on bearing capacity values calculated using procedures that are based in part on solutions obtained using the method of characteristics, which assumes a soil following an associated flow rule. In this paper, we use the finite element method to determine the vertical bearing capacity of strip and circular footings resting on a sand layer. Analyses were performed using an elastic–perfectly plastic Mohr–Coulomb constitutive model. To investigate the effect of dilatancy angle on the footing bearing capacity, two series of analyses were performed, one using an associated flow rule and one using a non-associated flow rule. The study focuses on the values of the bearing capacity factors N_q and N_γ and of the shape factors s_q and s_γ for circular footings. Relationships for these factors that are valid for realistic pairs of friction angle and dilatancy angle values are also proposed.     

Bearing capacity of foundations on rock mass using the method of characteristics

The method of stress characteristics has been used for computing the ultimate bearing capacity of strip and circular footings placed on rock mass. The modified Hoek‐and‐Brown failure criterion has been used. Both smooth and rough footing‐rock interfaces have been modeled. The bearing capacity has been expressed in terms of nondimensional factors N_σ0 and N_σ, corresponding to rock mass with (1) γ = 0 and (2) γ ≠ 0, respectively. The numerical results have been presented as a function of different input parameters needed to define the Hoek‐and‐Brown criterion. Slip line patterns and the pressure distribution along the footing base have also been examined. The results are found to compare generally well with the reported solutions.     

Magnetic anisotropy of hematite natural crystals: high field experiments

Hematite is one of the most important carriers of remanent magnetization in natural samples. Its strong magnetocrystalline anisotropy makes it difficult to determine one single value for the magnetic anisotropy constant and other magnetic properties. In particular, the anisotropy of hematite within its basal plane is controversial because an assumed triaxial anisotropy compatible with the crystallographic structure has not always been detected. This study presents a comparative analysis of rock magnetic properties, compositional analysis and determination of the magnetic anisotropy constant. Different models with anisotropy constant within the basal plane ranging from 0 to 13 (J m⁻³) are considered in the evaluation of the factors that control the presence or absence of a triaxial anisotropy. A linear relationship between saturation magnetization (M _s ) and coercitivity (B _c ) in measurements at increasing temperatures is observed in samples where anisotropy is either uniaxial or biaxial while those with significant triaxial anisotropies have a power–law relationship between M _s and B _c .     

Seismic Bearing Capacity of Shallow Strip Footing with Coulomb Failure Mechanism using Limit Equilibrium Method

In this paper, an effort is made to evaluate the seismic bearing capacity of shallow strip footing resting on c–ф soil. The formulation is developed to get a single coefficient of bearing capacity for simultaneous resistance of weight, surcharge and cohesion. Limit equilibrium method in Pseudo-static approach with Coulomb mechanism is applied here to evaluate the seismic bearing capacity. The seismic bearing capacity of footing (q_uE) is expressed in terms of single coefficient N_γE. The effect of various parameters viz. angle of internal friction of soil (ф), angle of wall friction (δ), cohesion (c), ratio of depth to width of footing (d_f/B₀), seismic acceleration (k_h, k_v) are studied on the variation of seismic bearing capacity co-efficients.     

Soil hydraulic properties on the steep karst hillslopes in northwest Guangxi, China

Soil hydraulic properties such as soil infiltration rate and hydraulic conductivity are closely linked to runoff generation and infiltration processes but little is known about them on karst hillslopes. The objectives of this paper were to investigate the change in soil stable infiltration rate (q _s) and near-saturated hydraulic conductivity (K _ns) in different slope positions and to understand their relationship with rock fragment content and soil texture within the topsoil in subtropical karst regions of southwest China. Tension infiltrometers (20 cm in diameter) were used to measure q _s and K _ns at pressure head of −20 mm on hillslopes 1 (a disintegrated landslide failure) and 2 (an avalanche slope). The change of q _s and K _ns was great and they mostly had a moderate variability with coefficient of variations (CV) between 0.1 and 1.0 in the different slope positions. On average, q _s ranged from 0.43 to 4.25 mm/min and K _ns varied from 0.75 to 11.00 mm/min. These rates exceed those of most natural rainfall events, confirming that overland flow is rare on karst hillslopes. From bottom to top, q _s and K _ns had a decrease–increase–decrease trend due to the presence of large rock outcrops (>2 m in height) on hillslope 1 but had an increasing trend on hillslope 2 with less complex landform. They tended to increase with increase in total rock fragment content (5–250 mm) within the topsoil as well as slope gradient on both hillslopes. Pearson correlation analysis suggested that higher coarse pebble (20–75 mm), cobble (75–250 mm), and sand (2–0.05 mm) contents as well as total rock fragment content could significantly facilitate water infiltration into soils, but higher clay (<0.002 mm) content could restrict water movement. This result indicated that rock fragment, sand, and clay contents may remarkably affect water flow in the topsoil layers, and should be considered in hydrological modeling on karst hillslopes in subtropical regions.     

Bearing capacity computation for a ring foundation using the stress characteristics method

The stress characteristics method (SCM) has been used to compute the bearing capacity of smooth and rough ring foundations. Two different failure mechanisms for a smooth footing, and four different mechanisms for a rough footing have been considered. For a rough base, a curvilinear non-plastic wedge has been employed below the footing. The analysis incorporates the stress singularities at the inner as well as outer edges of the ring footing. Bearing capacity factors, N_c, N_q and N_γ are presented as a function of soil internal friction angle (ϕ) and the ratio (r_i/r_o) of inner to outer radii of the footing.     

Behaviour of model footing on pond ash

This paper focuses on the effective utilization of pond ash, as foundation medium. A series of laboratory model tests have been carried out using square, rectangular and strip footings on pond ash. The effects of dry density, degree of saturation of pond ash, size and shape of footing on ultimate bearing capacity of shallow foundations are presented in this paper. Local shear failure of a square footing on pond ash at 37% moisture content (optimum moisture content) is observed up to the values of dry density 11.20 kN/m³ and general shear failure takes place at the values of dry density 11.48 kN/m³ and 11.70 kN/m³. Effects of degree of saturation on ultimate bearing capacity were studied. Experimental results show that degree of saturation significantly affects the ultimate bearing capacity of strip footing. The effect of footing length to width ratio (L/B), on increase in ultimate bearing capacity of pond ash, is insignificant for L/B ≥ 10 in case of rectangular footings. The effects of size of footing on ultimate bearing capacity for all shapes of footings viz., square, rectangular and strip footings are highlighted.     

Vertical uplift resistance of circular plate anchors in clays under undrained condition

The vertical uplift resistance of circular plate anchors, embedded horizontally in a clayey stratum whose cohesion increases linearly with depth, has been obtained under undrained ( = 0) condition. The axi-symmetric static limit analysis formulation in combination with finite elements proposed recently by the authors has been employed. The variation of the uplift factor (F_c) with changes in the embedment ratio (H/B) has been computed for several rates of increases of soil cohesion with depth. It is noted that in all the cases, the magnitude of F_c increases continuously with depth up to a certain value of H_cr/B beyond which the uplift factor becomes essentially constant. The proposed static limit analysis formulation is seen to provide acceptable results even for the two other simple chosen axi-symmetric problems.     

Relations between load and settlement of circular foundations on or in a dense sand expressed by a function of diameter and depth

When load acts on a circular foundation on or in a dense sand, average contact pressure on the lower surface of the foundation is q and settlement of the foundation is s. Diameter and depth of the foundation are B and D_f. When the sand, B and D_f are given, we can know the relation between q and s/B by, e.g. a loading test, i.e. the relation is determined by B and D_f for the sand. Using the results of numerical analyses, we express a relation between q and s/B up to s=0.1B by functions of a single variable which is a linear combination of B and D_f. Consequently when two foundations have different B's and different D_f's but have the same value of the variable, the relations are the same. Then we examine whether the functions can express the results of eleven tests of model foundations of wide range of B and/or D_f. In all the tests, the relations are expressed with sufficient accuracy. Copyright © 2005 John Wiley & Sons, Ltd.     

Reliability analysis of seismic bearing capacity of strip footing by stochastic slip lines method

In this research, the reliability analysis of seismic ultimate bearing capacity of strip footing is assessed with implementing slip lines method coupled with random field theory. The probability density functions of seismic and static bearing capacities which are log-normal and nearly normal distribution respectively are compared to each other. The predicted Probability Density Function (PDF) of the seismic bearing capacity by slip line method is verified, with those of the Terzaghi equation and Monte Carlo simulation (MCs). For uncertainties analysis by Terzaghi equation the N_c, N_q and N_γ are assessed stochastically.     

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.     

Kinematic slices approach for uplift analysis of strip foundations

A kinematic method of slices has been used in this article to deal with the stability problems of strip foundations subjected to uplift loads. The method is based on the upper bound theorem of limit analysis and satisfies the kinematic admissiblility of the chosen collapse mechanism. Assuming the global rupture surface as an arc of logarithmic spiral, uplift factors F_c, F_q and F_γ separately for the effects of cohesion, surcharge and density have been determined. The effect of the yielding of soil mass with partial soil shear strength parameters along the slice interfaces on the results has been examined. The ultimate uplift capacity increases with increase in soil shear strength along the interfaces of slices. The results compare reasonably well with the various existing theories and reported experimental tests data. Copyright © 1999 John Wiley & Sons, Ltd.     

Does AMS data from micaceous quartzite provide information about shape of the strain ellipsoid?

Anisotropy of magnetic susceptibility (AMS) in micaceous quartzites with mean susceptibility (K _m) >50 × 10⁻⁶ SI units is known to be on account of the orientation distribution of the para/ferromagnetic minerals (e.g. micas, magnetite), which comprise the minor phase in the rocks. However, the strain in such deformed micaceous quartzites is dominantly accommodated by the quartz grains, which are the major phase in them. The objective of this paper is to explore the extent to which AMS data from micaceous quartzites provide information about the shape of the strain ellipsoid. AMS analysis of 3 quartzite blocks is performed, and the shape of the AMS ellipsoid is recorded to be oblate. From AMS data, the three principal planes of the AMS ellipsoid are identified in each block and thin sections are prepared along them. Quartz grain shape (aspect ratio, R _q), intensity of quartz and mica shape preferred orientation (κ_q and κ_mi, respectively) and 2D strain (E) recorded by quartz are measured in each section. R _q, κ_q, κ_mi and E are all noted to be minimum in the section parallel to the magnetic foliation plane as compared to the other two sections. This indicates that the quartz grains have oblate shapes in 3D and accommodated flattening strain, which is similar to the shape of the AMS ellipsoid. The role of mica in causing Zener drag and pinning of quartz grain boundaries is discussed. It is concluded that during progressive deformation, migration of pinned grain boundaries is inhibited. This causes enhanced recrystallization at the grain boundaries adjacent to the pinned ones, thus guiding the shape modification of quartz grains. A strong correlation is demonstrated between κ_q and κ_mi as well as κ_mi and E. It is inferred that fabric evolution of quartz was controlled by mica. Hence, the shape of the AMS ellipsoid, which is on account of mica, provides information about shape of the strain ellipsoid.     

Comparing different models of aftershock rate decay: The role of catalog incompleteness in the first times after main shock

We evaluated the efficiency of various models in describing the time decay of aftershock rate of 47 simple sequences occurred in California (37) from 1933 to 2004 and in Italy (10) from 1976 to 2004. We compared the models by the corrected Akaike Information Criterion (AIC_c) and the Bayesian Information Criterion (BIC), both based on the log-likelihood function and also including a penalty term that takes into account the number of independent observations and of free parameters of each model. These criteria follow two different approaches (probabilistic and Bayesian respectively) well covering the wide spectra of current views on model comparison. To evaluate the role of catalog incompleteness in the first times after the main shock, we compared the performance of different models by varying the starting time T_s and the minimum magnitude threshold M_min for each sequence. We found that Omori-type models including parameter c are preferable to those not including it, only for short T_s and low M_min while the latters generally perform better than the formers for T_s longer than a few hours and M_min larger than the main shock magnitude M_m minus 3 units. For T_s > 1 day or M_min > M_m − 2.5, only about 15% of the sequences still give a preference to models including c. This clearly indicates that a value of parameter c different from zero does not represent a general property of aftershock sequences in California and Italy but it is very likely induced in most cases by catalog incompleteness in the first times after the main shock. We also considered other models of aftershock decay proposed in the literature: the Stretched Exponential Law in two forms (including and not including a time shift) and the band Limited Power Law (LPL). We found that such models perform worse than the Modified Omori Model (MOM) and other Omori-type models for the large majority of sequences, although for LPL, the relatively short duration of the analyzed sequences (one year) might also contribute to its poor performance. Our analysis demonstrates that the MOM with c kept fixed to 0 represent the better choice for the modeling (and the forecasting) of simple sequence behavior in California and Italy.     

Bearing capacity of a strip foundation on a sand layer overlying a smooth rigid stratum

The effect of a smooth rigid stratum, located beneath a dense sand layer, on the bearing capacity and settlement of surface and shallow strip footings is investigated using an advanced experimental model. A theoretical analysis is presented for the bearing capacity of surface footings. The results indicate that the bearing capacity reaches a minimum value at a specific sand-layer thickness. Any increase in the layer thickness above this value causes an increase in the bearing capacity up to that corresponding to a continuous media.Notation H= thickness of the sand layer - B= foundation width - N _q and N = bearing capacity factors for a semi-infinite layer - N _qs and N _s= bearing capacity factors for a finite layer - H _o /B= limiting depth - D _r= relative density - = angle of soil internal friction - M= model width - D= depth of surcharge - q= bearing stress, pressure applied on the footing - q _u= bearing capacity - = unit weight of sand