Ultimate bearing capacity of rigid footing under eccentric vertical load

In geotechnical engineering, the stability of rigid footings under eccentric vertical loads is an important issue. This is because the number of superstructure buildings has increased and the situation of structures being subjected to eccentric vertical loading is occurring more and more frequently. In this study, focus is placed on the ultimate bearing capacity of a footing against the eccentric load placed on two types of soil, namely, sandy soil and clayey soil, using a finite element analysis. For the sandy soil, the study newly introduces an interface element into the footing-soil system in order to properly evaluate the interaction between the footing and the soil, which greatly affects the failure mechanism of the footing-soil system. For the clayey soil, the study improves the analysis procedure by introducing a zero-tension analysis into the footing-soil system. Two friction conditions between the footing and the soils are considered; one models a perfectly rough condition and the other models a perfectly smooth condition. For a two-dimensional analysis of the footing-soil system, the rigid plastic finite element method (RPFEM) is applied to calculate the ultimate bearing capacity of the eccentrically loaded footing. The RPFEM is extended in this work to calculate not only the ultimate bearing capacity, but also the distribution of contact stress along the footing base. The study thoroughly investigates the effect of the eccentric vertical load on the ultimate bearing capacity in the normalized form of V/V_ult and e/B where e is the length of the eccentricity and B is the width of the footing. V_ult indicates the ultimate bearing capacity of the centric vertical load. The failure envelope in the plane of V/V_ult and M/BV_ult is further investigated under various conditions for the sandy and clayey soils. M is the moment load induced by the eccentric vertical load. This study examines the applicability of the failure envelope obtained for the eccentric vertical load to the cases where two variables, V and M, are independently prescribed. The obtained results are coincident and indicate the wide applicability of the failure envelope in the normalized V-M plane in practice. Finally, in a comparison with previous researches, the numerical data in the present study lead to the derivation of new equations for the failure envelopes of both sandy and clayey soils.     

Seismic bearing capacity of a strip footing on rock media

The bearing capacity factors for a rough strip footing placed on rock media, which is subjected to pseudo-static horizontal earthquake body forces, have been determined using the lower bound finite element limit analysis in conjunction with the power cone programming (PCP). The rock mass is assumed to follow the generalized Hoek-Brown (GHB) yield criterion. No assumption needs to be made to smoothen the GHB yield criterion and the convergence is found to achieve quite rapidly while performing the optimization with the usage of the PCP. While incorporating the variation in horizontal earthquake acceleration coefficient (k_h), the effect of changes in unit weight of rock mass (γ), ground surcharge pressure ($q_0$) and the associated GHB material shear strength parameters (geological strength index (GSI), yield parameter (m_i), uniaxial compressive strength (σ_ci)) on the bearing capacity factors has been thoroughly assessed. Non-dimensional charts have been developed for design purpose. The accuracy of the present analysis has been duly checked by comparing the obtained results with the different solutions reported in the literature. The failure patterns have also been examined in detail.     

End bearing capacity of a single incompletely end-supported pile based on the rigid plastic finite element method with non-linear strength property against confining stress

An Incompletely End Supported Pile (IESP) is a pile in a soft soil layer underlain by a hard soil layer that does not reach the bottom hard layer in practice. This study estimates the end bearing capacity of IESP by using an inhouse Rigid Plastic FEM code (RPFEM), considering shear strength non-linearity of soil against confining pressure, and soil-foundation interaction. The effect of the distance between the pile tip and the bottom hard soil layer (d/B) on the end-bearing capacity of IESP was mainly investigated for three types of soil: cohesive soils, cohesionless soils and intermediate soils. Also, theratio (r) of the end bearing capacity of the pile when it reaches the bottom hard layer to that of the pile when the bottom layer has no influence was was considered. By considering the shear strength non-linearity, the end bearing capacity was accurately estimated. The estimations were consistent with previous analytical, experimental and numerical solutions. It is found that the end bearing capacity inversely decreases with the distance d/B and becomes constant around d/B = 3. Based on the results, a formula for estimating the end bearing capacity of IESP is proposed. Comparisons with methods in existing literature confirmed the reliability of the proposed equation.     

Practical slip circle method of slices for calculation of bearing capacity factors

The slip circle method of slices is commonly used in the analyses of slope stability and bearing capacity for multi-layered ground. However, in the case of ground consisting of horizontal sandy layer, it is known that modified Fellenius׳ method tends to underestimate the factor of safety, while simplified Bishop׳s method tends to overestimate the factor of safety. In this study, a new slip circle method was proposed for the purpose of improving the accuracy of the analysis for a ground consisting of sand and clay layers. In the proposed method, β of the ratio of inter-slice shear force to inter-slice normal force i.e tan(βα_i) is assumed constant as 0.25 for all slices. This is named as circle bearing capacity factor (CBCF) method. It was found that the bearing capacity factors, N_c, N_q, and N_γ calculated for shallow foundation on horizontal ground from CBCF method agreed well with that obtained from the plastic solution. The back-analyses carried out for a few case studies on the stability of slopes on earth structures found in sand and clay layers showed that the factor of safety calculated from CBCF method explains the actual performance of earth structures well. The proposed CBCF method proves it reliability in calculating bearing capacity for shallow foundations. This was achieved from the results obtained from centrifugal model test, which were carried out for dense sand layer overlying soft clay with various conditions by Okamura et al. (1998). It was examined that the factor of safety calculated for the stability of slopes from CBCF method can explain the actual performance of geotechnical structures constructed on ground consisting of sand and clay layers.     

Behavior of zeolite-cement grouted sand under triaxial compression test

Permeation grouting with cement agent is one of the most widely used methods in various geotechnical projects,such as increasing bearing capacity,controlling deformation,and reducing permeability of soils.Due to air pollution induced during cement production as well as its high energy consumption,the use of supplementary materials to replace in part cement can be attractive.Natural zeolite(NZ),as an environmentally friendly material,is an alternative to reduce cement consumption.In the present study,a series of consolidated undrained(CU) triaxial tests on loose sandy soil(with relative density D_r=30%)grouted with cementitious materials(zeolite and cement) having cement replacement with zeolite content(Z) of 0%,10%,30%,50%,70% and 90%,and water to cementitious material ratios(W/CM) of 3,5 and 7 has been conducted.The results indicated that the peak deviatoric stress(q_(max)) of the grouted specimens increased with Z up to 50%(Z_(50)) and then decreased.The strength of the grouted specimens reduced with increasing W/CM of the grouts from 3 to 7.In addition,by increasing the stress applied on the grouted specimens from yield stress(q_y) to the maximum stress(q_(max)),due to the bond breakage,the effect of cohesion(c') on the shear strength reduced gradually,while the effect of friction angle(φ')increased.Furthermore,in some grouted specimens,high confining pressure caused breakage of the cemented bonds and reduced their expected strength.     

Bearing capacity of circular foundations reinforced with geogrid sheets

The ultimate bearing capacity of a circular footing, placed over a soil mass which is reinforced with horizontal layers of circular reinforcement sheets, has been determined by using the upper bound theorem of the limit analysis in conjunction with finite elements and linear optimization. For performing the analysis, three different soil media have been separately considered, namely, (i) fully granular, (ii) cohesive frictional, and (iii) fully cohesive with an additional provision to account for an increase of cohesion with depth. The reinforcement sheets are assumed to be structurally strong to resist axial tension but without having any resistance to bending; such an approximation usually holds good for geogrid sheets. The shear failure between the reinforcement sheet and adjoining soil mass has been considered. The increase in the magnitudes of the bearing capacity factors (N_c and N_γ) with an inclusion of the reinforcement has been computed in terms of the efficiency factors η_c and η_γ. The results have been obtained (i) for different values of ϕ in case of fully granular (c=0) and c−ϕ soils, and (ii) for different rates (m) at which the cohesion increases with depth for a purely cohesive soil (ϕ=0^○). The critical positions and corresponding optimum diameter of the reinforcement sheets, for achieving the maximum bearing capacity, have also been established. The increase in the bearing capacity with an employment of the reinforcement increases continuously with an increase in ϕ. The improvement in the bearing capacity becomes quite extensive for two layers of the reinforcements as compared to the single layer of the reinforcement. The results obtained from the study are found to compare well with the available theoretical and experimental data reported in literature.     

Effects of restraining conditions on the bearing capacity of footings near slopes

In evaluating the ultimate bearing capacity (q_u) of a strip footing adjacent to a slope, conventional correction formulas for the effect of load eccentricity may not be applicable because these formulas were developed exclusively for footings situated on horizontal grounds, where loads eccentric to opposite sides of the footing yield identical results for q_u. In this study, loading tests and analyses are conducted on a strip footing placed adjacent to a model slope with various slope angles. The experimental evidence shows that a load eccentric toward the heel of a footing leads to an increase in bearing capacity, whereas the analytical results based on conventional formulas show the opposite trend. To address this discrepancy, an approach is proposed that uses a bearing capacity correction formula for a footing with a setback from the crest of the slope. Results of a comparative study show that the experimental values for bearing capacity factor N_γ(test), with full corrections for load inclination, load eccentricity, and footing setback are comparable to the theoretical solutions. Furthermore, fully corrected values for N_γ(test) for the fixed footing approximately follow the line of the upper boundary; those for the free-rotating footing follow the lower boundary of the theoretical solutions reported in the literature. This discrepancy is due to the different failure mechanisms induced by the restraining conditions of the footing which have yet to be considered in engineering practice.     

Effect of Specimen Size on Unconfined Compressive Strength Properties of Natural Deposits

In order to use the advantages of unconfined compression tests, a new testing procedure using S (or Small size) specimens (15 mm in diameter and 35 mm in height) is proposed and a new portable unconfined compression test apparatus with suction measurement is outlined. The effect of specimen size on unconfined compressive strength properties of natural deposits is discussed from laboratory tests. The standard deviations of the ratios of q_u and E₅₀ values of the S specimens to O (or Ordinary size) specimens (35 mm d and 80 mm h) were in the range of 0.09 to 0.16. The 10% variation from the mean value reflects the homogeneity of soils since the coefficient of variations of the undrained shear strength for the undisturbed and reconstituted soils were 8% to 17% (Matsuo and Shogaki, 1988). In an engineering sense, there was no difference in shear strength and deformation characteristics between the S and O specimens for soils having plasticity indexes ranging from 10 to 370 and unconfined compressive strengths of 18 kPa to 1000 kPa, that were taken from 26 different sites in the United Kingdom, Korea and Japan. These soils consisted of Holocene and Pleistocene clays plus diatomaceous mudstone and highly organic soils.     

Pullout behavior of a bearing polymeric strap under monotonic and cyclic tensile loads

Soil-reinforcement interaction consists of three factors including frictional resistance, shear strength of the soil and passive resistance. In the ordinary polymeric strap (PS) reinforcement, only frictional resistance contributes to pullout resistance. In this study, in order to develop passive resistance in the soil, a number of angles as transversal elements were attached to PS reinforcement, which is called bearing polymeric strap (BPS). The post-cyclic pullout behaviour of the BPS is evaluated using a large-scale pullout apparatus adopting multistage pullout (MSP) test and one-stage pullout (OSP) test procedures. The results show that a spacing-to-high ratio of angles equal to 3.33 gives the maximum pullout resistance. MSP tests were performed on the BPS with an optimum arrangement to evaluate the influence of various factors including cyclic tensile load amplitude, load frequency and number of load cycles, and also the influence of vertical effective stress on the pullout resistance and the peak apparent coefficient of friction mobilized at the soil-BPS interface. Moreover, for BPS system with a single isolated transverse member, the bearing capacity factor N_q was calculated using equations based on three failure modes and it was found that the N_q calculated in the punching shear failure mode makes the best prediction.     

A Study on the Engineering Properties of Sand Improved by the Sand Compaction Pile Method

In order to directly evaluate the effects of soil improvement by the Sand Compaction Pile (SCP) method on the density, deformation, and static and liquefaction strength characteristics of sandy soils, a series of field and laboratory tests were performed. Laboratory tests were performed on high-quality undisturbed samples obtained from sandy soils both before and after soil improvement by the SCP method. The high-quality undisturbed samples were recovered by the in-situ freezing sampling method. The drained shear strength (internal friction angle, φ_d), liquefaction strength (R₁₅: cyclic stress ratio needed to cause 5% double amplitude axial strain in 15 cycles), and cyclic deformation characteristics (G~γ and h~γ relations) were determined by performing a series of laboratory tests on the undisturbed samples. Both the in-situ density and the relative density were measured on the undisturbed samples used in the laboratory tests. A standard penetration test (SPT) and a suspension-type P-S wave logging test were performed to investigate the soil profile of the test site before and after the sand compaction. Both the static and the liquefaction strengths of the sandy soils obtained in the laboratory tests were also compared with those estimated by empirical correlations used in practice based on the SPT N-value and soil gradations.     

In-Situ Evaluation of Strength and Dilatancy of Sands Based on CPT Results

In-situ tests have been increasingly used to estimate the shear strength of soils. In this paper, we propose methods to evaluate in-situ strength and dilatancy of sandy soils based on cone penetration test (CPT) results. It takes into account the silt content, relative density and stress state of the sand. A series of laboratory test results from fundamental property tests and triaxial tests are analyzed to develop methods for in-situ evaluation of strength and dilatancy for sands. Based on test results, modified and simplified dilatancy equations, in terms of the cone penetration resistance q_c and intrinsic soil variables, are proposed. Results from proposed and original dilatancy indexes show close agreements for various soil conditions. Values of intrinsic variables for the proposed dilatancy relationships were proposed as a function of silt content. Based on TX test results, a direct CPT-based correlation, applicable to both clean and silty sands, is proposed as well. In order to verify the proposed methods, calibration chamber CPT results obtained in this study and collected from the literature are adopted. It is observed that the results from the proposed methods show good agreement with the measured results.     

Strain localization characteristics of loose saturated Toyoura sand in undrained cyclic torsional shear tests with initial static shear

Strain localization, or the formation of shear bands, is a key aspect in understanding soil failure mechanisms. While efforts have been made in terms of measuring the shear band properties and the stress–strain behavior within shear bands, there are still uncertainties regarding when shear bands initiate and their influence on the development of large ground deformation. In this paper, the limiting value of shear strain, at which strain localization appears during undrained cyclic torsional shear tests with initial static shear, performed on loose Toyoura sand specimens (Dr=44–48%) up to a single amplitude of shear strain exceeding 50%, was evaluated. Non-uniform specimen deformation was observed at strain levels larger than 20%. However, the onset of strain localization could not be defined on the basis of visual observations. Therefore, the limiting values for half of the double amplitude (γ_DA/2) and single amplitude (γ_SA) shear strain, to initiate strain localization, were determined from test results based on changes in the deviator stress response and strain accumulation properties as well as changes in the strain-softening behavior during cyclic shear. It was found that γ_SA is a more appropriate parameter than γ_DA/2. Irrespective of the static shear stress level, the limiting strain value for γ_SA was evaluated to be in the range of 23–28% for liquefied loose Toyoura sand specimens (i.e., stress reversal and intermediate tests). Alternatively, the limiting strain value could not be properly defined when liquefaction did not occur (i.e., non-reversal stress tests), although various methods were employed.     

Undrained End Bearing Capacity of an Improved Soil Berm in an Excavation

For a wide excavation in soft soil, the excavation can be stabilized by an embedded improved soil berm to increase wall stability and control soil movement. An embedded stiff berm essentially behaves like a horizontal pile subjected to a load applied by the retaining wall and derives its resistance to horizontal movement from both end bearing and interfacial shear resistance on the top and bottom of the berm. This resistance helps to restrain the wall from moving inwards to the excavated side. However, to date, there is no known reported literature on the determination of the undrained ultimate bearing capacity of such a berm, especially for the unit end bearing, q_b. In this paper, the undrained end bearing of an improved berm under a plane strain condition was determined. The undrained end bearing capacity was first derived using a solution from a proposed upper bound analysis based on observations from centrifuge tests and then modified, taking on the basis of an equivalent finite element analyses. The proposed end bearing capacity factor N_c lies between the upper bound and lower bound solutions. The solution showed that the undrained end bearing capacity is not a constant but decreases during the excavation process. Furthermore, it was shown that the existence of an improved soil berm will provide an additional pressure relative to the passive pressure to control the wall displacement.     

Strength and dilatancy behaviors of deep sands in Shanghai with a focus on grain size and shape effect

With rapid development of infrastructures like tunnels and open excavations in Shanghai, investigations on deeper soils have become critically important. Most of the existing laboratory works were focused on the clayey strata up to Layer 6 in Shanghai, i.e. at depth of up to 40 m. In this paper, Layers 7, 9, and 11, which were mostly formed of sandy soils at depth of up to 150 m, were experimentally investigated with respect to physico-mechanical behaviors. The stress–strain behaviors were analyzed by the consolidated drained/undrained (CD/CU) triaxial tests under monotonic loading. One-dimensional (1D) oedometer tests were performed to investigate the consolidation properties of the sandy soils. Specimens were prepared at three different relative densities for each layer. Also, the micro-images and particle size analyzers were used to analyze the shape and size of the sand grains. The influences of grain size, density, and angularity on the stress–strain behaviors and compressibility were also studied. Compared to the other layers, Layer 11 had the smallest mean grain size (D₅₀), highest compressibility, and lowest shear strength. In contrast, Layer 9 had the largest mean grain size, lowest compressibility, and highest shear strength. Layer 7 was of intermediate mean grain size, exhibiting more compressibility and less shear strength than that of Layer 9. Also, the critical state parameters and maximum dilatancy rate of different layers were discussed.     

Effects of Curing Period and Stress Conditions on the Strength and Deformation Characteristics of Cement-mixed Soil

The effects of long-term curing on the strength and deformation characteristics of compacted cement-mixed soil were evaluated. A series of unconfined compression tests and drained triaxial compression (TC) tests were performed on moist cement-mixed sand compacted at various water contents, w_i, and cured at unconfined conditions for different periods up to more than eight years. TC tests were performed on cement-mixed gravel compacted at the optimum water content. The ageing effects on the compressive strength, q_max, from the present study were compared to those with various types of cement-mixed soils and concretes from the literature. An increase in q_max of cement-mixed soil continues for a very long period, up to several years, unlike ordinary concrete. This result indicates that the compressive strength at 28 days of cement-mixed soil, usually employed as the design strength, may largely underestimate the long-term strength. The increasing rate with time of the initial stiffness at small strains becomes continuously smaller than q_max with time. A large high-stiffness stress zone develops when monotonic loading is restarted at a certain high strain rate after some long sustained loading. This stress size is much larger than the one in the case without ageing effects. By positive interactions between the ageing effect and the inviscid yielding, q_max exhibits a larger extra gain when cured longer at more anisotropic stress states.     

砂砾软岩的极限承载力分析

利用Hoek-Brown强度准则建立砂砾软岩极限承载力分析方法,提出岩基剪切破坏模型,推求潜在破坏面上正应力计算公式。结合某工程现场载荷试验探讨砂砾软岩的极限承载能力及自重应力对极限承载能力的影响。研究结果表明:极限承载力的计算结果大于预估设计荷载,砂砾软岩在强度方面尚有很大潜力可挖;同时,极限承载力的计算结果弥补了现场载荷试验中由于试验条件所限造成的荷载–变形曲线上峰值荷载不能给出的缺陷,为建立完整的变形曲线模型奠定了理论基础。研究成果为研究砂砾岩一类软岩的承载力提供了新的途径。     

Predicting deformation of PVD improved deposit under vacuum and surcharge loads

A series of modified triaxial tests was conducted to investigate the deformation characteristics of mini-prefabricated vertical drain (PVD) unit cells. The factors considered are the (1) magnitudes of surcharge load (p_s) and vacuum pressure (p_vac); (2) pre-vacuum consolidation period (t_va) before applying surcharge load; (3) surcharge loading rate (SLR); and (4) initial effective stress state in the specimens. Based on the test results, relationships between the coefficient of earth pressure (K_es) at the end of surcharge load application and the normalized horizontal and vertical specimen strains are established. Further, a method is proposed for estimating the value of K_es, and therefore the horizontal and vertical strains of the PVD improved soil layer subjected to combined vacuum pressure and surcharge load using loading conditions and basic soil properties. Finally, the proposed method was applied to a case history reported in the literature and good agreement between the field-measured and calculated lateral displacement and settlement was obtained, which suggesting that the proposed method can be a useful tool for designing preloading projects involving combined vacuum and surcharge loads.     

Model tests comparing the behavior of pre-bored grouted planted piles and a wished-in-place concrete pile in dense sand

The compressive bearing capacity of wished-in-place (WIP) concrete piles and pre-bored grouted planted (PGP) piles in dense sand was investigated by means of model tests. In total, three model piles were tested. The load–displacement response, axial force and tip resistance of each model pile were measured in the static load test process. Several conclusions can be drawn from the model test results: the pre-bored grouted planted nodular (PGPN) pile and the pre-bored grouted planted pipe (PGPP) pile have ultimate skin friction 1.23–1.36 times and 1.34–1.46 times greater than the ultimate skin friction of the wished-in-place (WIP) pile, respectively. The tip bearing capacity of the PGP pile is similar to the tip bearing capacity of the WIP pile, and the hyperbolic model of normalized tip resistance (q_b/q_c) and normalized tip displacement (S_b/D) can represent the tip load–displacement response of the WIP and PGP piles well.     

Computation of Bearing Capacity Factor Nγ-Prandtl's Mechanism

In this paper, an analysis based on Prandtl's failure mechanism is proposed for the evaluation of bearing capacity factor, N_γ, using the limit equilibrium approach, coupled with Kotter's equation. Except for shape of the failure surface, no other assumptions are needed in the analysis. A methodology based on Kotter's equation and force equilibrium conditions is developed to identify the correct location of pole of the log spiral and hence the unique failure surface. Using moment equilibrium condition, the point of application of passive thrust is determined.The proposed N_γ values are compared with other available theoretical predictions and experimental results. They show a good agreement with some existing theoretical results and also show a better agreement with available experimental results. The analysis shows that pole of the log spiral lies at the footing edge for general shear failure conditions and the point of application of the passive thrust is strongly influenced by angle of soil internal friction.