Probabilistic stability analysis of geosynthetic-reinforced slopes under pseudo-static and modified pseudo-dynamic conditions

An efficient and accurate reliability-based design of the geosynthetic-reinforced slopes (GRS) using the pseudo-static and modified pseudo-dynamic framework is proposed in the present study. Deterministic formulation used in the present study is made robust with the help of nonlinear constrained optimization. The collocation based stochastic response surface method (CSRSM) is used to probabilistically analyze the GRS. The critical modes of failure pertaining to the internal and external stability of the GRS are considered in the formation of the performance functions. The horizontal seismic acceleration coefficient (k_h), internal friction angle of soil (φ), soil unit weight (γ), shear wave velocity (V_s), and friction angle at the interface between soil and reinforcement (φ_b) are chosen as the random variables, owing to their high influence on the stability of the GRS. The influence of correlation on the stability of the reinforced slope is illustrated considering the internal and external stability. System reliability analysis considering the internal and external modes of failure is also performed. An illustrative example is presented showing the steps to design a GRS using the proposed formulation. The results confirm the necessity of performing the system reliability analysis to estimate an accurate value of probability of failure of GRS.     

Dependency of Nγ on footing diameter for circular footings

By incorporating a variation in soil internal friction angle ? with mean principal stress σ_m, the dependency of bearing capacity factor N_γ with footing diameter B has been evaluated for circular footings. The evaluation has been performed by a lower bound finite element limit analysis in combination with a linear optimization. Two ?–σ_m curves, available from literature, were used. The magnitude of N_γ has been computed for several footing diameters, covering almost the entire possible range of model and field footing sizes. Factor N_γ is seen to decrease significantly with an increase in B. For B approximately greater than (i) 0.7 m for smooth footings (δ=0) and (ii) 0.35 m for rough footings (δ=?), N_γ varies almost linearly with B on a log–log scale. Once a relationship has been generated between N_γ and B, for a given design load, the required footing diameter can always be obtained.     

Effect of aspect ratio of footing on behavior of two closely-spaced footings on geogrid-reinforced sand

This paper presents the results of laboratory model tests carried out on two closely-spaced interfering footings resting on the surface of geogrid-reinforced and unreinforced sand bed. The effect of aspect ratio (or shape) of the footing on interference behavior is studied by adopting three pairs of model footings of different sizes. The length (L) to width (B) ratio (i.e., aspect ratio) of the footings is varied from 1.0 to 2.0. The effects of single layer of geogrid on footing interference and bearing capacity improvement are investigated. The optimum depth of the geogrid layer for both interfering and isolated footings is found to be one-third of the footing width and it is not dependent on the aspect ratio of the footing. The optimum spacing between the interfering footings is found to be 1.5 times the width of the footing. Lower efficiency factor is observed for interfering footings resting on the reinforced sand compared to the unreinforced sand. Higher bearing capacity ratio (BCR) is observed for isolated footing than that of interfering footings when BCR is measured based on ultimate bearing capacity values of reinforced and unreinforced cases and BCR value increases as the aspect ratio of the footing increases.     

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.     

Effects of Footing Size and Aspect Ratio on the Bearing Capacity of Sand Subjected to Eccentric Loading

The current practice of estimating bearing capacity usually employs the conventional bearing capacity formula originally developed for strip footings under vertical central loading. In order to account for the effect of footing shape and eccentricity and inclination of loads, correction factors are introduced in the formula, which are derived based on a number of small-scale model test observations.This paper describes research on the bearing capacity of rectangular footings on sand subjected to vertical eccentric loading. Two aspects, namely the effects of footing size and of footing shape on the bearing capacity and deformation characteristics, are focused on. A series of loading tests was conducted in a centrifuge on rectangular footings with aspect ratios from 1 to 5, at two different centrifugal accelerations. In addition, finite element analyses were performed in which factors influencing the angle of shear resistance including stress level dependency, anisotropy and coefficient of intermediate principal stress, were taken into account.It was found that the shape factor of footing apparently increased with increasing footing width. This indicates that the shape factor used in the current practice underestimates bearing capacity of footings. This was also the case for failure locus in the M/B-V (moment-vertical) load plane. Normalized failure locus for wider footings with a smaller aspect ratio is considerably larger than that reported in the literature. The stress level dependency of the angle of shear resistance appeared to be responsible for the scale effects of footings on the failure locus.     

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.     

Behavior evaluation of geogrid-reinforced ballast-subballast interface under shear condition

The effective functioning of a railway track under operating conditions depends largely on the performance of various rail track interfaces (e.g. ballast-subballast interface, subballast-subgrade interface). In this context, a series of large-scale direct shear tests were conducted to investigate the shear behavior of unreinforced and geogrid-reinforced ballast-subballast interfaces at different normal stresses (σ_n) and rates of shearing (S_r). Fresh granite ballast and subballast having average particle size (D₅₀) of 42?mm and 3.5?mm respectively, and five geogrids with different aperture shapes and sizes were used in this study. Tests were performed at different normal stresses (σ_n) ranging from 20 to 100?kPa and shearing rates (S_r) ranging from 2.5 to 10.0?mm/min. The laboratory test results confirmed that the shear strength of ballast-subballast interface was highly influenced by the applied normal stress (σ_n) and rate of shearing (S_r). The friction angle (φ) of unreinforced ballast-subballast interface was found to decrease from 63.24° to 47.82° and dilation angle (ψ) from 14.56° to 5.23° as the values of σ_n and S_r increased from 20 to 100?kPa and 2.5–10.0?mm/min, respectively. Further, the breakage of ballast (B_g) was found to increase from 2.84 to 6.69%. However, geogrid inclusions enhanced the shear strength of the ballast-subballast interface and also reduced the extent of B_g. The results indicate that it is possible to establish a relationship between the friction angle (φ) and breakage of ballast (B_g), wherein the friction angle (φ) of both unreinforced and geogrid-reinforced interfaces reduces with the increase in breakage (B_g). The interface efficiency factor, defined as the ratio of the shear strength of the geogrid-reinforced ballast-subballast interface to the original shear strength of ballast-subballast interface varies from 1.04 to 1.22. Moreover, the current study revealed that the shear behavior of ballast-subballast interface was influenced by geogrid aperture size (A).     

无黏性土斜坡地基承载力模型试验研究

采用缩尺模型试验对砂土斜坡地基的土压力分布、变形机制、破坏模式进行探索,并研究了斜坡坡角、基础尺寸、相对密度、基础形状对斜坡地基破坏形态及极限承载力的影响。结果表明：斜坡地基的破坏模式与Choudhury提出的破坏模式相近,破坏区域由不对称楔体、辐射向剪切区、被动楔体组成。斜坡地基的破坏区域长度随斜坡坡角、基础尺寸的增大而增大,但不随相对密度的变化而变化;而斜坡地基的极限承载力随斜坡坡角的增大而减小,随基础宽度、相对密度的增大而增大。对相同尺寸的基础而言,方形基础下的地基极限承载力和破坏区域长度均大于圆形基础。试验研究成果对斜坡地基变形特征、破坏形态和斜坡地基承载力影响因素的探究具有一定理论参考价值。     

Numerical parametric study of geosynthetic reinforced soil integrated bridge system (GRS-IBS)

A 2-D finite flement model was developed in this study to conduct a FE parametric study on the effects of some variables in the performance of geosynthetic reinforced soil integrated bridge system (GRS-IBS). The variables investigated in this study include the effect of internal friction angle of backfill material, width of reinforced soil foundation (RSF), secondary reinforcement within bearing bed, setback distance, bearing width and length of reinforcement. Other important parameters such as reinforcement stiffness and spacing were previously investgated by the authors. The performance of GRS-IBS were investgated in terms of lateral facing displacement, strain distribution along reinforcement, and location of potential failure zone. The results showed that the internal friction angle of backfill material has a significant impact on the performance of GRS-IBS. The secondary reinforcement, setback distance, and bearing width have low impact on the performance of GRS-IBS. However, it was found that the width of RSF and length of reinforcement have negligible effect on the performance of GRS-IBS. Finally, the potential failure envelope of the GRS-IBS abutment was found to be a combination of punching shear failure envelope (top) that starts under the inner edge of strip footing and extends vertically downward to intersect with Rankine active failure envelope (bottom).     

Modified ultimate bearing capacity formula of strip footing on sandy soils considering strength non-linearity depending on stress level

Most of the contemporary ultimate bearing capacity (UBC) formulas assume a linear yield function in shear stress-normal stress space. However, experimental investigations have corroborated the non-linearity in the failure envelopes of sandy soils. This study focused on the assessment of the stress level effect on the UBC of surface strip footings ascribed to the soil unit weight (γ), footing size (B), and uniform surcharge load (q). The rigid plastic finite element method (RPFEM) was employed for the analysis. The analysis method was validated against the centrifuge test results from the published references in the case of various sandy soils with different relative densities. The RPFEM, using the mean confining stress dependence property of Toyoura sand, is utilized in non-linear finite element analysis of model sandy soil. The normalized ground failure domains in the case of the non-linear shear strength model are gleaned smaller than those in the case of the linear shear strength one. The numerical results are compared with the guidelines of the Architectural Institute of Japan (AIJ) and the Japan Road Association (JRA). The modification coefficients are ascertained for the frictional bearing capacity factor (N_γ) and surcharge bearing capacity factor (N_q), and a modified UBC formula is proposed. The performance of the proposed UBC formula is examined against the analysis results and various prevailing UBC guidelines.     

Effect of shearing rate on the behavior of geogrid-reinforced railroad ballast under direct shear conditions

A series of large-scale direct shear tests were conducted to investigate the behavior of unreinforced and geogrid-reinforced ballast at different rates of shearing. Fresh granite ballast with an average particle size (D₅₀) of 42?mm and five geogrids having different aperture shapes and sizes was used in this study. Tests were performed at different normal stresses (σ_n) ranging from 35?kPa to 140?kPa and at different rates of shearing (S_r) ranging from 2.5 to 10.0?mm/min. The laboratory test results revealed that the shear strength of ballast was significantly influenced by the rate of shearing. The internal friction angle of ballast (φ) was found to decrease from 66.5° to 58° when the shearing rate (S_r) was increased from 2.5 to 10.0?mm/min. It is further observed that the interface shear strength has improved significantly when the ballast was reinforced with geogrids. The interface efficiency factor (α), defined as the ratio of the shear strength of the interface to the internal shear strength of ballast, varies from 0.83 to 1.06. The sieve analysis of samples after the testing reveals that a significant amount of particle breakage occurs during shearing. The value of breakage, evaluated in terms of Marsal's breakage index (B_g), increases from 5.12 to 13.24% with an increase in shearing rates from 2.5 to 10.0?mm/min. Moreover, the influence of aperture shape and size of geogrid on the behavior of ballast-geogrid interfaces was also examined in this study.     

Stability of long unsupported twin circular tunnels in soils

The stability of two long unsupported circular parallel tunnels aligned horizontally in fully cohesive and cohesive–frictional soils has been determined. An upper bound limit analysis in combination with finite elements and linear programming is employed to perform the analysis. For different clear spacing (S) between the tunnels, the stability of tunnels is expressed in terms of a non-dimensional stability number (γ_maxH/c); where H is tunnel cover, c refers to soil cohesion, and γ_max is maximum unit weight of soil mass which the tunnels can bear without any collapse. The variation of the stability number with tunnels’ spacing has been established for different combinations of H/D, m and ϕ; where D refers to diameter of each tunnel, ϕ is the internal friction angle of soil and m accounts for the rate at which the cohesion increases linearly with depth. The stability number reduces continuously with a decrease in the spacing between the tunnels. The optimum spacing (S_opt) between the two tunnels required to eliminate the interference effect increases with (i) an increase in H/D and (ii) a decrease in the values of both m and ϕ. The value of S_opt lies approximately in a range of 1.5D–3.5D with H/D = 1 and 7D–12D with H/D = 7. The results from the analysis compare reasonably well with the different solutions reported in literature.     

Investigation for the key technologies of ultra-high asphalt concrete core rockfill dams

The mechanical characteristics of ultra-high asphalt concrete core rockfill dams (UACCRDs) at different periods is investigated via Rankine’s earth pressure theory, and a shear safety control standard for UACCRDs is proposed. The reasonable material parameters of the asphalt concrete core (ACC) and transition material that independently and comprehensively satisfy the shear safety control standard are back-calculated. The engineering measures that reduce the stress level (shear stress) of the ACC are given. Moreover, the engineering measures (straight asphalt concrete core rockfill dams (SACCRDs) are designed as curved asphalt concrete core rockfill dams (CACCRDs)) that reduce the tensile stress of the ACC are proposed. Based on the theory of the straight beam and curved beam on Winkler elastic foundation, the simplified mechanical models of straight asphalt concrete core (SACC) and curved asphalt concrete core (CACC) are established. The improvement effect of CACC that reduces tensile stress is also investigated. The results show that the following value ranges of the internal friction angle, cohesion of ACC and the internal friction angle of transition material for the suitable construction of UACCRDs are recommended: φ_a ≥ 30.5°, C_a ≥ 0.25 MPa and φ_t ≤ 43.5° (h = 200 m), with the growth gradient adjusted by 0.5%, 1.5% and ?0.5%/25 m. The stress level of ACC can be obviously reduced by increasing the internal friction angle and cohesion of ACC, and reducing the internal friction angle of transition material. The simplified mechanical models of SACC and CACC can estimate the force and deformation characteristic of the ACC (SACC and CACC) well. The CACC can significantly reduce tensile stress to a level approximately 42.8% lower than that of SACC.     

Partially stiffened RHS sections under transverse bearing force

Concentrated force applied to rectangular hollow sections (RHS) members at loading or reaction points can lead to web crippling of the members. This paper investigates the possibility of improving the web crippling behaviour of RHS sections using internal stiffeners. Tests of RHS sections partially filled with concrete and with wood plus a bolt through the web are described. Both end-bearing and interior-bearing forces were applied. Design models are established for the four failure modes identified in the tests. The parameters varied include section aspect ratio (D/B) which ranges from 1.5 to 3.0, web depth to thickness ratio (D/t) which ranges from 15 to 75, and bearing length to section width ratio (γ=N/B) which ranges from 0.5 to 1.0.     

浅基础承载力离心模型试验研究

笔者利用容量为10gt的离心机对砂基上的浅基础进行了较为系统的试验,用以研究基础的尺寸、形状、埋深和砂土相对密度对浅基础承载力、承载力因数（Nr,Nq）、形状因数（ζr,ζq）及破坏型式的影响。笔者提出一种利用浅基础离心模拟试验资料确定浅基础的承载力因数和形状因数的方法。利用此方法确定的44T-4砂的承载力因数,形状因数与已有的各种理论解和试验解进行了对比。研究工作得出了一些有意义的结论。     

Load-settlement characteristics of large-scale square footing on sand reinforced with opening geocell reinforcement

This paper describes load-carrying characteristics of a series of large-scale steel square footing tests performed on sand reinforced with two types of reinforcement methods. These are full geocell reinforcement (FGR) and geocell with an opening reinforcement (GOR). A thick steel square plate with 500?mm by 500?mm dimensions and 30?mm thickness was used as foundation. The parameters varying in the tests include the depth of geocell mattress (u), width of opening in geocell in the GOR type (w), relative density of sand (D_r) and number of geocell layers (N). The results revealed that the use of GOR and FGR methods enhances significantly the footing load carrying capacity, decreases the footing settlement and decreases the surface heave. It has been found that the use of GOR with an opening width of w/B?<?0.92, has the same improvement effect on the footing load-carrying response as the FGR has (B?=?footing width). Furthermore, with increasing the number of geocell layers from 1 to 2 in both GOR and FGR methods, the footing bearing pressure increases and footing settlement, surface heave and difference of performance between FGR and GOR mattress decrease.     

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.     

Load-settlement response of shallow square footings on geogrid-reinforced sand under cyclic loading

To study the settlement and dynamic response characteristics of shallow square footings on geogrid-reinforced sand under cyclic loading, 7 sets of large scale laboratory tests are performed on a 0.5?m wide square footing resting on unreinforced and geogrid reinforced sand contained in a 3?m?×?1.6?m?×?2?m (length?×?width?×?height) steel tank. Different reinforcing schemes are considered in the tests: one layer of reinforcement at the depth of 0.3B, 0.6B and 0.9B, where B is the width of the footing; two and three layers of reinforcement at the depth and spacing both at 0.3B. In one of the two double layered reinforcing systems, the reinforcements are wrapped around at the ends. The footings are loaded to 160?kPa under static loading before applying cyclic loading. The cyclic loadings are applied at 40?kPa amplitude increments. Each loading stage lasts for 10?min at the frequency of 2?Hz, or until failure, whichever occurs first. The settlement of the footing, strain in the reinforcement and acceleration rate in the soil have been monitored during the tests. The results showed that the ultimate bearing capacity of the footings was affected by the number and layout of the reinforcements, and the increment of bearing capacity does not always increase with the number of reinforcement layers. The layout of the reinforcement layers affected the failure mechanisms of the footings. Including more layers of reinforcement could greatly reduce the dynamic response of the foundations under cyclic loading. In terms of bearing capacity improvement, including one layer of reinforcement at the depth of 0.6B was the optimum based on the test results. It is found that fracture of geogrid could occur under cyclic loading if the reinforcement is too shallow, i.e. for the cases with the first layer of reinforcement at 0.3B depth.     

Model testing and numerical investigation of interference effect of closely spaced ring and circular footings on reinforced sand

Due to heavy loads and the non-availability of suitable construction sites, engineers are often required to place footings at close spacing. These footings influence each other, including effects on load-settlement and bearing capacity behavior. In this research the bearing capacity of closely located ring and circular footings on reinforced sand has been investigated numerically and experimentally. The goal of this study is to evaluate the interference effect on the bearing capacity of adjacent circular and ring footings. Footings on reinforced and unreinforced sand have been investigated. In this research, interference effect of footings, shape effects, effect of spacing between footings and also the effect of reinforcement layer on the bearing capacity are studied. To achieve these objectives laboratory circular and ring footing models and also numerical models were used. Finite element computer code PLAXIS 3D Foundation was used for numerical modeling. Experimental and numerical analysis results show that the ultimate bearing capacity of two closely spaced circular and ring footings is greatest when they stand exactly beside each other and decreases with increase in the spacing to footing diameter ratio (Δ/D). It is found that for Δ/D > 4, the bearing capacity of each adjacent footing is almost the same as that for single footing. This means that for a center-to-center spacing greater than 4D, no significant interference effect was observed and each footing acted more or less independently, similar to a single footing.     

Behavior of strip footing on fiber-reinforced cemented sand adjacent to sheet pile wall

In urban areas, shallow foundations are often placed along the ground surface above a sheet pile wall. In this research, the potential benefits of reinforcing the active zone behind a model sheet pile wall by using polypropylene fiber and cement kiln dust have been investigated experimentally and numerically. Tests were conducted by varying parameters including fiber ratio (R_F), cement kiln dust (CKD) ratio, thickness of reinforced layer, footing location relative to the sheet pile wall and curing time of reinforced layer. Finite element computer code PLAXIS 2D foundation was used for numerical modeling. Close agreement between the experimental and numerical results was observed (maximum difference 14%). Experimental and numerical results clearly show that fiber insertion into the cemented soil causes an increase in ultimate bearing capacity of footing and significant reduction in the lateral deflection of the sheet pile wall. At higher fiber ratios (R_F ≥ 0.75%), the bearing capacity ratio (BCR) increased by about 42% and the effect of CKD ratio on BCR is more pronounced. The addition of fibers changed the brittle behavior of cemented sand to a more ductile one. Critical values of reinforcing parameters for maximum reinforcing effects are established.