Limit States Design Calibration for Internal Stability of Multi-Anchor Walls

The paper describes the methodology and results of limit states design calibration for two limit states of Japanese multi-anchor wall (MAW) earth retaining systems: anchor plate pullout and anchor rod rupture due to soil self-weight loading. Bias statistics are computed from measured loads from instrumented MAW structures and in-situ anchor load tests. Two different load models and two different plate load capacity equations are used in the calibrations. A load factor of γ_Q=2.25 is recommended to meet a 3% load exceedance criterion using a new load model by the writers which increases to 3.00 if the current approach recommended by PWRC (2002) is used. A target probability of failure P_f=1% is used in calibrations and is judged to be a reasonable value for the highly load-redundant MAW systems. Resistance factors of 0.80 and 0.95 are recommended for anchor plate and anchor rod rupture limit states using the new load and resistance models proposed by the writers. While the paper is focused on one particular wall system, the reliability-based limit states design calibration approach described in the paper provides an instructive template for limit states calibration of other reinforced soil retaining wall systems in Japan.     

Influence of Transient Flooding on Multi-Anchor Walls

The paper presents the results of three full-scale tests that were carried out to investigate the influence of transient flooding on the performance of multi-anchor reinforced soil walls (MAW). The walls were constructed to a height of 6 m and flooded from the front of the structures to about mid-height and then drained in two to four stages. The walls were constructed with three different sand soils varying with respect to permeability, fines content and shear strength. Earth pressures and anchor loads were monitored during the flooding and draining stages and in-situ anchor pullout tests were performed. The analysis of results showed that the wall facings were very permeable and thus prevented unbalanced hydrostatic or seepage forces from developing during drawdown that could increase anchor loads beyond drained condition values. The accuracy of the current PWRC (2002) analytical model to estimate anchor capacity of MAW systems was demonstrated to vary widely depending on soil type and whether the soil was flooded or drained. However, on the load side, the method proposed by Miyata et al. (2009) to predict anchor loads was judged to be more accurate than the current BS8006 (2005) and PWRC (2002) methods based on the mean and spread of bias statistics where bias is defined as the ratio of measured to predicted anchor load.     

Reliability analysis of soil-geogrid pullout models in Japan

The paper examines the accuracy of two geogrid pullout capacity models used in Japan (Public Works Research Center-PWRC, 2000a) by comparing measured capacities from a large database of laboratory pullout tests to predicted capacities. One model is the current default model (Model 1) used when project-specific laboratory pullout testing is not available and the other when this data is available (Model 2). The accuracy of the models is quantified using bias statistics where bias is defined as the ratio of measured pullout capacity to predicted value. Bias statistics are also a necessary precursor for reliability-based load and resistance factor design calibration for the ultimate pullout limit state in the internal stability design of geogrid reinforced soil walls. Bias statistics using Model 2 show that pullout predictions are very accurate with negligible scatter. However, the default model is shown to be very conservative on average with large scatter in bias values which also varies with magnitude of predicted pullout capacity. A modified formulation for Model 1 is proposed that has the same number of empirical coefficients as the current expression (i.e. two). The modified formulation gives improved accuracy based on the computed mean and coefficient of variation of bias values, and eliminates the significant model bias that is present for the current model. A final outcome from analysis of all available pullout data is that a factor of safety F=2 is recommended for allowable stress design (ASD) when using the current PWRC default Model 1, and a value of F=1.25 is recommended when using Model 2 with project-specific pullout testing.     

Measured and Predicted Loads in Multi-Anchor Reinforced Soil Walls in Japan

More than 3000 multi-anchor walls have been built in Japan over the last decade. The paper briefly reviews a total of eight instrumented wall sections that can be used to estimate anchor loads at the end of construction. Measured loads are compared to predicted values using equations found in current design guidelines. The comparison shows that the current Japanese and UK design methods to compute anchor loads are reasonably accurate for walls with frictional backfills provided K_a is calculated using the Rankine equation. For walls with cohesive-frictional backfills, current design methods over-predict anchor loads by as much as a factor of two. The eccentricity term in current UK and Hong Kong design methods is shown to not improve the accuracy of load predictions and it is recommended that this additional complexity be removed from these equations. A new load equation is proposed and constant coefficients are back-fitted to measured anchor load data. The new method is demonstrated to give quantitatively better predictions of anchor loads based on the statistics for load bias values computed as the ratio of measured to predicted anchor loads at the end of construction.     

Seismic Bearing Capacity of a Rigid Footing Adjacent to a Cohesionless Slope

At present, analytical or empirical formula for seismic bearing capacity of footings adjacent to slopes is not available. This study uses a pseudo-static-based approach in conjunction with rigorous Janbu's slice method to derive analytical values of seismic bearing capacity factors (N_γ) and correction factors for the effects of inertia of soil mass and load inclinations for a rigid footing adjacent to cohesionless slopes. It is shown that both the bearing capacity factors (N_γ) and the correction factors for the seismic bearing capacity of footings placed on level ground derived herein are comparable with those reported in the literature. Empirical equations regarding the effects of slope angles and load inclinations, expressed using generalized forms of those proposed in the literature, are also derived. It is also found that the empirical equations derived in the present study provide values of correction factors in good agreements with the analytical ones, indicating the validity of using these empirical equations for assessing the bearing capacity of rigid footings situated on the slope subjected to pseudo-static seismic loading.     

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.     

Experimental and numerical study on reinforcement effect of plate anchors or flip anchors on model slopes

Flip anchors are a kind of ground anchor that rotate and open in the ground to attain pull-out resistance without the use of grout. Compared to ordinary grouted ground anchors, flip anchors can be driven into the existing ground quickly and are suitable for the emergency reinforcement of slopes. However, little research has been done on the slope reinforcement effect of flip anchors. In this paper, experiments on a model slope reinforced by plate anchors or flip anchors were conducted. During the experiments, vertical loading with a rigid loading plate was applied to the shoulder of the model slope to investigate its stability. Experiments were firstly conducted with and without model plate anchors under a plane strain condition. Then, experiments were conducted using actual flip anchors under a three-dimensional condition. In these experiments, the depth of the anchor plates, h, and the installation state of the anchor heads of the flip anchors (open or closed anchor head condition) were varied. After the experiments, corresponding numerical simulations (FEM) were conducted, and a subloading t_ij model was applied to describe the soil behaviour. The numerical method used in this research successfully reproduced the reinforcing effect of the flip anchors. According to the test and calculated results, compared with the cases without reinforcement and with plate anchors, the effectiveness of the flip anchors for slope stability was verified. Moreover, the flip anchors installed under the closed anchor head condition required a larger displacement to produce a reinforcing effect than the anchors installed under the open anchor head condition.     

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.     

Analysis and calibration of default steel strip pullout models used in Japan

The calibration of default pullout capacity models for smooth and ribbed steel strip reinforcement, used in reinforced soil walls in Japan, was carried out more than two decades ago and was based on a small number of physical tests available at that time. The writers have collected and organized a much larger database of more than 600 laboratory pullout box and in situ pullout tests from among the Japanese literature. The new database is a useful reference for design engineers to match project-specific soils to previous pullout tests and to check the accuracy of the current lower-bound design curves proposed in the late 70s and 80s. Today, only the ribbed-type steel reinforcement strips are used. The new data show that a three-parameter exponential function better captures the trend in pullout data for ribbed steel reinforcement than the current bi-linear models adopted from European practice. The formulations also have the advantage of being smoothly continuous with depth. Parameter values are determined for default pullout models that can be used in load and resistance factor design (LRFD) and for the current lower-bound (factor of safety) allowable stress design (ASD). The current PWRC model and a newly proposed model for ribbed steel strip reinforcement, that include the soil coefficient of uniformity (U_c) in their formulations, are shown to be no more accurate than the simpler default models without this term.     

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.     

Seismic uplift capacity of shallow horizontal strip anchor under oblique load using pseudo-dynamic approach

In this paper, an analytical method to compute the uplift capacity of an obliquely loaded horizontal strip anchor under both static and seismic conditions is described using the limit equilibrium method. The distribution of the soil reactions on a simple planar failure surface is obtained through the use of Kötter's equation, and the pseudo-dynamic approach is used to obtain the net seismic vertical uplift capacity factor for the unit weight component of the soil (F_γd). The results for the static and seismic vertical uplift capacity factors are determined for various combinations of input parameters, such as the load inclination, the soil friction angle, the embedment ratio, the soil amplification and both horizontal and vertical pseudo-dynamic seismic accelerations. It is observed that the orientation of the load significantly affects the seismic uplift capacity of the horizontal strip anchor. F_γd is seen to decrease with an increase in both horizontal and vertical seismic accelerations and soil amplification, whereas it is seen to increase with an increase in the embedment ratio and the soil friction angle, as expected. The results in terms of the non-dimensional net seismic uplift capacity factor are presented in graphical and tabular forms. The present results are compared and found to be in good agreement with similar results available in literature.     

砂土中锚板拉拔模型试验及其抗拔力计算

锚板基础因其具有良好的抗拔特性而广泛应用于各类岩土工程问题中。在不同密实程度砂土中采用不同几何形状的锚板进行小比尺拉拔模型试验,分析锚板型式及尺寸对上拔承载特性的影响。试验结果表明,相同直径和埋深比的螺旋锚与平板锚上拔承载特性无明显差别;相同埋深比时,直径为50 mm的锚板上拔承载力系数略小于直径为20mm锚板的上拔承载力系数,而其上拔破坏位移比明显高于小直径锚板。进一步根据破坏位移比与埋深比关系曲线确定中密及密砂中浅、深破坏模式的临界埋深比,同时结合已有试验结果假设两种破坏模式的滑裂面,利用极限平衡分析推导并给出两种破坏模式下上拔承载力公式;通过与41个拉拔试验数据进行比较,验证了所提理论公式的适用性及准确性。     

Comparison of sand liquefaction in cyclic triaxial and simple shear tests

The liquefaction resistance and correction factors K_σ and K_α of Nakdong River sand obtained from cyclic triaxial (CTX) tests were compared with those determined by cyclic simple shear (CSS) tests to ascertain the importance of the reduction factor C_r and correction factors K_σ and K_α in liquefaction evaluations, especially in view of the lack of comparative liquefaction assessments based on different laboratory test apparatuses. All samples used for the comparisons were obtained from the same type of sand by using similar preparation methods and they were subjected to similar stress states to minimize the number of factors influencing the comparison results; moreover, the apparatuses used in the two tests were manufactured by the same company and all tests were conducted by a single operator. It was found that the liquefaction resistance in CTX tests was always greater than that in CSS tests. Furthermore, C_r varied from 0.63 to 0.36, and it depended on the relative density D_r and initial static shear ratio α. K_σ, which increased with the normal effective stress σ′_nc in CTX tests, was identical to K_σ observed in CSS tests when α was increased up to 0.1. By contrast, K_α in the CSS tests was 58%–97% of K_α measured in the CTX tests, and it depended on the combined effect of D_r, σ′_nc, and α. The relationship between K_α and α in both CTX and CSS tests was well represented by a parabolic function. Moreover, the differences in K_α values between the CTX and CSS tests were also found to be a parabolic function of α. This information can be used for converting CTX (or CSS) values into equivalent CSS (or CTX) values.     

Uplift capacity of horizontal anchor plate in geocell reinforced sand

The paper investigates the uplift performance of horizontal anchor plate in geocell reinforced sand through a series of model tests. It is noted that the unreinforced anchor plate undergoes a clear failure at a displacement of about 3% of its width, whereas with the provision of geocell and a layer of geotextile right below the geocell mattress significantly increases the uplift capacity by about 4.5 times higher than that of unreinforced sand and could sustain anchor displacement of more than 60%. Results indicates that the geocell mattress by virtue of its rigidity distributes the uplift load in the lateral directions to a larger area, thereby reducing the stress in the overlying soil mass and hence increases the performance of anchor plate system. The provision of the additional geotextile layer right below the geocell mattress is found to be very effective in increasing the stiffness as well as load carrying capacity of anchor plate system. The optimum size (i.e., width and length) of geocell mattress giving adequate load carrying capacity of anchor plate is found to be 5.4 times of anchor width (5.4B). The comparison of model tests results with 3D numerical analysis shows good agreement, indicating that the proposed model is able to capture the uplift load-displacement behaviour of geocell reinforced anchor plate system.     

砂土中锚板抗拔承载力研究

首先回顾了砂土中锚板抗拔承载力理论与公式,然后进行密实度不同的砂土中的模型锚板上拔试验,结合以往的研究成果,阐明了砂土密实度、锚板埋深率、锚板的几何形状和上拔倾斜角度对锚板承载能力的影响,并对锚板极限承载力的计算公式进行了评价。按照从条形锚板到矩形锚板、从竖直锚板到倾斜锚板的思路,引入形状系数和倾斜系数,提出了方便工程应用的砂土中浅埋锚板统一抗拔极限承载力计算公式,并对模型试验的尺寸效应和计算公式与现场实测的比较作了说明。     

Study of the Ultimate Load Capacity of K-Type Tube-Gusset Plate Connections

In order to investigate the ultimate load capacity of K-type tube-gusset plate connections with stiffened plate, the static tests of five full-scale specimens were conducted in this study. The results indicate that the end stiffened plate is critical for improving the load capacity of the connections. In addition, the parametric nonlinear finite element analysis of the K-type tube-gusset plate specimens was performed with account of such non-dimensional parameters as chord diameter-to-thickness ratio (γ), plate width-to-chord diameter ratio (α), plate thickness-to-chord thickness ratio (\(\tau_{1}\)), stiffened plate thickness (t_d), and nominal-to-yield stress ratio (η). The above analysis implies that the ultimate load capacity decreases with the increment of γ and increases with the increment of α and \(\tau_{1}\), while it is only slightly affected by the stiffened plate thickness. Compare the results of the finite element analysis with assessment by design guides existing. Based on the former results, an equation for estimating the load capacity of K-type tube-stiffened gusset plate is proposed.     

Evaluation of liquefaction probability of earth-fill dam over next 50 years using geostatistical method based on CPT

A method for evaluating the liquefaction probability of an earth-fill dam over the next 50 years is presented through the use of a geostatistical method for the measured values from cone penetration tests (CPTs). In particular, this paper discusses a new procedure for evaluating the liquefaction probability based on CPTs. Although the fines content, F_c, and the N-value are required in the Japanese standards to evaluate the liquefaction risk, the number of test data is not enough for the statistical modeling. Herein, F_c and the N-value are derived directly from CPTs. The statistical modeling procedure for F_c and the N-value is the unique point of this study. Since CPTs can be conducted with short intervals, especially in the horizontal direction, the geostatistical parameters can be determined, and the geostatistical simulation method is applicable for evaluating the liquefaction probability. In addition, since the frequency of the seismic load at the studied site will affect the liquefaction probability, the seismic hazard should be evaluated properly. An illustrative example, assessing the liquefaction probability of an earth-fill dam in Japan, is presented to demonstrate the capability of the proposed method. Finally, the spatial average of the liquefaction probability of the dam over the next 50 years is calculated. The proposed procedure is confirmed to work well for actual design problems.     

Mechanism of Bearing Capacity of Spread Footings Reinforced with Micropiles

The Hyogoken-Nambu Earthquake in 1995 caused extensive damages to the foundations of bridges. Ever since, methods to improve the bearing capacity of existing foundations have become an important aspect of foundation engineering in Japan. Micropiles are considered to provide promising solutions. The mechanism which enhances the bearing capacity of surface footings reinforced with micropiles is the subject of investigation in this study. As an initial phase, model tests were conducted to understand the load-displacement behavior of surface footings with and without micropiles on loose, medium dense, and dense layers of sands. Salient factors which influence the behavior of the footings were selected and their influence on bearing capacity was examined through a comprehensive series of model tests. Notable improvements in the bearing capacity of surface footings reinforced with vertical micropile groups were observed in the case of dense sand which is dilative during shear. To assess quantitatively the degree of improvement in the bearing capacity of surface footings reinforced with micropiles, an index R called “Network Effect Index” was introduced in this study. The index R of unity means that the bearing capacity of footings reinforced with micropiles is simply equal to the summation of the individual value of the surface footing and that of the micropile group. An index R of more than two is achieved in this study where surface footings reinforced with a group of vertical micropiles bear on a dense layer of dilative sand. By contrast, with loose and medium dense sand, which are contractive in nature, the index R is found to be less than unity.     

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.     

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.