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In the literature, the influence of spatial variability of the undrained shear strength of foundation soils on the bearing capacity of footings is limited to footings seated directly on the foundation. This is an unlikely arrangement in practice. This paper revisits the footing problem by considering a thin granular layer between a strip footing and soft foundation soil using analytical and stochastic numerical modeling. The analyses are extended to the case of a geosynthetic-reinforced granular layer and to the idealized case of no granular layer. The study shows that the probability that the ultimate bearing capacity for the footing is smaller than the deterministic design value is greater for all three scenarios with randomly uniform clay soil than for the same soil with isotropic or anisotropic spatial variability of strength at practical levels of reliability index β (e.g., β≥3.09 for a permanent footing). The reason for this outcome, which may appear counterintuitive, is explained. Design charts are provided to estimate the deterministic design bearing capacity of a rigid strip footing required to meet a range of target reliability index for the three footing scenarios examined in this study. [ABSTRACT FROM AUTHOR]

This paper presents the results of load and resistance factor design (LRFD) calibration of the facing limit states for soil nail walls. The current AASHTO facing load model and a modified model together with the AASHTO facing resistance models for both permanent and temporary facing load cases are considered. The facing design includes flexure, punching shear, and headed-stud tensile limit states. The calibration of resistance factors captures uncertainty in the accuracy of the load and resistance models, uncertainties in the nominal load and resistance values at time of design, and bias dependencies between model bias and nominal values. Resistance factors are calibrated for a range of load factors and target reliability indexes. Example designs for facing limit states demonstrate the implementation of the calibrated resistance factors in a LRFD framework using the current AASHTO and modified load models for the permanent facing load case. The practical values of this study are calibrated load and resistance factors for facing limit states of soil nail walls that are of interest to code writers for future editions of LRFD codes in the United States and Canada. [ABSTRACT FROM AUTHOR]

A numerical finite-difference method (FLAC) model was used to investigate the influence of constitutive soil model on predicted response of two full-scale reinforced soil walls during construction and surcharge loading. One wall was reinforced with a relatively extensible polymeric geogrid and the other with a relatively stiff welded wire mesh. The backfill sand was modeled using three different constitutive soil models varying as follows with respect to increasing complexity: linear elastic-plastic Mohr-Coulomb, modified Duncan-Chang hyperbolic model, and Lade's single hardening model. Calculated results were compared against toe footing loads, foundation pressures, facing displacements, connection loads, and reinforcement strains. In general, predictions were within measurement accuracy for the end-of-construction and surcharge load levels corresponding to working stress conditions. However, the modified Duncan-Chang model which explicitly considers plane strain boundary conditions is a good compromise between prediction accuracy and availability of parameters from conventional triaxial compression testing. The results of this investigation give confidence that numerical FLAC models using this simple soil constitutive model are adequate to predict the performance of reinforced soil walls under typical operational conditions provided that the soil reinforcement, interfaces, boundaries, construction sequence, and soil compaction are modeled correctly. Further improvement of predictions using more sophisticated soil models is not guaranteed. DOI: 10.1061/(ASCE)GT.1943-5606.0000092 CE Database subject headings: Soil stabilization; Walls; Constitutive models; Numerical models; Reinforcement.

The paper investigates the accuracy of the AASHTO simplified method by using load measurements reported in a large database of full-scale instrumented walls for bar mat, welded wire, and steel strip soil reinforced walls. The accuracy of the AASHTO simplified method is quantified by computing the mean and coefficient of variation of the ratio (bias) of measured loads under operational conditions to predicted loads. The paper shows that for steel strip walls, the AASHTO simplified method is reasonably accurate for granular backfill soils with friction angles less than 45[degrees]. For bar mat walls, the method is demonstrated to be slightly conservative. The simplified method underpredicts reinforcement loads at shallow overburden depths for steel strip walls with backfill friction angles greater than 45[degrees] due to compaction-related effects. It is concluded that these compaction-induced loads near the wall top do not contribute to internal instability due to pullout. DOI: 10.1061/(ASCE) 1090-0241 (2009) 135:2(177) CE Database subject headings: Soil stabilization; Walls; Steel; Static loads; Statistics; Data analysis.

Needle-punched geosynthetic clay liner (GCL) specimens subjected to 0, 5, and 12 freeze-thaw cycles in the laboratory, and GCL specimens recovered from a composite barrier wall in the Canadian Arctic after 1 and 3 years were examined to assess the hydraulic conductivity/permeability with respect to both deionized deaired water and Jet A-1. The GCL specimens recovered from the field after 3 years had a hydraulic conductivity with respect to water that was approximately 30% less than that of the GCL specimens subjected to 12 initial freeze-thaw cycles in the laboratory, suggesting that the laboratory conditions are more severe than field conditions. The combined effects of both the freeze-thaw cycles and Jet A-1 permeation increased the permeability. This increase is attributed to the creation of macropores in the GCL due to freezing and to an expansion of free-pore space due to contraction of the double layer caused by permeation of Jet A-1. Although there was an increase in permeability due to the combined effect of freeze-thaw and permeation by Jet A-1, the effect was relatively small and the results suggest that the GCL continued to exhibit good performance as a hydraulic barrier when subject to extreme climatic conditions and hydrocarbons both in the laboratory and in the field. DOI: 10.1061/(ASCE)1090-0241(2006)132:12(1526) CE Database subject headings: Geosynthetics: Hydraulic conductivity; Freeze-thaw; Permeability: Pore water: Bentonite: Hydrocarbons.

The construction and surcharge loading response of foul' full-scale reinforced-soil segmental retaining walls is simulated using the program FLAC. The numerical model implementation is described and constitutive models for the component materials (i.e., modular block facing units, backfill, and tour different reinforcement materials) are presented. The influence of backfill compaction and reinforcement type on end-of-construction and surcharge loading response is investigated. Predicted response features of each test wall are compared against measured boundary loads, wall displacements, and reinforcement strain values. Physical test measurements are unique in the literature because they include a careful estimate of the reliability of measured data. Predictions capture important qualitative features of each of the four walls and in many instances the quantitative predictions are within measurement accuracy. Where predictions are poor, explanations are provided. The comprehensive and high quality physical data reported in this paper and the lessons learned by the writers are of value to researchers engaged in the development of numerical models to extend the limited available database of physical data for reinforced soil wall response. DOI: 10.1061/(ASCE)1090-0241(2006) 132:6(673) CE Database subject headings: Retaining walls; Soil stabilization; Numerical analysis; Numerical models: Surcharge; Loads.

The paper describes a new working stress design methodology introduced by the writers for geosynthetic reinforced soil walls (K-Stiffness Method) that is now extended to steel reinforced soil walls. A large database of full-scale steel reinforced soil walls (a total of 20 fully instrumented wall sections) was used to develop the new design methodology. The effects of global wall stiffness, soil strength, reinforcement layer spacing, and wall height were investigated. Results of simple statistical analyses using the ratio of measured to predicted peak reinforcement loads (i.e., method bias) demonstrate the improved prediction accuracy. The AASHTO Simplified Method results in an average method bias of 1.1 with a coefficient of variation (COV) of 45%, whereas the proposed K-Stiffness Method results in an average bias of 0.95 and a COV of 32%. Soil strength was found to have limited influence on reinforcement loads for steel reinforced soil walls, especially for high shear strength soils, while global wall stiffness and wall height had a major influence on reinforcement loads. CE Database subject headings: Retaining walls; Earth reinforcement, Design; Geosynthetics; Soil structure: Stiffness.

In this paper, upper bound limit analysis that includes a horizontal pseudostatic seismic force is used for the first time to obtain the limit load on strip footings seated on cohesive-frictional soils reinforced with a single geosynthetic layer. Reinforcement tensile rupture and sliding failure modes for the geosynthetic layer are included in the analyses. Results of analyses are presented as optimum reinforcement depths and a bearing capacity equation with a single term and different bearing capacity factors for tensile rupture and sliding failure modes. The bearing capacity factors are presented in tables and capture the combined influence of the reinforcement strength, soil frictional strength and cohesion, soil unit weight, footing geometry, uniform surcharge, and magnitude of horizontal ground acceleration. [ABSTRACT FROM AUTHOR]

The paper demonstrates load and resistance factor design (LRFD) calibration for tensile strength and pullout strength limit states for steel strip mechanically stabilized earth (MSE) walls using a reliability theory-based approach. The analyses adopt load models found in current North American LRFD specifications in combination with a coupled mechanical-corrosion model for the reinforcement tensile strength and pullout models found in design guidelines and in the research literature. Resistance factors for prescribed load factors and different load and resistance model combinations are compiled in tables. The limitations of the LRFD approach to generate resistance factors that are judged to be acceptable based on current practice are demonstrated. The challenges to generate consistent design outcomes with the same margin of safety expressed probabilistically are identified, and the link to reliability-based design is described. Example designs are provided to show the impact on steel reinforcement quantities and length when using different models in combination with proposed and current specified load and resistance factors. The calibration outcomes will be of value to code writers in Canada and the US for MSE wall design sections in the next editions of national geotechnical foundation LRFD codes. [ABSTRACT FROM AUTHOR]

Numerical modelers are often faced with the challenge to numerically reproduce the physical behavior of soil-geosynthetic interaction problems using assumed values for missing soil and interface model parameters. This paper examines two such examples using the finite-difference method, (1) horizontal pullout of a geosynthetic (geogrid) reinforcement layer in a pullout box and (2) a geosynthetic (geotextile)-reinforced soil layer over a void. It also presents the results of parametric sensitivity analyses for the missing soil and interface model parameter values and identifies the values that give the best agreement with measured data. The paper further demonstrates that correct modeling of geometrical nonlinearity is key to accurately predicting the performance of geosynthetic-reinforced soil systems controlled by the tensioned membrane effect. The lessons learned in this study will be of interest to numerical modelers during numerical model design of geosynthetic-reinforced soil systems. [ABSTRACT FROM AUTHOR]

A total of 123 measured maximum nail-load data were collected from instrumented soil nail walls reported in the literature. Filtered data sets corresponding to short-term and long-term measurements were used to evaluate the accuracy of the current Federal Highway Administration (FHWA) simplified method to calculate maximum nail loads under operational conditions. The accuracy of load predictions was quantified by the mean and coefficient of variation (COV) of the ratio (bias) of measured load to predicted load. Data in short-term and long-term categories were also investigated according to frictional-cohesive and frictional soil types. Based on the available data, the current FHWA simplified method was found to overestimate both long-term and short-term maximum nail loads on average. The spreads in prediction accuracy measured by the COVof bias were 38 and 52% for long-term and short-term data, respectively. Large spreads in prediction accuracy were also found using data for walls with cohesive-frictional soils alone. With the exception of the frictional soil data set, there was an undesirable correlation (dependency) between method accuracy and predicted maximum nail load using the current FHWA simplified method. A modified FHWA simplified method equation is proposed that has fewer empirical coefficients than the current formulation (i.e., three compared to five) and is shown to be more accurate on average and to have less spread in prediction accuracy for all data sets. Furthermore, hidden dependencies between method accuracy and magnitude of predicted load are not present. [ABSTRACT FROM AUTHOR]

The paper reports numerical model details and predictions of the end-of-construction performance for two instrumented and well-documented mechanically stabilized earth (MSE) walls. The walls were constructed as part of the highway SR-18 approach fills for a bridge near Seattle, Washington. The geogrid reinforced block face walls were modeled using a commercially available two-dimensional (2D) finite-difference program. The paper provides details on how material properties were selected from laboratory testing of wall components and how the computer modeling was carried out. The paper shows that predicted wall deformations and reinforcement strains were in reasonable agreement with measured data using both linear elastic-plastic and nonlinear elastic-plastic constitutive models for the soil. The geogrid reinforcement was simulated using a nonlinear load-strain-time secant stiffness model and cable elements. The paper compares numerical predictions of reinforcement loads at end of construction with measured values and predictions using a AASHTO Simplified Method, K-stiffness Method, and Simplified Stiffness Method. The paper is a useful benchmark for modelers because it demonstrates what the authors believe are reasonable expectations of model accuracy for Class C predictions of deformations and reinforcement strains for these types of walls when high-quality project information is available. [ABSTRACT FROM AUTHOR]

The Simplified Method as reported in AASHTO and Federal Highway Administration (FHWA) manuals has been demonstrated to give poor predictions of unfactored reinforcement loads and strains, especially for geosynthetic reinforced soil walls. The writers have proposed the K-stiffness Method to improve the load prediction accuracy for walls under working stress (operational) conditions. However, it has also been recognized in recent publications by the writers and others that further improvements to the K-stiffness Method are needed. Furthermore, acceptance of the K-stiffness Method has been hindered due to its perceived complexity and the use of the plane strain friction angle to quantify the strength of the reinforced soil. This paper takes a fresh look at both methods and uses lessons learned from the K-stiffness Method development to improve the accuracy of the AASHTO/FHWA Simplified Method. Key parameters introduced during the development of the K-stiffness Method are applied to the Simplified Method and updated to further improve load prediction accuracy. Additional wall case histories have been added to the database used for the original K-stiffness Method to calibrate the new model and to broaden its utility. An important improvement is a single model that allows for seamless load prediction across a range of walls constructed with relatively extensible geosynthetic reinforcement and inextensible steel reinforcement materials. The quantitative improvement of the new model (Simplified Stiffness Method) compared to the current AASHTO/FHWA Simplified Method is demonstrated through statistical analysis of load bias values (i.e., the ratio of measured to predicted reinforcement load). [ABSTRACT FROM AUTHOR]

Steel bar mat is a common reinforcing material in mechanically stabilized earth (MSE) walls. The current method to calculate the pullout capacity of these materials is an empirical-based formulation found in AASHTO and Federal Highway Administration (FHWA) design guidance documents. The accuracy of the current formulation is evaluated using a large database of laboratory pullout tests including data that were not available at the time the current model was developed. A new model is proposed, and it is shown to have advantages over the current formulation particularly when pullout capacity design and analysis will be carried out in a load and resistance factor design (LRFD) framework. Calibration of the new model and quantitative comparisons of the accuracy of the two models are evaluated using statistical characteristics of bias values where bias is the ratio of measured pullout capacity to predicted pullout capacity. The accuracy of both models is evaluated for two cases: (1) when project-specific pullout data are not available (the typical case) and presumptive default coefficients must be used; and (2) when project-specific laboratory pullout box data are available. The influence on calibration outcomes of data sets corresponding to markedly different soils and test methodology is demonstrated in the paper. The data reported in the paper are a necessary precursor to future LRFD calibration of the pullout limit state in the internal stability design of bar mat reinforced soil walls. [ABSTRACT FROM AUTHOR]

A high-density polyethylene (HDPE) geogrid soil-reinforced dry-cast concrete block retaining wall 6.3-m high was designed using the K-stiffness method as part of a highway-widening project southeast of Seattle, Washington. The amount of reinforcement needed for the original wall design using the K-stiffness method was approximately 50% of that required using the AASHTO simplified method. This paper describes the construction, instrumentation program, and interpretation of the measurements. Geogrid strains were measured using strain gauges and extensometers attached to reinforcement layers. An extensive materials testing program was conducted to characterize the backfill soil properties and geogrid stiffness properties and to calibrate strain gauge readings. The reinforcement loads deduced from the measured strains are compared with Class A, B, and C1 predictions using the AASHTO simplified and K-stiffness methods. These comparisons demonstrate that the simplified method significantly overestimated reinforcement loads, whereas the K-stiffness method provided estimates that were consistent with the measured results. This paper describes lessons learned, the influence of construction activities on wall performance, and the limitations of both methods in estimating connections loads. [ABSTRACT FROM AUTHOR]

The paper reports the results of load and resistance factor design (LRFD) calibration for pullout and yield limit states for steel strip reinforced soil walls under self-weight loading. An important feature of the calibration method is the use of bias statistics to account for prediction accuracy of the underlying deterministic models for reinforcement load, pullout capacity and yield strength of the steel strips, and random variability in input parameters. To improve the accuracy of reinforcement load predictions, small adjustments to current semiempirical American Association of State Highway and Transportation Officials (AASHTO) load design charts are proposed. Similarly, current empirical-based design charts found in AASHTO and Federal Highway Administration (FHWA) guidance documents for the estimation of the pullout resistance factor for smooth and ribbed steel strips are adjusted to improve the accuracy of pullout capacity predictions. The results of calibration lead to a load factor of 1.35 that is consistent with current practice and resistance factors that together give a consistent probability of failure of 1% for all three limit states considered. Furthermore, comparison with allowable stress design (ASD) past practice (AASHTO simplified method) shows that the operational factors of safety using a rigorous LRFD approach give the same or higher factors of safety and lower probabilities of failure. In this study, data for steel strip reinforced soil walls are used as an example to illustrate rigorous reliability theory-based LRFD calibration concepts. However, the general approach is applicable to other reinforced soil wall technologies and calibration outcomes can be updated as more data become available. [ABSTRACT FROM AUTHOR]

The results of load and resistance factor design (LRFD) calibration are reported for the pullout limit state in geogrid reinforced soil walls under self-weight loading and permanent uniform surcharge. Bias statistics are used to account for the prediction accuracy of the underlying deterministic models for load and pullout capacity and the random variability in the input parameters. The paper shows that the current AASHTO simplified method to calculate reinforcement loads under operational conditions is overly conservative leading to poor prediction accuracy of the underlying deterministic model used in LRFD calibration. Refinements to the load and default pullout capacity models in the AASHTO and Federal Highway Administration guidance documents are proposed. These models generate reasonable resistance factors using a load factor of 1.35 and give a consistent probability of pullout failure of 1%. A comparison with the allowable stress design (ASD) past practice shows that the operational factors of safety using a reliability-based LRFD approach give factors of safety greater than 1.5. Regardless of the design approach (ASD or LRFD), the analysis results demonstrate that the current empirical minimum reinforcement length criteria will likely control the design for pullout. [ABSTRACT FROM AUTHOR]

A response is from the authors to the reviewers of their article “Predicted Loads in Steel Reinforced Soil Walls Using the AASHTO Simplified Method” which is in Volume 135 of the February 2009 issue is presented.

A numerical finite-difference method (FLAC) model was used to investigate the influence of constitutive soil model on predicted response of two full-scale reinforced soil walls during construction and surcharge loading. One wall was reinforced with a relatively extensible polymeric geogrid and the other with a relatively stiff welded wire mesh. The backfill sand was modeled using three different constitutive soil models varying as follows with respect to increasing complexity: linear elastic-plastic Mohr-Coulomb, modified Duncan-Chang hyperbolic model, and Lade’s single hardening model. Calculated results were compared against toe footing loads, foundation pressures, facing displacements, connection loads, and reinforcement strains. In general, predictions were within measurement accuracy for the end-of-construction and surcharge load levels corresponding to working stress conditions. However, the modified Duncan-Chang model which explicitly considers plane strain boundary conditions is a good compromise between prediction accuracy and availability of parameters from conventional triaxial compression testing. The results of this investigation give confidence that numerical FLAC models using this simple soil constitutive model are adequate to predict the performance of reinforced soil walls under typical operational conditions provided that the soil reinforcement, interfaces, boundaries, construction sequence, and soil compaction are modeled correctly. Further improvement of predictions using more sophisticated soil models is not guaranteed. [ABSTRACT FROM AUTHOR]

A rigorous probabilistic-based approach for load and resistance factor design (LRFD) calibration of internal stability tensile rupture and pullout limit states for geogrid reinforced mechanically stabilized earth (MSE) walls is presented. Load and resistance factors are provided for different combinations of the load model with pullout model and the tensile strength model used in current practice. The load models are the AASHTO Simplified Method and the Simplified Stiffness Method. Resistance factors are tabulated for use in LRFD foundation practice in Canada which rewards designers with larger resistance factors for greater project level of understanding. Resistance factors are also provided that are amenable to US practice where the notion of level of understanding is not explicitly considered in LRFD practice. The paper demonstrates the application of the load and resistance factors for tensile rupture and pullout internal stability limit states using a design example and shows the reduction in required reinforcement strength using the Simplified Stiffness Method. The paper is of value to practitioners and LRFD code writers in the United States and Canada for future revisions of design specifications in their jurisdictions. [ABSTRACT FROM AUTHOR]