Richard J. Bathurst

• PhD, FRSC, FCAE FEIC, FCSCE
• Professor (Emeritus) at Royal Military College of Canada

The mean (point) estimate of reliability index (β) for simple limit state performance functions is most often based on load and resistance model bias statistics taken from bias data of limited size. The paper shows how the confidence in the point estimate of β can be computed using the bootstrap method and a closed-form solution for the special cas...

Analytical and numerical solutions for the problem of geosynthetic reinforced fills over a void have been the subject of investigation for the last four decades. A common feature of this prior work is that all methods have treated the analytical solutions as deterministic. While the treatment of some input parameters must be taken as deterministic,...

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 an...

Thin granular fill layers are routinely used to aid the construction of shallow footings seated over undrained soft clay foundations and to increase their load capacity. The influence of time- and strain-dependent reduction in reinforcement stiffness on the bearing capacity and load-settlement response of a footing seated on a thin reinforced granu...

The paper demonstrates load and resistance factor design (LRFD) calibration for tensile strength, connection strength, pull-out, and soil failure internal stability limit states for polyester strap mechanically stabilized earth (MSE) walls using a reliability theory-based approach. The calibrations are carried out using the simplified and stiffness...

Current design methods for the problem of a thin reinforced fill over a void are based on analytical solutions which are most often solved using an allowable (working) stress deterministic (factor of safety) approach. However, in practice there are uncertainties in the estimate of the input parameter values that appear in the analytical equations....

Reinforced soil walls (RSWs) have proven to be a reliable and resilient solution in many geotechnical applications (e.g., bridge abutments, highway and railway embankments, soil retaining walls, dikes, among others). Moreover, the reduced impact of these types of structures over traditional solutions has been compared using life cycle analysis (LCA...

The bearing capacity of a footing seated directly on a soft clay foundation with constant undrained shear strength is the classical Prandtl geotechnical problem. However, a footing seated directly on an undrained clay soil is an unlikely arrangement in practice. Rather, a granular layer is used as a working platform for the construction of the foot...

The problem of a reinforced fill over a void has been the subject of much research in the geosynthetics literature. Previous studies have mainly focused on finding closed-form solutions to predict the tensile loads and strains in the reinforcement layer once a void develops below the fill. In this paper, a 2D finite difference (FLAC) model that imp...

The estimation of the resistance factor in load and resistance factor design (LRFD) calibration for simple soil–structure limit states is most often based on model bias data of limited size. Frequently, the bias data are only available or required for the resistance term. In this study, the confidence in the estimate of the mean of the resistance f...

Several closed-form analytical methods for the design of a geosynthetic-reinforced fill spanning a void appear in national standards and codes in the UK, France, Germany and in the Eurocode. In this paper, the reinforced void problem is examined using the UK BS 8006-1 (2010) method. A simple hyperbolic stiffness model for reinforcement geosynthetic...

The paper makes the argument for a fully probabilistic approach to quantify the margins of safety for the internal stability limit states for geosynthetic mechanically stabilized earth (MSE) walls. The three limit states considered are tensile strength, pullout and the soil failure limit state that appears in the stiffness method. The methodology i...

The role of temperature and relative humidity on long-term mechanical and chemical degradation of polyester fibres due to hydrolysis and creep is well documented. This study presents the results of a thermo-hydraulic 2D finite-element model used to estimate the magnitude and distribution of in-situ temperature, relative humidity, and degree of satu...

Constructing geosynthetic mechanically stabilized earth walls with recycled backfill materials reduces environmental impacts and financial cost compared with their gravity wall counterparts. While a large database of column-scale tests to evaluate the hydraulic performance of recycled backfill materials exists in the literature, clogging potential...

In the most recent edition of the AASHTO LRFD Bridge Design Specifications published in 2020, the Stiffness Method is specified for the internal stability design of geosynthetic MSE walls. A key feature of this approach is the use of the creep-reduced tensile stiffness of the reinforcement as a key parameter to compute the magnitude of reinforcemen...

Most often the focus on the mechanical contribution of reinforcement geosynthetics in soil reinforcement applications has been on the strength of the material. In fact, under operational conditions the performance of these systems is controlled by the stiffness of the geosynthetic, not its strength. An appreciation of the role of geosynthetic stiff...

This document provides a summary of the different topics presented at the Special Session organized by the International Geosynthetics Society (IGS) Technical Committee on Soil Reinforcement (TC-R). This Special Session brings together very interesting studies regarding soil reinforcement in the field of geosynthetics. Studies presented include top...

Analytical solutions for geosynthetic reinforced fills over a void have appeared in the literature starting in the 1980s. Current solutions pay little or no attention to the influence of the creep-reduced stiffness of the geosynthetic reinforcement under tensile loading. This paper addresses this gap by introducing a reinforcement stiffness limit s...

The paper describes load and resistance factor design (LRFD) calibration for the resistance factor used in the Stiffness Method internal stability soil failure limit state for geogrid mechanically stabilized earth (MSE) walls. The Stiffness Method was recently adopted in the current American Association of State Highway and Transportation Officials...

The paper examines the quantitative influence of uncertainty in the estimate of geosynthetic reinforcement stiffness on numerical outcomes using analytical solutions for a) the maximum outward facing deformation in mechanically stabilized earth (MSE) walls, b) maximum reinforcement tensile loads and strain in MSE walls under operational conditions,...

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, pun...

Pile model penetration tests were conducted in a transparent plane strain container filled with granular mechanoluminescent-coated particles. The pile models were constructed with flat- and cone-shaped tips. Load transmission through the analogue granular soil was captured by taking images of the light emissions from one side of the container that...

Reliability-based design (RBD) can overcome some limitations and ambiguities in the partial factor design approach found in Eurocode 7 (EC7) and the load and resistance factor design (LRFD) method used in North America. The aim of this study is to show how RBD via the first-order reliability method (FORM) can complement LRFD and EC7 codes. Three ge...

Soil-facing mechanical interactions play an important role in the behaviour of earth retaining walls. Generally, numerical analysis of earth retaining structures requires the use of interface elements between dissimilar component materials to model soil-structure interactions and to capture the transfer of normal and shear stresses through these di...

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...

ABSTRACT Over a period of 40 years, fuels spills and leaks have occurred at Canadian sub-Arctic and Arctic Distant Early Warning Line (DEW Line) sites. The Canadian Department of National Defence has initiated cleanup program of these sites estimated to cost $320 million (Cdn). Access to these sites is often limited and the environmental conditions...

This paper reports the results of calculations for the margins of safety for internal stability limit states for two as-built geosynthetic MSE walls constructed in 2006 in Washington State, U.S.A. The walls are unique because a) the internal stability design for the reinforcement was based on a working stress design method which includes the stiffn...

The authors investigated a temperature-accelerated creep test under confining pressure conditions on a single-rib geogrid placed in a soil layer. A basic study was conducted on the fixing method of the geogrid to the loading device, the applying method of creep load considering the friction between soil and geogrid, and the adjusting method of the...

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 mecha...

Ports, waterways and related coastal structures are very common in most countries. Geosynthetics as used in many other applications are also applicable to these structures for their better performance and cost-effectiveness compared with traditional materials. In this chapter, the applications of geosynthetics for quay walls, breakwaters, river emb...

Many analytical and numerical analysis and design methods for geosynthetic-reinforced soil structures require a single-value (constant) estimate of reinforcement stiffness. However, geosynthetic reinforcement products are rate-dependent polymeric materials meaning that they exhibit time and strain-dependent behaviour under load. Hence, the appropri...

With the growing interest in risk-based design, the choice of analysis method to estimate deformation, damage, and failure of geotechnical structures is important. The authors aimed to develop a SPH analysis method for analysis of reinforced soil walls. The general approach is based on the framework of the existing SPH analysis method. The fill mat...

During the historical development of the mechanics of deformable solids, the problems in geotechnical engineering are often categorized into two distinct groups, namely elasticity and stability (e.g., Terzaghi 1943; Terzaghi and Peck. 1948; Chen 1975). The ela sticity problems deal with stress or deformation of soil without failure, such as point s...

This paper reports the results of 3D numerical modelling of a 6-m-high mechanically stabilised earth (MSE) wall constructed with concrete panels and steel or polymeric strip reinforcement. These systems pose numerical challenges as a result of the discontinuous reinforcement arrangement which is not the case for MSE walls constructed with continuou...

Many analytical and numerical analysis and design methods for geosynthetic-reinforced soil structures require a single-value (constant) estimate of reinforcement stiffness. However, geosynthetic reinforcement products are rate-dependent polymeric materials meaning that they exhibit time and strain-dependent behaviour under load. Hence, the appropri...

Compaction grouting (CPG) is an in-situ grout injection technique used to improve the liquefaction resistance of loose sandy ground by densification and increasing lateral confining pressure. The present study investigates ground response during grout injection using a transparent granular soil and a natural sand soil. The injection process was sim...

The design and analysis of geosynthetic-reinforced walls, embankments and slopes are presented earlier in this book for structures under static loading conditions. This chapter focuses on the seismic aspects of these structures. It describes the properties and behaviour of cohesionless soils, geosynthetic reinforcement and facing components under d...

Geotechnical data used for reliability-based design (RBD) and load and resistance factor design (LRFD) calibration can be parsed into subgroups based on material type, location, test method, and so on. Most often statistical analyses assume all data fall within a representative envelope, and pool (combine) all data into a single large data set with...

Polyester (PET) strap MSE walls are gaining popularity in many countries. The writers compared measured tensile reinforcement loads from instrumented field walls under operational (working stress) conditions with predictions using the Coherent Gravity Method and the Simplified Stiffness Method. These methods are specified in the latest AASHTO code...

This paper explains simple probabilistic analysis and design for tensile strength and pullout internal stability limit states for geosynthetic reinforced soil walls. The general approach uses a closed-form solution for reliability index which is easily implemented in a spreadsheet and thus eliminates the need for Monte Carlo simulation. A novel fea...

The paper demonstrates deterministic and reliability-based assessment of strength limit states (tensile resistance and pullout) and the service limit state for soil failure for mechanically stabilized earth (MSE) walls constructed with polyester (PET) strap reinforcement. The general approach considers the accuracy of the load and resistance models...

This paper demonstrates reliability-based design (RBD) and analysis for tensile strength (rupture) and pullout limit states for mechanically stabilized earth (MSE) walls constructed with steel grid reinforcement in combination with frictional soils. Five different reinforcement tensile load models for walls under operational conditions are consider...

Design for internal limit states of steel grid reinforcement in mechanically stabilized earth (MSE) walls must provide for loss of steel thickness due to corrosion. The paper combines key features of zinc and steel corrosion models used in North American practice with corrosion rate statistics reported in the literature for the zinc coating on buri...

Mechanically stabilized earth (MSE) walls constructed with steel and geosynthetic reinforcing elements are now well-established technologies. The paper gives a brief historical overview and then a review of current approaches to the internal stability design of these systems including strength-based limit equilibrium methods and reinforcement stiff...

Earth retaining walls are common geotechnical structures with a wide range of solutions available to perform the same function. More and more, geotechnical engineers are asked to find the best solution among several options in different civil engineering applications based on environmental impact, cost and societal/functional issues. Evaluation of...

This paper demonstrates reliability-based analysis of tensile strength and pullout limit states for mechanically stabilized earth (MSE) walls constructed with steel-strip reinforcement. Five different reinforcement tensile load models, three different pullout models, and one tensile strength model were examined. The accuracy of each model was asses...

A shortcoming of the typical use of the frequentist probabilistic approach in reliability analysis of limit state equations that appear in the geotechnical literature is that estimates of the uncertainty in reliability index (probability of failure) are not made. A Bayesian approach is demonstrated in the paper to overcome this shortcoming using th...

Model checking, evaluation and comparison are critical steps in Bayesian data analysis but not routinely considered in statistical analysis of geotechnical data. This paper presents an overview of model checking and comparison concepts and techniques employed in modern Bayesian data analysis that are useful for analysis of geotechnical engineering...

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 th...

Reinforcement stiffness is a key parameter that influences the magnitude of tensile loads in geosynthetic mechanically stabilized earth (MSE) walls under operational conditions. An estimate of reinforcement creep stiffness at 2% strain and 1000 hours is required to carry out internal stability design using the Simplified Stiffness Method. This pape...

Glass beads were coated with a mixture of mechanoluminescent (ML) paint and epoxy resin in order to visualize particle-level force distribution through an analog granular material. SEM observation and X-ray CT scanning was used to verify that the application of the ML coating on the glass beads was uniform. Load tests were conducted on single colum...

Polyester (PET) straps are being used more frequently in mechanically stabilized earth (MSE) walls. At present, there is no consensus on a model or models that are suitable for design codes to calculate the pullout capacity of these materials. A database of 296 pullout tests from 81 test series with single and closely-spaced parallel double PET str...

Mechanically stabilized earth (MSE) walls must be designed with adequate margins of safety against internal stability failure described by tensile strength and pullout limit states. Probabilities of failure (or reliability index) will vary strongly with the accuracy of the underlying models that appear in limit state performance functions. In this...

The results of probabilistic analyses of a mechanically stabilized earth (MSE) wall with geosynthetic reinforcement are presented. The analyses consider spatial variability of reinforced and foundation soil properties using the 2D non-circular random limit equilibrium method (RLEM). In this study, it is assumed that the reinforced soil is a purely...

This paper explains probabilistic analysis and design for simple internal stability limit states for mechanically stabilized earth (MSE) walls using the example of reinforcement pullout of a steel strip reinforcement layer. The general approach uses a closed-form solution for reliability index which is easily implemented in a spreadsheet and thus e...

The results of probabilistic analyses of a mechanically stabilized earth (MSE) wall with geosynthetic reinforcement are presented. The analyses consider spatial variability of reinforced and foundation soil properties using the 2D non-circular Random Limit Equilibrium Method (RLEM). In this study, it is assumed that the reinforced soil is a purely...

Design for the tensile strength limit state of steel strip reinforcement in mechanically stabilized earth (MSE) walls must provide for loss of steel thickness due to corrosion. The paper combined key features of zinc and steel corrosion models found in the literature with corrosion rate statistics for buried galvanized steel strips. Examples of los...

The focus of this paper is on quantitative evaluation of four different methods that use closed-form equations to calculate the nominal load in steel grid-reinforced soil walls under operational (end of construction) conditions. The four methods are the Coherent Gravity Method used in the UK, the AASHTO Simplified Method (USA), the PWRC Method used...

In North America, the design of earth structures for transportation applications is most often carried out using load and resistance factor design (LRFD). In the U.S., the AASHTO LRFD Bridge Design Specifications are followed. In Canada, the primary code is the Canadian Highway Bridge Design Code. The premise behind LRFD is that when a limit state...

Non-circular Random Limit Equilibrium Method (RLEM) uses a combination of non-circular limit equilibrium method, 2D random field theory, and Monte Carlo simulation. Non-circular RLEM has the ability to seek out the weakest failure path in a slope stability analysis using optimization techniques such as Surface Altering, while considering spatial va...

A general approach for calibration of resistance factors for load and resistance factor design (LRFD) of pullout and tensile failure internal limit states of soil nail walls is presented. The calibration of resistance factor values includes the influence of nominal load and nominal resistance model type and accuracy (method bias), bias dependencies...

Probabilistic analysis of slopes with several random variables, complex geometries, and spatial variability of soil properties can be carried out using a non-circular random limit equilibrium method (RLEM) search together with an optimization technique. Two optimization techniques are coupled with non-circular slope stability analysis in this paper...

This paper demonstrates reliability-based design for tensile rupture and pullout limit states for mechanically stabilized earth (MSE) walls constructed with geosynthetic (geogrid) reinforcement. The general approach considers the accuracy of the load and resistance models that appear in each limit state equation plus uncertainty due to the confiden...

Energy Grade Line Analysis (EGLA) of tsunami run-up has been proposed as a simple tool to predict inundation heights and tsunami loads. A large database of more than 500 inundation measurements collected on the Sendai Plain on the east coast of Japan after the Tohoku earthquake of 2011 provided the writers the opportunity to evaluate the accuracy o...

There are conflicting opinions regarding whether or not mechanically stabilized earth (MSE) walls constructed with polyester (PET) straps should be classified as relatively inextensible type, and thus fall into the same category as steel reinforced soil walls, or they should be viewed as relatively extensible and grouped with MSE walls that are des...

In an earlier paper, the writers proposed modifications to the AASHTO simplified method to address shortcomings in the method and to improve reinforcement load predictions for walls under operational conditions. The new method is called the simplified stiffness method to emphasize the importance of reinforcement stiffness on reinforcement loads rat...

The paper describes the first reported attempt to numerically simulate the performance of full-scale steel multi-anchor reinforced soil walls (MAWs) during construction using a commercially available two-dimensional finite element method (FEM) model. The numerical simulation results are compared to the measurements taken from three 6 m-high MAW str...

The response surface method (RSM) with a quadratic polynomial was used to formulate three equations for the calculation of the maximum reinforcement loads in steel-reinforced mechanically stabilized earth (MSE) walls under operational (working stress) conditions. The RSM models were formulated using control variables found in the simplified stiffne...

A general approach for reliability-based analysis and design for pullout and tensile failure internal limit states of soil nail walls is presented. Reliability index values are computed using a closed-form solution that captures the influence of nominal load and nominal resistance model type and accuracy (method bias), bias dependencies, uncertaint...

The Random Limit Equilibrium Method (RLEM) is a relatively new method of probabilistic slope stability analysis which uses a combination of 2D random field theory, limit equilibrium methods, and Monte Carlo simulation. The Random Finite Element Method (RFEM) uses a combination of 2D random field theory, finite element method of analysis, strength r...

The results of probabilistic analysis of simple and layered slopes with linearly increasing (mean) undrained shear strength with depth, and spatial variability using the 2D non-circular Random Limit Equilibrium Method (RLEM) are presented. For the case of simple slopes, the results of the circular RLEM approach and the Random Finite Element Method...

Steel grids in the form of bar mat and welded wire mesh are a common reinforcing material in mechanically stabilized earth (MSE) walls. This paper uses a large database of laboratory steel grid pullout tests from multiple sources to evaluate the accuracy of different ultimate pullout capacity models in a consistent statistical framework. Included i...

A general closed-form solution to compute the reliability index of a simple limit state function with two load terms and one resistance term is derived. The formulation considers contributions to margins of safety expressed in probabilistic terms due to the choice of load and resistance models, bias values, dependencies between nominal values and b...

This paper describes the use of X-ray tomography imaging of natural gravel specimens to create repeatable assemblages of bonded gravel-size resin specimens using a 3D printer. The paper describes how the resulting resin-based surrogate specimens have particle geometry and interparticle bonds that are a function of the original scanning image resolu...

This paper presents the results of numerical simulations of one physical full-scale unreinforced embankment and two reinforced embankments taken to failure using a strip footing. The embankments were 3.4 m in height and were constructed with the same slope using the same sand backfill. One reinforced embankment was constructed with a relatively wea...

This paper extends the numerical parametric study previously reported by the writers for the vertical load distribution and vertical gap compression between facing panel units in steel reinforced soil walls ranging in height from 6 m to 24 m. The presented study demonstrates how gap compression and magnitude of vertical load transmitted between hor...

The paper demonstrates the use of the response surface method (RSM) to carry out probabilistic assessment of selected performance features of geosynthetic-reinforced segmental retaining walls under operational conditions. The method substantially reduces the number of Monte Carlo simulations required to carry out probabilistic analysis of numerical...

The Random Limit Equilibrium Method (RLEM) is a relatively new method of probabilistic slope stability analysis which uses a combination of 2D random field theory and circular or non-circular limit equilibrium methods. This study uses data available from the Mount Polley Tailings Dam breach in order to 1) compute soil property correlation lengths,...