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This study first develops a database containing 56 measured facing tensile forces from instrumented soil nail walls during or at completion of construction. Based on the compiled database, the accuracies of both default and modified federal highway administration (FHWA) simplified models for estimation of short-term facing tensile forces are evaluated. Here, accuracy is defined by the model bias computed as the ratio of measured to predicted facing tensile force. The analysis results show that predictions are highly conservative and highly dispersive using the default model, and moderately conservative and medium dispersive using the modified model. Moreover, the prediction accuracy is statistically correlated with magnitudes of the computed facing tensile forces and several model input parameters. An out-of-sample approach is used to develop and validate a recalibrated FHWA model which is then demonstrated to have least empirical constants but best accuracy compared to the default and modified models. The biases for the three models are characterized as lognormal random variables. An example of reliability-based analysis for facing flexure limit state is illustrated to both elaborate the application and highlight the benefit of using the recalibrated model for design practice from the perspective of cost-effectiveness.

This study first presents accuracy assessments of two default models proposed in two popular soil nail wall design specifications and their calibrated versions for estimation of maximum soil nail loads under operational conditions. The assessments are based on a general nail load database reported in the literature. Evaluation results showed that predictions using the default and calibrated models are unsatisfactory as the dispersions are high to extremely high. Simple calibration terms are introduced to the calibrated models for performance enhancement. The recalibrated models are shown to be accurate on average, and the prediction dispersions are significantly reduced. The model biases for the above six models are demonstrated to be lognormal random variables. Individual reliability-based designs for the nail pullout and nail-in-tension limit states using the six models are carried out. System reliability of nails against internal failures is also explored. The correlation between the two limit states is investigated, and its influences on system reliability evaluation are discussed. The practical value of model calibration is demonstrated as using the recalibrated models for nail designs leads to the most cost-effective design outcomes. This study represents a solid step toward development of reliability-based design framework for soil nail walls.

Statistical evaluation of the accuracy of effective stress method (ESM) equations for prediction of the ultimate bond strength of soil nails was performed using the maximum likelihood method. Over 500 pullout tests were examined for soil nails installed in two different Hong Kong soils. The data were parsed into tests that reached pullout failure before reaching 90% of the nail tendon yield strength (uncensored data) and tests terminated at the 90% yield strength criterion (censored data). A log-likelihood function was constructed to include both types of bias data, where bias is the ratio of measured to predicted ultimate nail bond strength. The accuracy of two ESM equations previously reported in the literature was evaluated using both uncensored data alone and then combined censored and uncensored data. A revised ESM equation with two empirical coefficients is calibrated using the larger combined data sets, and its accuracy is compared to the two earlier formulations using the same expanded database. The revised formulation has the advantage that mean of bias values is 1 for both soil types and there are no bias dependencies with magnitude of predicted pullout capacity or overburden pressure. However, for one soil type the COV of bias values is less using the larger database and for the other soil type the value is greater. A practical lesson for calibration of equations of the type investigated here is that including censored data for calibration is of great importance to reach a better and more thorough understanding of the performance of the model.

Soil nails are extensively used to stabilize existing slopes and new cuts in Hong Kong. The current method adopted for estimation of nail bond strength is the effective stress method (ESM), which h...

The design of soil nail walls in China is dictated by two national technical specifications, namely, Technical Specification for Retaining and Protection of Building Foundation Excavations by China Academy of Building Research (CABR) and Specifications for Soil Nailing in Foundation Excavations by China Association for Engineering Construction Standardization (CECS). Each specification proposes a method for computation of maximum nail loads while the prediction accuracy of the method is still not yet fully assessed. To fill the gap, this study evaluates the accuracies of the two methods using 144 measured nail loads collected from fully instrumented soil nail walls in China. The influences of three wall working conditions on the prediction accuracy of the methods are also examined. The results show that the two default methods overestimate the maximum nail loads by about 40% on-average and the spread in prediction generally ranges from 70% to 100%. However, the prediction accuracy is not significantly influenced by wall working conditions. Simple calibrations with two or three empirical constants are introduced to the two methods to achieve great improvements in prediction accuracy. The calibrated CABR and CECS methods are demonstrated to be unbiased on average and the prediction dispersions are reduced to about 50%.

Resistance factors for load and resistance factor design (LRFD) of pullout limit state of both permanent and temporary soil nails are calibrated against a wide design space using the current Federa...

The technique of pit-in-pit excavations is increasingly used in China to provide an efficient solution of maximizing the utilization of underground space while minimizing the amount of solid waste due to excavations. One of the critical steps toward the successful implementation of the pit-in-pit excavation technique is to rationally estimate the passive earth pressure, which is typically done using approaches such as numerical modeling, field monitoring, or traditional Coulomb or Rankine earth pressure theories. This paper presents a simplified approach for computing passive earth pressures for pit-in-pit excavations. A trapezoidal-shaped failure wedge is formed between two levels of retaining walls. A complete symmetric soil arch is used to describe the stress field of soils in the rectangular zone, whereas a half arch with one base acting on the wall and another base acting on the inclined shear surface is proposed for soils in the triangular zone. The soil arching effect is explicitly considered to derive the earth pressure for both cohesionless and cohesive soils at any intermediate passive state. A parametric study is conducted to demonstrate that the mobilized passive earth pressure increases nonlinearly with the magnitude of wall movement and soil shear strength parameters. The allowable spacing between two walls is also defined to produce a design chart. In the end, the proposed model is assessed against experimental measurements from model-scale tests.

Reliability analyses of nail pullout, nail-in-tension, and system reliability of internal limit states are presented for both permanent and temporary soil nails that are designed using defa...

The accuracy of the default Federal Highway Administration (FHWA) simplified model for estimation of facing tensile forces for soil nail walls under in-service conditions was evaluated using a large quantity of measured long-term and short-term facing tensile force data collected from the literature. The estimation accuracy was quantified by the mean and coefficient of variation (COV) of the bias where bias is defined as the ratio of measured to calculated facing tensile force. Based on the available data, the default FHWA simplified model equation was found to overestimate long- and short-term facing tensile forces by about 15% and 23% on average, respectively. The corresponding spreads in estimation accuracy expressed as the bias COV were about 43% and 67%. Undesirable correlations between bias values and calculated facing tensile forces using the default FHWA simplified model equation were detected. A modified FHWA simplified model was proposed to improve the on average accuracy, reduce the spread in estimation accuracy, and remove the hidden correlations noted above. In addition, the modified equation has fewer empirical coefficients than the current formulation (i.e., four versus five). The facing tensile force equations developed in this study are a contribution to the design of facing of soil nail walls within the current FHWA soil nail wall design framework.

Cross correlations between nominal load and resistance terms in limit state functions for geotechnical soil–structure interaction problems can be expected. A closed-form solution for the reliability index for a simple linear limit state function is used to examine the influence of nominal load and resistance correlations on computed margins of safety. The formulation also includes the contribution of the underlying accuracy of the load and resistance equations (method bias) and bias dependencies with the magnitude of nominal load and resistance values assumed in the limit state design function. Sensitivity analyses and example problems for the external sliding limit state for a cantilever wall and the pullout limit state for internal stability of reinforced soil walls with different soil reinforcement types are presented. Ignoring nominal correlations where they exist is shown to underestimate the reliability index in some cases and to overestimate the reliability index in other cases. In the example problems, these differences are shown to exceed one order of magnitude in terms of probability of failure, but in the sensitivity analyses using a wider range of input parameter values, the differences can be several orders of magnitude.

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 mechan...

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. T...

The model uncertainty in prediction of facing tensile forces using the default Federal Highway Administration (FHWA) simplified equation is assessed in this study based on the Bayesian inference method and a large number of measured lower and upper bound facing tensile force data collected from the literature. Model uncertainty was quantified by model bias which is the ratio of measured to nominal facing tensile force. The Bayesian assessment was carried out assuming normal and lognormal distributions of model bias. Based on the collected facing tensile force data, it is shown that both the on-average accuracy and the spread in prediction accuracy of the default FHWA simplified facing tensile force equation depend largely upon the distribution assumptions. Two regression approaches were used to calibrate the default FHWA simplified facing tensile force equation for accuracy improvement. The Bayesian Information Criterion was adopted to quantitatively compare the rationality between the competing normal and lognormal statistical models that were intended for description of model bias. A case study is provided in the end to demonstrate both the importance of model uncertainty and the influence of distribution assumptions on model bias in reliability-based design of soil nail walls against facing flexural limit state.

Subgrade soils experience repeated traffic loads, such that dynamic stress and displacement are accumulated to jeopardize the stability of pavement foundations. Laboratory element testing is often conducted to apply cyclic loads to the soil. In fact, the stress state of subgrade soil is complex due to the constant rotation of principal stress induced by moving vehicles. It is hard to select constitutive relations for unsaturated subgrade soils in numerical or analytical calculation, since most models are developed without proper consideration of principal stress rotation. Furthermore, most available earth pressure sensors cannot provide stress measurements in three orthogonal directions for a soil element at the same time. A novel orthogonal earth pressure transducer is developed to measure dynamic stresses of subgrade soils in three directions under a roadway at Chencun, China. The cumulative effect of dynamic stress with load cycles is observed explicitly. Results indicate that the dynamic stress becomes negligible at 2 m from the roadway, and stabilization is suggested to be limited within this width. A series of constitutive relations is proposed to correlate the dynamic stress with the resulted displacement in different directions, which can be used to guide the design of unsaturated subgrade soils in South China.

Uncertainty in the predicted ultimate pullout strength of soil nails can be significant due to the complexity of nail–soil interactions, inherent variability in soil properties and the effects of nail installation. The paper first presents a statistical evaluation of the accuracy of ultimate bond strength of soil nails using the effective stress method (ESM) equation that has been adopted in Hong Kong. A total of 113 ultimate nail capacity data points from field pullout tests were collected from the literature and used to estimate the accuracy of the current ESM. Based on the available data, the current ESM default pullout model is found to be excessively conservative (on average) by at least a factor of three. The spread in prediction accuracy measured by the coefficient of variation (COV) of bias is in the range of 36–43 % after removing anomalous test data. Here, bias is the ratio of measured to predicted pullout load capacity. In addition, the accuracy of the current ESM equation for prediction of nail bond strength is shown to be dependent on the magnitude of predicted ultimate bond strength and magnitude of nominal vertical effective stress which is undesirable. The paper examines four candidate-modified bond strength equations with empirical coefficients that have been back-fitted to measured bond strengths to improve the overall accuracy of the equation and to reduce or remove the undesirable dependencies noted above. One equation with an empirically corrected stress-dependent term is judged to be the best candidate model based on the mean of bias values, spread (COV) of bias values, lack of dependencies and simplicity. Finally, the relative contributions of random variability in soil shear strength to measurement bias in bond strength (prediction accuracy) for each soil type are computed for the best bond strength model. Analysis of the contribution of soil shear strength to prediction accuracy showed that the combination of variability due to factors other than soil shear strength was greater than the variability in soil shear strength alone, where the latter is defined by the soil secant friction coefficient.

This paper presents reliability analyses of soil nail walls against two external ultimate limit states, global and sliding stabilities, which are related to the external stability failures of soil nail walls. Reliability analyses are conducted using Monte Carlo simulation technique. Soil nailing is a popular retaining system in highway construction and slope stabilization, and its current design practice is still based on the working stress design. There remains a need to establish a more rational design framework—load and resistance factor design—based on the concept of limit state design and reliability analysis for soil nail walls. The development of load and resistance factor design approach must consider multiple ultimate limit states, associated with external, internal, and facing failures. The analyses of resistance factors against two external failures are conducted in this study considering various influencing factors, including statistical parameters of soil friction angle, ultimate bond strength between soil and nails, soil type, wall geometry (wall height, back slope angle, and face batter angle), and nail configurations (nail inclination angle, drillhole diameter, and nail spacing). In the end, a series of resistance factors are proposed for potential application of load and resistance factor design approach against external failures for soil nail walls according to different design codes.

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 usi...

This paper presents the development of a simplified model for estimation of maximum nail loads during or at completion of construction of soil nail walls. The developed simplified nail load model consists of two multiplicative components: the theoretical nail load and the correction factor. The theoretical nail load is computed as the product of lateral active Earth pressure at nail depth and the nail tributary area. The correction factor is introduced to account for the difference between the theoretical and the measured nail loads. A total of 85 measured nail load data were collected from the literature; out of which, 74 were used to develop a simple formulation for the correction factor, whereas the remaining 11 were used for validation. After the validation, the model was updated using all 85 data. The updated simplified nail load model was demonstrated to be accurate on average (mean of model factor equal to 1), and the spread in prediction quantified as the coefficient of variation of the model factor was about 40%. Here, model factor is the ratio of measured to estimated nail load. The randomness of the model factor was also verified. Finally, the model factor was demonstrated to be a lognormal random variable. The proposed simplified nail load model is beneficial due to its simplicity and quantified model uncertainty; thus it is practically valuable to both direct reliability-based design and load and resistance factor design of soil nail wall internal limit states.

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 COV of 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-f...

Due to the characteristics of dispersion of guided waves, the waveforms recorded in ultrasonic nondestructive testing (NDT) of rock bolts are complicated to interpret. With a goal to increase the inspection sensitivity and accuracy in NDT of rock bolts, an approach of waveform interpretation based on wave modes identification is developed. The numerical simulation of full rock bolt and rock bolts with grout defect by Finite Element Method (FEM) is applied to illustrate the approach; it is found that the sensitive and low attenuation wave modes exist. Laboratory tests on full rock bolt and rock bolt with grout loss using NDT are conducted to evaluate the efficacy of the approach of waveform interpretation. In addition to that, a parametric study was conducted on rock bolt models with different sectional defect size. Based on the waveform interpretation, the mode-based reflection coefficientRis proposed to evaluate the sensitivity of wave modes to the defect size of sectional area. It is found that the sensitivity of the wave mode does not change with the defect sectional area, and the amplitude depends on the size of the defect.

This study presents reliability analyses of soil nail walls (SNWs) against global and sliding stability failures in layered ground. The load and resistance factor design (LRFD) has been studied and advocated for SNW design over the past few years. However, the majority of those studies were exclusively focused on SNWs in single-layer ground and few have investigated the case of layered ground. In this paper, the reliability is evaluated using the first-order reliability method (FORM) for SNWs that are designed based on traditional working stress design (WSD) methods. Based on analyses of a great variety of combinations of two soils, a stiff clay layer and a dense sand layer, reliability indices calibrated from traditional WSD exceed 3.0 for global stability designs but may be lower than 3.0 for sliding stability designs. This study also reveals that the sequence and the thickness ratio of layers are two important factors for the reliability of both global and sliding stability modes. SNWs in layer...

Accuracy evaluation of the default Federal Highway Administration (FHWA) simplified equation for prediction of maximum soil nail loads under working conditions is presented in this study using the maximum likelihood method and a large amount of measured lower and upper bound nail load data reported in the literature. Accuracy was quantitatively expressed as model bias where model bias is defined as the ratio of measured to predicted nail load. The maximum likelihood estimation was carried out assuming normal and lognormal distributions of bias. Analysis outcomes showed that, based on the collected data, the default FHWA simplified nail load equation is satisfactorily accurate on average and the spread in prediction accuracy expressed as the coefficient of variation of bias is about 30%, regardless of the distribution type. Empirical calibrations were proposed to the default FHWA simplified nail load equation for accuracy improvement. The Bayesian Information Criterion was adopted to perform a comparison of suitability between the competing normal and lognormal statistical models that were intended for description of model bias. Example of reliability-based design of soil nail walls against internal pullout limit state of nails is provided in the end to demonstrate the benefit of performing model calibration and using calibrated model for design of soil nails.