Bearing capacity of spatially random rock masses obeying Hoek–Brown failure criterion

This paper presents a probabilistic analysis to compute the probability density function of the bearing capacity of a strip footing resting on a spatially varying rock mass. The rock is assumed to follow the generalised Hoek–Brown failure criterion. The uniaxial compressive strength of the intact rock (σc) was considered as a random field and the geological strength index was modelled as a random variable. The uncertainty propagation methodology employed in the analysis is the sparse polynomial chaos expansion. A global sensitivity analysis based on Sobol indices was performed. Some numerical results were presented and discussed.     

Effect of rock mass disturbance on the stability of rock slopes using the Hoek–Brown failure criterion

The process of creating man made or “cut” slopes in rock invariably leads to stress relief within the rock mass which in turn induces a certain degree of fracturing and disturbance. The level of disturbance can be particularly significant when the slope is formed using blasting techniques. However, the effects of this disturbance on the overall rock slope stability have not been investigated thoroughly in the current literature. In order to account for rock mass disturbance during construction, a disturbance factor has been included in the Hoek–Brown failure criterion [1]. This paper uses finite element upper and lower bound limit analyses to estimate rock slope stability based on the Hoek–Brown failure criterion whilst including the effect of rock mass disturbance. A rigorous set of analyses have been performed where the level of disturbance is considered as constant or linearly varying throughout the slope. The results are then compared to a number of reported case histories for verification purposes. From the results of this study, the disturbance factor was found to have significant influence on the rock slope stability assessment, especially for poorer quality rock masses. Hence, cautious engineering judgement must be exercised when estimating the level of disturbance. In addition, utilising stability charts to estimate the stability of cut rock slopes without considering the rock mass disturbance may lead to significant overestimations.     

Pseudo-dynamic stability of rock slope considering Hoek–Brown strength criterion

Rock slopes with planar joints or weak structural planes are vulnerable in nature, especially suffering from the natural hazards, instabilities of slopes are more prone to occur. Therefore, concerning to the influence of earthquakes, this paper performs a new procedure to evaluate slope stability in a geomaterial governed by Hoek–Brown strength criterion. A rotational failure mechanism determined by 21 dependent angle variables is introduced to respect the Hoek–Brown strength criterion. The earthquake load is characterized by a modified pseudo-dynamic method that does not violate the zero boundary condition and considers the damping properties of geomaterials. A slice approach is adopted to calculate the earthquake-induced inertial force work rate. The stability number of rock slope is considered to measure the safety. The stability number is formulated as a classical optimization problem controlled by 21 dependent angle variables and a time variable which need to be optimized by the genetic algorithm toolbox. Comparisons with the literature are made to prove rationality and accuracy of the proposed procedure. Parametric study is carried out to reveal the influence of dynamic properties. For engineering application, stability charts are provided for a quick assessment of slope safety.

     

A generalized three-dimensional Hoek–Brown strength criterion

Summary  Although the Hoek–Brown strength criterion has been widely used in rock mechanics and rock engineering, it does not take account of the influence of the intermediate principal stress. Much evidence, however, has been accumulating to indicate that the intermediate principal stress does influence the rock strength in many instances. Therefore, researchers have developed three-dimensional (3D) versions of the Hoek–Brown strength criterion. In this paper, three existing 3D versions of the Hoek–Brown strength criterion are reviewed and evaluated. The evaluation shows that all of the three 3D versions of the Hoek–Brown strength criterion have limitations. To address the limitations, a generalized 3D Hoek–Brown criterion is proposed by modifying the generalized Hoek–Brown strength criterion. The proposed 3D criterion not only inherits the advantages of the Hoek–Brown strength criterion but can take account of the influence of the intermediate principal stress. At a 2D stress state (triaxial or biaxial), the proposed 3D criterion will simply reduce to the form of the generalized Hoek–Brown strength criterion. To validate the proposed 3D strength criterion, polyaxial or true triaxial compression test data of intact rocks and jointed rock masses has been collected from the published literature. Predictions of the proposed generalized 3D Hoek–Brown strength criterion are in good agreement with the test data for a range of different rock types. The difference of the proposed generalized 3D Hoek–Brown strength criterion from and its advantages over the existing 3D versions of the Hoek–Brown strength criterion are also discussed. It should be noted that the proposed 3D criterion is empirical in nature because it is an extension of the 2D Hoek–Brown strength criterion, which is empirical. Because of the non-convexity of the yield surface for a biaxial stress state, the proposed 3D criterion may have problems with some stress paths. Correspondence: L. Zhang, Department of Civil Engineering and Engineering Mechanics, The University of Arizona, Tucson, Arizona 85721, USA     

Prediction of underground cavity roof collapse using the Hoek–Brown failure criterion

Preventing roof collapse in underground cavities is a challenge to geotechnical engineering. In this study, three independent methods have been used to evaluate the roof collapse of underground rectangular cavities for a range of geometries and rock properties. The rock mass strength has been described by the Hoek–Brown failure criterion. The results of the analysis allow for prediction of roof collapse and to determine whether the failure surface that develops in the rock mass remains localised or extends through the full depth of cover. This is of significance if there are overlying cavities and when estimating surface subsidence.     

A three-dimensional Hoek–Brown failure criterion based on an elliptical Lode dependence

A new three-dimensional (3D) Hoek–Brown (HB) failure criterion based on an elliptical Lode dependence is proposed to describe failure of rocks and concrete under multiaxial stress states. This criterion not only inherits all benefits of the classical HB criterion that is developed for the triaxial compression (TXC) of rocks but also accounts for the effect of the intermediate principal stress. It is capable of representing the strength difference between the triaxial extension (TXE) and TXC with the introduction of an additional coefficient k (0.5 ≤ k ≤ 1.0), which can be derived from TXE tests or taken as 0.53 for rocks in cases where the TXE test data is unavailable. Other two material constants (m_i and σ_ci) involved in this criterion can be obtained from TXC tests. Additionally, the failure surface of this criterion is smooth and convex on the deviatoric stress plane when 0.5 < k ≤ 1.0. The new criterion achieves very good fit to the test data of TXC/TXE, biaxial compression, and polyaxial compression (PXC) on a wide variety of rock materials and concrete, reported in the literature. Comparison of the new criterion with an existing 3D HB criterion based on the same Lode dependence has demonstrated that the new criterion performs better than the latter for test data of rock and concrete under multiaxial stress states except for PXC test data of one rock type. Finally, the influence of values of k on the accuracy of the new criterion is discussed.     

Parametric Monte Carlo studies of rock slopes based on the Hoek–Brown failure criterion

Probabilistic evaluation of slope failures is increasingly seen as the most appropriate framework for accounting for uncertainties in design. This paper performs reliability assessments for rock slopes based on the latest version of the Hoek–Brown failure criterion. The purpose of this study is to demonstrate the use of a new form of stability number for rock slope designs that has been recently developed from finite element upper and lower bound limit analysis methods, and to provide guidance for its use in probabilistic assessments. The analyses show that by using this newly proposed stability number, the probability of failure (P_f) obtained from case studies agrees well with the true state of the slope. In addition, this paper details a procedure to determine the magnitude of safety factor required for rock slope design.     

Probabilistic back analysis of slope failure – A case study in Taiwan

In this paper, the authors present a probabilistic back-analysis of a recent slope failure at a site on Freeway No. 3 in northern Taiwan. Post-event investigations of this failure found uncertain strength parameters and deteriorating anchor systems as the most likely causes for failure. Field measurement after the event indicated an average slip surface of inclination 15°. To account for the uncertainties in input parameters, the probabilistic back analysis approach was adopted. First, the Markov Chain Monte Carlo (MCMC) simulation was used to back-calculate the geotechnical strength parameters and the anchor force. These inverse analysis results, which agreed closely with the findings of the post-event investigations, were then used to validate the maximum likelihood (ML) method, a computationally more efficient back-analysis approach. The improved knowledge of the geotechnical strength parameters and the anchor force gained through the probabilistic inverse analysis better elucidated the slope failure mechanism, which provides a basis for a more rational selection of remedial measures.     

An empirical relation for parameter mi in the Hoek–Brown criterion of anisotropic intact rocks with consideration of the minor principal stress and stress-to-weak-plane angle

Acta Geotechnica - The parameter mi accounts for the anisotropy of rock strength, and the accurate determination of mi is a primary requirement of the Hoek–Brown (H–B) strength...     

Value of information analysis in rock engineering: a case study of a tunnel project in Äspö Hard Rock Laboratory

Geoengineering prognoses are often based on data from a limited number of investigations of soil and rock mass. There is generally a desire to reduce the uncertainty in the prognoses while minimising the investigation costs. Value of Information Analysis (VOIA) is a support for decisions regarding investigation strategies and the aim of this paper is to present methodology for VOIA that takes into account four decision alternatives where the input data could be provided by experts. The methodology will be applied in a case study where the value of information related to an investigation borehole will be calculated. The results indicate that the value of information of the borehole is low compared with the realisation costs of the investigation. It was found that models for VOIA in underground construction projects are complex but that the analysis can be simplified with extensive use of expert knowledge and calculations of the value of perfect information as a benchmark for investigation strategies.     

Instantaneous Friction Angle and Cohesion of 2-D and 3-D Hoek–Brown Rock Failure Criteria in Terms of Stress Invariants

The Mohr–Coulomb (M–C) failure criterion is one of the most widely used failure criteria in rock mechanics, although it has a number of shortcomings such as neglecting the nonlinear strength observed in rock or the effect of the intermediate principal stress σ ₂. Other failure criteria have been proposed to effectively include in the predictions of failure the non-linear response of rock to confinement or the effects of the intermediate principal stress. The M–C criterion is still widely used, and it is arguably the criterion most used in practice. For example, stability evaluations of shallow rock structures such as slopes and foundations are routinely carried out by estimating a friction angle and a cohesion of the rock mass. To include the dependency of cohesion and friction angle on stresses, efforts are being made to estimate equivalent values of the M–C parameters for the range of stresses applicable to a particular design. The paper suggests a new and convenient approach to find the equivalent friction angle and cohesion from any failure criterion that can be expressed in terms of the Nayak and Zienkiewicz’s stress invariants. To demonstrate the capabilities and application of the methodology, the new approach is applied to two failure criteria: the Hoek–Brown (H–B) criterion and the Hoek–Brown and Willam–Warnke (HB–WW) criterion, 2-D and 3-D failure criteria, respectively. Results from the new method, in terms of equivalent friction and cohesion for the H–B criterion, are exactly the same as the results obtained from Balmer’s theory, which confirms the validity of the new method. The predicted equivalent friction and cohesion for the HB–WW criterion show a dependency on σ ₂, which does not occur for a 2-D failure criterion.     

A multiphase approach to the stability analysis of reinforced earth structures accounting for a soil–strip failure condition

A multiphase model, developed in the context of elastoplasticity, is applied to the simulation and design of reinforced earth retaining structures. The main feature of this model is to combine the advantage of a homogenization approach, as regards its computational efficiency, with the ability to account for a specific failure condition at the interface between the soil and the reinforcing strips, which may have a decisive influence on the behavior of the structure. A particular emphasis is put on the stability analysis of this kind of reinforced soil structures, formulated within the framework of the yield design theory. Making use of a generalized rigid block failure mechanism, the stability of a reinforced earth retaining wall is investigated by means of the kinematic approach, leading to upper bound estimates for the stability factor of the structure, which are then favorably compared with the results of an elastoplastic analysis. Special attention is paid to assessing in a quantitative way how a specific soil–strip failure condition affects the stability of the reinforced earth structure as a whole.     

The challenge of numerically implementing numerous force–resultant models in the stability analysis of long on-bottom pipelines

Plasticity models written directly in terms of force and displacement are finding increased popularity in describing the behaviour of offshore foundations. However, when applied to the on-bottom stability analysis of pipelines under random storm loading, hundreds, if not thousands, of models must be incorporated with structural elements in a three-dimensional analysis and simultaneously solved. This necessitates extremely efficient and accurate numerical integration techniques. This paper scrutinizes constitutive integration algorithms within both explicit and implicit frameworks, and applies them to a two-surface mixed hardening model that describes the force–displacement behaviour of a pipe partially embedded in sand. Detailed solutions are provided, allowing implementation of the pipe–soil model into any standard structural finite-element program. Through use of practical examples, the efficiency and accuracy of the solution methods are assessed.     

Assessing the influence of a rapid water drawdown on the seismic response characteristics of a reservoir rock slope using time–frequency analysis

Acta Geotechnica - To investigate the influence of a rapid water drawdown (RWD) on the seismic response characteristics of reservoir rock slopes, numerical dynamic analyses and shaking table tests...     

Sensitivity analysis of parameters influencing the ice–seabed interaction in sand by using extreme learning machine

Ice gouging problem is a significant challenge threatening the integrity of subsea pipelines in the Arctic (e.g., Beaufort Sea) and even non-Arctic (e.g., Caspian Sea) offshore regions. Determining the seabed response to ice scour through the subgouge soil deformations and the keel reaction forces are important aspects for a safe and cost-effective design. In this study, the subgouge soil deformations and the keel reaction forces were simulated by the extreme learning machine (ELM) for the first time. Nine ELM models (ELM 1–ELM 9) were developed using the key parameters governing the ice–seabed interaction. The number of neurons in the hidden layer was optimized and the best activation function for the ELM network was identified. The premium ELM model, resulting in the lowest level of inaccuracy and complexity and the highest level of correlation with experimental values was identified by performing a sensitivity analysis. The gouge depth ratio and the shear strength of the seabed soil were found to be the most influential input parameters affecting the subgouge soil deformations and the keel reaction forces. A set of the ELM-based equations were proposed to approximate the ice gouging parameters. The uncertainty analysis showed that the premium ELM model slightly underestimated the subgouge soil deformation.

     

δ13C analysis of bulk organic matter in speleothems using liquid chromatography–isotope ratio mass spectrometry

The determination of δ¹³C values in speleothems is of considerable importance in palaeoenvironmental research, but has focussed solely on analysis of the carbonate. Here we demonstrate a new method for analysing the δ¹³C values of organic matter (OM) trapped in speleothems, utilising flow injection liquid chromatography–isotope ratio mass spectrometry (LC–IRMS). Developmental analysis using a homogenised speleothem powder showed that the method is robust, with repeated digests and analyses having an average standard deviation of 0.1‰. Dilution tests with samples of 4–23 μg total organic carbon (TOC) show relatively small linearity effects, with the overall standard deviation across a peak response range of 1700–9000 mV being 0.2‰.     

Qualitative analysis and mapping of heavy metals in an abandoned Au–Ag mine area using NIR spectroscopy

Reflectance spectroscopy covering the visible and near-infrared ranges (400–2,400 nm) is known as a rapid and nondestructive method in the characterization and quantitative analysis of many components of interest. In this study, the potential use of spectral absorption feature parameters (SAFPs) in the range of 400–2,400 nm was investigated in terms of the prediction of heavy metals and mapping of their distribution. Parameters such as absorption depth, area, and peak ratio were derived from variations in spectral absorption shape associated with concentrations of heavy metals. Heavy metals were quantified from SAFPs using stepwise multiple linear regression (SMLR) and enter multiple linear regression (EMLR). The EMLR model showed qualitative prediction performance for As and Cu, with R ² values of 0.60 and 0.81, respectively. A contour map of As and Cu concentrations based on EMLR-derived values showed similar spatial patterns to a map based on measured values.     

Trend analysis of hydroclimatological variables in Urmia lake basin using hybrid wavelet Mann–Kendall and Şen tests

This paper investigates monthly, seasonal, and annual trends in rainfall, streamflow, temperature, and humidity amounts at Urmia lake (UL) basin and analyzes the interaction between these variables and UL’s water level fluctuation during the 1971–2013 period. Two new methods including nonparametric hybrid wavelet Mann–Kendall test and ?en’s methodology have been used to determine potential trends in the variables and their dominant periods. The results showed significant decreasing trends in the water level and streamflow series, moderate decreasing trend in the rainfall and relative humidity series, and increasing trends in the observed temperature data. The 8- , 12-month, and 2-year periods were detected as the dominant periods of the variables in monthly, seasonal, and annual timescales, respectively. The results from the interaction analysis revealed that the main factor influencing the water level at UL is decreasing trend in the streamflow series. Both the monthly series of UL’s water level and the streamflow series of the stations indicated two start points of significant decreasing trend in 1973 and 1998. Furthermore, a comparative analysis among the applied methods indicated a good agreement between the results of hybrid wavelet Mann–Kendall test and ?en’s trend analyzing method.