Hoek-Brown Model Research Articles

Investigation of the Geomechanical Situation in the Rock Mass in the Zone of Influence of Cleaning Operations in the Conditions of the Khromtau Mine Field

Goal. The forecast of the stress-strain state (VAT) in the rock mass in the zone of influence of cleaning operations when using the self-destruction development system and the calculation of the bearing capacity of the supports of the mine workings used at the Khromtau mine. Methodology. The complex of geological and engineering data on the properties of the host rocks is analyzed. Numerical modeling of the stress-strain state of the rock mass and calculation of the bearing capacity of the types of supports used at the mine in the RS2 program, which works on the basis of the Finite Element Method in a two-dimensional formulation, which allowed us to take into account a significant number of factors affecting the state of the array. The HoekBrown model was used as a model of array behavior, the distinctive advantage of which is its nonlinearity. Results. The values of the main stresses and the load on the support are obtained. According to the results of numerical analysis of the stress-strain state of the rock mass at a depth of 900 m (horizon – 480 m), the dominant stresses are close to hydrostatic σ1 = σ3 = σz = 24.8 MPa. A predictive assessment of the stability reserve of mine workings before and after the cleaning work has been carried out, according to the results of which it should be assumed that the stability reserve of the workings passed in the cleaning area is below the minimum allowable, therefore, collapses and an increase in the load on the support are possible. The reference pressure on the support of the workings at a depth of 900 m (-480 m) is calculated. Calculation of the parameters of the support for workings laid at a horizon of 480 m was carried out.. Scientific novelty. The nature and features of the regularities of the formation of the stress-strain state within the boundaries of the influence of various variants of cleaning operations of block 20-28 on the horizon of 480 m are established and a quantitative assessment of the values of loads on the support of the pumping orts of the workings of the horizon is given. Practical significance. The results of the research can be applied to the creation of a geomechanical model of the deposit and the design of stable parameters of the support of mine workings

BARIK: an extended Hoek–Brown-based anisotropic constitutive model for fractured crystalline rock

Abstract. The disposal of heat-generating radioactive waste in deep geologic formations is a global concern. Numerical methods play a key role in understanding and assessing the disposal scenarios of radioactive waste in deep geological repositories. However, the complexities of the thermal, hydrological, mechanical, chemical, and biological processes associated with the disposal of radioactive waste in porous and fractured materials constitute significant challenges. One of the most challenging issues in this field is the complex material behavior of fractured crystalline rock. The presence of fractures makes the rock anisotropic, nonlinear, and dependent on loading paths. Additionally, the Biot coefficient cannot be considered constant throughout the critical and subcritical fracture development regions. These factors make the development of an accurate constitutive model for fractured crystalline hard rock a critical component of any deep geological disposal project. Furthermore, to demonstrate the integrity of the containment-providing rock zone in crystalline host rock, the qualitative integrity criteria must be quantified so that numerical simulation can be performed with concrete numerical values. Part of this assessment for a crystalline host rock is a dilatancy criterion, which is currently based on the Hoek–Brown constitutive model. BARIK is the German acronym for the research project on which this paper is based. This contribution provides an overview of the development and verification of the BARIK constitutive model, an extended Hoek–Brown model for fractured crystalline hard rock that takes into account up to three fracture systems. The model enables the consideration of the matrix and joint behavior of the rock separately, with each component having unique strength characteristics and failure criteria. These criteria are formulated such that suitable consideration of the strength-reducing properties of the respective fracture systems during barrier integrity verification is possible. The BARIK model has been implemented into two computer codes, FLAC3D and MFront for OpenGeoSys, allowing for the identification and evaluation of any inaccuracies that may arise from the use of different codes. The model enables isotropic–elastic, orthotropic–elastic, isotropic–elasto-plastic, and orthotropic–elasto-plastic calculations of the matrix, making it a valuable tool for the site selection process and for the construction and long-term safety of underground repositories. Furthermore, this poster presentation will show how the constitutive model was evaluated in relation to the dilatancy criterion and how the BARIK constitutive model's suitability for conducting an integrity assessment was validated. In conclusion, the development of BARIK is a significant step forward in the understanding and modeling of the complex material behavior of fractured crystalline hard rock. This contribution will provide insights into the development and verification of this model for the safe disposal of radioactive waste.

Return mapping scheme for the Hoek-Brown model with tension cut-off

The present paper revisits a stress update procedure for the Hoek-Brown plasticity model enhanced by a Rankine type of tension cut-off failure criterion. Limiting tensile stresses not only supports the behavior of weak rock masses with a very low tensile strength but in combination with the original Hoek-Brown model improves robustness of the stress update procedure, i.e. the stress return mapping algorithm. Herein, the primary focus is on the stress return from a space of inadmissible trial stresses for which neither the Hoek-Brown yield surface nor its derivative can be evaluated. All potential scenarios are thoroughly discussed both in the framework of single- and multi-surface plasticity. The presented procedures were implemented and verified with the help of the Geo5 FEM software.

Development of models of ice interaction with waves and structures

Mathematical models used to study the interaction of sea ice with ocean waves and hydraulic structures are analyzed. Works focusing on general and specific scenarios of this interaction are reviewed. General scenarios include wave-ice interactions with a focus on various prevailing physical and mechanical processes, while specific scenarios include ice-structure interactions. The specific scenarios within the framework of this work include changes in ice pressure as the ice field thickens between the offshore platform supports, the effect of seasonal variations on the resulting ice load, and ice floe bending failure using the Hoek-Brown model. Based on the results obtained, a classification of existing models was developed according to modeling methods, details of accounting for various natural phenomena, complexity of use, and predictive accuracy. For each model in the classification, advantages and disadvantages were identified, and recommendations for their improvement for further application in scientific research and practical calculations were proposed.

Modelling of progressive failure mechanism of mine pillars

Rock fracturing process around underground openings is mainly a process of progressive slabbing with the generation of surface-parallel fractures in the initial stage, and shear failure is likely to occur in the final process. The difficulty of capturing this behaviour through conventional continuum modelling has led to the development of advanced constitutive laws for use in continuum models. Recently, an enhanced continuum constitutive approach to simulate strain-softening based on the Hoek-Brown failure criterion has been presented. This advanced Hoek-Brown model with Softening introduces a hyperbolic decay of the material properties affecting the post-peak response and the nonlinear dilation, thus enabling to investigate failure modes in the form of dilatant shear bands. Moreover, to restore the objectivity of the numerical solution during the development of strain localization phenomena, a viscous regularization technique has been implemented within the model. The performance of this constitutive model has been proved and, in this paper, further numerical computations are reported concerning the brittle failure process occurring in mine pillars, thus confirming the capability to capture failure mechanisms during excavation within a strain localization regime.

A Modified Hoek–Brown Model for Determining Plastic-Strain-Dependent Post-peak Strength of Brittle Rock

A Modified Hoek–Brown Model for Determining Plastic-Strain-Dependent Post-peak Strength of Brittle Rock

A New Method for Predicting Residual Strength of Rock in Water Diversion Tunnel Using Drilling Process Monitoring

The peak and residual strengths of rock materials are important parameters for the stability evaluation of rock engineering, especially water diversion tunnels. A friction-strengthening model based on Hoek–Brown model is proposed to determine peak and residual strength of rock. The proposed model parameter, contact friction coefficient of rock, controls the nonlinearity of the peak strength and residual strength. With a great amount of data from publications examined, the relationship between the friction coefficient and the parameters in the Hoek–Brown model is studied. A new field method using drilling process monitoring was proposed to predict the peak strength and residual strength. The results show that the predicted strength for four types of rock is in good agreement with those of the standard tests in laboratory. Their errors are within the error range of 15% compared to the results from the tested results in laboratory. Although the proposed model is empirical, the parameters in the proposed model have clear physical meaning, and it can successfully predict the peak strength and residual strength of hard rock, medium rock, and weak rock using drilling process monitoring in the field. This practical method should have a great potential for field application in rock engineering.

Numerical simulation of triaxial tests on cement-treated clays using Hoek–Brown criterion

Triaxial tests are generally conducted to establish the mechanical behaviour of cement-treated clays. Numerical simulations of these tests involve selection of the correct constitutive model, which can capture the key features of the stress–strain response of the geomaterial. However, as cement-treated clays behave differently to untreated clay in its natural state, the classic constitutive models may not give reasonable results and the failure envelope has been found to be non-linear. An attempt was made in this work to simulate the behaviour of cement-treated clays using the Hoek–Brown model and the experimental and numerical simulation results were compared.

Safety factor calculation of a road structure with cement-modified loess as subgrade

The deformation and failure parameters of six mixtures of cement-modified loess have been determined based on direct tensile stress testing, indirect tensile test testing and unconfined compressive stress testing. Results have been used to determine the parameters of the Mohr-Coulomb failure criterion and the parameter of the Hoek-Brown failure criterion. The Hoek-Brown model clearly shows that results from indirect tensile stress measurement must be weighted to describe materials properly. Both models’ results were then used to calculate the safety factor of a road structure with cement-modified loess used as subgrade material using reduction techniques. Specifically, for the Hoek-Brown model, a new calculation adapted to structures with tensile stresses is proposed. Results vary by around 8.9 for the Mohr-coulomb model and around 3.2 for the Hoek-Brown model.This shows, at the laboratory scale, that resource-based economies could be expected if cement-modified loess mechanical parameters were considered in the design of structures. It also shows that the Hoek-Brown model is a promising tool to study tensile stressed structures made with cement-modified materials.

COMPARING THE HOEK-BROWN AND MOHR-COULOMB FAILURE CRITERIA IN FEM ANALYSIS

This paper revisits the issue of a potential substitutions of the Hoek-Brown failure model by the standard Mohr-Coulomb model in the stability analysis of rock masses. The derivation of equivalent shear strength parameters of the Mohr-Coulomb proposed by Hoek et al. [1] is addressed with emphases on the suitable range of stresses for which the equivalence of the two failure criteria applies. To that end, a simple numerical analysis of the oedometric test is carried out. It is seen that a correct choice of the upper limit of the minimum compressive principal stress is crucial for the Mohr-Coulomb model to provide predictions comparable to the Hoek-Brown model. This issue is addressed next in the light of the solution of slope stability problem. All the presented results were derived with the help of the GEO5 FEM finite element software [2].

Research into rock mass geomechanical situation in the zone of stope operations influence at the 10th Anniversary of Kazakhstan’s Independence mine

Purpose. Predicting the stress-strain state (SSS) of the rock mass in the zone of stope operations influence using the self-caving mining system and the calculation of the load-bearing capacity of mine workings support at the 10th Anniversary of Kazakhstan’s Independence mine. Methods. An engineering-geological data complex of the host rocks properties has been analyzed. Numerical modelling of the rock mass stress-strain state and the calculation of the load-bearing capacity of the support types used at the mine have been performed with the help of the RS2 software. This program, based on the Finite Element Method in a two-dimensional formulation, makes it possible to take into account a significant number of factors influencing the mass state. The Hoek-Brown model with its distinctive advantage of nonlinearity is used as a model for the mass behaviour. Findings. The values of the main stresses and load on the support have been obtained. According to the numerical analysis results of the rock mass stress-strain state at a depth of 900 m (horizon -480 m), the principal stresses are close to hydrosta-tic ones σ1 = σ2 = σz = 24.8 MPa. Predicting assessment of mine workings stability margin is performed before and after stope operations. Based on its results, it can be assumed that the stability margin of the mine workings driven in the stope zone is below the minimum permissible, therefore, caving and an increase in the load on the support are possible. Abutment pressure on mine workings support at a mining depth of 900 m (-480 m) has been calculated. The parameters of support in mine workings driven at the horizon -480 m have been calculated. Originality.The nature and peculiarities of patterns of the stress-strain state formation within the boundaries of various stope operations influence in blocks 20-28 at the horizon -480 m have been determined. The quantitative assessment of the values of loads on the support of haulage cross-cuts of the horizon mining is given. Practical implications. The research results can be used for creating a geomechanical model of the field and to design stable parameters of mine workings support. Keywords: stress-strain state, principal stresses, support, mine, ore, rock mass

Model Technics to Predict the Impact of the Particle Size Distribution (PSD) of the Sand on the Mechanical Properties of the Cement Mortar Modified with Fly Ash

Despite many of the research studies on the effect of the particle size distribution of the sand and fly ash content on the mechanical behavior of the cement mortar, there has not been a comprehensive study investigating the effect of particle size distribution curve corresponding to 10% of finer (d10), fly ash content, curing time, sand particle size distribution properties (d10), and water to cement ratio (w/c) on the compressive (σc), tensile (σt), and flexural (σf) strengths of cement mortar. Therefore, this study investigates the subject which could be beneficial for the geotechnical and building and construction field. In this study, more than 1000 data on the mechanical properties of the cement mortar modified with different percentages of fly ash varied from 5 to 75% (by dry weight of the cement) collected from the literature. Statistical analysis and modeling were performed on the collected data. Vipulanandan p-q model was used and compared to the Logistic Growth model to predict the particle size distribution of sands used in the cement mortar. The water to cement ratio (w/c) of the cement mortar ranged between 0.20–0.80 percent and the compressive strength (σc), tensile strength (σt) and flexural strength (σf) of cement mortar modified with fly ash up to 90 days of curing were ranged between 15–88 MPa, 0.4–5 MPa, and 1–10 MPa, respectively. Vipulanandan correlation model was also used and compared with the Hoek–Brown model to correlate the mechanical properties of cement mortar modified with fly ash. The analysis and modeling results of the present study showed that there is a good relationship between the compressive strength (σc) with w/c, curing time, fly ash content and d10. Based on the coefficient of determination (R2) and root mean square error (RMSE) the compressive strength (σc), flexural strength (σf) and tensile strength (σt) of cement mortar quantified well as a function of w/c, the percentage of fly ash, curing time, and d10 using nonlinear relationship.

Stability of Unsupported Conical Slopes in Hoek-Brown Rock Masses

This paper presents new plasticity stability solutions of unsupported conical rock slopes, obeying generalised Hoek-Brown failure criterion. To solve the problem, a finite element limit analysis framework is selected to investigate the stability of the conical rock slopes. Four dimensionless parameters influencing the stability factor of the conical slopes including excavated height ratios, slope inclinations, geological strength index and yield parameter of Hoek-Brown model are considered in this study. The numerical solutions of the stability factor of the conical slopes are proposed as design charts. The failure mechanism of conical slopes influenced by the four dimensionless parameters is also presented and discussed in the paper.

Numerical Analysis of Stress Distribution During Tunneling in Clay Stone Rock

Modern technology has been used to build tunnels in recent years by means of drilling machines (TBM) that were used for civil engineering work in large cities to reduce the harmful effects of spending on the surface of the earth significantly. To build the tunnel, numerical modeling was used on the basis of the finite element method to predict stress behavior during the tunnel construction process. Tunnel simulation model by using the numerical method (FEM) with the Hoek-Brown model, which includes calculating the behavior of predicting stress-that surrounds the tunnel and analysis during the process of building the tunnel and compared with the natural state of the rocks during the different tunnel construction stages. Vertical stresses at the top and bottom of the tunnel are reduced during the advance of tunneling while horizontal stresses are increased. TBM progression is reflected in phases through one to five by performing an axial symmetric FE analysis, math calculation results revealed significant stress changes occurring in rock regions near the boundary of the tunnel. In other words, proximity to rocks is mostly affected by the tunnel. These pressure variations decrease as you move away from the tunnel horizontally and the seams reach extremely small values for distances greater than (2D) meters from the edge of the tunnel, where D is the diameter of tunnel.

The Characterization and Modeling the Mechanical Properties of High Strength Concrete (HSC) Modified with Fly Ash (FA)

One of the main challenges facing Civil Engineering community is to modify cement quantity in the mix design by admixtures to enhance the mechanical properties. According to more than 1000 data from literature, mechanical characteristics of concrete modified with FA were discussed. The statistical variation with modeling were achieved by set of data. The cement was replaced up to 70% with FA (weight of dry cement) and by cube of concrete testing up to 90 days of curing time and different w/c ratio. The compressive strength of concrete varied from 18-67 MPa, while, for modified concrete with FA, compressive strength ranged from 21-94 MPa, tensile strength ranged from 1-9 MPa and flexural strengths ranged from 3 - 10 MPa. The w/c ratio of concrete modified with FA varied from 0.24-0.53, also the FA content varied from 0-50 %. Vipulanandan correlation model was effective by connecting mechanical properties and compare with Hoek-Brown model. The nonlinear model was used to investigate the effect of FA on properties of normal and high strength concrete. Study results presented a worthy correlation between compressive strength and curing time, w/c ratio and FA content. By using the interactive linked (model) for compressive, tensile, and flexural strengths of concrete quantified well as a function of w/c ratio, curing time and FA content by using a nonlinear relationship.

Statistical variations and new correlation models to predict the mechanical behaviour of the cement mortar modified with silica fume

ABSTRACT Despite many of the research studies on the effect of the silica fume content on the mechanical properties of the cement mortar, there has not been a comprehensive study investigating the effect of silica fume content, curing time and water to cement ratio on the compressive, tensile and flexural strengths of cement mortar. In this study investigates the subject which could be beneficial for building and construction field. More than 1000 data on the mechanical properties of the cement mortar modified with different percentages of silica fume varied from 5% to 55% (by dry weight of the cement) collected from the literature. The statistical analysis, modelling and non-linear regression analysis were performed on the collected data. The water to cement ratio (w/c) ranged between 0.20% and 1% and the compressive strength, tensile strength and flexural strength of cement mortar modified with silica fume up to 90 days of curing were ranged between 2.5MPa and 87 MPa; 2 MPa and 6.8 MPa; and 1.2 MPa and 9.2 MPa, respectively. Vipulanandan correlation model was used and compared with the Hoek-Brown model to correlate the mechanical properties of cement mortar modified with silica fume. The Vipulanandan correlation model has a lower root mean square error (RMSE) compared to the Hoek-Brown model. The results of the present study showed that there is a good relationship between the compressive strength with flexural strength and tensile strength for cement mortar modified with silica fume. Based on the data analysis the per cent of silica fume up to 55% had the lowest effect on increasing the compressive strength compared with w/c and curing time.

Numerical Study of P-Waves Propagating across Deep Rock Masses Based on the Hoek–Brown Model

Strong dynamic disturbances constitute an important problem threatening the safety of deep underground engineering projects. The mechanical mechanisms responsible for such disturbances in deep rock masses can be revealed by studying stress waves propagating across them. In this study, the propagation of P-waves across a deep rock mass was investigated both numerically and theoretically. The Hoek–Brown (HB) model, which is able to account for the stress state and nonlinear failure of the rock mass, was employed. In particular, the time-domain recursive method was extended to analyze the propagation of P-waves across the rock mass following the HB failure criterion. Good agreement is found between the theoretical results and simulations, which demonstrates that using the Universal Distinct Element Code (UDEC) with the HB model to study the transmission of P-waves across rock masses is eminently feasible. The effects of the disturbance factor, confining pressure, incident amplitude, and coupling of joints and rock mass quality on wave propagation were also studied using the UDEC in a systematic manner. The results show that for an incident P-wave of given amplitude, the greater the rock mass quality and smaller the disturbance factor, the greater the transmission coefficient. In addition, there is an upper limit to the effect the confining pressure has on the transmission coefficient. The amplitude of the incident wave also has an important influence on the transmission coefficient. Finally, if the quality of the rock mass is good and the disturbance slight, then the attenuation of the wave is primarily caused by the joints.

Quantification the effect of microsand on the compressive, tensile, flexural strengths, and modulus of elasticity of normal strength concrete

ABSTRACT The objective of this study is to identify and quantify the effect of microsand content (MS) or silica fume (SF), water-cement-ratio (w/c) and curing time (t) on the compressive and tensile strengths of concrete at different strength ranges varied from 4 MPa to 55 MPa. In this study, over 1000 data were used to characterise the compressive and tensile strength behaviour. The range of w/c for modified concrete with different percentages of microsand up to 40% (by dry weight of cement) was in the range of 0.17% to 0.80%, compressive and tensile strengths were in the range of 4–55 MPa, and 1–7 MPa, respectively. Vipulanandan model correlated the relationship between mechanical properties of concrete modified with MS with a varied range of w/c and curing time, and the results were compared with the Hoek-Brown correlation model used in the literature. Based on the NLM parameters, the effect of MS was less than w/c and curing time on the compressive strength of modified concrete with MS in different strength range up to 55 MPa.

Numerical study of the circular opening effect on mechanical behaviour of rock under confinement

Opening holes in rock including their size and distribution can affect the performance of rock-related structures. A good understanding on this will contribute to, for example, rock cavern design, and construction, tunnelling, and mining engineering. To improve the understanding, a comprehensive investigation of the opening hole effect on the rock mechanical behaviour under biaxial loading condition is carried out by virtue of a hybrid continuum-discrete element method. Laboratory specimens with both single hole and multi-hole of various radii are investigated and compared with the cases subjected to uniaxial compression. It is demonstrated that the confining pressure can increase both the stiffness and strength due to delaying the crack initiation and propagation. The increase due to the confining pressure is more evident for the compressive strength. For single hole specimens with 0.75 mm radius hole, the increase ratio of the compressive strength is a linear increasing function with width and the increase ratio ranges from 2.15 for the specimen with 3.5 mm width to 2.45 for 10 mm width. For the single hole specimen with 10 mm width, the increase ratio starts at 2.13 for the specimen with 0.75 mm radius hole, ascending to the peak of 2.37 for the specimen with 1 mm radius hole, followed by a decline to 2.2 for the specimen with 1.25 mm radius hole. However, for the multi-hole specimens, the increase ratio varies from 1.66 to 3.13. In addition, to verify the influence of confining pressure magnitude on the performance of the rock specimens, totalling 10 confining pressure levels are applied and modelled. The simulation results show that even though there are opening holes in the specimens, the simulated compressive strength generally follows the generalised Hoek-Brown model.

Modeling the effect of silica fume on the compressive, tensile strengths and durability of NSC and HSC in various strength ranges

The objective of this study is to identify and quantify the effect of silica fume content (SF), water–cement-ratio (w/c) and curing time (t) on the compressive and tensile strengths of concrete at different strength ranges varied from 4 to 100 MPa. In this study, over 1000 data were used to characterize the compressive and tensile strengths behavior. The range of w/c for modified concrete with different percentage of silica fume up to 40% (by dry weight of cement) was in the range of 0.17–0.80%, compressive and tensile strengths were in the range of 4–100 MPa, and 1–7 MPa, respectively. Vipulanandan model correlated the relationship between mechanical properties of concrete modified with SF with a varied range of w/c and curing time and the result were compared with the Hoek–Brown correlation model used in the literature. Based on the coefficient of determination (R2) and root mean square error (RMSE) the compressive strength (σc), tensile strength (σt) of concrete as a function of w/c, percentage of silica fume and curing time using nonlinear (NLM) relationship quantified very well. Based on the NLM parameters, the effect of SF was less than w/c and curing time on the compressive strength of modified concrete with SF in different strength range. According to the coefficient of determination (R2) and root mean square error (RMSE), the Vipulanandan correlation model and Hoek–Brown model both are very close in predicting the mechanical behavior of concrete modified with SF for normal and high strengths concrete (NSC and HSC).