Seismic prediction of cracks is of great significance in many disciplines,for which the rock physics model is indispensable.However,up to now,multitudinous analytical models focus primarily on the cracked rock with th...Seismic prediction of cracks is of great significance in many disciplines,for which the rock physics model is indispensable.However,up to now,multitudinous analytical models focus primarily on the cracked rock with the isotropic background,while the explicit model for the cracked rock with the anisotropic background is rarely investigated in spite of such case being often encountered in the earth.Hence,we first studied dependences of the crack opening displacement tensors on the crack dip angle in the coordinate systems formed by symmetry planes of the crack and the background anisotropy,respectively,by forty groups of numerical experiments.Based on the conclusion from the experiments,the analytical solution was derived for the effective elastic properties of the rock with the inclined penny-shaped cracks in the transversely isotropic background.Further,we comprehensively analyzed,according to the developed model,effects of the crack dip angle,background anisotropy,filling fluid and crack density on the effective elastic properties of the cracked rock.The analysis results indicate that the dip angle and background anisotropy can significantly either enhance or weaken the anisotropy degrees of the P-and SH-wave velocities,whereas they have relatively small effects on the SV-wave velocity anisotropy.Moreover,the filling fluid can increase the stiffness coefficients related to the compressional modulus by reducing crack compliance parameters,while its effects on shear coefficients depend on the crack dip angle.The increasing crack density reduces velocities of the dry rock,and decreasing rates of the velocities are affected by the crack dip angle.By comparing with exact numerical results and experimental data,it was demonstrated that the proposed model can achieve high-precision estimations of stiffness coefficients.Moreover,the assumption of the weakly anisotropic background results in the consistency between the proposed model and Hudson's published theory for the orthorhombic rock.展开更多
Accurate modelling of the potential failure modes in the rock mass is an essential task towards a robust design of roof support systems in coal mines.The use of generalised rock mass properties based on averaged prope...Accurate modelling of the potential failure modes in the rock mass is an essential task towards a robust design of roof support systems in coal mines.The use of generalised rock mass properties based on averaged properties(e.g.Hoek-Brown model) has been found to limit the capability to reproduce the actual rock mass behaviour which may include a wide range of interacting and complex failure mechanisms such as shear and tension fracturing of the intact rock and shear and separation of pre-existing discontinuities,including re-activation.Recent studies have also shown that traditional models,such as the Mohr-Coulomb,may not accurately describe the behaviour of the intact rock,particularly for stress induced failures where spalling and slabbing are observed.This is mainly due to the cohesion and friction components of the shear strength of the intact rock not being mobilised at the same rate with strain-softening of the former component playing an essential role in the post peak behaviour.In addition,coal measure rocks are often transversely isotropic,both by way of the preferred orientation of clay particles within the finer grained lithology and by bedding textures and bedding partings,and this is often ignored in computer simulations.A newly developed transversely isotropic brittle rock mass model is applied in the simulation of a hypothetical and simple roadway development.A Cohesion Weakening-Friction Strengthening(CWFS) approach is adopted to describe the intact rock where the mobilisation and strain-softening of the two shear strength components are linked to plastic deformation.The impacts of anisotropy and brittle rock on the development of the excavation disturbed zone or height of softening,as often referred to,are investigated and their implication in the roof support design discussed.展开更多
Fully grouted bolts are a key component of the support system for underground openings.Although considerable effort has been made in the simulation of the reinforcement effect of the fully grouted bolts on the rock ma...Fully grouted bolts are a key component of the support system for underground openings.Although considerable effort has been made in the simulation of the reinforcement effect of the fully grouted bolts on the rock masses surrounding underground openings,most of the work has limited significance since the structural element approach is used.This study proposes a local homogenization approach(L-H approach)that integrates elastoplastic mechanics,composite mechanics,and analytical approaches with numerical simulation to effectively simulate the reinforcement effect of the fully grouted bolt on deep surrounding rock masses.In the L-H approach,the representative volume of bolted rock mass(RVBRM)with a fully grouted bolt is established based on the original mesh model utilized in the rockbolt element approach.The RVBRM is a regular quadrangular prism with a cross-sectional size equal to the bolt spacing and a length equal to the bolt length.The RVBRM is homogenized by the L-H approach from a unidirectional bolt-reinforced composite into a homogeneous transversely isotropic medium whose mechanical properties are described by a new transversely isotropic elastoplastic model.The L-H parameters for the RVBRM are obtained using analytical approaches,composite mechanics,and known parameters of the rock mass and bolt.Using the L-H approach,the reinforcement effect of the fully grouted bolt on the bolted rock specimen and the surrounding rock mass in Jinping II Diversion Tunnel#2 with a depth greater than 2000 m is simulated.The results show that the predictions of the L-H approach are more in agreement with the physical model results of bolted rock specimen and provide a more realistic response of the bolted surrounding rock mass.The L-H approach demonstrates that fully grouted bolts with common bolt spacings and diameters substantially enhance the elastic modulus,shear strength,and tensile strength of the rock mass in the direction of the bolt axis.展开更多
In this paper numerical analysis of underground structures, taking account the transverse isotropy system of rocks, was done using CAST 3M code by varying the shape of excavation and the coefficient of earth pressure ...In this paper numerical analysis of underground structures, taking account the transverse isotropy system of rocks, was done using CAST 3M code by varying the shape of excavation and the coefficient of earth pressure k. Numerical results reveal that the anisotropy behavior, the shape of hole and the coefficient of earth pressure k have significant influence to the mining induced stress field and rock deformations which directly control the stability of underground excavation design. The magnitude of horizontal stress obtained for the horse shoe shape excavation(25.2 MPa for k = 1; 52.7 MPa for k = 2)is lower than the magnitude obtained for circular hole(26.4 MPa for k = 1; 59.5 MPa for k = 2).Therefore, we have concluded that the horse shoe shape offers the best stability and the best design for engineer. The anisotropy system presented by rock mass can also influence the redistribution of stresses around hole opened. Numerical results have revealed that the magnitude of redistribution of horizontal stresses obtained for transverse isotropic rock(12.1 MPa for k = 0.5; 25.2 MPa for k = 1 and52.7 MPa for k = 2) is less than those obtained in the case of isotropic rock(27.6 MPa for k = 1;48.6 MPa for k = 2 and 90.81 MPa for k = 2). The more the rock has the anisotropic behavior, the more the mass of rock around the tunnel is stable.展开更多
Non-consistency of stress results is of ten observed during field measurements. In some cases, even the rneasurernents are made at the same location in a massive rockrnass, the results can vary widely. In order to sol...Non-consistency of stress results is of ten observed during field measurements. In some cases, even the rneasurernents are made at the same location in a massive rockrnass, the results can vary widely. In order to solve the problem, extensive research has been carried out to study the major factors wh1ch rnay affect stress deterrnlnation. They include the rock behaviour and the stress state. For rocks showing non-isotropic behaviour, the values of Young’s modulus and Poisson ratio vary with the orientation of loading and measurement. Stress condition in the rock affects the rock behaviour. Furtherrnore, the loading condition on rock samples durlng laboratory tests is different from in the field and therefore the determined e1astic constants may not represent the field condi tion. In general , the Young’s modulus may depend on the orientation, the loading path, the stress magnitude and the stress ratio. This paper examines in detail the effects of those factors, especially for rocks showing transversely isotropic behaviour. It is found that the discrepancy of stress results from field measurernents in this type of rock is mainly due to over simplification of the rock behavior and inadequate use of elastic constants of the rock during stress calculation. A case study is given,which indicates the significance of these factors and demonstrates the proper procedure for stress calculation from measurements.展开更多
Compared with hyperbolic velocity estimation methods,nonhyperbolic methods(such as shifted hyperbola)are better choices for large offsets or vertical transverse isotropy(VTI)media.Since local seismic event slope conta...Compared with hyperbolic velocity estimation methods,nonhyperbolic methods(such as shifted hyperbola)are better choices for large offsets or vertical transverse isotropy(VTI)media.Since local seismic event slope contains subsurface information,they can be used to estimate zero-offset two-way traveltime and normal moveout velocity.The traditional velocity estimation methods require a great deal of manual work and are also prone to human error.In order to estimate the traveltime parameters for VTI media automatically,in this paper,we propose to use predictive painting and similarity-weighted clustering to obtain traveltime parameters.The predictive painting is used to estimate zero-offset two-way traveltime,and the shifted-hyperbola traveltime equation is used to obtain velocity and anisotropy attributes.We first map local slopes to zero-offset two-way traveltime and moveout-parameters domain and then use similarity-weightedk-means clustering to find the maximum likelihood anisotropy parameters of the main subsurface structures.In order to demonstrate that,we apply the similarity-weighted clustering method to synthetic and field data examples and the results are of higher accuracy when compared to the ones obtained using multiparameter semblance-based method.From estimation error section,it can be seen that the estimation error of multiparameter semblance-based method is about 3-5 times that of the proposed method.展开更多
The dispersion curves of real-valued modes in a fluid-filled borehole are widely used in acoustic well logging.The accurate dispersion curves are the precondition of theoretical analysis and inversion process.Generall...The dispersion curves of real-valued modes in a fluid-filled borehole are widely used in acoustic well logging.The accurate dispersion curves are the precondition of theoretical analysis and inversion process.Generally,these curves can be obtained by solving the conventional dispersion equation for isotropic formations and most vertically transverse isotropy(VTI)formations.However,if the real-valued solutions exist when the radial wavenumbers for the formation quasi-P and quasi-S equals to each other,the existed methods based on the conventional dispersion equation could lead to incorrect results for some VTI formations.Few studies have focused on the influence of these real-valued solutions on dispersion curve extraction.To remove these real-valued solutions,we have proposed a modified dispersion equation and its corresponding solving process.When solving the dispersion equation,the Scholte wave velocity of VTI formation at high frequency is used as the initial guess.The two synthetic examples including fast and slow VTI formations validate that these real-valued solutions do not contribute to the wavefield,and the new dispersion curve extraction method is suitable for all kinds of VTI formations.Consequently,the method can provide reliable dispersion curves for both theoretical analysis and anisotropic parameters inversion in VTI formations.展开更多
基金We would like to acknowledge all the reviewers and editors and the sponsorship of National Natural Science Foundation of China(42030103)the Marine S&T Fund of Shandong Province for Pilot National Laboratory for Marine Science and Technology(Qingdao)(2021QNLM020001-6)the Laoshan National Laboratory of Science and Technology Foundation(LSKJ202203400).
文摘Seismic prediction of cracks is of great significance in many disciplines,for which the rock physics model is indispensable.However,up to now,multitudinous analytical models focus primarily on the cracked rock with the isotropic background,while the explicit model for the cracked rock with the anisotropic background is rarely investigated in spite of such case being often encountered in the earth.Hence,we first studied dependences of the crack opening displacement tensors on the crack dip angle in the coordinate systems formed by symmetry planes of the crack and the background anisotropy,respectively,by forty groups of numerical experiments.Based on the conclusion from the experiments,the analytical solution was derived for the effective elastic properties of the rock with the inclined penny-shaped cracks in the transversely isotropic background.Further,we comprehensively analyzed,according to the developed model,effects of the crack dip angle,background anisotropy,filling fluid and crack density on the effective elastic properties of the cracked rock.The analysis results indicate that the dip angle and background anisotropy can significantly either enhance or weaken the anisotropy degrees of the P-and SH-wave velocities,whereas they have relatively small effects on the SV-wave velocity anisotropy.Moreover,the filling fluid can increase the stiffness coefficients related to the compressional modulus by reducing crack compliance parameters,while its effects on shear coefficients depend on the crack dip angle.The increasing crack density reduces velocities of the dry rock,and decreasing rates of the velocities are affected by the crack dip angle.By comparing with exact numerical results and experimental data,it was demonstrated that the proposed model can achieve high-precision estimations of stiffness coefficients.Moreover,the assumption of the weakly anisotropic background results in the consistency between the proposed model and Hudson's published theory for the orthorhombic rock.
基金Project support from the Specialist Technical Apprentice Scheme from Coffey Geotechnics Ltd. Pty
文摘Accurate modelling of the potential failure modes in the rock mass is an essential task towards a robust design of roof support systems in coal mines.The use of generalised rock mass properties based on averaged properties(e.g.Hoek-Brown model) has been found to limit the capability to reproduce the actual rock mass behaviour which may include a wide range of interacting and complex failure mechanisms such as shear and tension fracturing of the intact rock and shear and separation of pre-existing discontinuities,including re-activation.Recent studies have also shown that traditional models,such as the Mohr-Coulomb,may not accurately describe the behaviour of the intact rock,particularly for stress induced failures where spalling and slabbing are observed.This is mainly due to the cohesion and friction components of the shear strength of the intact rock not being mobilised at the same rate with strain-softening of the former component playing an essential role in the post peak behaviour.In addition,coal measure rocks are often transversely isotropic,both by way of the preferred orientation of clay particles within the finer grained lithology and by bedding textures and bedding partings,and this is often ignored in computer simulations.A newly developed transversely isotropic brittle rock mass model is applied in the simulation of a hypothetical and simple roadway development.A Cohesion Weakening-Friction Strengthening(CWFS) approach is adopted to describe the intact rock where the mobilisation and strain-softening of the two shear strength components are linked to plastic deformation.The impacts of anisotropy and brittle rock on the development of the excavation disturbed zone or height of softening,as often referred to,are investigated and their implication in the roof support design discussed.
基金funded by the National Natural Science Foundation of China(Nos.51979268,U1765206,and 52079027)。
文摘Fully grouted bolts are a key component of the support system for underground openings.Although considerable effort has been made in the simulation of the reinforcement effect of the fully grouted bolts on the rock masses surrounding underground openings,most of the work has limited significance since the structural element approach is used.This study proposes a local homogenization approach(L-H approach)that integrates elastoplastic mechanics,composite mechanics,and analytical approaches with numerical simulation to effectively simulate the reinforcement effect of the fully grouted bolt on deep surrounding rock masses.In the L-H approach,the representative volume of bolted rock mass(RVBRM)with a fully grouted bolt is established based on the original mesh model utilized in the rockbolt element approach.The RVBRM is a regular quadrangular prism with a cross-sectional size equal to the bolt spacing and a length equal to the bolt length.The RVBRM is homogenized by the L-H approach from a unidirectional bolt-reinforced composite into a homogeneous transversely isotropic medium whose mechanical properties are described by a new transversely isotropic elastoplastic model.The L-H parameters for the RVBRM are obtained using analytical approaches,composite mechanics,and known parameters of the rock mass and bolt.Using the L-H approach,the reinforcement effect of the fully grouted bolt on the bolted rock specimen and the surrounding rock mass in Jinping II Diversion Tunnel#2 with a depth greater than 2000 m is simulated.The results show that the predictions of the L-H approach are more in agreement with the physical model results of bolted rock specimen and provide a more realistic response of the bolted surrounding rock mass.The L-H approach demonstrates that fully grouted bolts with common bolt spacings and diameters substantially enhance the elastic modulus,shear strength,and tensile strength of the rock mass in the direction of the bolt axis.
文摘In this paper numerical analysis of underground structures, taking account the transverse isotropy system of rocks, was done using CAST 3M code by varying the shape of excavation and the coefficient of earth pressure k. Numerical results reveal that the anisotropy behavior, the shape of hole and the coefficient of earth pressure k have significant influence to the mining induced stress field and rock deformations which directly control the stability of underground excavation design. The magnitude of horizontal stress obtained for the horse shoe shape excavation(25.2 MPa for k = 1; 52.7 MPa for k = 2)is lower than the magnitude obtained for circular hole(26.4 MPa for k = 1; 59.5 MPa for k = 2).Therefore, we have concluded that the horse shoe shape offers the best stability and the best design for engineer. The anisotropy system presented by rock mass can also influence the redistribution of stresses around hole opened. Numerical results have revealed that the magnitude of redistribution of horizontal stresses obtained for transverse isotropic rock(12.1 MPa for k = 0.5; 25.2 MPa for k = 1 and52.7 MPa for k = 2) is less than those obtained in the case of isotropic rock(27.6 MPa for k = 1;48.6 MPa for k = 2 and 90.81 MPa for k = 2). The more the rock has the anisotropic behavior, the more the mass of rock around the tunnel is stable.
文摘Non-consistency of stress results is of ten observed during field measurements. In some cases, even the rneasurernents are made at the same location in a massive rockrnass, the results can vary widely. In order to solve the problem, extensive research has been carried out to study the major factors wh1ch rnay affect stress deterrnlnation. They include the rock behaviour and the stress state. For rocks showing non-isotropic behaviour, the values of Young’s modulus and Poisson ratio vary with the orientation of loading and measurement. Stress condition in the rock affects the rock behaviour. Furtherrnore, the loading condition on rock samples durlng laboratory tests is different from in the field and therefore the determined e1astic constants may not represent the field condi tion. In general , the Young’s modulus may depend on the orientation, the loading path, the stress magnitude and the stress ratio. This paper examines in detail the effects of those factors, especially for rocks showing transversely isotropic behaviour. It is found that the discrepancy of stress results from field measurernents in this type of rock is mainly due to over simplification of the rock behavior and inadequate use of elastic constants of the rock during stress calculation. A case study is given,which indicates the significance of these factors and demonstrates the proper procedure for stress calculation from measurements.
基金supported by the National Natural Science Foundation of China(41574113)the Important National Science and Technology Specific Projects of China(Grant 2016ZX05026-002-006).
文摘Compared with hyperbolic velocity estimation methods,nonhyperbolic methods(such as shifted hyperbola)are better choices for large offsets or vertical transverse isotropy(VTI)media.Since local seismic event slope contains subsurface information,they can be used to estimate zero-offset two-way traveltime and normal moveout velocity.The traditional velocity estimation methods require a great deal of manual work and are also prone to human error.In order to estimate the traveltime parameters for VTI media automatically,in this paper,we propose to use predictive painting and similarity-weighted clustering to obtain traveltime parameters.The predictive painting is used to estimate zero-offset two-way traveltime,and the shifted-hyperbola traveltime equation is used to obtain velocity and anisotropy attributes.We first map local slopes to zero-offset two-way traveltime and moveout-parameters domain and then use similarity-weightedk-means clustering to find the maximum likelihood anisotropy parameters of the main subsurface structures.In order to demonstrate that,we apply the similarity-weighted clustering method to synthetic and field data examples and the results are of higher accuracy when compared to the ones obtained using multiparameter semblance-based method.From estimation error section,it can be seen that the estimation error of multiparameter semblance-based method is about 3-5 times that of the proposed method.
基金financial support provided by the National Natural Science Foundation of China(Grant No.42104127 and 42004117)the Fundamental Research Funds for the Central Universities,China University of Geosciences(Wuhan)(Grant No.162301192696).
文摘The dispersion curves of real-valued modes in a fluid-filled borehole are widely used in acoustic well logging.The accurate dispersion curves are the precondition of theoretical analysis and inversion process.Generally,these curves can be obtained by solving the conventional dispersion equation for isotropic formations and most vertically transverse isotropy(VTI)formations.However,if the real-valued solutions exist when the radial wavenumbers for the formation quasi-P and quasi-S equals to each other,the existed methods based on the conventional dispersion equation could lead to incorrect results for some VTI formations.Few studies have focused on the influence of these real-valued solutions on dispersion curve extraction.To remove these real-valued solutions,we have proposed a modified dispersion equation and its corresponding solving process.When solving the dispersion equation,the Scholte wave velocity of VTI formation at high frequency is used as the initial guess.The two synthetic examples including fast and slow VTI formations validate that these real-valued solutions do not contribute to the wavefield,and the new dispersion curve extraction method is suitable for all kinds of VTI formations.Consequently,the method can provide reliable dispersion curves for both theoretical analysis and anisotropic parameters inversion in VTI formations.
