CN113326551A - Surrounding rock excavation damage analysis method under thermal coupling condition and application thereof - Google Patents

Surrounding rock excavation damage analysis method under thermal coupling condition and application thereof Download PDF

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CN113326551A
CN113326551A CN202110623136.8A CN202110623136A CN113326551A CN 113326551 A CN113326551 A CN 113326551A CN 202110623136 A CN202110623136 A CN 202110623136A CN 113326551 A CN113326551 A CN 113326551A
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rock
excavation
surrounding rock
thermal
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CN113326551B (en
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鲁功达
陶剑
石安池
周家文
杨兴国
李洪涛
范刚
李海波
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Sichuan University
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    • G06F30/00—Computer-aided design [CAD]
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    • G—PHYSICS
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    • G06F2119/00—Details relating to the type or aim of the analysis or the optimisation
    • G06F2119/08—Thermal analysis or thermal optimisation
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
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    • G06F2119/00—Details relating to the type or aim of the analysis or the optimisation
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Abstract

The invention discloses a surrounding rock excavation damage analysis method under a thermal coupling condition and application thereof, wherein the analysis method comprises the following steps: and (3) establishing an excavation blasting-unloading-cooling whole-process model of the tunnel, and solving a process control equation comprising superposition coupling of thermal stress, dynamic stress and ground stress, so as to obtain rock thermal-force coupling response of the model under different geological conditions and excavation modes. The analysis method of the invention can determine the distribution range of the excavated damage area, can reveal the formation stage and the formation reason of the rock mass damage, has the advantages of high calculation efficiency, short required time, low manpower and material resource consumption and the like, and can provide prediction and guidance for the adaptive excavation design of the underground chambers under the conditions of high temperature and high pressure.

Description

Surrounding rock excavation damage analysis method under thermal coupling condition and application thereof
Technical Field
The invention relates to the technical field of underground chamber excavation.
Background
With the increasing depletion of mineral resources in shallow layers of the earth surface, resource exploration and exploitation activities are continuously moving to the deep part of the earth. However, according to Lucier et al, the highest ground stress magnitude actually measured in a certain gold mine in south Africa can reach 100MPa, and according to the research of Belle and Biffi, the ground temperature gradient currently disclosed in a certain coal mine in Australia can reach 7 ℃/100 m. Therefore, the problems of high ground stress and high ground temperature caused by the increase of the resource occurrence depth form a serious technical challenge for deep geotechnical engineering practices such as deep resource exploitation, deep energy development, high-level waste geological disposal and the like.
During underground chamber excavation, the reserved rock body can form unrecoverable dynamic damage due to blasting load impact and dynamic stress redistribution. In addition, for a geothermal abnormal area or a deep high-temperature mine, after the excavation of the high-temperature chamber is finished, cold air is generally introduced into an underground tunnel by adopting modes of artificial ventilation and the like so as to reduce the temperature of a working environment, so that the cooled rock body generates temperature redistribution and causes continuous adjustment of a secondary stress field, thereby possibly generating additional thermal damage on the basis of the formed dynamic excavation damage and seriously threatening the stability and construction safety of the chamber. Therefore, a rock thermal-force coupling behavior model and an analysis method in the whole process of deep-buried high-temperature chamber excavation blasting-unloading-cooling are established, a formation mechanism, a mechanical mechanism and an influence range of surrounding rock excavation damage are further revealed, and important practical help can be provided for deep chamber excavation design under high ground stress and high ground temperature environments.
In order to solve the above problems, some feasible schemes are proposed in the prior art, such as a numerical simulation method by using memories and the like, and the distribution condition of the surrounding rock damage zone induced by explosion load and transient unloading under the condition of high ground stress is researched by using finite elements, but the method has the following defects:
(1) the numerical calculation is usually limited by the grid division mode, if the grid divided by the model is dense, the calculation efficiency is low, and the required time is long; if the model grid is thick, the accuracy of the calculation result cannot be effectively guaranteed;
(2) rock thermal-force coupling response under the coupling action of high ground stress and high ground temperature is not considered, so that a surrounding rock excavation damage evolution mechanism under the deep high-temperature and high-pressure condition cannot be described, and an accurate operation scheme under the condition cannot be obtained.
Or as the chinese patent application CN201911400238.2 proposes a method of laying sound wave monitoring points in the tunnel excavation region and calculating the rock mass damage value according to the obtained sound wave monitoring data, but the method has the following disadvantages:
(1) the arrangement of sound wave monitoring points is complex, the monitoring process needs long time, and the consumption of manpower and material resources is large.
(2) The actual monitoring method can only obtain the distribution range of the surrounding rock damage area, but cannot reflect the rock stress evolution trend in the blasting-unloading-cooling process, so that the formation mechanism and the mechanical mechanism of excavation damage are difficult to reveal, and an accurate operation scheme cannot be obtained.
Disclosure of Invention
Aiming at the defects of the prior art, the invention aims to provide a surrounding rock excavation damage analysis method under the thermal coupling condition, which can accurately judge the formation mechanism, the mechanical mechanism and the influence range of a surrounding rock damage area under different geological conditions and excavation modes based on the processes of thermal coupling analysis, stress trajectory projection and the like, so that the optimal operation schemes under different conditions and modes can be further obtained, and the limitations that the traditional numerical calculation and in-situ monitoring method is low in calculation efficiency, long in required time, large in manpower and material resource consumption, and incapable of distinguishing the formation mechanism and the mechanical mechanism of the surrounding rock damage and the like are overcome.
It is also an object of the present invention to provide some specific applications of the above method.
The invention firstly discloses the following technical scheme:
the method for analyzing the surrounding rock excavation damage under the thermal coupling condition comprises the following steps:
establishing a tunnel excavation whole-process thermodynamic coupling model containing variable parameters, wherein the thermodynamic coupling model comprises the coupling of ground stress, dynamic stress and thermal stress;
setting basic design parameters of the overall process thermodynamic coupling model, wherein the basic design parameters comprise blasting related parameters and rock thermodynamic parameters;
setting a stress model of the surrounding rock mass at the boundary of the excavated tunnel based on the overall process thermodynamic coupling model and the basic design parameters;
setting process control equations of the surrounding rock mass in different excavation processes based on the overall process thermal coupling model and the basic design parameters, wherein the process control equations comprise state equations and boundary conditions, the state equations comprise dynamic stress conduction equations and heat conduction equations, and the boundary conditions comprise stress models at the boundaries;
solving the process control equation to obtain the dynamic stress and the thermal stress of the surrounding rock mass in different processes;
obtaining a surrounding rock thermodynamic coupling model according to the dynamic stress, the thermal stress and the coupling of the dynamic stress and the thermal stress with the initial ground stress;
projecting the obtained surrounding rock thermal coupling model to a stress invariant space through stress projection to obtain a surrounding rock mass stress trajectory curve in the whole surrounding rock excavation process under different variable parameters;
and obtaining the distribution range, the formation stage and the formation reason of the surrounding rock mass excavation damage under different variable parameters according to the stress trajectory curve.
Wherein, the blasting-related parameters may further include such as: explosive properties, blast hole arrangement, charging mode and the like; the thermodynamic parameters of the rock mass may further include, for example: rock density ρrYoung's modulus E, rock Poisson ratio upsilon, rock yield stress under different confining pressure conditions, rock thermal expansion coefficient beta, thermal conductivity coefficient kappa, specific heat capacity C and the like.
The forming stage (or the forming mechanism according to the embodiment) refers to each stage of the whole tunnel excavation process, such as excavation blasting, ground stress unloading, or temperature reduction after unloading, which will be described later.
Wherein, the formation cause (or the mechanical mechanism in the embodiment) refers to a thermodynamic cause generating loss of the surrounding rock body, such as formation by a tensioning mechanism, a shear-expansion mechanism or a shear-contraction mechanism.
According to some preferred embodiments of the invention, the coupling is in the form of: the coupling force is obtained by the ground stress superimposed dynamic stress superimposed heating stress.
According to some preferred embodiments of the present invention, the whole tunnel excavation process includes three stages of excavation blasting, ground stress unloading and cooling after unloading; the variable parameters comprise tunnel excavation radius a and unloading time tduGround stress P0And temperature T of original rock0。
In the preferred embodiment, the stress model at the tunnel boundary may use, for example, a pressure function f (t) of uniform blasting and unloading waves, which is determined by integrating blasting design parameters, ground stress magnitude and unloading time.
According to some preferred embodiments of the present invention, the establishment of the full process thermodynamic coupling model includes the following setup conditions:
the tunnel is excavated in an infinite elastic homogeneous rock body by a full-section drilling and blasting method, the axis of the tunnel is long enough, the section of the tunnel is a circle with the radius of a, and the profile surface of the tunnel is formed by one-step excavation under the condition of plane strain;
the initial temperature of the elastic homogeneous rock mass is the original rock temperature T0And is subjected to far-field hydrostatic pressure, i.e. the ground stress P0The function of (1);
during excavation, when the pressure of the explosion wave is attenuated to be equal to the initial ground stress of the excavation boundary, transient unloading of the ground stress is generated, and the ground stress P is simulated by applying reverse traction force on the wall of the hole along a linear path0At unloading time tduThe dynamic response of the lower excited rock mass;
after the chamber profile, namely the profile of the circular tunnel with the section radius of a, is formed, the chamber profile is cooled by cold air, and when the chamber profile is cooled to a specified time, the whole excavation process is completed.
It will be appreciated by those skilled in the art that although the preferred embodiment involves processes that are not physically manipulated on the surface, such as an infinitely large elastically homogeneous rock mass, a tunnel with a sufficiently long axis, etc., it is operable in the model set-up of the art, such as set-up conditions based on an infinitely large elastically homogeneous rock mass, and those skilled in the art will appreciate that r → ∞ may be used as a boundary condition in the set-up or solution of the model. That is, the description of the preferred embodiment can be specifically implemented within the technical scope of the field.
According to some preferred embodiments of the invention, the base design parameters include: the explosive density, the detonation wave velocity, the detonation product isentropic index, the detonation product thermal insulation constant, the charge diameter, the blast hole spacing, the charge length, the rock density, the rock elastic modulus, the rock Poisson ratio, the rock thermal expansion coefficient, the rock thermal conduction coefficient, the rock specific heat capacity and the rock heat exchange coefficient.
According to some preferred embodiments of the invention, the solving is performed by a laplace transform method.
More specifically, the laplace method can be further applied to the solution of the dynamic stress transfer equation described later to obtain the dynamic stress evolution characteristics of the rock mass around the excavation boundary; the method can also be applied to the solution of the heat conduction equation described later to obtain the thermal stress distribution of the rock mass in the ventilation and cooling process of the tunnel.
According to some preferred embodiments of the invention, the force model at the tunnel boundary comprises:
Figure BDA0003100840230000041
wherein the content of the first and second substances,
Figure BDA0003100840230000042
tr＝L/Vd，td＝2πtr/ln(2)，Fb0＝dbFe0/S；
wherein t represents time, Fb0Representing the equivalent peak pressure, d, acting on the tunnel profilebIndicating the diameter of the hole, S the distance between adjacent holes, Fe0Indicating the peak pressure of the blast hole wall, delta indicating the attenuation coefficient of the explosion stress wave, trIndicating the time at which the explosive load reaches a peak, L the length of the charge, VdIndicates detonation wave velocity, tdRepresenting the duration of the blast wave, tuIndicates the unloading end time (i.e., the earth stress unloading end time), tduDenotes the unloading time, P0Representing the ground stress.
According to some preferred embodiments of the invention, the borehole wall peak pressure is obtained by:
Figure BDA0003100840230000051
where ρ iseDenotes the density of the explosive, deRepresenting the charge diameter, and gamma and eta represent the isentropic index and adiabatic constant, respectively, of the detonation product.
According to some preferred embodiments of the invention, the process control equation comprises:
Figure BDA0003100840230000052
wherein r represents the distance between the surrounding rock constitution point and the center of the chamber under the cylindrical coordinate system,
Figure BDA0003100840230000055
representing the displacement potential function, v, of the mass point of the surrounding rock mass in a cylindrical coordinate systempRepresents the longitudinal wave velocity of the dynamic stress wave when the dynamic stress wave propagates in the surrounding rock mass medium,
Figure BDA0003100840230000053
and (3) representing the radial dynamic stress function of the surrounding rock mass under the cylindrical coordinate system.
According to some preferred embodiments of the invention, the process control equation further comprises:
Figure BDA0003100840230000054
wherein T (r, T) represents a redistribution function of rock mass temperature, rhorRepresenting rock density, C representing specific heat capacity of rock, k representing heat conduction coefficient of rock, H ═ H/k, wherein H represents heat exchange coefficient of rock, T (a, T) represents temperature of cavity wall unit obtained according to redistribution function T (r, T) of rock temperature, T (a, T) represents temperature of cavity wall unit obtained according to redistribution function T (r, T) of rock temperatureuIndicating the end time of unloading, TbIndicating the cooling gas temperature.
According to some preferred embodiments of the present invention, the surrounding rock thermodynamic coupling model comprises:
Figure BDA0003100840230000061
wherein σr、σθAnd σzRespectively representing radial total coupling stress, circumferential total coupling stress and out-of-plane normal direction total coupling stress of the surrounding rock mass under a cylindrical coordinate system; tau isrθRepresents the total coupled shear stress;
Figure BDA0003100840230000062
and
Figure BDA0003100840230000063
respectively representing the dynamic radial stress, the circumferential stress and the out-of-plane normal direction stress of the surrounding rock mass under a cylindrical coordinate system,
Figure BDA0003100840230000064
Representing a dynamic shear stress obtained by solving the dynamic stress conduction equation;
Figure BDA0003100840230000065
and
Figure BDA0003100840230000066
respectively show the columnRadial thermal stress, circumferential thermal stress and out-of-plane normal direction thermal stress applied to surrounding rock mass under coordinate system,
Figure BDA0003100840230000067
Representing the shear stress resulting from a temperature change (e.g., drop in temperature) obtained by solving the heat conduction equation.
According to some preferred embodiments of the present invention,
Figure BDA0003100840230000068
and
Figure BDA0003100840230000069
obtained by the following process:
according to the conduction equation described in equation (3), the following dynamic stress components are obtained using generalized hooke's law:
Figure BDA00031008402300000610
wherein, lambda and mu represent Lame constants which can be obtained by calculating the rock elastic modulus E and Poisson ratio upsilon;
wherein, the solution of the displacement potential function can be obtained by:
solving the equation (3) by a Laplace transform method and substituting the equation into each edge value condition to obtain a dynamic displacement potential function of rock mass particles under a complex domain, wherein the dynamic displacement potential function comprises the following steps:
Figure BDA00031008402300000611
wherein k isd＝p/vp，vpRepresents the velocity of the longitudinal wave, p represents the laplacian,
Figure BDA00031008402300000612
representing the Laplace transform result of the force model F (t) at the tunnel boundary, K0And K1Second class of modified Bessel functions representing zeroth and first order, respectivelyA derivative of (a);
further solving by the numerical inverse transformation method proposed by Durbin yields:
Figure BDA0003100840230000071
wherein α represents an arbitrary real number between 0 and Re (p), Re () represents a real part, k represents the number of calculations, N represents the maximum number of calculations, i represents an imaginary unit, Im () represents an imaginary part, TiRepresents a solution time interval and T is more than or equal to 0 and less than or equal to Ti/2。
According to some preferred embodiments of the present invention,
Figure BDA0003100840230000072
and
Figure BDA0003100840230000073
the expression is obtained by the following procedure:
solving the equation (7) by a Laplace transform method to obtain the redistribution of the rock mass temperature in the tunnel ventilation process as follows:
Figure BDA0003100840230000074
wherein u represents an integral variable, TbIndicating the cooling gas temperature, T0Denotes the temperature of the original rock, J0、J1And Y0、Y1Zero and first order bezier functions representing the first and second classes, respectively.
Then, each thermal stress component can be obtained by the following formula:
Figure BDA0003100840230000075
where β represents the linear thermal expansion coefficient of the rock.
According to some preferred embodiments of the invention, the process of stress projection comprises:
a) converting the stress component under the cylindrical coordinate system into a Cartesian coordinate system as follows:
σx＝σrcos2θ+σθsin2θ-2τrθsinθcosθ
σy＝σrsin2θ+σθcos2θ+2τrθsinθcosθ
τxy＝(σr-σθ)sinθcosθ+τrθ(cos2θ-sin2θ) (11)；
b) obtaining the hydrostatic pressure I of the rock units in the model by1And difference of principal stress J2：
Figure BDA0003100840230000081
C) With I1Is shown as the abscissa of the graph,
Figure BDA0003100840230000082
and drawing stress tracks of the rock units under different variable parameters and basic design parameters in the whole process for the vertical coordinate.
According to some preferred embodiments of the invention, the method of analysis comprises: and determining the distribution range, the formation stage and the formation reason of the surrounding rock excavation damage by analyzing the relative position relationship between the stress track of the rock mass around the excavation outline and the yield surface of the rock mass.
The invention further provides an application of any one of the analysis methods, which is used for excavating the deep-buried high-temperature chamber.
According to some preferred embodiments of the invention, the applying comprises: and selecting proper variable parameters to form an optimal excavation scheme according to the distribution range, the formation stage and the formation reason of the surrounding rock excavation damage determined under different variable parameters.
The invention has the following beneficial effects:
(1) the analysis method of the invention establishes an analysis model of the whole process of tunnel excavation blasting-unloading-cooling under the condition of deep burying of a high-temperature chamber and the like, and solves the rock heat-force coupling response of the model under different geological conditions and excavation modes through a Laplace transform method and stress superposition in some specific embodiments, so that an accurate analysis and evaluation scheme can be obtained before actual excavation;
(2) the analysis method of the invention converts the complex rock mechanical behavior under different time scales into a stress invariant space through a stress projection technology, and further can visually judge the influence range of excavation damage, formation mechanisms (such as blasting, unloading and cooling) and mechanical mechanisms (such as tensioning, shearing expansion and shearing shrinkage) according to the relative position relationship between a stress track and a rock yield surface in specific implementation;
(3) compared with a numerical calculation or actual monitoring method, the analysis method disclosed by the invention can determine the distribution range of the excavation damage area, can also reveal the formation mechanism and the mechanical mechanism of rock mass damage, has the advantages of high calculation efficiency, short required time, low manpower and material resource consumption and the like, and can provide prediction and guidance for the adaptive excavation design of the underground chamber under the conditions of high temperature and high pressure.
Drawings
Fig. 1 is a schematic view of a thermal coupling model in the excavation process of a deep-buried high-temperature chamber according to the invention.
Fig. 2 is a surrounding rock stress trajectory evolution diagram under different excavation sizes obtained in example 1.
Fig. 3 shows the distribution characteristics of the surrounding rock damage areas of different excavation sizes obtained in example 1.
FIG. 4 is a surrounding rock stress trajectory evolution diagram obtained in example 1 at different unloading rates.
FIG. 5 is a distribution characteristic diagram of a surrounding rock damage zone at different unloading rates obtained in example 1.
FIG. 6 is a graph showing the evolution of stress traces of surrounding rocks under different stress conditions obtained in example 1.
FIG. 7 is a distribution characteristic diagram of the damaged area of the surrounding rock under different stress conditions obtained in example 1.
Fig. 8 is a graph showing the change of excavation damage with the temperature of the original rock under different stresses obtained in example 1.
Detailed Description
The present invention is described in detail below with reference to the following embodiments and the attached drawings, but it should be understood that the embodiments and the attached drawings are only used for the illustrative description of the present invention and do not limit the protection scope of the present invention in any way. All reasonable variations and combinations that fall within the spirit of the invention are intended to be within the scope of the invention.
According to the technical scheme of the invention, the specific surrounding rock excavation damage identification method comprises the following steps:
(1) establishing an overall process model for excavating and building the deep-buried high-temperature chamber, wherein the overall process of excavating and building comprises excavation blasting, ground stress unloading and cooling after unloading of the chamber, and the overall process model of excavation blasting, unloading and cooling of the deep-buried high-temperature chamber is obtained;
more specifically, a full process model as shown in FIG. 1 can be built, which includes the following variable parameters: excavation radius a and unloading time t of underground chamberduGround stress P0And temperature T of original rock0And the model based on the variable parameters is set as follows:
the chamber is obtained by excavating a circular tunnel with a long enough axis and a radius of a section in an infinite elastic homogeneous rock body by a full-section drilling and blasting method, and the profile surface of the tunnel is regarded as being formed by one-step excavation under the condition of plane strain;
the initial temperature of the elastic homogeneous rock mass is T0And is subjected to far-field hydrostatic pressure, i.e. ground stress P0The function of (1);
during the excavation process, when the pressure of the explosion wave is attenuated to be equal to the initial ground stress of the excavation boundary, the transient unloading of the ground stress is generated, and the ground stress P is simulated by applying reverse traction force on the wall of the hole along a linear path0At unloading time tduThe dynamic response of the lower excited rock mass;
after the chamber profile, namely the profile of the circular tunnel with the section radius of a, is formed, the chamber profile is cooled by cold air, and when the chamber profile is cooled to a specified time, the whole excavation process is completed.
Under the above configuration, the overall process model shown in fig. 1 can be embodied as follows: the thermal-force coupling response model of the deep-buried high-temperature chamber surrounding rock in the blasting-unloading and cooling processes as shown in fig. 1(a) is a dynamic mechanical response model caused by the blasting and unloading waves as shown in fig. 1(c) and a surrounding rock secondary stress adjustment model caused by the chamber ventilation and cooling as shown in fig. 1(d) which are superposed on the initial ground stress model as shown in fig. 1 (b).
Under the above arrangement, the present invention further comprises:
(2) obtaining basic design parameters required by the whole process model;
more specifically, in the overall process model shown in fig. 1, the required basic design parameters include:
explosive density, detonation wave velocity, detonation product isentropic index, detonation product thermal insulation constant, charge diameter, blast hole spacing, charge length, rock density, rock elastic modulus, rock poisson ratio, rock thermal expansion coefficient, rock thermal conduction coefficient, rock specific heat capacity and rock heat transfer coefficient.
(3) Setting a boundary stress model of the whole process model;
more specifically, in the overall process model illustrated in fig. 1, the chamber excavation boundary is determined by the following equispaced blast-relief wave pressure function f (t):
Figure BDA0003100840230000101
wherein the content of the first and second substances,
Figure BDA0003100840230000102
tr＝L/Vd，td＝2πtr/ln(2)，Fb0＝dbFe0/S；
wherein t represents time, Fb0Representing the equivalent peak pressure, d, acting on the tunnel profilebIndicating the diameter of the hole, S the distance between adjacent holes, Fe0Indicating the peak pressure of the blast hole wall, delta indicating the attenuation coefficient of the explosion stress wave, trIndicating the time at which the explosive load reaches a peak, L the length of the charge, VdIndicates detonation wave velocity, tdRepresenting the duration of the blast wave, tuIndicates the unloading end time (i.e., the earth stress unloading end time), tduDenotes the unloading time, P0Representing the ground stress.
Wherein the peak pressure F of the blast hole walle0The method can be further calculated by the following C-J detonation theoretical model:
Figure BDA0003100840230000111
where ρ iseDenotes the density of the explosive, deRepresenting the charge diameter, and gamma and eta represent the isentropic index and adiabatic constant, respectively, of the detonation product.
(4) Setting process control equations of the whole process model at different time periods, wherein the process control equations comprise: the propagation equation of dynamic stress waves in surrounding rocks in the excavation blasting-unloading process and the heat conduction equation for describing the temperature change of the surrounding rocks in the tunnel ventilation cooling process are adopted;
more specifically, the propagation model of the dynamic stress wave in the surrounding rock is shown in fig. 1(c), and the propagation equation is set as follows:
Figure BDA0003100840230000112
wherein r represents the distance between the surrounding rock constitution point and the center of the chamber under the cylindrical coordinate system,
Figure BDA0003100840230000113
representing the displacement potential function, v, of the mass point of the surrounding rock mass in a cylindrical coordinate systempRepresents the longitudinal wave velocity of the dynamic stress wave when the dynamic stress wave propagates in the surrounding rock mass medium,
Figure BDA0003100840230000114
and (3) representing the radial dynamic stress function of the surrounding rock mass under the cylindrical coordinate system.
More specifically, the heat conduction model in the tunnel ventilation and cooling process is shown in fig. 1(d), and the conduction equation is set as follows:
Figure BDA0003100840230000121
wherein T (r, T) represents a redistribution function of rock mass temperature, rhorRepresenting rock density, C representing specific heat capacity of rock, k representing heat conduction coefficient of rock, T (a, T) representing temperature of hole wall unit, TuIndicating the ground stress unloading end time, TbAnd H is H/k, wherein H represents the heat exchange coefficient of the rock.
(5) Solving the process control equation, obtaining the dynamic stress of the surrounding rock mass at different times according to the propagation equation of the dynamic stress wave in the surrounding rock, and obtaining the thermal stress of the surrounding rock mass at different times according to the heat conduction equation in the tunnel ventilation cooling process;
more specifically, solving the propagation equation may include:
according to the propagation equation, the dynamic stress component of the rock mass in the excavation process is obtained by utilizing the generalized Hooke's law as follows:
Figure BDA0003100840230000122
wherein the content of the first and second substances,
Figure BDA0003100840230000123
and
Figure BDA0003100840230000124
respectively representing dynamic radial stress, hoop stress and out-of-plane normal direction stress of the surrounding rock mass under a cylindrical coordinate system; λ and μ represent Lame constants which can be obtained by calculating the elastic modulus E and Poisson ratio upsilon of rock mass;
Figure BDA0003100840230000125
representing dynamic shear stress；
Solving the control equation (3) by a Laplace transform method and substituting the solution into each edge value condition to obtain a dynamic displacement potential function of rock mass particles under a complex domain, wherein the dynamic displacement potential function comprises the following steps:
Figure BDA0003100840230000131
wherein k isd＝p/vp，vpRepresents the velocity of the longitudinal wave, p represents the laplacian,
Figure BDA0003100840230000134
representing the Laplace transform result of the force model F (t), K0And K1Derivatives of a second class of modified Bessel functions representing zeroth and first orders, respectively;
further solving by the numerical inverse transformation method proposed by Durbin yields:
Figure BDA0003100840230000132
wherein α represents an arbitrary real number between 0 and Re (p), Re () represents a real part, k represents the number of calculations, N represents the maximum number of calculations, i represents an imaginary unit, Im () represents an imaginary part, TiRepresents a solution time interval and T is more than or equal to 0 and less than or equal to Ti/2。
More specifically, solving the heat transfer equation may include:
solving the heat conduction control equation (7) by adopting a Laplace transform method to obtain the following redistribution of the rock mass temperature in the tunnel ventilation process:
Figure BDA0003100840230000133
wherein u represents an integral variable, J0、J1And Y0、Y1The 0 th order and 1 st order bezier functions represent the first and second classes, respectively.
The thermal stress in the retained rock mass produced by the aeration cooling process can then be obtained by:
Figure BDA0003100840230000141
wherein beta represents the linear thermal expansion coefficient of the rock,
Figure BDA0003100840230000142
and
Figure BDA0003100840230000143
respectively representing radial thermal stress, circumferential thermal stress and out-of-plane normal direction thermal stress of the surrounding rock mass under the cylindrical coordinate system;
Figure BDA0003100840230000144
representing the shear stress resulting from cooling;
(5) obtaining a surrounding rock thermal coupling response model through the dynamic stress borne by the surrounding rock mass, the thermal stress borne by the surrounding rock mass and the initial ground stress;
more specifically, the thermodynamic coupling response model is set as follows:
Figure BDA0003100840230000145
wherein σr、σθAnd σzRespectively representing radial total coupling stress, circumferential total coupling stress and out-of-plane normal direction total coupling stress of the surrounding rock mass under a cylindrical coordinate system; tau isrθRepresenting the total shear stress of the coupling.
(6) Projecting the obtained surrounding rock thermal coupling response model to a stress invariant space through stress projection, and further obtaining a rock stress track curve in the whole process of blasting, unloading and cooling, wherein the rock stress track curve contains variable parameters representing different geological conditions and excavation modes and basic design parameters;
more specifically, it may comprise
a) Converting the stress component under the cylindrical coordinate system into a Cartesian coordinate system as follows:
σx＝σrcos2θ+σθsin2θ-2τrθsinθcosθ
σy＝σrsin2θ+σθcos2θ+2τrθsinθcosθ
τxy＝(σr—σθ)sinθcosθ+τrθ(cos2θ-sin2θ) (11)；
b) obtaining the hydrostatic pressure I of the rock units in the model by1And difference of principal stress J2：
Figure BDA0003100840230000151
C) With I1Is shown as the abscissa of the graph,
Figure BDA0003100840230000152
and drawing stress tracks of the rock units under different variable parameters and basic design parameters in the whole process of blasting, unloading and cooling for the ordinate.
(7) And analyzing the relative position relation between the rock stress track around the excavation outline and the yield surface of the rock stress track through the obtained rock stress track curve, obtaining the relation between the variable parameter and the distribution range, formation mechanism and mechanical mechanism of rock excavation damage, obtaining rock thermal power coupling response and the time-space evolution rule of the surrounding rock damage area under different geological conditions and excavation modes, and further determining the actual excavation scheme.
Wherein the forming mechanism comprises blasting, unloading or cooling, and the mechanical mechanism comprises tensioning, shear expansion or shear contraction.
When the blasting, unloading or cooling stress track intersects with the yield surface, the surrounding rock is considered to be respectively subjected to blasting, unloading and cooling damage. Meanwhile, the mechanical mechanism of the surrounding rock damage can be judged according to the intersection point position of the stress track and the yielding surface, such as:
a. when the intersection point is positioned at the tensile yield section, the surrounding rock generates tensile damage;
b. when the intersection point is positioned at the shear-expansion yield section, the surrounding rock generates shear-expansion damage;
c. when the intersection point is located the cap section, the country rock produces the damage of shearing shrinkage.
Example 1
The simulation experiment is carried out by the specific scheme of the specific embodiment under the condition that the rocks around the deep-buried high-temperature chamber are mainly indiana limestone.
Wherein, the excavation design scheme is shown in the following table 1, and the use temperature T is used in the cooling processaAirflow at 15 ℃, ventilation time 15 days:
TABLE 1 model protocol
Figure BDA0003100840230000153
Figure BDA0003100840230000161
The basic design parameters are shown in table 2 below:
TABLE 2 excavation blasting-unloading-cooling model base design parameters
Figure BDA0003100840230000162
In the process of solving the numerical inverse transformation, taking alpha to be 0.2, TiThe number of iterations N is 5000 for 40 ms.
Under the above conditions, a lesion analysis chart as shown in FIGS. 2 to 8 can be obtained, in which:
fig. 2 shows stress track evolution of a tunnel boundary unit surrounding rock mass under different excavation radius parameters a in the whole process of blasting, unloading and cooling, wherein a solid circle represents an intersection point of different stress tracks and an initial yield surface, namely a point representing that a rock starts to form damage, and corresponding surrounding rock damage distribution characteristics caused by excavation blasting, unloading and cooling are shown in fig. 3.
FIG. 4 shows different unloading rates (unloading time t)du) And (3) evolving the surrounding rock mass stress track of the boundary unit of the tunnel, wherein the solid circles represent intersection points of different stress tracks and the initial yielding surface, namely represent points where the rock starts to form damage, and the corresponding surrounding rock excavation damage distribution characteristics are shown in the attached drawing 5.
Fig. 6 shows the evolution of the stress trajectories of the surrounding rock masses of the boundary unit of the tunnel under different stresses, wherein the solid circles represent the intersection points of the different stress trajectories and the initial yielding surface, namely the points representing the initial damage formation points of the rock, and the corresponding surrounding rock excavation damage distribution characteristics are shown in fig. 7.
Fig. 8 is a statistical graph of the change rule of the surrounding rock damage under different stresses along with the temperature of the original rock, namely a heat damage development rule graph, wherein the temperature values are different temperatures of the original rock, and the time values are the time for generating heat damage to the surrounding rock mass of the boundary unit of the tunnel.
As can be seen from the above figures:
under different chamber excavation radius parameters a:
as can be seen from fig. 2, under the action of the blasting load, the stress trace of the tunnel boundary unit with a smaller excavation radius exceeds the shear yield surface, and finally blasting shear-expansion damage is caused in the reserved rock body (fig. 3 (a)). As the excavation radius increases, the stress path created by the blast loading becomes flatter and does not intersect the rock yield face, so the blast loading cannot cause excavation damage to the retained rock mass (fig. 3(b) and (c)). During the transient unloading process of the ground stress, the unloading stress track is further extended out of the shear yield surface due to the larger excavation radius (figure 2), so that stronger unloading shear expansion damage is caused in the reserved rock body (figure 3). During the subsequent aeration cooling process, the thermal damage range of the surrounding rock gradually expands along with the increase of the radius of the chamber (figure 3).
At different unloading rates (unloading time t)du) The following:
as can be seen from fig. 4-5, the tendency of the stress trace to move toward the tensile yield surface is more pronounced as the unloading rate increases. When the rate of unloading is sufficiently fast, dynamic tensile stresses will be induced in the rock mass due to the rapid release of the ground stress, which may lead to the formation of unloading tensile damage. After the radial stress unloading is finished, due to the influence of inertia effect, additional annular dynamic stress is generated in the rock mass, the higher the unloading speed is, the larger the dynamic stress amplitude is, the more the stress track exceeds the shear yield surface, and finally stronger unloading shear expansion damage is caused in the reserved rock mass (fig. 5).
At different ground stress P0The following:
as can be seen from fig. 6 and 7, as the magnitude of the ground stress increases, the blasting stress trajectory gradually shifts to the upper right in the stress invariant space and continuously moves away from the shear yield plane as the initial stress state changes due to the increase of the ground stress, thereby suppressing the formation of blasting damage. However, in the process of releasing the ground stress, the higher the confining pressure magnitude is, the higher the circumferential additional dynamic stress is caused, and further stronger unloading damage is generated. In addition, since the ground stress can suppress the relaxation of the rock mass pressure caused by temperature reduction, the thermal damage range tends to decrease monotonically as the ground stress increases.
Under different geothermal conditions (i.e. different stresses and temperature T of the source rock)0) The following:
as can be seen from fig. 8, under a given geostress condition, the surrounding rock with higher temperature will generate a larger range of thermal damage under the same cooling medium, and the increase of the magnitude of the geostress will inhibit the development of the thermal damage of the surrounding rock under the same geothermal environment. In addition, under the same cooling air flow, the higher the initial temperature of the surrounding rock, the faster the heat exchange rate, so the secondary stress adjustment is more severe, and the heat damage of the surrounding rock occurs earlier (fig. 8). Meanwhile, the rise of the confining pressure offsets the relaxation of the rock mass pressure caused by the temperature reduction of the tunnel, so that the occurrence time of the thermal damage is remarkably delayed along with the increase of the magnitude of the ground stress under the same geothermal condition (figure 8).
In conclusion, the analysis method disclosed by the invention effectively reveals the formation mechanism, the mechanical mechanism and the evolution characteristics of the damage of the surrounding rock under different ground pressure and ground temperature conditions and excavation modes, and can provide important practical assistance for the excavation design of the underground chamber under the deep high-temperature and high-pressure conditions.
The above examples are merely preferred embodiments of the present invention, and the scope of the present invention is not limited to the above examples. All technical schemes belonging to the idea of the invention belong to the protection scope of the invention. It should be noted that modifications and embellishments within the scope of the invention may be made by those skilled in the art without departing from the principle of the invention, and such modifications and embellishments should also be considered as within the scope of the invention.

Claims (10)

1. The method for analyzing the surrounding rock excavation damage under the thermal coupling condition is characterized by comprising the following steps of: the method comprises the following steps:
establishing a tunnel excavation whole-process thermodynamic coupling model containing variable parameters, wherein the thermodynamic coupling model comprises the coupling of ground stress, dynamic stress and thermal stress;
setting basic design parameters of the overall process thermodynamic coupling model, wherein the basic design parameters comprise blasting related parameters and rock thermodynamic parameters;
setting a stress model of the surrounding rock mass at the tunnel boundary based on the whole-process thermodynamic coupling model and the basic design parameters;
setting process control equations of the surrounding rock mass in different excavation processes based on the overall process thermal coupling model and the basic design parameters, wherein the process control equations comprise state equations and boundary conditions, the state equations comprise dynamic stress conduction equations and heat conduction equations, and the boundary conditions comprise stress models at the boundaries;
solving the process control equation to obtain the dynamic stress and the thermal stress of the surrounding rock mass in different processes;
obtaining a surrounding rock thermodynamic coupling model according to the dynamic stress, the thermal stress and the coupling of the dynamic stress and the thermal stress with the initial ground stress;
projecting the obtained surrounding rock thermal coupling model to a stress invariant space through stress projection to obtain a surrounding rock mass stress trajectory curve in the whole surrounding rock excavation process under different variable parameters;
obtaining the distribution range, the formation stage and the formation reason of the surrounding rock mass excavation damage under different variable parameters according to the stress trajectory curve;
preferably, the formation cause includes a tension formation, a shear bulge formation or a shear shrink formation.
2. The analytical method of claim 1, wherein: the whole tunnel excavation process comprises three stages of excavation blasting, ground stress unloading and cooling after unloading; the variable parameters comprise tunnel excavation radius a and unloading time tduGround stress P0And temperature T of original rock0。
3. The analytical method of claim 2, wherein: the establishment of the whole-process thermodynamic coupling model comprises the following setting conditions:
the tunnel is excavated in an infinite elastic homogeneous rock body by a full-section drilling and blasting method, the axis of the tunnel is long enough, the section of the tunnel is a circle with the radius of a, and the profile surface of the tunnel is formed by one-step excavation under the condition of plane strain;
the initial temperature of the elastic homogeneous rock mass is the original rock temperature T0And is subjected to far-field hydrostatic pressure, i.e. the ground stress P0The function of (1);
during excavation, when the pressure of the explosion wave is attenuated to be equal to the initial ground stress of the excavation boundary, transient unloading of the ground stress is generated, and the ground stress P is simulated by applying reverse traction force on the wall of the hole along a linear path0At unloading time tduThe dynamic response of the lower excited rock mass;
after the chamber profile, namely the profile of the circular tunnel with the section radius of a, is formed, the chamber profile is cooled by cold air, and when the chamber profile is cooled to a specified time, the whole excavation process is completed.
4. The analytical method of claim 1, wherein: the basic design parameters include: the explosive density, the detonation wave velocity, the detonation product isentropic index, the detonation product thermal insulation constant, the charge diameter, the blast hole spacing, the charge length, the rock density, the rock elastic modulus, the rock Poisson ratio, the rock thermal expansion coefficient, the rock thermal conduction coefficient, the rock specific heat capacity and the rock heat exchange coefficient.
5. The analytical method of claim 1, wherein: the solution is implemented by the laplace transform method.
6. The analytical method of claim 1, wherein: the stress model at the tunnel boundary comprises:
Figure FDA0003100840220000021
wherein the content of the first and second substances,
Figure FDA0003100840220000022
tr＝L/Vd，td＝2πtr/ln(2)，Fb0＝dbFe0/S；
wherein t represents time, Fb0Representing the equivalent peak pressure, d, acting on the tunnel profilebIndicating the diameter of the hole, S the distance between adjacent holes, Fe0Indicating the peak pressure of the blast hole wall, delta indicating the attenuation coefficient of the explosion stress wave, trIndicating the time at which the explosive load reaches a peak, L the length of the charge, VdIndicates detonation wave velocity, tdRepresenting the duration of the blast wave, tuIndicating the end time of unloading, tduDenotes the unloading time, P0Representing the ground stress.
7. The analytical method of claim 6, wherein: the process control equation includes:
Figure FDA0003100840220000031
wherein r represents a column seatMarking the distance between the mass point of the lower surrounding rock and the center of the chamber,
Figure FDA0003100840220000032
representing the displacement potential function, v, of the mass point of the surrounding rock mass in a cylindrical coordinate systempRepresents the longitudinal wave velocity of the dynamic stress wave when the dynamic stress wave propagates in the surrounding rock mass medium,
Figure FDA0003100840220000033
representing a radial dynamic stress function of the surrounding rock mass under a cylindrical coordinate system;
and/or:
Figure FDA0003100840220000034
wherein T (r, T) represents a redistribution function of rock mass temperature, rhorRepresenting rock density, C representing specific heat capacity of rock, k representing heat conduction coefficient of rock, H ═ H/k, wherein H represents heat exchange coefficient of rock, T (a, T) represents temperature of cavity wall unit obtained according to redistribution function T (r, T) of rock temperature, T (a, T) represents temperature of cavity wall unit obtained according to redistribution function T (r, T) of rock temperatureuIndicating the end time of unloading, TbIndicating the cooling gas temperature.
8. The analytical method of claim 7, wherein: the surrounding rock thermal coupling model comprises:
Figure FDA0003100840220000035
wherein σr、σθAnd σzRespectively representing radial total coupling stress, circumferential total coupling stress and out-of-plane normal direction total coupling stress of the surrounding rock mass under a cylindrical coordinate system; tau isrθRepresents the total coupled shear stress;
Figure FDA0003100840220000041
and
Figure FDA0003100840220000042
respectively representing the dynamic radial stress, the circumferential stress and the out-of-plane normal direction stress of the surrounding rock mass under a cylindrical coordinate system,
Figure FDA0003100840220000043
Representing a dynamic shear stress obtained by solving the dynamic stress conduction equation;
Figure FDA0003100840220000044
and
Figure FDA0003100840220000045
respectively representing the radial thermal stress, the circumferential thermal stress and the out-of-plane normal direction thermal stress of the surrounding rock mass under the cylindrical coordinate system,
Figure FDA0003100840220000046
Represents the shear stress resulting from the temperature change, which is obtained by solving the heat conduction equation.
9. The analytical method of claim 8, wherein: the process of stress projection comprises:
a) converting the stress component under the cylindrical coordinate system into a Cartesian coordinate system as follows:
σx＝σrcos2θ+σθsin2θ-2τrθsinθcosθ
σy＝σrsin2θ+σθcos2θ+2τrθsinθcosθ
τxy＝(σr—σθ)sinθcosθ+τrθ(cos2θ-sin2θ)(11)；
b) obtaining the hydrostatic pressure I of the rock units in the model by1And difference of principal stress J2：
Figure FDA0003100840220000047
C) With I1Is shown as the abscissa of the graph,
Figure FDA0003100840220000048
and drawing stress tracks of the rock units under different variable parameters and basic design parameters in the whole excavation process for the vertical coordinate.
10. Use of the analytical method of any one of claims 1 to 9 for excavating deep-buried high-temperature chambers.
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