CN113155699A - Rock statistical damage calculation method under combined action of heat, water and force and application thereof - Google Patents
Rock statistical damage calculation method under combined action of heat, water and force and application thereof Download PDFInfo
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Abstract
The invention provides a heat-water-force combined rock statistical damage calculation method, and also provides a test device applying the calculation method, which comprises the following steps: high temperature heating device (<100 ℃), seepage device, pressure chamber, base testboard, pressure applying element, top plate, stress detecting element, strain detecting element, temperature detecting element, water flow detecting element and automatic detecting data acquisition device. The calculation process of the invention is more complex, the invention has stronger comprehensiveness, and the invention is applied to the rock triaxial compression seepage test, and the proposed new model has stronger comprehensiveness and applicability than the existing model, and has higher fitting degree to the stress-strain curve obtained by the test. The deformation and damage characteristics of the rock under the action of different temperatures are reflected, the trend of the post-peak stage is fully reflected, and the stress-strain relation of the high-temperature rock under the condition of the triaxial compression-seepage coupling test can be better reflected.
Description
Technical Field
The invention relates to the technical field of a rock statistical damage model calculation method, in particular to a rock statistical damage calculation method under the combined action of heat, water and force and application thereof.
Background
With the continuous development of high-temperature rock mass and underground engineering construction such as geothermal resource development, deep mineral resource exploitation and the like, the related research on the physical and mechanical properties of high-temperature rock is more and more. Under normal conditions, the mechanical properties of the rock are degraded under the action of high temperature, and the bearing capacity and the stability of the rock are further influenced, so that the establishment of an objective and reasonable constitutive model is the key for understanding and judging the mechanical properties of the rock under the action of high temperature.
For the research aspect of the constitutive model, the statistical damage constitutive model can reasonably describe the defects of the rock damage evolution process, and can better reflect the mechanical mechanism of the rock damage under the action of high temperature. But the research on the statistical damage constitutive relation of the rock under the condition of high-temperature-seepage coupling is rarely related.
Disclosure of Invention
The invention aims to solve the problem that the prior art has no research on a calculation method for statistical damage under the condition of high-temperature-seepage coupling, and particularly provides a calculation method for statistical damage of rocks, which can reflect the stress-strain process of the rocks under the action of high-temperature-seepage coupling and has high fitting degree with a partial stress-strain curve, and the calculation method is applied to an actual test and compared with a test value to verify the rationality of a constructed model.
In order to achieve the purpose, the technical scheme of the invention is as follows:
a heat-water-force combined rock statistical damage calculation method comprises the following steps:
s1: defining a thermal damage parameter DTSaid thermal damage parameter DTThe method is used for representing the influence of temperature on the stress performance of the rock;
s2: defining a force damage parameter D for representing the influence of the load on the stress performance of the rock, and establishing an constitutive relation of the rock damage under the action of force to represent the influence of the force on the stress performance of the rock;
s3: and (3) establishing a statistical damage constitutive model of the rock under the combined action of heat, water and force so as to represent the influence of the combined action of heat, water and force on the stress performance of the rock.
Further, the specific method of S1 is as follows:
s11: definition for characterizing thermal damage D of rock under temperature TTComprises the following steps:
in the formula: eTIs the modulus of elasticity under the influence of the temperature T, E0Is the modulus of elasticity at normal temperature;
s12: assuming that the strength of the rock infinitesimal body under the action of the temperature T follows the Weibull distribution function, then
In the formula: x is the intensity value of infinitesimal body, mTIs a parameter affecting the shape of the rock infinitesimal under the action of temperature T, KTIs a parameter influencing the size of the rock infinitesimal body under the action of the temperature T;
s13: the formula characterizing the effect of temperature on the statistical constitutive model of rock damage is as follows:
in the formula: m is0Is a parameter affecting the shape of the rock infinitesimal body at normal temperature, K0The parameters influencing the size of the rock infinitesimal body at normal temperature; m isTFor parameters affecting the shape of the rock infinitesimal under the effect of the temperature T, KTIs a parameter influencing the size of the rock infinitesimal body under the action of the temperature T.
Further, the specific method of S2 is as follows:
s21: defining a continuous damage variable D characterizing the rock under force:
in the formula: n is a radical ofFThe number of rock micro-elements which are damaged under the action of temperature T under a certain stress state; n is the total number of rock micro-elements; f (sigma'ij) Is micro element strength, sigma'ijIs the effective stress tensor under the seepage effect;
s22: correcting the effective stress principle aiming at the seepage problem to obtain:
σ’ij＝σij-b△Pδij (5)
in the formula: sigmaijThe stress tensor is under the seepage effect, and the delta P is the osmotic pressure difference; deltaijIs a unit second order tensor; b is the Biot coefficient;
s23: introducing a damage correction coefficient eta, and establishing a rock damage constitutive relation under the action of force:
in the formula,
stress-effective stress under percolation; sigmaiStress under stress-seepage action;
the effective stress tensor under stress-seepage action is derived from the formula (5) and the formula (6):
in the formula, σ* ijIs the effective stress tensor, delta, under stress-seepageij＝1；
S24: according to the generalized Hooke's law, the axial stress-strain relation of rock stress-strain under the action of temperature T is obtained as follows:
in the formula, σ1、σ2、σ3Respectively principal stress in three directions under stress-seepage action, wherein sigma1Is the axial stress under the action of stress-seepage; sigma2Is the shear stress under the action of stress-seepage; sigma3Is confining pressure under the action of stress-seepage;
for effective axial stress under stress-seepage action,
is the effective shearing stress under the stress-seepage action,
effective confining pressure under the action of stress-seepage; mu.sTIs the poisson's ratio at temperature T.
Further, the specific method of S3 is as follows:
s31: and (3) respectively substituting the effective stress tensor of the formula (7) into a formula (8) to obtain the axial stress-strain relation under the action of the osmotic pressure:
σ1＝ETε1(1-ηD)+2μTσ3+(1-2μT)△P (9)
s32: the rock infinitesimal body strength is calculated as follows:
in the formula phiTThe internal friction angles of the rock under the action of the temperature T are respectively;
combining equations (7) and (9), equation (10) converts to:
axial offset stress sigma recorded according to triaxial seepage test1tIn fact the axial stress sigma1With confining pressure σ3The difference of (a) is:
σ1t＝σ1-σ3 (12)
loaded biasing force σ1tFirst of all the confining pressure σ is loaded3And pore water pressure, i.e. osmotic pressure difference, Δ P, so that the initial strain, ε, has been established0Comprises the following steps:
micro element strength f (sigma'ij) Of1tMeasuring strain values epsilon for the test1With initial strain epsilon0And (c) the sum, i.e.:
ε1t＝ε1+ε0 (14)
by substituting formula (12) and formula (14) into formula (11), there can be obtained:
according to the formula (9), the constitutive models of the statistical damage of the rock considering the combined action of heat, water and force under the triaxial condition can be obtained through the formulas (12) to (15):
further, said mT、KTThe determination method of (2) is as follows:
the model parameters are solved by using a linear fitting method, and the formula (16) is converted into:
two sides of the equation are logarithmized twice at the same time and simplified, and the following can be obtained:
Y＝mTX-B (18)
wherein,
X＝lnf(σ’ij) (19)
B＝mT ln KT (21)
linear fitting by experimental dataTo obtain mTAnd B value, and then K can be obtainedTComprises the following steps:
a test device applying the rock statistical damage calculation method is characterized by comprising the following steps: the device comprises a high-temperature heating device, a seepage device, a pressure chamber, a base test board, a pressing element, a top plate, a stress detection element, a strain detection element, a temperature detection element, a water flow detection element and an automatic data acquisition device; the data automatic acquisition device comprises a data processor and a data monitor, wherein the data processor is used for obtaining the influence result of the combined action of heat-water-force on the stress performance of the rock under the test condition through the rock statistical damage constitutive model under the combined action of heat-water-force; the data monitor is used for monitoring the influence result of the combined action of heat, water and force on the stress performance of the rock under the test condition;
the high-temperature heating device is connected with the pressure chamber and is used for adjusting the temperature in the pressure chamber;
the pressure chamber is arranged on the base test bench, and the pressing element is arranged between the pressure chamber and the top plate;
the seepage device comprises two water permeable gaskets, a water inlet and a water outlet and is arranged in the pressure chamber, and the rock to be tested is placed between the two water permeable gaskets in the seepage device; the pore water enters the seepage device through the water inlet via the seepage gasket, and then flows out of the test piece through the water outlet via the seepage gasket.
The stress detection element, the strain detection element and the temperature detection element are all fixed on the rock to be detected;
the water flow detection element is arranged above the seepage device and is used for detecting the water flow passing through the interior of the rock within a fixed time;
the automatic data acquisition device is connected with the stress detection element, the strain detection element, the temperature detection element and the water flow detection element so as to acquire the acquired heat, water and force related parameters of the rock to be detected.
Has the advantages that: the calculation process is complex, the comprehensive performance is high, the method is applied to the rock triaxial compression seepage test under the action of heat-water-force, the provided new calculation method is high in comprehensive performance and applicability compared with the existing model, and the fitting degree of the stress-strain curve obtained by the test is high.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings needed to be used in the description of the embodiments or the prior art will be briefly introduced below, and it is obvious that the drawings in the following description are some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to these drawings without creative efforts.
FIG. 1 is a schematic diagram of a testing apparatus applying the statistical damage calculation method for rocks according to the present invention;
fig. 2(a) is a graph comparing the experimental values with the theoretical curve under the environment of 30MPa ambient pressure and 5MPa osmotic pressure difference at 90 ℃ in T obtained in the example of the present invention;
fig. 2(b) is a graph comparing the experimental values with the theoretical curve under the environment of 30MPa ambient pressure and 5MPa osmotic pressure difference at 70 ℃ in T obtained in the example of the present invention;
fig. 2(c) is a graph comparing the experimental values with the theoretical curve under the environment of 30MPa ambient pressure and 5MPa osmotic pressure difference at 50 ℃ in T obtained in the example of the present invention;
fig. 2(d) is a graph comparing the experimental values with the theoretical curves at 40 ℃ under the environment of 30MPa ambient pressure and 5MPa osmotic pressure difference obtained in the example of the present invention;
FIG. 3 is a diagram of the steps of a statistical damage calculation method for rock under the combined action of heat, water and force according to the invention;
FIG. 4 is a diagram illustrating the evolution rule of permeability of red sandstone under the action of 5MPa of osmotic pressure difference and different temperatures in one embodiment of the present invention;
FIG. 5 is a schematic illustration of a seepage test in one embodiment of the present invention;
FIG. 6(a) shows the confining pressure and different osmotic pressures of the invention at 10MPaPermeability k and damage index D under differenceTThe associated characteristic curve of (a);
FIG. 6(b) is a graph showing the permeability k and the damage index D of the present invention under a confining pressure of 20MPa and different osmotic pressure differencesTThe associated characteristic curve of (a);
FIG. 6(c) is a graph showing the permeability k and the damage index D of the present invention under a confining pressure of 30MPa and different osmotic pressure differencesTThe associated characteristic curve of (1).
In the figure: 1. high temperature heating device (<100 ℃); 2. a seepage device; 3. a pressure chamber; 4. a base test bench; 5. a pressing member; 6. a top plate; 7. a stress detection element; 8. a strain detecting element; 9. a temperature detection element; 10. a water flow detection element 11 and an automatic detection data acquisition device; 21. pore water; 22. a water permeable gasket; 23. a water inlet; 24. a water outlet; 11-1, a data processor; 11-2 and a data monitor.
Detailed Description
In order to make the objects, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are some, but not all, embodiments of the present invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
A method for calculating statistical damage to a rock under thermal-hydraulic-force effect, the method comprising the steps of:
s1: when the temperature is high, a large number of microscopic cracks are generated in the rock and gradually spread with the increase of the temperature, so that the elastic modulus is remarkably reduced, thereby defining the thermal damage DTTo characterize the effect of temperature on the stress performance of the rock; because the invention considers rock damage under the combined action of heat, water and force, the high temperature in the invention is less than 100 ℃.
S11: definition for characterizing thermal damage D of rock under temperature TTComprises the following steps:
in the formula: eTIs the modulus of elasticity under the influence of the temperature T, E0Is the modulus of elasticity at normal temperature (20 ℃);
s12: under the action of the temperature T, the rock material particles are not uniform and are distributed randomly, and meanwhile, the rock micro-elements contain a large number of micro-cracks and cracks, and the strength values of the rock micro-elements are also changed randomly. Assuming that the strength of the rock infinitesimal body under the action of the temperature T follows the Weibull distribution function, then
In the formula: x is the intensity value of infinitesimal body, mTAnd KTAre parameters relating to the shape, respectively the size of the rock infinitesimal directly influenced by the temperature T of the Weibull distribution function, where mTIs a parameter affecting the shape of the rock infinitesimal under the action of temperature T, KTIs a parameter influencing the size of the rock infinitesimal body under the action of the temperature T;
s13: the formula characterizing the effect of temperature on the statistical constitutive model of rock damage is as follows:
in the formula: m is0Is a parameter affecting the shape of the rock microelement at normal temperature (20 ℃), K0The parameters influencing the size of the rock infinitesimal body at normal temperature (20 ℃); m isTFor parameters affecting the shape of the rock infinitesimal under the effect of the temperature T, KTIs a parameter influencing the size of the rock infinitesimal body under the action of the temperature T.
S2: under the action of force, the original micro cracks in the rock expand and evolve, so that the rock is continuously damaged, and therefore the constitutive relation of the rock damage under the action of force is established to represent the influence of load on the stress performance of the rock;
s21: the continuous damage variable D, which is defined to characterize the rock under force, is:
in the formula: n is a radical ofFThe number of rock micro-elements which are damaged under the action of temperature T under a certain stress state; n is the total number of rock micro-elements; f (sigma'ij) Is micro element strength, sigma'ijIs the effective stress tensor under the seepage effect;
s22: in the porous medium elastic theory framework, the M.A.Biot corrects the effective stress principle aiming at the seepage problem to obtain:
σ’ij＝σij-b△Pδij (5)
in the formula: sigmaijThe stress tensor is under the seepage effect, and the delta P is the osmotic pressure difference; deltaijIs a unit second order tensor, δij1(i ═ j), otherwise δij0(i ≠ j); b is a Biot coefficient, the value range is 0-1, and for convenience of research, b is taken as 1;
s23: according to the Lemailtre strain equivalence principle and the effective stress concept, the strain generated by the rock under the stress condition (nominal stress) measured in the test is equal to the effective strain generated by the damaged rock under the effective stress condition. Because of the influence of the friction force and the confining pressure of the test piece, the internal infinitesimal body still has the capability of transmitting the compression shear stress after being damaged, and certain residual strength exists, so that a damage correction coefficient eta is introduced, and the rock damage constitutive relation is established:
in the formula,
stress-effective stress under percolation; sigmaiStress under stress-seepage action;
the effective stress tensor under stress-seepage action is derived from the formula (5) and the formula (6):
in the formula, σ* ijIs the effective stress tensor, delta, under stress-seepageij＝1；
S24: because the rock stress-strain has an obvious elastic stage under the action of the temperature T, the axial stress-strain relation of the rock stress-strain under the action of the temperature T is obtained according to the generalized Hooke's law as follows:
in the formula, σ1、σ2、σ3Respectively principal stress in three directions under stress-seepage action, wherein sigma1Is the axial stress under the action of stress-seepage; sigma2Is the shear stress under the action of stress-seepage; sigma3Is confining pressure under the action of stress-seepage;
for effective axial stress under stress-seepage action,
is the effective shearing stress under the stress-seepage action,
is the effective confining pressure under the action of stress-seepage.
S3: establishing a statistical damage constitutive model of the rock under the combined action of heat, water and force so as to represent the influence of the combined action of heat, water and force on the stress performance of the rock; and further, a stress-strain relation of the rock reflected by the stress-strain relation provides a guidance basis for the stability evaluation and design parameter adjustment of the fire tunnel.
S31: in conventional triaxial rock testing, σ1>σ2＝σ3Since in conventional calculations, σij＝σiTherefore, the effective stress tensor of the formula (7) is respectively substituted into the formula (8), and the stress-strain relation in the axial direction under the consideration of osmotic pressure is obtained:
σ1＝ETε1(1-ηD)+2μTσ3+(1-2μT)△P (9)
s32: during the uniaxial and triaxial tests of the rock, when the temperature is increased, the internal friction angle of the rock is gradually increased, and conversely, the cohesive force is reduced, so that the internal friction angle is gradually reduced. Because the M-C strength criterion has the characteristics of simple parameters, easy calculation, suitability for rock analysis and the like, the M-C strength criterion is adopted in the embodiment to describe the rock infinitesimal body strength as follows:
in the formula phiTThe internal friction angles of the rock under the action of the temperature T are respectively;
combining equations (7) and (9), equation (10) converts to:
axial offset stress sigma recorded according to triaxial seepage test1tIn fact the axial stress sigma1With confining pressure σ3The difference of (a) is:
σ1t＝σ1-σ3 (12)
in tests, the biasing force σ was loaded1tFirst of all the confining pressure σ is loaded3And pore water pressure, i.e. osmotic pressure difference, Δ P, so that the initial strain, ε, has been established0Comprises the following steps:
micro element strength f (sigma'ij) Of1tMeasuring strain values epsilon for the test1With initial strain epsilon0And (c) the sum, i.e.:
ε1t＝ε1+ε0 (14)
by substituting formula (12) and formula (14) into formula (11), there can be obtained:
according to the formula (9), the constitutive models of the statistical damage of the rock considering the combined action of heat, water and force under the triaxial condition can be obtained through the formulas (12) to (15):
in the above-described established model, the parameter m needs to be determinedT、KTUnder the combined action of the tail tooth, osmotic pressure and temperature, the peak stress and the peak strain of the rock are different, and the model parameter m isT、KTAnd also has close relation with the action temperature.
Therefore, the model parameters are found by using a linear fitting method, and equation (16) is converted into:
two sides of the equation are logarithmized twice at the same time and simplified, and the following can be obtained:
Y＝mTX-B (18)
wherein,
X＝lnf(σ’ij) (19)
B＝mT ln KT (21)
obtaining m by linear fitting of experimental dataTAnd B value, and then K can be obtainedTComprises the following steps:
a testing device for applying the method for calculating the statistical damage of the rock under the action of heat-water-force is disclosed, as shown in the attached figure 1, and comprises the following components: the device comprises a high-temperature heating device (T <100 ℃), a seepage device 2, a pressure chamber 3, a base test bench 4, a pressing element 5, a top plate 6, a stress detection element 7, a strain detection element 8, a temperature detection element 9, a water flow detection element 10 and an automatic data acquisition device 11; the data automatic acquisition device 11 comprises a data processor 111 and a data monitoring detector 112; the data processor 111 is used for obtaining the influence result of the combined action of the heat-water-force on the stress performance of the rock under the test condition through the rock statistical damage constitutive model under the combined action of the heat-water-force; the data monitor 112 is used for monitoring the influence of the combined action of heat, water and force on the stress performance of the rock under test conditions;
the high-temperature heating device 1 is connected with the pressure chamber 3 and is used for adjusting the temperature in the pressure chamber to provide a medium-high temperature test environment for the rock to be tested; the pressure chamber 3 is arranged on the base test bench 4, and the pressure applying element 5 is arranged between the pressure chamber 3 and the top plate 6;
the seepage device 2 comprises two water permeable gaskets 22, a water inlet 23 and a water outlet 24, and is arranged in the pressure chamber 3, and the rock to be tested is placed between the two water permeable gaskets 22 in the seepage device 2;
the stress detection element 7, the strain detection element 8 and the temperature detection element 9 are all fixed on the rock to be detected; the water flow detection element 10 is arranged above the seepage device 2 and is used for detecting the water flow passing through the interior of the rock within a fixed time; the stress detection element 7, the strain detection element 8, the temperature detection element 9 and the water flow detection element 10 are all connected with an automatic data acquisition device 11. As shown in fig. 5, pore water 21 enters the seepage device 2 through a water inlet 23 and a seepage gasket 22 to perform a seepage test on the test piece, and then flows out of the test piece through a water outlet 24 through the seepage gasket 22;
preferably, an application process of the invention, which takes red sandstone as an example, is as follows:
in order to verify the reasonability of the model, the full stress-strain curves of the red sandstone acted at 20, 50, 70 and 90 ℃ under the conditions of 30MPa and 5MPa of osmotic pressure difference delta P are selected, the Poisson ratios of the red sandstone acted at various temperatures are respectively 0.24, 0.23 and 0.24 through test data processing, the internal friction angles are respectively 45 degrees, 42 degrees, 40 degrees and 39 degrees, and the model parameters obtained through calculation are shown as the following table:
and (3) obtaining a theoretical curve of the full stress-strain relation of the red sandstone under different temperature actions according to the established model, and comparing the theoretical curve with a test curve, wherein the theoretical curve is shown in figures 2(a) to (d). The theoretical value calculated by the rock statistical damage calculation method considering the combined action of heat, water and force is proved to be not much different from the test value, and the trend of the post-peak stage is fully reflected.
Meanwhile, in order to deeply research the correlation between the permeability k and the high-temperature rock damage, the experimental data under the action of 50 ℃, 70 and 90 ℃ are taken as examples for analysis, and the method is shown in the attached figure 4. Selecting thermal damage DTAs a measure of the degree of damage, it can be calculated from equation (23).
In the formula, k is permeability, and xi is the order of magnitude of permeability (10-20 m)2)，DTFor thermal damage, and for damage index, a, b, c are fitting parameters, obtained by experiment.
The permeability was calculated by fitting using the above test data, as shown in fig. 6(a) to (c). As can be seen from the figure, the permeability and the damage index (thermal damage D)T) Exist ofExponential relationship and fitting the correlation coefficient R of the curve2All reach 0.99, so that the evolution rule that the permeability increases along with the damage degree can be obtained. In addition, the method further clarifies that the thermal damage can represent rock damage, and simultaneously discloses a permeability evolution mechanism in the red sandstone gradual cracking process under the action of thermal-force coupling, and reflects the evolution rule that the permeability of the red sandstone increases along with the increase of the temperature.
The embodiment of the invention has the following beneficial effects:
the method considers the influence of temperature and osmotic pressure on the constitutive model parameters, and determines the solving process of the parameters; the M-C strength criterion has the characteristics of simple parameters, easiness in calculation, suitability for rock analysis and the like, so that the M-C strength criterion is adopted to describe the rock infinitesimal body strength. The theoretical value calculated by the rock statistical damage calculation method considering the combined action of heat, water and force constructed by the invention is not greatly different from the test value, the trend of the post-peak stage is fully reflected, and the stress-strain relation of the red sandstone under the action of high temperature and osmotic pressure can be better reflected. The invention further clarifies that the thermal damage can represent the rock damage, simultaneously discloses a permeability evolution mechanism in the red sandstone gradual cracking process under the action of thermal-force coupling, and reflects the evolution rule that the permeability of the red sandstone is increased along with the increase of the temperature.
Therefore, by constructing a rock statistical damage calculation method considering the combined action of heat, water and force, the stress-strain relationship of the red sandstone under the action of high temperature and osmotic pressure and the permeability evolution mechanism of the red sandstone in the gradual cracking process under the action of heat-force coupling are disclosed, the deformation and damage characteristics of the rock under the action of different temperatures are reflected, the trend of the post-peak stage is fully reflected, the stress-strain relationship of the rock under the condition of a triaxial compression-seepage coupling test can be better reflected, and a scientific basis is provided for the stability evaluation of the fire tunnel.
Finally, it should be noted that: the above embodiments are only used to illustrate the technical solution of the present invention, and not to limit the same; while the invention has been described in detail and with reference to the foregoing embodiments, it will be understood by those skilled in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some or all of the technical features may be equivalently replaced; and the modifications or the substitutions do not make the essence of the corresponding technical solutions depart from the scope of the technical solutions of the embodiments of the present invention.
Claims (6)
1. A statistical damage calculation method for rock under combined action of heat, water and force is characterized by comprising the following steps:
s1: defining a thermal damage parameter DTSaid thermal damage parameter DTThe method is used for representing the influence of temperature on the stress performance of the rock;
s2: defining a force damage parameter D for representing the influence of the load on the stress performance of the rock, and establishing an constitutive relation of the rock damage under the action of force to represent the influence of the force on the stress performance of the rock;
s3: a rock statistical damage constitutive model under the combined action of heat, water and force is established to represent the influence of the combined action of heat, water and force on the stress performance of the rock, and further the stress-strain relation of the rock under the condition of a triaxial high-temperature-seepage coupling test is determined.
2. The method for calculating statistical damage of rock under combined action of heat, water and force according to claim 1, wherein the specific method of S1 is as follows:
s11: definition for characterizing thermal damage D of rock under temperature TTComprises the following steps:
in the formula: eTIs the modulus of elasticity under the influence of the temperature T, E0Is the modulus of elasticity at normal temperature;
s12: assuming that the strength of the rock infinitesimal body under the action of the temperature T follows the Weibull distribution function, then
In the formula: x is the intensity value of infinitesimal body, mTIs a parameter affecting the shape of the rock infinitesimal under the action of temperature T, KTIs a parameter influencing the size of the rock infinitesimal body under the action of the temperature T;
s13: the formula characterizing the effect of temperature on the statistical constitutive model of rock damage is as follows:
in the formula: m is0Is a parameter affecting the shape of the rock infinitesimal body at normal temperature, K0Is a parameter influencing the size of the rock infinitesimal body at normal temperature.
3. The method for calculating statistical damage of rock under combined action of heat, water and force according to claim 2, wherein the specific method of S2 is as follows:
s21: defining a continuous damage variable D characterizing the rock under force:
in the formula: n is a radical ofFThe number of rock micro-elements which are damaged under the action of temperature T under a certain stress state; n is the total number of rock micro-elements; f (sigma'ij) Is micro element strength, sigma'ijIs the effective stress tensor under the seepage effect;
s22: correcting the effective stress principle aiming at the seepage problem to obtain:
σ′ij＝σij-b△Pδij (5)
in the formula: sigmaijThe stress tensor is under the seepage effect, and the delta P is the osmotic pressure difference; deltaijIs a unit second order tensor; b is the Biot coefficient;
s23: introducing a damage correction coefficient eta, and establishing a rock damage constitutive relation under the action of force:
in the formula,
stress-effective stress under percolation; sigmaiStress under stress-seepage action;
the effective stress tensor under stress-seepage action is derived from the formula (5) and the formula (6):
in the formula, σ* ijIs the effective stress tensor, delta, under stress-seepageij＝1；
S24: according to the generalized Hooke's law, the axial stress-strain relation of rock stress-strain under the action of temperature T is obtained as follows:
in the formula, σ1、σ2、σ3Respectively principal stress in three directions under stress-seepage action, wherein sigma1Is the axial stress under the action of stress-seepage; sigma2Is the shear stress under the action of stress-seepage; sigma3Is confining pressure under the action of stress-seepage;
for effective axial stress under stress-seepage action,
is the effective shearing stress under the stress-seepage action,
effective confining pressure under the action of stress-seepage; mu.sTIs the poisson's ratio at temperature T.
4. The method for calculating statistical damage of rock under combined action of heat, water and force according to claim 3, wherein the specific method of S3 is as follows:
s31: and (3) respectively substituting the effective stress tensor of the formula (7) into a formula (8) to obtain the axial stress-strain relation under the action of the osmotic pressure:
σ1＝ETε1(1-ηD)+2μTσ3+(1-2μT)△P (9)
s32: the rock infinitesimal body strength is calculated as follows:
in the formula phiTThe internal friction angles of the rock under the action of the temperature T are respectively;
combining equations (7) and (9), equation (10) converts to:
axial offset stress sigma recorded according to triaxial seepage test1tIn fact the axial stress sigma1With confining pressure σ3The difference of (a) is:
σ1t＝σ1-σ3 (12)
loaded biasing force σ1tFirst of all the confining pressure σ is loaded3And pore water pressure, i.e. osmotic pressure difference, Δ P, so that the initial strain, ε, has been established0Comprises the following steps:
micro element strength f (sigma'ij) Of1tMeasuring strain values epsilon for the test1With initial strain epsilon0And (c) the sum, i.e.:
ε1t＝ε1+ε0 (14)
by substituting formula (12) and formula (14) into formula (11), there can be obtained:
according to the formula (9), the constitutive models of the statistical damage of the rock considering the combined action of heat, water and force under the triaxial condition can be obtained through the formulas (12) to (15):
5. the method for calculating statistical damage of rock under combined action of heat, water and force according to claim 4, wherein m is a value obtained by calculating the statistical damage of rock under combined action of heat, water and forceT、KTThe determination method of (2) is as follows:
the model parameters are solved by using a linear fitting method, and the formula (16) is converted into:
two sides of the equation are logarithmized twice at the same time and simplified, and the following can be obtained:
Y＝mTX-B (18)
wherein,
X＝ln f(σ′ij) (19)
B＝mTln KT (21)
obtaining m by linear fitting of experimental dataTAnd B value, and then K can be obtainedTComprises the following steps:
6. a test device applying the statistical damage calculation method for rocks according to claim 5 is characterized by comprising: the device comprises a high-temperature heating device (1), a seepage device (2), a pressure chamber (3), a base test bench (4), a pressing element (5), a top plate (6), a stress detection element (7), a strain detection element (8), a temperature detection element (9), a water flow detection element (10) and an automatic data acquisition device (11); the automatic data acquisition device (11) comprises a data processor (111) and a data monitor (112), wherein the data processor (111) is used for obtaining the influence result of the combined action of the heat-water-force on the stress performance of the rock under the test condition through a rock statistical damage constitutive model under the combined action of the heat-water-force; the data monitor (112) is used for monitoring the result of the influence of the combined action of heat, water and force on the stress performance of the rock under the test condition;
the high-temperature heating device (1) is connected with the pressure chamber (3) and is used for adjusting the temperature in the pressure chamber;
the pressure chamber (3) is arranged on the base test bench (4), and the pressure applying element (5) is arranged between the pressure chamber (3) and the top plate (6);
the seepage device (2) comprises two water permeable gaskets (22), a water inlet (23) and a water outlet (24), and is arranged in the pressure chamber (3), and the rock to be tested is placed between the two water permeable gaskets (22) in the seepage device (2); the pore water (21) enters the seepage device (2) through the water inlet (23) and the seepage gasket (22), and then flows out of the test piece through the water outlet (24) through the seepage gasket (22).
The stress detection element (7), the strain detection element (8) and the temperature detection element (9) are all fixed on the rock to be detected;
the water flow detection element (10) is arranged above the seepage device (2) and is used for detecting the water flow passing through the interior of the rock within a fixed time;
and the automatic data acquisition device (11) is connected with the stress detection element (7), the strain detection element (8), the temperature detection element (9) and the water flow detection element (10) to acquire the acquired heat, water and force related parameters of the rock to be detected.
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