CN117540553A - Construction method of fractional creep damage constitutive model of weakly cemented soft rock - Google Patents
Construction method of fractional creep damage constitutive model of weakly cemented soft rock Download PDFInfo
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Abstract
The invention provides a construction method of a creep damage constitutive model of weak consolidated soft rock suitable for grading and relieving confining pressure, which comprises the following steps: developing a weak cemented soft rock grading confining pressure unloading creep test to obtain creep test data; drawing a creep variable-time relation curve and a creep rate-time relation curve based on creep test data, and analyzing creep characteristics of the weak cementing soft rock under the pressure of the unloading enclosure; introducing a Riemann-Liouville fractional order integral operator and a negative time index damage evolution variable, defining a nonlinear damage Abel adhesive kettle, and constructing a weak cementing soft rock creep damage constitutive model suitable for grading relief; based on the result of the stress relief creep test, the Levenberg-Marquardt algorithm is adopted to carry out preliminary identification of model parameters, then the ant colony algorithm is utilized to carry out model parameter optimization, and finally the optimal model parameters are determined. The model established according to the method can be used for describing the creep damage characteristics of the whole process of the weakly consolidated soft rock under the excavation unloading condition, and has important significance for predicting the long-term stability of the surrounding rock of the underground engineering.
Description
Technical Field
The invention relates to the technical field of geotechnical engineering, in particular to a method for constructing a fractional creep damage constitutive model of weakly cemented soft rock.
Background
The rock mass material can generate transient deformation and creep characteristics under the action of long-term load, and the total strain under the long-term static load comprises transient strain and creep, wherein the creep comprises three stages of damping creep, constant-speed creep and accelerating creep. The creep property of rock mass materials is an important factor for long-term stability of rock mass engineering such as foundations, slopes, chambers and the like. The creep model of the rock mass material reflects the mechanical nature of creep of the rock mass material, and is a foundation for carrying out long-term stable analysis of rock mass engineering, promoting mine construction, safety and high efficiency exploitation and improving the design level of mine engineering. The weak cemented soft rock has a large number of defects such as microcracks, holes and the like, when the soft rock is subjected to load for a long time, the internal damage of the soft rock is accumulated more, the crack development is more severe, and finally the soft rock is damaged. Therefore, the creep damage characteristic of the weak consolidated soft rock under the relief pressure is studied to have important engineering significance.
The mechanical characteristics of the rock mass under the excavation unloading condition are obviously different from those of the rock mass under the loading state, students at home and abroad develop a series of rock mass mechanical parameter tests under the unloading confining pressure condition, such as the documents of Xue Y, ranjith P, gao F, et al mechanical behaviour and permeability evolution of gas-containing coal from unloading confining pressuretests [ J ]. Journal of Natural Gas Science and Engineering,2017,40 ] "the influence of the unloading rate on the mechanical behavior and permeability evolution (including energy evolution and fractal dimension) of the coal rock is quantitatively researched. The literature Chen Xiutong, li Lu is that under the condition of high confining pressure and high water pressure, the rock unloading mechanical property test research [ J ]. The report of rock mechanics and engineering is 2008, (S1): 2694-2699.) is that the mechanical property weakening rule and the damage type of the rock under the unloading effect are researched. The literature Cheng Jianlong, yang Shengji, yan Pengfei, etc. composite rock deformation and strength characteristic confining pressure unloading test research [ J ]. University of Chinese mining university, 2018,47 (06): 1233-1242, "the law of influence of confining pressure unloading rate on ultimate bearing strength and real-time confining pressure of composite rock samples is studied. It can be seen that scholars at home and abroad obtain great achievements in aspects of strength degradation, energy evolution rule, deformation damage mode research and the like of the rock mass for unloading confining pressure. However, the surrounding rock is in a single-side unloading state for a long time after the underground chamber is excavated, the strength damage performance of the weakly cemented soft rock is particularly remarkable in the single-side unloading state for a long time, and the problem of the deformation of the soft rock caused by the underground chamber excavation is still a key technical problem faced by the soft rock underground engineering.
At present, certain results are achieved for research on creep models, particularly nonlinear creep models, of geotechnical materials. Such as documents Liu Quansheng, luo Ciyou and Peng Xingxin. Soft rock field rheological test and nonlinear fractional order creep model [ J ]. Coal school report, 2020,45 (04): 1348-1356. A nonlinear fractional order creep model of a soft rock mass is established by carrying out field staged loading compression creep test. Document "Liu Gushun, jing Hong Wen, meng Bo, etc. under hydrous conditions, creep characteristics and fractional creep model study of weakly cemented soft rock [ J ]. Geotechnical mechanics, 2020,41 (08): 2609-2618." use Abel adhesive pot to replace adhesive pot element in Kelvin model, plastic element to replace elastic element, four-element fractional creep model of weakly cemented soft rock was established which can describe accelerated creep. Literature Liu Wenbo, zhang Shuguang, chen Lei. Based on the rock aging creep model [ J ]. Mining and safety engineering report, 2021,38 (02): 388-395 ". Instant the viscosity coefficient of the clay is unsteady to construct an unsteady Abel clay, on the basis of which the fraction order is unsteady, and further a sandstone aging creep constitutive model based on the unsteady fraction order is established.
Based on the fractional order creep constitutive model, some scholars began to study the rock damage and creep coupling constitutive model. The method is characterized in that a rock salt creep constitutive model considering the hardening and damage effects is established by taking element combination models as a basis and combining fractional calculus theory on the basis of the element combination models, namely, the rock salt creep constitutive model research [ J ]. Rock soil mechanics, 2023,44 (10): 2953-2966 ] taking the hardening and damage effects into consideration. The literature "Hao K, chuan H, wenbo Y, et al a Fractional Nonlinear Creep Damage Model for Transversely Isotropic Rock [ J ]. Rock Mechanics and Rock Engineering,2022,56 (2): 831-846 et al," assume poisson's ratio as a constant, generalized the creep equation for isotropic rock to transverse isotropic rock, and built a nonlinear damage creep model for transverse isotropic rock. The literature is "ice, lei Qing, zhao Tongde et al," full time nonlinear creep injury model of rock based on stress and time double threshold rock full time nonlinear creep injury model [ J ]. Rock mechanics and engineering report 2023,42 (08): 1928-1944, "full time nonlinear creep injury model of rock is constructed by combining nonlinear elements and injury mechanics treatments. It can be seen that the creep characteristics of soft rock can be better described by introducing fractional calculus theory and damage theory into the rock mass rheological constitutive model. It can be seen that the scholars at home and abroad have obtained great achievements in the aspect of rock damage and creep coupling constitutive models. However, the surrounding rock is in an unloading state for a long time after the underground chamber is excavated, the strength damage performance of the weakly cemented soft rock is particularly remarkable in the long-time unloading state, and the problem of the deformation of the soft rock caused by the underground chamber excavation is still a key technical problem faced by the soft rock underground engineering.
Disclosure of Invention
In order to solve the problems, the invention provides a construction method of a fractional creep damage constitutive model of weak cemented soft rock. The model can describe the attenuation creep stage, the constant-speed creep stage and the acceleration creep stage of creep, and provides basis for carrying out long-term stability analysis of rock mass engineering, promoting mine construction, safe and efficient exploitation and improving mine engineering design level.
In order to achieve the above purpose, the present invention provides the following technical solutions:
the construction method of the fractional creep damage constitutive model of the weakly cemented soft rock specifically comprises the following steps:
s1: and carrying out a grading ring pressure unloading creep test of the weakly cemented soft rock to obtain creep data of the weakly cemented soft rock.
S2: drawing a creep quantity-time curve and a creep rate-time curve based on creep data, and determining the long-term strength of the weak consolidated soft rock by using a steady-state creep rate reciprocal-stress relation curve inflection point method.
S3: and introducing a Riemann-Liouville fractional order integral operator and a negative time index damage evolution variable, defining a nonlinear damage Abel adhesive kettle, and constructing a six-element fractional creep damage constitutive model comprising an elastic element, a fractional order Kelvin viscoelastic damage model, a viscous damage element and a nonlinear viscoelastic damage element.
S4: based on the result of the confining pressure unloading test, carrying out parameter identification on the fractional creep damage model by adopting a Levenberg-Marquardt algorithm, and carrying out model parameter optimization by utilizing an improved ant colony algorithm;
s5: substituting the model parameters obtained by the parameter identification into the weak cementation soft rock fractional order damage model, obtaining a fractional order creep damage model calculation result, comparing the model calculation result with test data, and verifying the reliability of the model.
Preferably, the method for constructing the weak cemented soft rock fractional creep damage constitutive model is constructed based on the Riemann-Liouville fractional integral operator theory and the damage mechanics theory, and specifically comprises the following steps:
step S3, establishing a fractional Kelvin viscoelastic damage model and a nonlinear viscoelastic damage element based on Riemann-Liouville fractional integral operator theory and damage mechanics theory, and connecting the fractional Kelvin viscoelastic damage model and the nonlinear viscoelastic damage element with an elastic element and a viscous damage element in series; the elastic element is used for representing the instantaneous deformation characteristic of the weakly cemented soft rock, the fractional Kelvin viscoelastic damage element is used for representing the attenuation creep characteristic of the weakly cemented soft rock, the viscous damage element is used for representing the constant-speed creep characteristic of the weakly cemented soft rock, and the nonlinear viscoplastic damage element is used for representing the acceleration creep characteristic of the weakly cemented soft rock.
And establishing a weak cementation soft rock fractional order creep damage model based on the creep equation of the elastic element, the creep equation of the fractional order Kelvin viscoelastic damage model, the creep equation of the viscous damage element and the creep equation of the nonlinear viscoplastic damage element.
Preferably, the creep equation of the elastic element is:
wherein: epsilon e For the strain, sigma, of the elastic element 0 Stress of elastic element E 0 Is the elastic modulus of the elastic element;
preferably, the fractional order Kelvin viscoelastic damage element is formed by connecting a nonlinear damage Abel and a spring in parallel, and the constitutive equation is as follows:
order theEpsilon when t=0 ve1 (t) =0, then the above formula can be written as:
laplace transformation is carried out on the above method to obtain:
and (3) finishing to obtain:
performing Laplace inverse transformation on the obtained product to obtain the product:
wherein:solving the above equation, and substituting a and b to obtain:
introducing attenuated creep stage damage variable D 1 The damage evolution equation of the weak cementing soft rock attenuation creep stage is assumed to be negative exponential relation with time, namely, the damage evolution equation of the attenuation creep stage is:
the damage viscosity coefficient eta of the viscous body ve1,D The method comprises the following steps:
the creep equation for the fractional order Kelvin viscoelastic damage element is:
wherein: η (eta) 1 The viscosity coefficient, η, of the fractional order Kelvin viscoelastic element ve1.D The viscosity coefficient, beta, of the fractional order Kelvin viscoelastic damage element 1 Order of fractional order of Kelvin viscoelastic damage element, alpha 1 Is the correlation coefficient of rock mass material, t is loading time, E 1 Is the elastic modulus of the fractional Kelvin viscoelastic damage element.
Preferably, the constitutive equation of the viscous injury element is:
introduction of constant velocity creep stage damage variable D 2 The evolution of soft rock creep damage is assumed to be a negative exponential function relation with time, namely, a damage evolution equation of a constant-speed creep stage is:
the damage viscosity coefficient eta of the viscous body ve2,D The method comprises the following steps:
the creep equation of the viscous injury element is as follows:
wherein: η (eta) 2 Is the viscosity coefficient of the viscous element, eta ve2,D Is the viscosity coefficient alpha of the viscous injury element 2 Is the correlation coefficient of the rock mass material, and t is the loading time.
Preferably, the constitutive equation of the Abel-pot in the nonlinear viscoplastic element is:
the creep equation of the Abel adhesive pot in the nonlinear adhesive plastic element is as follows:
introducing an accelerated creep phase damage variable D 3 The evolution of soft rock creep damage is assumed to be a negative exponential function relation with time, namely, an accelerated creep stage damage evolution equation is:
the damage viscosity coefficient eta of the nonlinear viscoplastomer vp,D The method comprises the following steps:
the creep equation of the nonlinear viscoplastic damage element is:
wherein: η (eta) 3 Is the viscosity coefficient, eta of the nonlinear viscoplastic element vp,D Is the viscosity coefficient beta of the nonlinear viscoplastic damage element 2 Order of fractional order of nonlinear viscoplastic damaged element, alpha 3 Is the correlation coefficient of rock mass material, t is loading time, sigma s To accelerate creep stress, the value can be taken as the long-term strength sigma of weak cemented soft rock ∞ 。
Preferably, the nonlinear viscoplastic damage element means that when the level of the bias stress is less than the long-term strength, the friction plate in the nonlinear viscoplastic damage element is a rigid body and does not function; when the nonlinear viscoplastic damage element means that the friction plate in the nonlinear viscoplastic damage element is triggered to play a role when the bias stress level is greater than the long-term strength. The creep-time relationship of the nonlinear viscoplastic damaged element is:
preferably, the fractional order creep damage constitutive equation of the weakly cemented soft rock is established based on the creep equation of the elastic element, the creep equation of the fractional order Kelvin viscoelastic damage element, the creep equation of the viscous damage element and the creep equation of the nonlinear viscoelastic damage element.
Step S4, according to the creep amount-time relation curve, carrying out parameter identification on the fractional creep damage model by adopting a Levenberg-Marquardt algorithm in Matlab so as to obtain fractional creep damage model parameters, and carrying out model parameter optimization by utilizing an improved ant colony algorithm;
and S5, substituting the model parameters obtained by the parameter identification into a weak cementation soft rock fractional order damage model, obtaining a fractional order creep damage model calculation result, comparing the model calculation result with test data, and verifying the reliability of the model.
The invention has the beneficial effects that: the method for constructing the fractional creep damage constitutive model of the weakly cemented soft rock can accurately describe the characteristics of the whole process of instantaneous deformation, attenuation creep, constant-speed creep and acceleration creep of the weakly cemented soft rock, and accurately judge and predict the whole creep deformation process of the weakly cemented soft rock. The creep damage characteristics of the weak cementation soft rock under the excavation unloading condition of the underground engineering are more accurate in predicting the long-term stability of the underground engineering.
Drawings
FIG. 1 is a flow chart of a method of constructing a creep damage constitutive model of weakly cemented soft rock of the present invention;
FIG. 2 is a graph of a laboratory test of creep in weakly cemented soft rock in accordance with an embodiment of the present invention;
FIG. 3 is a graph of a single-stage loading creep test of a weak consolidated soft rock based on the Boltzmann linear superposition principle;
FIG. 4 is a graph of creep rate versus time for a first stage based on a creep rate versus time curve in accordance with the present invention;
FIG. 5 is a graph of creep rate versus time for a second stage based on a creep rate versus time curve in accordance with the present invention;
FIG. 6 is a third stage creep rate versus time curve based on a creep rate versus time curve in accordance with the present invention;
FIG. 7 is a graph of creep rate versus time for a fourth stage based on a creep rate versus time curve in accordance with the present invention;
FIG. 8 is a graph of creep rate versus time for a fifth stage based on a creep rate versus time curve in accordance with the present invention;
FIG. 9 is a graph of a fractional creep damage architecture model of weakly cemented soft rock in accordance with an embodiment of the present invention;
fig. 10 is a flowchart of an improved ant colony algorithm optimization model parameter proposed by the present invention;
FIG. 11 is a graph comparing the results of the model calculation and the results of the test in example 2 of the present invention.
Detailed Description
The invention is further illustrated by the following examples. The examples are given solely for the purpose of illustration and are not intended to limit the scope of the invention.
Example 1
The invention provides a construction method of a fractional creep damage constitutive model of weakly cemented soft rock, and the construction flow is shown in figure 1. The method for constructing the fractional creep damage constitutive model specifically comprises the following steps:
s1: performing a grading ring pressure unloading creep test of the weakly cemented soft rock to obtain creep data of the weakly cemented soft rock;
s2: drawing a creep quantity-time curve and a creep rate-time curve based on creep data, and determining the long-term strength of the weak consolidated soft rock by using a steady-state creep rate reciprocal-stress relation curve inflection point method;
s3: introducing a Riemann-Liouville fractional order integral operator and a negative time index damage evolution variable, defining a nonlinear damage Abel adhesive kettle, and constructing a six-element fractional creep damage constitutive model comprising an elastic element, a fractional order Kelvin viscoelastic damage model, a viscous damage element and a nonlinear viscoelastic damage element;
s4: based on the result of the confining pressure unloading test, carrying out parameter identification on the fractional creep damage model by adopting a Levenberg-Marquardt algorithm, and carrying out model parameter optimization by utilizing an improved ant colony algorithm;
s5: substituting the model parameters obtained by the parameter identification into the weak cementation soft rock fractional order damage model, obtaining a fractional order creep damage model calculation result, comparing the model calculation result with test data, and verifying the reliability of the model.
Preferably, the method for constructing the weak cemented soft rock fractional creep damage constitutive model is constructed based on the Riemann-Liouville fractional integral operator theory and the damage mechanics theory, and specifically comprises the following steps:
step S3, establishing a fractional Kelvin viscoelastic damage model and a nonlinear viscoelastic damage element based on Riemann-Liouville fractional integral operator theory and damage mechanics theory, and connecting the fractional Kelvin viscoelastic damage model and the nonlinear viscoelastic damage element with an elastic element and a viscous damage element in series; the elastic element is used for representing the instantaneous deformation characteristic of the weakly cemented soft rock, the fractional Kelvin viscoelastic damage element is used for representing the attenuation creep characteristic of the weakly cemented soft rock, the viscous damage element is used for representing the constant-speed creep characteristic of the weakly cemented soft rock, and the nonlinear viscoplastic damage element is used for representing the acceleration creep characteristic of the weakly cemented soft rock.
And establishing a weak cementation soft rock fractional order creep damage model based on the creep equation of the elastic element, the creep equation of the fractional order Kelvin viscoelastic damage model, the creep equation of the viscous damage element and the creep equation of the nonlinear viscoplastic damage element.
Preferably, the creep equation of the elastic element is:
wherein: epsilon e For the strain, sigma, of the elastic element 0 Stress of elastic element E 0 Is the elastic modulus of the elastic element;
preferably, the fractional order Kelvin viscoelastic damage element is formed by connecting a nonlinear damage Abel and a spring in parallel, and the constitutive equation is as follows:
order theEpsilon when t=0 ve1 (t) =0, then formula (2) can be written as:
performing Laplace transformation on the formula (3) to obtain:
and (3) finishing to obtain:
performing Laplace inverse transformation on the formula (5) to obtain:
wherein:
solving the formula (6) and substituting a and b to obtain:
introducing attenuated creep stage damage variable D 1 Supposing weak bond soft rock failureThe damage evolution of the creep reduction stage is in a negative exponential function relation with time, namely, the damage evolution equation of the creep reduction stage is as follows:
the damage viscosity coefficient eta of the viscous body ve1,D The method comprises the following steps:
the creep equation for the fractional order Kelvin viscoelastic damage element is:
wherein: η (eta) 1 The viscosity coefficient, η, of the fractional order Kelvin viscoelastic element ve1.D The viscosity coefficient, beta, of the fractional order Kelvin viscoelastic damage element 1 Order of fractional order of Kelvin viscoelastic damage element, alpha 1 Is the correlation coefficient of rock mass material, t is loading time, E 1 Is the elastic modulus of the fractional Kelvin viscoelastic damage element.
Preferably, the constitutive equation of the viscous injury element is:
introduction of constant velocity creep stage damage variable D 2 The evolution of soft rock creep damage is assumed to be a negative exponential function relation with time, namely, a damage evolution equation of a constant-speed creep stage is:
the damage viscosity coefficient eta of the viscous body ve2,D The method comprises the following steps:
the creep equation of the viscous injury element is as follows:
wherein: η (eta) 2 Is the viscosity coefficient of the viscous element, eta ve2,D Is the viscosity coefficient alpha of the viscous injury element 2 Is the correlation coefficient of the rock mass material, and t is the loading time.
Preferably, the constitutive equation of the Abel-pot in the nonlinear viscoplastic element is:
the creep equation of the Abel adhesive pot in the nonlinear adhesive plastic element is as follows:
introducing an accelerated creep phase damage variable D 3 The evolution of soft rock creep damage is assumed to be a negative exponential function relation with time, namely, an accelerated creep stage damage evolution equation is:
the damage viscosity coefficient eta of the nonlinear viscoplastomer vp,D The method comprises the following steps:
the creep equation of the nonlinear viscoplastic damage element is:
wherein: η (eta) 3 Is the viscosity coefficient, eta of the nonlinear viscoplastic element vp,D Is the viscosity coefficient beta of the nonlinear viscoplastic damage element 2 Order of fractional order of nonlinear viscoplastic damaged element, alpha 3 Is the correlation coefficient of rock mass material, t is loading time, sigma s To accelerate creep stress, the value can be taken as the long-term strength sigma of weak cemented soft rock ∞ 。
Preferably, the nonlinear viscoplastic damage element means that when the level of the bias stress is less than the long-term strength, the friction plate in the nonlinear viscoplastic damage element is a rigid body and does not function; when the nonlinear viscoplastic damage element means that the friction plate in the nonlinear viscoplastic damage element is triggered to play a role when the bias stress level is greater than the long-term strength. The creep-time relationship of the nonlinear viscoplastic damaged element is:
preferably, the weak cementitious soft rock fractional order creep damage constitutive equation is established based on the creep equation (1) of the elastic element, the creep equation (10) of the fractional order Kelvin viscoelastic damage element, the creep equation (14) of the viscous damage element and the creep equation (20) of the nonlinear viscoplastic damage element, and is shown in the formula (21).
Step S4, according to the creep amount-time relation curve, carrying out parameter identification on the fractional creep damage model by adopting a Levenberg-Marquardt algorithm in Matlab so as to obtain fractional creep damage model parameters, and carrying out model parameter optimization by utilizing an improved ant colony algorithm;
and S5, substituting the model parameters obtained by the parameter identification into a weak cementation soft rock fractional order damage model, obtaining a fractional order creep damage model calculation result, comparing the model calculation result with test data, and verifying the reliability of the model.
Example 2
(1) And carrying out a weak cemented soft rock grading confining pressure unloading creep test. The stress relief creep test uses a stress control module in a GDSLAB advanced loading module to load a sample into sigma at a loading rate of 0.1MPa/min 10 ＝σ 30 And remain constant. Thereafter, the shaft pressure sigma is maintained 10 And (3) constantly, discharging the confining pressure to a preset value at a confining pressure discharging rate of 0.05MPa/s, keeping the stress state of the sample constant for about 50 hours, and then performing next confining pressure discharging. The confining pressure is discharged according to 5 stages, the bias stress after each stage of confining pressure discharge is valued according to 30%,40%,50%,55% and 60% of the uniaxial compressive strength of the rock, and the grading confining pressure discharge test scheme is shown in table 1.
Table 1 table for testing scheme of step-by-step ring-down pressure
(2) Creep data of weakly cemented soft rock is obtained, and a creep amount-time relation curve is drawn based on the creep data, as shown in fig. 2.
(3) The graded loading creep test data are processed according to the linear superposition principle, and creep amount-time curves and creep rate-time curves under different stress levels are drawn, as shown in fig. 3-8.
(4) Based on Riemann-Liouville fractional order integration operator theory and damage mechanics theory, an elastic element is connected with a fractional order Kelvin viscoelastic damage element, a viscous damage element and a nonlinear viscoplastic damage element in series to construct a six-element weak cementation soft rock fractional order creep damage model, as shown in figure 9.
(5) And establishing a fractional order creep damage constitutive equation of the weakly cemented soft rock based on the creep equation of the elastic element, the creep equation of the fractional order Kelvin viscoelastic damage element, the creep equation of the viscous damage element and the creep equation of the nonlinear viscoplastic damage element.
(6) And carrying out parameter identification on the fractional order creep damage model according to the creep amount-time relation curve to obtain creep model parameters. Identifying a weak cemented soft rock fractional order creep damage model parameter E by adopting Trust-Region algorithm in Matlab 0 、E 1 、β 1 、β 2 、η 1 、η 2 、η 3 、α 1 、α 2 、α 3 、t 1 、t 2 Is set to be a constant value.
(7) Model parameter optimization is performed by using the improved ant colony algorithm, and a preferred flow is shown in fig. 10. The preferred model parameters are shown in Table 2.
TABLE 2 parameter optimization results for fractional creep damage constitutive models
(8) The model parameters after optimization are substituted into the weak cemented soft rock fractional creep damage constitutive model (formula (21)), and the model calculation result is compared with the test data, as shown in fig. 11.
The model calculation result and the test data comparison analysis result show that the fractional creep damage constitutive model of the weakly cemented soft rock can accurately describe the whole process characteristics of instantaneous deformation, attenuation creep, constant-speed creep and acceleration creep of the weakly cemented soft rock, accurately reflect the creep damage characteristics of the weakly cemented soft rock under the excavation unloading condition, and has important significance for guaranteeing the long-term stability of underground engineering.
The principles and embodiments of the present invention have been described with reference to specific examples, which are provided to facilitate understanding of the method and core ideas of the present invention; also, it is within the scope of the present invention to be modified by those of ordinary skill in the art in light of the present teachings. In view of the foregoing, this description should not be construed as limiting the invention.
Claims (8)
1. The construction method of the fractional creep damage constitutive model of the weakly cemented soft rock is characterized by comprising the following steps of:
s1: performing a grading ring pressure unloading creep test of the weakly cemented soft rock to obtain creep data of the weakly cemented soft rock;
s2: drawing a creep quantity-time curve and a creep rate-time curve based on creep data, and determining the long-term strength of the weak consolidated soft rock by using a steady-state creep rate reciprocal-stress relation curve inflection point method;
s3: introducing a Riemann-Liouville fractional order integral operator and a negative time index damage evolution variable, defining a nonlinear damage Abel adhesive kettle, and constructing a six-element fractional creep damage constitutive model comprising an elastic element, a fractional order Kelvin viscoelastic damage model, a viscous damage element and a nonlinear viscoelastic damage element;
s4: based on the result of the confining pressure unloading test, carrying out parameter identification on the fractional creep damage model by adopting a Levenberg-Marquardt algorithm, and carrying out model parameter optimization by utilizing an improved ant colony algorithm;
s5: substituting the model parameters obtained by the parameter identification into the weak cementation soft rock fractional order damage model, obtaining a fractional order creep damage model calculation result, comparing the model calculation result with test data, and verifying the reliability of the model.
2. The method for constructing a fractional creep damage constitutive model of weakly cemented soft rock according to claim 1, wherein the data of the fractional relief pressure creep test of weakly cemented soft rock in step 1 specifically comprises: creep amount versus time and creep rate versus time.
3. The method for constructing a fractional creep injury constitutive model of weakly cemented soft rock according to claim 1, wherein the fractional creep injury constitutive model in step 3 specifically comprises:
establishing a fractional Kelvin viscoelastic damage model and a nonlinear viscoelastic damage element based on Riemann-Liouville fractional order integral operator theory and damage mechanics theory, and respectively connecting the fractional Kelvin viscoelastic damage model and the nonlinear viscoelastic damage element with an elastic element and a viscous damage element in series;
establishing a creep equation of the elastic element, a creep equation of the fractional-order Kelvin viscoelastic damage element, a creep equation of the viscous damage element and a creep equation of the nonlinear viscoelastic damage element according to creep-time relation curves under different stress levels;
and establishing a fractional order creep damage constitutive model of the weak cemented soft rock based on the creep equation of the elastic element, the creep equation of the fractional order Kelvin viscoelastic damage model, the creep equation of the viscous damage element and the creep equation of the nonlinear viscoplastic damage element.
4. The method for constructing a fractional creep injury constitutive model of weakly cemented soft rock according to claim 3, wherein the elastic element, the viscous injury element, the fractional Kelvin viscoelastic injury model and the nonlinear viscoelastic injury element constitutive equation are specifically as follows:
the constitutive equation of the elastic element is:
wherein: epsilon e For the strain, sigma, of the elastic element 0 Stress of elastic element E 0 Is the elastic modulus of the elastic element;
the fractional order Kelvin viscoelastic damage element is formed by connecting a nonlinear damage Abel and a spring in parallel, and the constitutive equation is as follows:
order theEpsilon when t=0 ve1 (t) =0, then the above formula can be written as:
laplace transformation is carried out on the above method to obtain:
and (3) finishing to obtain:
performing Laplace inverse transformation on the obtained product to obtain the product:
wherein:solving the above equation, and substituting a and b to obtain:
introducing attenuated creep stage damage variable D 1 The damage evolution equation of the weak cementing soft rock attenuation creep stage is assumed to be negative exponential relation with time, namely, the damage evolution equation of the attenuation creep stage is:
the damage viscosity coefficient eta of the viscous body ve1,D The method comprises the following steps:
the creep equation for the fractional order Kelvin viscoelastic damage element is:
wherein: η (eta) 1 The viscosity coefficient, η, of the fractional order Kelvin viscoelastic element ve1.D The viscosity coefficient, beta, of the fractional order Kelvin viscoelastic damage element 1 Order of fractional order of Kelvin viscoelastic damage element, alpha 1 Is the correlation coefficient of rock mass material, t is loading time, E 1 Is the elastic modulus of the fractional Kelvin viscoelastic damage element.
The constitutive equation of the viscous injury element is as follows:
introduction of constant velocity creep stage damage variable D 2 The evolution of soft rock creep damage is assumed to be a negative exponential function relation with time, namely, a damage evolution equation of a constant-speed creep stage is:
the damage viscosity coefficient eta of the viscous body ve2,D The method comprises the following steps:
the creep equation of the viscous injury element is as follows:
wherein: η (eta) 2 Is the viscosity coefficient of the viscous element, eta ve2,D Is the viscosity coefficient alpha of the viscous injury element 2 Is the correlation coefficient of the rock mass material, and t is the loading time.
The constitutive equation of the Abel adhesive pot in the nonlinear adhesive plastic element is as follows:
the creep equation of the Abel pot in the nonlinear viscoplastic element is:
introducing an accelerated creep phase damage variable D 3 The evolution of soft rock creep damage is assumed to be a negative exponential function relation with time, namely, an accelerated creep stage damage evolution equation is:
the damage viscosity coefficient eta of the nonlinear viscoplastomer vp,D The method comprises the following steps:
the creep equation for the nonlinear viscoplastic damage element is:
wherein: η (eta) 3 Is the viscosity coefficient, eta of the nonlinear viscoplastic element vp,D Is the viscosity coefficient beta of the nonlinear viscoplastic damage element 2 Order of fractional order of nonlinear viscoplastic damaged element, alpha 3 Is the correlation coefficient of rock mass material, t is loading time, sigma s To accelerate the creep stress threshold, the value may be taken as the long-term strength sigma of weakly cemented soft rock ∞ ；
The established fractional creep damage constitutive equation of the weakly cemented soft rock is shown in the following formula,
5. the method for constructing a fractional creep injury constitutive model of weakly cemented soft rock according to claim 4, wherein the nonlinear viscoplastic injury element is characterized in that when the level of the bias stress is smaller than the long-term strength, the friction plate in the nonlinear viscoplastic injury element is rigid and does not function; when the nonlinear viscoplastic damage element means that the friction plate in the nonlinear viscoplastic damage element is triggered to play a role when the bias stress level is greater than the long-term strength. The creep-time relationship of the nonlinear viscoplastic damaged element is:
wherein: η (eta) 3 Is the viscosity coefficient, eta of the nonlinear viscoplastic element vp,D Is the viscosity coefficient beta of the nonlinear viscoplastic damage element 2 Order of fractional order of nonlinear viscoplastic damaged element, alpha 3 Is the correlation coefficient of rock mass material, t is loading time, sigma s To accelerate the creep stress threshold, the value may be taken as the long-term strength sigma of weakly cemented soft rock ∞ 。
6. The method for constructing a fractional creep injury constitutive model of weakly cemented soft rock according to claim 1, wherein the step 3 is based on a creep equation of the elastic element, a creep equation of a fractional Kelvin viscoelastic injury element, a creep equation of a viscous injury element and a creep equation of a nonlinear viscoplastic injury element, and specifically comprises:
using elastic elements to describe the instantaneous deformation characteristics of the creep of weak cemented soft rock;
describing the attenuation creep characteristics of the creep of the weak cemented soft rock by adopting a fractional Kelvin viscoelastic damage model;
using a viscous injury element to describe the constant-speed creep characteristics of the creep of the weakly consolidated soft rock;
the accelerated creep is characterized by a nonlinear viscoplastic damaging element.
7. The method for constructing the fractional creep injury structure model of the weakly cemented soft rock according to claim 1, wherein the step 4 is specifically to adopt a Levenberg-Marquardt algorithm in Matlab to perform parameter identification on the fractional creep injury model of the weakly cemented soft rock according to the experimental creep-time relation curve to obtain creep model parameters, and perform model parameter optimization by using an improved ant colony algorithm.
8. The method for constructing fractional creep injury constitutive model of weakly cemented soft rock according to claim 1, wherein step 5 comprises identifying parameters to obtain 10 model parameters E 0 、E 1 、β 1 、β 2 、η 1 、η 2 、η 3 、α 1 、α 2 And alpha 3 Substituting the model into the weak cementation soft rock fractional order damage model in the step (3), calculating to obtain fractional order creep damage model calculation results, and feeding the model calculation results and test data into the model calculation resultsAnd (5) comparing the rows, and verifying the reliability of the model.
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