CN-121598711-B - Rock equivalent GSI parameter value method based on three-dimensional strength and strain softening

CN121598711BCN 121598711 BCN121598711 BCN 121598711BCN-121598711-B

Abstract

The invention belongs to the technical field of geotechnical engineering, and discloses a rock equivalent GSI parameter value method based on three-dimensional strength and strain softening, which comprises the steps of determining rock mechanical parameters and tunnel excavation parameters, calculating a model plastic region radius R p,epp by adopting a peak GSI p and an ideal elastoplastic model, calculating an attenuation factor k according to the determined parameters, determining a proportionality coefficient beta by an exponential attenuation relation based on the attenuation factor k and the model plastic region radius R p,epp , further obtaining an equivalent parameter GSI eq , and finally calculating surrounding rock mechanical response by adopting the equivalent parameter GSI eq and the ideal elastoplastic model. According to the invention, by introducing equivalent GSI parameters, the complex strain softening problem is converted into the ideal elastoplasticity problem of high-efficiency calculation, the calculation efficiency is obviously improved while the calculation precision is ensured, the influence of the three-dimensional stress state is fully considered, and a practical and reliable technical means is provided for the stability analysis of tunnel engineering.

Inventors

SU CHENLONG
Cai Wuqiang
ZHU HEHUA
LIANG WENHAO
XIAO JUNHUA
CHEN LIKANG
Ma Yaocai
WEI XIANGYANG

Assignees

同济大学
中交简石数字科技(苏州)有限公司
中南大学

Dates

Publication Date: 20260508
Application Date: 20260128

Claims (7)

1. The rock mass equivalent GSI parameter value method based on three-dimensional strength and strain softening is characterized by comprising the following steps: s1, determining mechanical parameters and tunnel excavation parameters of a strain softened rock mass; The mechanical parameters of the strain softened rock body comprise uniaxial compressive strength sigma c , elastic modulus E, poisson ratio v, geological strength index peak value GSI p , geological strength index residual value GSI r , rock mass characteristic parameter m i , disturbance coefficient D, shear expansion angle psi and critical plastic bias strain gamma p* ; The tunnel excavation parameters comprise an excavation radius R 0 , a static water stress p of the original rock, an axial stress q of the original rock and a supporting stress p s after excavation; The post-peak strain softening behavior of the rock mass is characterized by a geological strength index GSI, the geological strength index GSI linearly decreases along with the increase of plastic deflection gamma p in the strain softening stage, and the geological strength index residual value GSI r is kept unchanged after the critical plastic deflection gamma p* is reached; S2, calculating the mechanical response of the excavated surrounding rock by adopting a geological strength index peak GSI p and an ideal elastoplastic model to obtain a model plastic region radius R p,epp ; The mechanical response of surrounding rock after excavation is calculated, an excavation scene is simulated by adopting a thick-wall cylindrical model, and the surrounding rock is judged to enter a plastic region according to a three-dimensional Hoek-Brown strength criterion; the expression of the three-dimensional Hoek-Brown intensity criterion is: ; Wherein sigma m,2 =(σ 1 +σ 3 )/2 is the average value of the maximum and minimum principal stresses, tau oct is octahedral shearing stress, m b , s, a is rock mass material parameter, and is obtained by converting geological strength index GSI, rock mass characteristic parameter m i and disturbance coefficient D: ; s3, calculating an attenuation factor k according to the parameters determined in the step S1; s4, calculating a proportionality coefficient beta according to the proportionality coefficient beta, the model plastic region radius R p,epp and the excavation radius R 0 according to an exponential decay relation: ; The equivalent parameter GSI eq is obtained by combining the definition of the proportion coefficient beta, wherein the proportion coefficient beta is defined as follows: ; wherein GSI r is a geological strength index residual value; S5, calculating the mechanical response of the surrounding rock by adopting an equivalent parameter GSI eq and an ideal elastoplastic model.
2. The method for calculating the equivalent GSI parameters of the rock mass based on the three-dimensional strength and the strain softening as set forth in claim 1, wherein the mechanical response of the excavated surrounding rock in the step S2 comprises the stress-strain calculation of an elastic region, the stress-radius calculation of a plastic region and the strain-displacement calculation of the plastic region.
3. The method for evaluating the equivalent GSI parameters of the rock mass based on the three-dimensional strength and the strain softening as set forth in claim 2, wherein the elastic region stress strain is calculated by adopting an elastic mechanics solution, and the expression is: , Wherein sigma r 、σ θ 、σ z is radial stress, tangential stress and axial stress respectively, epsilon r 、ε θ 、u r is radial strain, tangential strain and radial displacement respectively, G=E/(1+v)/2 is shear modulus, and r is radial distance; When the post-excavation supporting stress p s is smaller than the plastic region critical stress p c , the surrounding rock is in a plastic region, the radius R p of the plastic region and the critical stress p c of the plastic region are used for replacing R 0 and p s in the formula respectively, and an elastic region stress strain expression when the plastic region exists is obtained.
4. The method for evaluating the equivalent GSI parameters of the rock mass based on the three-dimensional strength and the strain softening as set forth in claim 2, wherein the stress of the plastic region is calculated by adopting a finite difference method, the plastic region is divided into n rings according to the equal radial stress difference delta sigma r = –(p c – p s )/n, and the stress components of the rings are calculated gradually from the boundary i=0 of the plastic region to the wall i=n of the hole, wherein the expression is as follows: ; and solving the radius of each circular ring by combining the differential format of the balance equation to obtain the radius R p of the plastic region.
5. The method for evaluating the equivalent GSI parameters of the rock mass based on the three-dimensional strength and strain softening according to claim 2, wherein the strain of the plastic region is calculated by adopting an elastoplastic separation method, the total strain is decomposed into elastic strain and plastic strain, the elastic strain is calculated by the Hooke's theorem, and the plastic strain is calculated according to a non-associated flow rule considering the shear expansion angle and a plastic strain compatibility equation, and the expression is: , wherein λ= (1+sin ψ)/(1-sin ψ) is a shear expansion coefficient, and ψ is a shear expansion angle; radial displacement u r of each point is combined with geometric equation by strain of plastic region And (5) calculating to obtain the product.
6. The method for evaluating the equivalent GSI parameters of the rock mass based on the three-dimensional strength and the strain softening as set forth in claim 1, wherein the attenuation factor k and the rock mass and tunnel parameters in the step S3 satisfy the empirical formula: , wherein S i is the calculated parameters of each input, and c i is the corresponding empirical coefficients.
7. The method for evaluating the equivalent GSI parameters of the rock mass based on the three-dimensional strength and strain softening according to claim 1 is characterized in that beta=1, namely GSI eq = GSI p , is adopted when R p,epp = R 0 , and beta=0, namely GSI eq = GSI r , is adopted when R p,epp ≥3R 0 .

Description

Rock equivalent GSI parameter value method based on three-dimensional strength and strain softening Technical Field The invention belongs to the technical field of surrounding rock analysis of underground engineering, and particularly relates to a rock mass equivalent GSI parameter value method based on three-dimensional strength and strain softening, which is suitable for surrounding rock stability analysis and support design of underground engineering such as tunnels, roadways and the like, and can improve engineering design and analysis efficiency while ensuring calculation accuracy. Background In the design and construction of underground engineering such as tunnels, mine roadways and the like, surrounding rock stability analysis is a core link for guaranteeing engineering safety, numerical simulation is an important means for realizing the analysis, and the accuracy and the efficiency of the analysis directly depend on the adopted rock mass constitutive model. At present, rock mass constitutive models widely applied in engineering are mainly divided into two types of ideal elastoplastic models (ELASTIC PERFECT PLASTIC model, EPP) and strain softening models (ELASTIC STRAIN softening model, ESS), but both have significant application limitations: The ideal elastoplastic model is favored by engineers in the form of simple, easily obtained parameters and stable and efficient numerical calculation. However, this model has a key drawback-assuming that the load bearing capacity remains unchanged after the rock mass reaches peak strength, which is in serious contrast to the strain softening behavior (i.e. the gradual decrease in strength with increasing deformation) that most rock masses (especially weak rock masses) exhibit after the peak in practice. Therefore, the adoption of an ideal elastoplastic model can overestimate the residual strength of the surrounding rock, so that the self-bearing capacity of the calculated surrounding rock is larger, the required supporting force is smaller, and the potential risk is brought to engineering safety. In order to describe the post-peak behaviour of the rock mass more accurately, strain softening models have been proposed and developed. The model can simulate the process of the attenuation of the rock mass intensity from the peak value to the residual value, and is more practical in theory. However, the strain softening model has a complex structure and huge calculation amount, and the related softening parameters (such as softening modulus, critical plastic strain and the like) are difficult to accurately determine through field tests, so that the strain softening model is difficult to popularize in engineering practice, and particularly cannot meet the requirements of rapid design and multi-scheme comparison. In summary, the contradiction between "high efficiency but inaccurate" and "accurate but low efficiency" in the prior art is outstanding, so the engineering world is urgent to need a method for taking account of the calculation precision and efficiency, and not only considers the three-dimensional strength and the strain softening characteristics of the rock mass, but also has simplicity and practicability. Disclosure of Invention The invention aims to overcome the limitation of the existing rock mass constitutive model in engineering application, provides a rock mass equivalent GSI parameter value method based on three-dimensional strength and strain softening, and provides a reliable technical support for rapid and safe design of underground engineering such as tunnels and the like by introducing attenuation factors and proportional coefficients related to the plastic region range, converting the complex rock mass strain softening problem into an ideal elastoplasticity problem adopting an equivalent GSI parameter (GSIeq), and fully reflecting the three-dimensional strength characteristic and strain softening behavior of the rock mass while keeping the calculation efficiency of the ideal elastoplasticity model. In order to achieve the above purpose, the present invention adopts the following technical scheme: A rock mass equivalent GSI parameter value method based on three-dimensional strength and strain softening comprises the following steps: s1, determining mechanical parameters and tunnel excavation parameters of a strain softened rock mass; S2, calculating the mechanical response of the excavated surrounding rock by adopting a geological strength index peak GSI p and an ideal elastoplastic model (EPP) to obtain a model plastic region radius R p,epp; s3, calculating an attenuation factor k according to the parameters determined in the step S1; S4, calculating a proportion coefficient beta based on the attenuation factor k and the model plastic region radius R p,epp, and defining an equivalent parameter GSI eq by combining the proportion coefficient beta; S5, calculating the mechanical response of the surrounding rock by adopting an equivalent parameter G