Cooperative bearing analysis method for surrounding rock-support system in construction period

Abstract

The invention discloses a construction period surrounding rock-support system cooperative bearing analysis method, which is characterized in that the radial stress release process of the tunnel inner wall surrounding rock in the construction period is divided into n calculation steps, and after a support system is constructed, each calculation step comprises a preliminary approach analysis stage and a precise convergence analysis stage; in the initial approaching analysis stage, the displacement increment of the ith calculation step is utilized to estimate the support load increment of the (i + 1) th calculation step, and the stress, strain and displacement of the surrounding rock are solved; if the absolute value of the difference value of the surrounding rock displacement and the support displacement is smaller than a set error threshold value, calculation is ended; otherwise, entering a precise convergence stage to correct the support load. The method has the advantages that the complex iterative calculation process in the traditional dichotomy is simplified, and the solving process of the surrounding rock-support system is divided into two stages of preliminary approaching and accurate convergence. The calculation times are obviously reduced, and the calculation precision is ensured.

Description

Technical Field

[0001] The present invention relates to the technical field of load-bearing analysis, and is particularly applicable to a collaborative load-bearing analysis method of a surrounding rock-support system during construction. Background Art

[0002] In fields such as water conservancy projects, civil engineering, and transportation engineering, analyzing the coordinated bearing capacity of surrounding rock and support systems during construction is crucial for ensuring construction safety and structural stability. Accurately analyzing the synergistic effects of surrounding rock and support provides scientific support for support structure selection, construction sequence optimization, and emergency response plan development. This optimizes support design and avoids under- or over-support, thereby reducing construction risks, improving efficiency, and lowering costs. Furthermore, it provides real-time insights for construction decision-making, effectively minimizing project delays.

[0003] At present, the analysis of the synergistic bearing of surrounding rock and support system is mostly carried out by constructing theoretical models to accurately simulate the mechanical behavior of surrounding rock and support response, and dynamically reflect the synergistic evolution process of surrounding rock and support system. For example, the “Incremental Support Load Method (ISLM)” proposed by Ren Mingyang is Picture 2 As shown in the figure, based on the theoretical model, the stress release of the surrounding rock is divided into multiple calculation steps. By gradually increasing the support load by equal values ​​and calculating the surrounding rock stress, strain, and displacement, it is determined whether the error between the surrounding rock displacement and the support displacement meets the accuracy requirements. However, this method has difficulty balancing computational efficiency and accuracy. If the load increase is small, the calculation accuracy improves but efficiency decreases; if the load increase is large, the calculation efficiency increases but accuracy decreases. (For details, see Ren Mingyang's "Research on the Mechanism of Synergistic Bearing of Surrounding Rock and Support System in Deep Tunnel Construction Excavation", Shandong University).

[0004] While the traditional dichotomy method can perform mechanical calculations of the surrounding rock-support system, it requires considering all stresses released by the surrounding rock in each calculation step, resulting in a large calculation scope and requiring improved efficiency. (For details, see Fei Song's "Numerical solutions for tunnels excavated in strain-softening rock masses considering a combined support system").

[0005] Therefore, it is of great significance to develop a construction period surrounding rock-support system collaborative bearing analysis method with high computational efficiency, accurate computational accuracy and wide applicability. Summary of the Invention

[0006] The purpose of the present invention is to provide a collaborative bearing analysis method for the surrounding rock support system during the construction period, which is used to solve the problem of simply, quickly and accurately solving the dynamic evolution process of the collaborative bearing of the surrounding rock support system during the construction period for various rock mass types such as elastic rock mass, elastoplastic rock mass, and post-peak softening rock mass.

[0007] To achieve the above object, the present invention adopts the following technical solutions: The collaborative bearing analysis method for the surrounding rock support system during construction, described in the present invention, divides the radial stress release process of the surrounding rock on the inner wall of the tunnel during construction into n calculation steps. After the support system is constructed, each calculation step includes a preliminary approach analysis stage and a precise convergence analysis stage. The preliminary approximation analysis stage uses the displacement increment of the i-th calculation step to estimate the support load increment of the i+1-th calculation step to solve the stress, strain and displacement of the surrounding rock; if the absolute value of the difference between the surrounding rock displacement and the support displacement is less than the set error range, the calculation ends; otherwise, the precise convergence stage is entered to correct the support load.

[0008] Furthermore, the support load is adjusted using a dichotomy method in the precise convergence stage.

[0009] Furthermore, the support displacement is compared with the surrounding rock displacement. If the support displacement is greater than the surrounding rock displacement, the support load increment is gradually reduced until the support displacement is less than the surrounding rock displacement, and the dynamic adjustment range of the support load increment is obtained. Then, the support load increment is adjusted within the dynamic adjustment range using the dichotomy method until the absolute value of the difference between the surrounding rock displacement and the support displacement meets the set error threshold. If the support displacement is less than the surrounding rock displacement, the support load increment is gradually increased until the support displacement is greater than the surrounding rock displacement, and the dynamic adjustment range of the support load increment is obtained. Then, the support load increment is adjusted within the dynamic adjustment range using the dichotomy method until the absolute value of the difference between the surrounding rock displacement and the support displacement meets the set error threshold.

[0010] Furthermore, in the preliminary analysis stage, the value of each change in the support load increment of the i+1th calculation step is 5% to 10% of the load increment of the i-th calculation step.

[0011] Furthermore, after the precise convergence phase is completed, the load and displacement borne by the surrounding rock, as well as the load and displacement borne by the support, are obtained.

[0012] The advantages of the present invention include: First, this invention simplifies the complex iterative calculation process used in the traditional bisection method, dividing the solution process for the surrounding rock-support system into two stages: preliminary approximation and precise convergence. The preliminary approximation stage rapidly approximates the actual support load through a single calculation, significantly reducing the number of calculations. The precise convergence stage uses the bisection method to fine-tune the support load within a very small range to ensure calculation accuracy. Compared to the traditional bisection method, this invention significantly improves calculation efficiency while maintaining accuracy.

[0013] Second, the present invention simulates the tunnel excavation process as a process of multiple, uniform releases of radial stress in the rock mass of the tunnel wall. It uses elastic-plastic theory and the differential method to solve for surrounding rock deformation, and combines it with the "support load approximation method" to fine-tune the support load, ensuring high-precision calculation results and accurately reflecting the collaborative load-bearing evolution of the surrounding rock and support system. Real-time analysis of surrounding rock stress, strain, displacement, support response, and load bearing provides a scientific basis for adjusting support parameters during construction, ensuring the safety and economy of the support structure, significantly reducing project costs, and providing a scientific basis for construction decision-making.

[0014] Third, the present invention is applicable to a variety of rock types, including elastic rock, elastoplastic rock and post-peak softening rock. It can be widely used in different types of engineering scenarios such as tunnels, underground caverns, mine tunnels, etc., and has strong universality. BRIEF DESCRIPTION OF THE DRAWINGS

[0015] Picture 1 This is a schematic diagram of the model of the collaborative bearing analysis method of surrounding rock and support system during the construction period described in the present invention.

[0016] Picture 2 Schematic diagram of the solution of the incremental support load method for the current surrounding rock-support system collaborative bearing analysis.

[0017] Picture 3 This is a schematic diagram of solving the collaborative bearing analysis method of surrounding rock and support system during construction period described in the present invention.

[0018] Picture 4 This is a flow chart of the collaborative bearing analysis method of surrounding rock and support system during construction period shown in the present invention.

[0019] Picture 5 This is a schematic diagram of a surrounding rock lining system model in Example 2.

[0020] Picture 6 Calculation results for the surrounding rock lining system in Example 2.

[0021] Picture 7 This is the calculation result of the radial stress of the surrounding rock in Example 2.

[0022] Picture 8 This is the calculation result of the radial strain of the surrounding rock in Example 2.

[0023] Picture 9 This is the calculation result of the radial displacement of the surrounding rock in Example 2. DETAILED DESCRIPTION

[0024] The following is a clear and complete description of the technical solutions in the embodiments of the present invention. Obviously, the embodiments described are only part of the embodiments of the present invention, not all of them. All other embodiments obtained by ordinary technicians in this field based on the embodiments of the present invention without making any creative efforts are within the scope of protection of the present invention.

[0025] Example 1 The proposed method for analyzing the coordinated load-bearing of the surrounding rock and support system during construction considers the surrounding rock and support system as an axisymmetric problem with isotropic materials, assuming a hydrostatic initial stress state. The tunnel excavation process is simulated as multiple uniform radial stress releases in the rock mass, with each stress release step treated as an independent solution step.

[0026] like Picture 1 The figure shows the model of the collaborative load analysis method of surrounding rock and support system during construction period of the present invention. R a The surrounding rock-support system is under stress of σ 0 in the hydrostatic stress field. Taking lining support as an example, the inner radius of the lining is R b , when the internal support force P i + Psi Below critical support force P ic When the radius is formed around the tunnel R p The plastic zone. P i is the virtual support force of the tunnel face, Ps i The load borne by the support.

[0027] The concept of “load release” is used to analyze and solve the collaborative bearing of surrounding rock and support system. σ 0 released n The whole collaborative load analysis and solution process is divided into n calculation steps, n The larger the value, the more accurate the calculation result; otherwise, the more ambiguous the calculation result.

[0028] Before supporting, only the surrounding rock characteristics need to be analyzed. The surrounding rock mass includes elastic rock mass and plastically softened rock mass. For the solution method of the surrounding rock mass, please refer to relevant papers, such as A new numerical procedure for elasto-plastic analysis of a circular opening excavated in a strain-softening rock mass; or A new large strain approach for predicting tunnel deformation in strain-softening rock mass based on the Generalized Zhang-Zhustrength criterion. The elastic zone rock mass is solved using elasticity theory, and the plastic zone rock mass is solved using the difference method. For ease of understanding, the present invention stipulates that compressive stress is positive and the shrinkage displacement in the tunnel is positive.

[0029] After supporting, the present invention divides each calculation step of the surrounding rock-support system collaborative bearing analysis solution process during the construction period into a preliminary approach analysis stage and a precise convergence analysis stage.

[0030] The goal of the preliminary approach analysis stage is to make the support load quickly approach the actual value. This stage only needs to be calculated once. After that, by judging whether the error between the surrounding rock displacement and the support displacement exceeds the allowable range, it is decided whether to enter the precise convergence analysis stage; the goal of the precise convergence analysis stage is to use the dichotomy method to make subtle adjustments to the support load.

[0031] Assume that i After the calculation step is completed, the virtual support force of the tunnel face is P i The load borne by the support is Ps i The load borne by the surrounding rock is Pri , P i = Ps i+Pr i The support displacement is us i , the surrounding rock displacement is uri The surrounding rock displacement at the moment of support application is u 0 ,therefore us i = uri - u 0.

[0032] In the i In the +1 calculation step, the virtual support force of the tunnel face is given by P i Reduce to P i+1 , the reduced load is∆P i+1 , ∆P i+1 The calculation is carried out by the surrounding rock and support. The main analysis in this step is ∆P i+1 distribution of . ∆Ps(a)i+1 Indicates the additional load of the support, ∆P i+1 - ∆Ps(a)i+1 During the whole construction process, the virtual support force of the tunnel face will be increased from the original rock stress σ 0 is reduced to 0.

[0033] Since adjacent calculation steps (such as i Hedi i +1 step) between the surrounding rock displacement increments ( ∆us i and ∆us i+1 ) are almost the same, and according to the common support bearing capacity calculation formula, such as The calculation formula for the bearing capacity of the lining is: (1) P l represents the bearing capacity of the lining, K l represents the lining stiffness, u l represents the radial displacement of the lining, E l represents the elastic modulus of the lining, v l represents the Poisson's ratio of the lining, σ rl represents the radial stress of the lining, σ θl represents the tangential stress of the lining, r Indicates the distance from the center of the tunnel.

[0034] The calculation formula for the bearing capacity of anchor rods is as follows: (2) In the above formula, P b represents the bearing capacity of the anchor rod, K b represents the stiffness of the anchor rod, u b represents the displacement of the anchor rod, ϕ 、 s l 、 s t Respectively represent the diameter, spacing and row spacing of the anchor rods. E b and lb They represent the elastic modulus and length of the anchor respectively.

[0035] The calculation formula for the bearing capacity of I-beam is as follows: (3) In the above formula: P st is the bearing capacity of the I-beam, K st is the stiffness of the I-beam, u st is the displacement of the I-beam, E st is the elastic modulus of steel, A set is the cross-sectional area of ​​the I-beam, d is the longitudinal spacing of I-beams, R a is the tunnel excavation radius, h set is the cross-sectional height of the I-beam.

[0036] It can be seen that the support load increment ∆P s and displacement increment ∆u s There is a linear relationship between them. Therefore, the support load increment between adjacent calculation steps is ∆Ps i and ∆Ps i+1 Based on this rule, we can i Displacement increment of calculation step ∆us i Estimated i +1 calculation step support load increment, that is, ∆Ps i+1=∆us i×K. Then, the stress, strain and displacement of the surrounding rock are solved, and the displacement of the surrounding rock is determined. uri+1 - u 0 and support displacement us i+1 Is the absolute value of the difference less than the set error threshold? ε min .

[0037] If the conditions are met, then i +1 calculation step ends; otherwise, it enters the precise convergence stage and further corrects the support load.

[0038] like Picture 3 As shown, the initial approximation stage includes three situations: No. 1 in the figure represents that the estimated value is too small, No. 2 represents that the estimated value is accurate, and No. 3 represents that the estimated value is too large.

[0039] In the precise convergence stage, the dichotomy method is used to make fine adjustments to the support load to ensure that the calculation accuracy meets the requirements.

[0040] Specifically, first, by comparing the support displacement us i+1 Displacement of surrounding rock uri+1 - u 0 is not used to determine the support load increment ∆Ps(1)i+1 Too big or too small. If us i+1 > uri+1 - u 0, indicating that the support displacement exceeds the surrounding rock displacement, indicating that the support load increment ∆Ps(1)i+1 Too large, which is unreasonable. Therefore, it is necessary to gradually reduce ∆Ps(1)i+1 to ∆Ps(a)i+1 , so that the support displacement us i+1 Less than surrounding rock displacement uri+1 - u 0, thus determining the support load increment ∆Ps i+1 Dynamic adjustment range ∆Ps(1)i+1 to ∆Ps(a)i+1 . Then, in ∆Ps(1)i+1 and ∆Ps(a)i+ 1 Use the dichotomy method to make fine adjustments until the calculation error meets the requirements, so that us i+1 ≈ uri+1 - u 0, and finally obtain the support load increment ∆Ps i+1 .

[0041] Through multiple calculations, it is found that the differences between the surrounding rock displacement increment and the support load increment between adjacent calculation steps are usually small. ∆Ps i and ∆Ps i+1 The error is usually kept within 5%. ∆Ps i+1 The gradual reduction amount is set to ∆Ps(1)i+1 ×10%, that is, K is 10%. Generally, only one calculation is needed at this stage to determine the dynamic adjustment range of the support load. After that, the dichotomy method is continued to be used for gradual and fine adjustment until the surrounding rock displacement is uri+1 - u 0 and support displacement us i+1 The absolute value of the difference is less than the set error threshold ε min .

[0042] like us i+1 < uri+1 - u 0, use the similar method as above to calculate. i After the +1 calculation step is completed, the load borne by the surrounding rock can be obtained Pri+1 and displacement uri+1 , and the load borne by the support Ps i+1 and displacement us i+1 .like Picture 4As shown, the entire calculation logic of the surrounding rock-support system collaborative bearing analysis method during the construction period shown in the present invention is demonstrated.

[0043] Example 2 The construction period surrounding rock-support system collaborative bearing analysis method of the present invention can be automatically calculated by programming on the MATLAB platform.

[0044] like Picture 5 As shown in the figure, a surrounding rock is in a hydrostatic stress field, with an initial ground stress of 7.5 MPa and a surrounding rock density of 2630 kg / m 3 , deformation modulus is 5GPa, softening modulus is 3.0GPa, Poisson's ratio is 0.35, cohesion is 2.2MPa, softening cohesion is 1.7MPa, internal friction angle is 40°, and tunnel excavation radius is 3.75m. The lining adopts a linear elastic model, the elastic modulus of the lining is 25GPa, the Poisson's ratio is 0.2, and the lining thickness is 0.5m. Assuming that the stress release coefficient of the surrounding rock of the inner wall of the tunnel is 80% during lining, the construction period surrounding rock-support system collaborative bearing analysis method described in the present invention is used to analyze the synergistic effect of the surrounding rock and the support structure during the construction process, such as Picture 6 shown.

[0045] Picture 6 is the calculation result of the surrounding rock-lining bearing system, Picture 6 (a) is the dynamic evolution process of the coordinated bearing of the surrounding rock-lining system during the construction period. Picture 6 (b) Picture 6 (a) Enlarged view of the part after lining application.

[0046] Picture 6 (a) contains three curves: the surrounding rock characteristic curve, the virtual support force curve, and the support characteristic curve. The surrounding rock characteristic curve consists of two parts: the elastic section and the elastoplastic section. The surrounding rock characteristic curve, the virtual support force curve, and the support characteristic curve are often used to describe and analyze the interaction between the surrounding rock and the support structure in the underground space. The surrounding rock characteristic curve is usually a curve that describes the relationship between the rock support force and radial displacement around the tunnel. The virtual support force curve describes in detail the changes in the virtual support force provided by the tunnel face in the underground space. The support characteristic curve is used to describe the correlation between the support force of the support structure and its displacement. By combining the surrounding rock characteristic curve and the support characteristic curve, the load shared by the surrounding rock and the support structure can be obtained.

[0047] When not supported, Picture 6There are only surrounding rock characteristic curves and virtual support force curves, and the surrounding rock characteristic curves and virtual support force curves coincide. After the support is applied, the support characteristic curve is added, and the bearing capacity of the support structure at any moment plus the virtual support force is equal to the support force acting on the tunnel wall. It can be observed from the figure that the surrounding rock characteristic curve consists of two parts: one part represents the surrounding rock in a purely elastic state (green curve), and the other part represents the surrounding rock entering an elastic-plastic state (red curve). The bearing capacity of the support structure is mainly related to its support structure installation time and support stiffness (curve slope). From Picture 6 It can be seen from the figure that the construction period surrounding rock-support system collaborative bearing analysis method proposed in the present invention can be used to analyze the evolution law of the collaborative effect of surrounding rock and support structure during the construction process.

[0048] In order to fully verify the rationality of the construction period surrounding rock-support system collaborative bearing analysis method proposed in this invention, the surrounding rock radial stress, radial strain and radial displacement are selected as the analysis objects. Picture 7 The figure shows the radial stress of the surrounding rock after the construction is completed. Picture 8 Shown is the radial strain of the surrounding rock, as Picture 9 Shown is the radial displacement of the surrounding rock.

[0049] in, Picture 7 a is the radial stress curve of surrounding rock, Picture 7 b is the radial stress cloud diagram of the surrounding rock. Picture 7 Observations consistently show that radial stress is minimum at the tunnel inner wall, but not equal to 0 MPa. This is because the support structure provides a certain amount of bearing capacity. As the radial stress increases deeper into the surrounding rock along the tunnel inner wall, it gradually returns to its original rock stress state. This observation is consistent with traditional research results, validating the rationality of the radial stress variation pattern in the surrounding rock.

[0050] Picture 8 a is the radial strain curve of surrounding rock, Picture 8 b is the radial strain cloud diagram of surrounding rock. Picture 8 Observations show that the radial strain of the surrounding rock is greatest at the inner wall of the tunnel. As one moves deeper into the surrounding rock, the radial strain gradually decreases, eventually returning to the original rock state of zero, or zero strain. This result is consistent with traditional research, validating the rationality of the radial strain variation pattern of the surrounding rock.

[0051] Picture 9 a is the radial displacement curve of surrounding rock, Picture 9 b is the cloud diagram of the radial displacement of the surrounding rock. Picture 9Observations show that the radial displacement of the surrounding rock is greatest at the inner wall of the tunnel. As one moves deeper into the surrounding rock, the radial displacement gradually decreases and eventually approaches zero. The calculated results are consistent with traditional research, validating the rationality of the variation pattern of the surrounding rock radial displacement.

[0052] By analyzing the synergistic effect of the surrounding rock and the support system in detail, it is verified that the proposed theoretical model can be used to describe the synergistic effect between the surrounding rock and the support structure. The variation patterns of the radial stress, radial strain, and radial displacement of the surrounding rock are consistent with traditional research, which once again verifies the rationality of the theoretical model.

Claims

1. A method for analyzing the coordinated bearing capacity of surrounding rock and support system during construction, which divides the radial stress release process of the surrounding rock on the inner wall of a tunnel during construction into n calculation steps, is characterized by: After the support system is constructed, each calculation step includes a preliminary approach analysis phase and an exact convergence analysis phase; The preliminary approximation analysis stage uses the displacement increment of the i-th calculation step to estimate the support load increment of the i+1-th calculation step to solve the stress, strain and displacement of the surrounding rock; If the absolute value of the difference between the surrounding rock displacement and the support displacement is less than the set error threshold, the calculation ends; otherwise, it enters the precise convergence stage to correct the support load.

2. The method for analyzing the coordinated bearing capacity of surrounding rock and support system during construction period according to claim 1, characterized in that: The support load is adjusted using a dichotomy method during the precise convergence stage.

3. The method for analyzing the coordinated bearing capacity of surrounding rock and support system during construction period according to claim 2 is characterized by: Compare the support displacement with the surrounding rock displacement. If the support displacement is greater than the surrounding rock displacement, gradually reduce the support load increment until the support displacement is less than the surrounding rock displacement, obtain the dynamic adjustment range of the support load increment, and then use the dichotomy method to adjust the support load increment within the dynamic adjustment range until the absolute value of the difference between the surrounding rock displacement and the support displacement meets the set error threshold; if the support displacement is less than the surrounding rock displacement, gradually increase the support load increment until the support displacement is greater than the surrounding rock displacement, obtain the dynamic adjustment range of the support load increment, and then use the dichotomy method to adjust the support load increment within the dynamic adjustment range until the absolute value of the difference between the surrounding rock displacement and the support displacement meets the set error threshold.

4. The method for analyzing the coordinated bearing capacity of surrounding rock and support system during construction according to claim 3, characterized in that: During the preliminary analysis phase, the value of each change in the support load increment of the i+1th calculation step is 5% to 10% of the load increment of the i-th calculation step.

5. The method for analyzing the coordinated bearing capacity of surrounding rock and support system during construction period according to claim 3 is characterized by: After the precise convergence stage is completed, the load and displacement borne by the surrounding rock, as well as the load and displacement borne by the support, are obtained.

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