Method for evaluating stability of lining tunnel under fluctuating load with asymmetric force

Abstract

The present application relates to the asymmetric force under fluctuating load bearing lining tunnel stability evaluation method, including: obtaining the two-way ground stress state around the tunnel, solving the asymmetric coefficient of stress;Establish the underground tunnel pressure bearing model and carry out stress analysis;Set the asymmetric load stress function, the elastic stress distribution is obtained by solving;Determine the function that the limit elastic principal stress of the first yield point of the tunnel satisfies, the first yield point position and its stress state are obtained by solving;Derive the stability condition of the tunnel structure under any stress, determine the safety load space and construct the plastic stress distribution conforming to the stability condition;Establish the self-balancing stress equation set of arbitrary load disturbance, the maximum value of the allowable stress value of the tunnel is obtained, and the safety allowable load range is drawn. The present application considers the asymmetric load condition of the tunnel, and has higher calculation accuracy and better application effect;The tunnel is analyzed in full plasticity, and the safety load obtained can well guarantee the stability of the structure.

Description

TECHNICAL FIELD

[0001] The application belongs to the field of tunnel stability evaluation, and particularly relates to a lining tunnel stability evaluation method under asymmetric force and fluctuating load. BACKGROUND

[0002] After tunnel excavation, the surrounding stress often changes, and the surrounding rock mass undergoes irreversible deformation after the stress is redistributed. In order to ensure the stability of the underground structure after excavation, lining materials are often used for support in engineering. The pressure of the surrounding rock is borne by the internal support lining and the tunnel together, and only for the tunnel, the internal and external pressure acts simultaneously, and in the later construction and service process, the entire structure simultaneously bears various load fluctuations from the external environment. Therefore, the stress of the tunnel needs to be limited to prevent excessive plastic deformation or direct collapse. For convenience of calculation, the existing technology simplifies the action of the stratum on the tunnel as a ring-shaped symmetric pressure with equal size, but in most cases, the ground stress distribution at the tunnel location is not equal, especially in the geological structure zone, the imbalance is very obvious, and the stress concentration phenomenon is very obvious, resulting in excessive deformation or direct collapse of the tunnel. SUMMARY

[0003] The purpose of the present application is to solve the above problems, and provide a lining tunnel stability evaluation method under asymmetric force and fluctuating load, which considers the effect of asymmetric load on the tunnel, models and analyzes the irregular fluctuating load that the tunnel may bear, determines the conditions for the tunnel structure to remain stable under asymmetric fluctuating load, calculates the maximum value of the allowable stress of the tunnel under asymmetric conditions, and analyzes and judges the safety of the lining tunnel bearing fluctuating load according to the above.

[0004] The technical scheme of the present application is a lining tunnel stability evaluation method under asymmetric force and fluctuating load, comprising the following steps:

[0005] Step 1: Obtain the two-way ground stress state around the tunnel, and solve the asymmetric coefficient of the stress;

[0006] Step 2: Establish a pressure-bearing model of the underground tunnel, and analyze the stress of the underground tunnel;

[0007] Step 3: Set the stress function that satisfies the compatibility under the asymmetric load condition, and solve and calculate the elastic stress distribution;

[0008] Step 4: Determine the stress function that the limit elastic principal stress of the first yield point of the tunnel under the asymmetric load condition satisfies, and solve the position of the first yield point and its stress state;

[0009] Step 5: Deriving the stability condition of the tunnel structure under any stress action, determining the safe load space and constructing the plastic stress distribution conforming to the stability condition according to the result of Step 4;

[0010] Step 6: Establishing the self-balanced stress equation set under any load disturbance, solving the maximum value of the allowable stress value of the tunnel, and thus delimiting the safe allowable load range of the tunnel.

[0011] Further, Step 1 specifically comprises the following sub-steps:

[0012] Step 1.1: Selecting a representative stratum point in the well section, rotating 45° along the horizontal axis of the stratum vertical profile to drill three samples in sequence, and processing into rock block standard samples;

[0013] Step 1.2: Testing the samples for ground stress to obtain the ground stress distribution law at the sampling point and solve the lateral pressure coefficient.

[0014] Further, Step 2 specifically comprises the following sub-steps:

[0015] Step 2.1: Modeling the underground tunnel as an ideal elastic-plastic structure model bearing internal and external pressure, and setting two-way stress inequality according to the actual situation.

[0016] Step 2.2: Setting the mechanical boundary conditions of the tunnel according to the contact condition of the tunnel with the outside world.

[0017] Further, Step 3 specifically comprises the following sub-steps:

[0018] Step 3.1: Determining the stress function form containing undetermined coefficients and satisfying the continuity equation and compatibility equation under the condition of asymmetric load;

[0019] Step 3.2: Substituting the boundary conditions to solve the undetermined coefficients of the stress function and obtaining the elastic stress distribution.

[0020] Optionally, Step 4 specifically comprises the following sub-steps:

[0021] Step 4.1: Solving the stress distribution and the first yield point of the yield region by simultaneously solving the plastic equilibrium equation and the yield condition.

[0022] Step 4.2: Calculating the condition of complete failure of the structure during loading.

[0023] Optionally, Step 5 specifically comprises the following sub-steps:

[0024] Step 5.1: Clearly stating the mechanical mechanism of the structural stability requirement and giving the specific mechanical condition.

[0025] Step 5.2: Determining the stress field form under the actual problem of the project.

[0026] Optionally, step 6 specifically includes the following sub-steps:

[0027] Step 6.1: Calculate the residual strain caused by loading and unloading;

[0028] Step 6.2: Calculate the stress magnitude at which the structure fails during the unloading stage;

[0029] Step 6.3: Discuss the safe allowable load.

[0030] Compared with the prior art, the beneficial effects of the present invention include:

[0031] 1) This invention takes into account the situation of tunnels subjected to asymmetric loads, which is very close to the actual engineering situation. It considers the problems comprehensively, has higher calculation accuracy, and has better application effect.

[0032] 2) This invention performs a full plastic analysis on the tunnel, which can better utilize the material's load-bearing capacity than the previous purely elastic analysis. At the same time, this analysis method is conservative, and the safety load can well ensure the stability of the structure, which has very good engineering value.

[0033] 3) This invention analyzes the irregular fluctuation loads that the tunnel experiences throughout the construction and service process, and provides the critical safety load. It does not require specifying the stress path and loading history of various load fluctuations, which is convenient for providing reference for on-site engineers. Attached Figure Description

[0034] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0035] Figure 1 This is a flowchart illustrating the tunnel stability evaluation method according to an embodiment of the present invention.

[0036] Figure 2 This is a schematic diagram of the tunnel structure according to an embodiment of the present invention.

[0037] Figure 3 This is a stress analysis diagram of a tunnel according to an embodiment of the present invention.

[0038] Figure 4 This is a schematic diagram of the yield zone of a tunnel under symmetrical conditions.

[0039] Figure 5 This is a schematic diagram of the yield zone of a tunnel under asymmetric conditions.

[0040] Explanation of reference numerals in the attached drawings: stratum 1, tunnel 2, elastic zone 201, yield zone 202, lining 3. Detailed Implementation

[0041] like Figure 1 As shown, the stability evaluation method for lined tunnels subjected to wave loads under asymmetric forces includes the following steps:

[0042] Step 1: Sampling is carried out around the tunnel, Kaiser effect and acoustic emission experiment are carried out on the sample, the maximum horizontal principal stress of the stratum where the tunnel is located and the maximum horizontal principal stress σ1 and σ2 are obtained, and according to the spatial orientation of the tunnel, it is converted to the two-direction maximum and minimum principal stress of the tunnel section, which is denoted as σ H and σ h . The asymmetric coefficient ω = σ H / σ h is calculated. Obviously, ω is greater than 1, and the greater ω is, the more uneven the stress distribution is, the higher the stress concentration degree is, and the greater the adverse effect on the tunnel is.

[0043] Step 2: The tunnel construction structure is shown in Figure 2 , the inner and outer diameters of the tunnel are r0 and r1 respectively, the action of the stratum on the tunnel can be simplified as a two-direction asymmetric load, wherein P1 = σ h , P2 = σ H = ωP1, the action of the lining on the tunnel can be simplified as a pressure p0, and the stress condition of the tunnel is shown in Figure 3 .

[0044] According to the stress condition shown in Figure 3 , the following boundary conditions can be established at the boundary:

[0045] At the inner boundary,

[0046] At the outer boundary,

[0047] In the formula, σ r , σ θ are the radial and tangential normal stresses of a microelement on the cement body in polar coordinates, τ rθ is the shear stress; r represents the radial direction; and θ represents the polar angle.

[0048] Step 3: In the case of asymmetric load, the elastic solution has no explicit analytical solution, so the stress function is assumed to be in the form of formula (3), which satisfies the compatibility condition,

[0049]

[0050] In the formula, X1-X8 are undetermined coefficients.

[0051] The boundary conditions are brought in, and the unknown coefficients X1-X8 are solved to be in the form of matrix

[0052]

[0053] According to the meaning of the stress function, the elastic stress distribution is expressed as:

[0054]

[0055] where the superscript "e" represents the elastic state, σ r , σ θ , τ rθ , respectively, in the elastic state.

[0056] Step 4: For the symmetric case, when the structure yields due to the action of internal and external pressure, the whole region consisting of the yield radius and the inner diameter yields, and the yield region is a symmetric circular ring, as shown in Fig. 4a. For the asymmetric case, due to the existence of stress concentration, the points on the same radial line yield out of step, which leads to the yield region not being a central symmetric shape, as shown in Fig. 4b. Figure 4 Figure 5

[0057] The limit elastic principal stresses σ e 1 and σ e 2 of the first yield point at the inner diameter satisfy the Mohr-Coulomb condition, i.e., equation (6), and the derivative of the angle θ is 0, i.e., equation (7), according to which the position of the first yield point and its stress state can be determined.

[0058]

[0059]

[0060] where

[0061]

[0062] Step 5: To keep the structure stable under arbitrary stress, it is necessary to ensure that 1) the accumulation of plastic strain increment of the structure is reduced to prevent excessive deformation; and 2) the internal plastic work of the structure is avoided to prevent low-cycle fatigue failure.

[0063] Here it is assumed that the structure is subjected to a series of fluctuating external forces p i (x, t), i = 1, 2,... n, whose range of variation is p i (x, t) = {p i (x, t) - , p i (x, t) +} = (u i - , u i + p 0 i (x, t), where p 0 i (x, t) is the reference load, and ui - and ui + are load multipliers.​​

[0064] Therefore, the fluctuating load region Ω can be expressed as

[0065] Ω = {p = ∑p 0 i (x, t), u i ∈ (u i - , u i + )]} (9)

[0066] If the structure is to avoid the above two types of damage, then in this fluctuating load space Ω, each physical quantity must satisfy the following conditions

[0067]

[0068]

[0069]

[0070]

[0071] Δu i = 0 on S u (10)

[0072] where v is the load multiplier; σ E ij is the elastic stress generated by the fluctuating load; is the plastic strain rate cycle allowed by the mechanism; is the plastic dissipation power; Δu i and are the plastic displacement increment and strain increment within a cycle, respectively. V represents the region of the force body, and in V represents on the force body.

[0073] From equation (10), it can be found that the difficulty of solving is to construct a suitable self-balancing residual force field and to deal with the very explicit yield condition, so as to reduce the calculation scale of solving the engineering complex actual problem. Therefore, the plastic analysis of a certain fluctuating cycle can be used here to help construct the stress field that meets the conditions.

[0074] When the tunnel reaches plasticity, a point that occurs plastic deformation satisfies the balance equation, i.e. equation (11) at the same time. Due to the existence of plastic deformation, the stress is redistributed, which can be calculated approximately according to the elastic zone and without losing accuracy,

[0075] The plastic zone stress distribution is

[0076]

[0077]

[0078] wherein respectively represent σ r , σ θ in the plastic state.

[0079] Step 6: after obtaining the elastic and plastic stress distribution, the expression of residual strain can be written as

[0080]

[0081] respectively represent σ r , σ θ in the self-balanced stress field. This indicates in mechanics that the residual strain is a function of internal and external pressure and unbalanced coefficient, when the structure is damaged or large deformation occurs, the residual strain satisfies the reverse Mohr-Coulomb yield condition, and after being brought in, we get

[0082]

[0083] When formula (14) is just established, it is explained that P1 reaches the maximum allowable stress value, that is, P1=P max , and P max is solved. Formula (14) is an implicit function, and the physical quantity is substituted into formula (14) to specifically obtain P max .

[0084] In particular, when ω=1, formula (14) can be degenerated to the symmetric case, that is, formula (15),

[0085]

[0086] The application innovatively calculates the safety load of the wellbore structure from the theoretical analysis, simplifies the complex calculation process of general elastic-plastic analysis, does not need to consider the complex loading history, and considers the size of the wellbore, the stress size of the surrounding stratum, the material properties of the wellbore structure, and the prediction result is high in accuracy.

[0087] Taking a Guangdong tunnel as an example, the inner and outer diameters are 4.49m and 5.76m respectively, the cohesion of the tunnel is 6.87MPa, the internal friction angle is 27.2°, the unbalanced coefficient ω calculated through the ground stress test is 1.23, and P1=22.45MPa. P max =16.11MPa is calculated, so the load borne by the tunnel can be adjusted to be less than the value, so that the tunnel is always in a stable state.

Claims

1. A method for evaluating the stability of lined tunnels subjected to wave loads under asymmetric forces, characterized in that, include: Step 1: Obtain the biaxial stress state around the tunnel and solve for the stress asymmetry coefficient; Step 1.1: Select representative formation points in the well section, drill multiple samples in the vertical profile of the formation, and process them into standard rock samples; Step 1.2: Conduct in-situ stress tests on the sample to obtain the in-situ stress distribution pattern at the sampling points and solve for the asymmetry coefficient; Step 2: Establish a pressure-bearing model and perform stress analysis on the underground tunnel; Step 2.1: Establish an elastic-plastic structure model subjected to internal and external pressure; Step 2.2: Based on the contact between the tunnel and the outside world, set the mechanical boundary conditions of the tunnel; Step 3: Define the stress function that satisfies the compatibility condition under asymmetric load, solve and calculate the elastic stress distribution; Step 3.1: Determine the stress function form containing undetermined coefficients and satisfying the continuity equation and compatibility equation under asymmetric load conditions; Step 3.2: Substitute the boundary conditions and solve for the undetermined coefficients of the stress function to obtain the elastic stress distribution; Step 4: Determine the stress function satisfied by the ultimate elastic principal stress at the first yield point of the tunnel under asymmetric load, and solve for the location of the first yield point and its stress state. Step 5: Derive the stability conditions of the tunnel structure under arbitrary stress, determine the safe load space, and construct the plastic stress distribution that meets the stability conditions based on the results of Step 4. Step 6: Establish a set of self-balancing stress equations for arbitrary load disturbances, solve for the maximum allowable stress value of the tunnel, and determine the safe allowable load range of the tunnel accordingly.

2. The method for evaluating the stability of lined tunnels according to claim 1, characterized in that, In step 1.1, three samples are drilled sequentially by rotating 45° along the horizontal axis from the vertical profile of the strata to form standard rock block samples.

3. The method for evaluating the stability of lined tunnels according to claim 2, characterized in that, In step 2.1, based on the actual external conditions of the tunnel, the biaxial stresses are set to be unequal.

4. The method for evaluating the stability of lined tunnels according to claim 3, characterized in that, In step 1, the sample is subjected to Kessel upper acoustic emission experiments to determine the maximum and minimum horizontal principal stresses of the strata where the tunnel is located. σ 1 and σ 2. Based on the spatial orientation of the tunnel, convert it to the two-dimensional maximum and minimum principal stresses of the tunnel cross section, denoted as... σ H and σ h asymmetric coefficients ω The ratio of the two is, i.e. ω=σ H / σ h .

5. The method for evaluating the stability of lined tunnels according to claim 4, characterized in that, In step 2, the effect of the strata on the tunnel is modeled as a two-dimensional asymmetric load; Boundary conditions in polar coordinates at the tunnel boundary: ；（1） ；（2） r 0、 r 1 represents the inner and outer diameters of the tunnel, respectively; This indicates the radial pressure exerted by the tunnel lining. Radial and tangential normal stresses of a cementitious micro-element in a tunnel under polar coordinates; ; r Indicates the radial direction of the western tower circumferential direction; Polar angle; This indicates the overburden pressure of the tunnel; This indicates the lateral pressure of the tunnel.

6. The method for evaluating the stability of lined tunnels according to claim 5, characterized in that, In step 3, under asymmetric loading, the stress function that satisfies the compatibility condition is as follows: ；（3） In the formula Stress function that satisfies compatibility conditions; All are undetermined coefficients; After substituting the boundary conditions, the undetermined coefficients are solved. , , , , , , , , ；（4） The expression for elastic stress distribution is as follows: ；（5） In the formula They represent the elastic state respectively , 7. The method for evaluating the stability of lined tunnels according to claim 6, characterized in that, In step 4, under asymmetric loading, points on the same radius vector yield at different times, resulting in a non-symmetrical shape of the yield zone. The ultimate elastic principal stress at the inner diameter point yields first is... σ e 1 and σ e 2. Satisfies the Mohr-Coulomb condition, and the angle θ The derivative is 0, that is ；（6） ；（7） To simplify the formula derivation, complex algebraic expressions in the formula are represented by... , Simplified representation, , ；（8） The location of the first yield point and its stress state can be determined according to equations (6), (7), and (8).

8. The method for evaluating the stability of lined tunnels according to claim 7, characterized in that, In step 5, the two necessary conditions for the tunnel structure to remain stable under arbitrary stress are: 1) reducing the cumulative increase of the structure's plastic strain to prevent excessive deformation; 2) Avoid unlimited plastic work within the structure to prevent low-cycle fatigue failure; Assume the tunnel structure is subjected to multiple wave-like external forces. p i ( x , t ), i =1,2,... n ,in n This indicates the amount of external force exerted by the fluctuation. p i ( x , t )express t The moment received i A fluctuating external force, its range of variation is ( p i ( x , t ) - , p i ( x , t ) + ), p i ( x , t ) + , p i ( x , t ) - } represent wave-like external forces respectively p i ( x , t The upper and lower bounds of ) p i ( x , t ) - = u i - × p 0 i ( x , t ) p i ( x , t ) + = u i + × p 0 i ( x , t ) ； In the formula p 0 i ( x , t ) is the reference load. u i - , u i + All are load multipliers; The fluctuating load region can be represented as ； （9） In the formula Ω Represents the space of fluctuating loads. u i Indicates the first i A load multiplier of a fluctuating external force; In order for the tunnel structure to satisfy conditions 1) and 2), then in the space of the wave load... Ω In this process, each physics element must satisfy the following conditions. ； ； ； ； （10） In the formula, ν For load multipliers; σ E ij To generate elastic stress for fluctuating loads; ε ij p Cycles at the permissible plastic strain rate for maneuverability; D ( ε ij p ) represents plastic power dissipation; Δu i , Δε ij p These represent the plastic displacement increment and strain increment within a cycle, respectively; V represents the stressed body region, and in V represents the stressed body. As can be seen from equation (10), the difficulty in solving the problem lies in constructing a suitable self-balancing residual force field and handling the very explicit yield condition, so as to reduce the computational scale of solving complex engineering problems. Therefore, plastic analysis of a certain wave cycle can help construct a stress field that meets the conditions. When the tunnel reaches the plastic stage, the points where plastic deformation occurs simultaneously satisfy equation (11), i.e., the equilibrium equation. Due to the existence of plastic deformation, the stress is redistributed, and it can be approximated as an elastic zone calculation without loss of accuracy. ；（11） Solving (11) yields the following stress distribution in the plastic region: ；（12） In the formula , They represent the plastic state, respectively. .

9. The method for evaluating the stability of lined tunnels according to claim 8, characterized in that, In step 6, the expression for residual strain. ； （13） In the formula , They represent the residual stress state respectively. ; Equation (13) shows that the residual strain is a function of the internal and external pressures and the unbalance coefficient. When the structure fails or undergoes large deformation, the residual strain satisfies the reverse Mohr-Coulomb yield condition. Substituting this into the equation yields... ； (14) When equation (14) is exactly true, it means P 1. The maximum allowable stress value has been reached, that is... P 1= P max Equation (14) is an implicit function. Substituting each physical quantity into equation (14) yields the result. P max ; when ω= 1. Equation (14) becomes the symmetrical case. ；（15）。

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