Method for determining the timing of underground cavern support

Abstract

The application provides a method for determining the supporting time of underground caverns, which is based on the crack closure degree to determine the supporting time of rock mass at each part of surrounding rock in the time-dependent deformation process. For the cavern surrounding rock in the low confining pressure compression state, the crack closure degree C3 in the radial stress direction is taken as the time-dependent supporting basis of the surrounding rock. The crack closure degree C3 changes with time in three cases. By setting anchor cables and anchor rods, additional radial compressive stress can be provided to compensate for the radial stress released by the surrounding rock, thereby reducing the difference between the tangential stress and the radial stress, maintaining the crack closure degree in a non-destructive stage, and ensuring the safety and smooth progress of the underground cavern construction. Such measures help to maintain the stability of the surrounding rock and can optimize the supporting design, improve the engineering efficiency and safety.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of geotechnical engineering, in particular to a method for determining the supporting time of underground caverns. BACKGROUND

[0002] The underground powerhouse of a hydropower station has a large buried depth. After the excavation of the cavern is completed, part of the initial ground stress near the cavern wall is immediately released, and the remaining stress needs to be fully released after a certain period of time. This indicates that the deformation of the surrounding rock will not be completed in a short time or even instantaneously, but will tend to converge after a long time. Therefore, the supporting time of the surrounding rock needs to be determined. The so-called timely support is to allow the surrounding rock to exert the maximum self-bearing capacity. During the time-dependent deformation after excavation, the strain of the surrounding rock before failure reaches the ultimate strain. At present, the stress release coefficient is commonly used as an evaluation for determining the initial support of the timely support. It mainly considers the time effect of stress release. Many studies have shown that when the stress release amount reaches 100%, the stress at the arch top reaches the minimum, and the stress at the sidewall reaches the maximum. Therefore, it is believed that when the stress release of the surrounding rock reaches 70-80%, the stress at the arch top gradually dissipates without generating tensile stress, and the stress near the arch springing has not reached the compressive strength of the surrounding rock. At this time, it is the supporting time. However, in actual engineering, the stress state of the surrounding rock at different positions after the excavation of the underground cavern is not the same, and the stress release amount and release time are also different, making it difficult to give a quantitative evaluation. SUMMARY

[0003] The main purpose of the present application is to provide a method for determining the supporting time of underground caverns, which solves the problems in the background art.

[0004] To solve the above technical problems, the technical solution adopted by the present application is as follows: based on the crack closure degree, the supporting time of the rock mass at different positions of the surrounding rock during the time-dependent deformation process is given. For the surrounding rock in the low confining pressure compression state, the crack closure degree C3 in the radial stress direction is taken as the time-dependent support basis of the surrounding rock. The change of the crack closure degree C3 with time has three cases, i.e. the time-dependent support method of the cavern after excavation is:

[0005] S1, the surrounding rock with a rock mass crack closure degree C3 < x is regarded as failure, and immediate support is required;

[0006] S2, for the surrounding rock with x < C3 < 0, the tangential and radial stress of the rock mass is allowed to be further released, the inflection point of C3 is determined according to the change curve of the C3 value, and it is regarded as the optimal supporting time;

[0007] S3, in combination with the actual engineering support method, the surrounding rock is divided into three regions, i.e. the arch top, the upstream sidewall and the downstream sidewall. If there is a rock mass that needs to be supported in a certain region at a certain level of excavation, the surrounding rock in this region at this level is fully supported.

[0008] Preferably, the maximum principal stress in the surrounding rock is the tangential stress which is parallel to the tunnel wall, and the minimum principal stress is the radial stress which is perpendicular to the tunnel wall;

[0009] Rock mass failure is dominated by the radial stress direction of crack propagation, and for the surrounding rock of the excavated cavern, the ground stress is released, and the surrounding rock of the tunnel wall is considered to be in a uniaxial compression state under no confining pressure stress or a triaxial compression state under low confining pressure stress;

[0010] In a conventional triaxial test, as the confining pressure increases, the failure mode of the rock gradually changes from elastic softening to elastic-plastic hardening, so the increase of the confining pressure is taken as the basis for rock failure;

[0011] Under the action of time effect, the tangential and radial stresses of the tunnel wall will gradually release, and the corresponding anchor cables and anchor rods provide radial compressive stress for the surrounding rock, compensate for the radial pressure released by the surrounding rock itself, reduce the difference between the tangential stress and the radial stress compared to the unsupported working condition, and further make the crack closure degree C3 of the rock mass in the non-destructive stage.

[0012] Preferably, the axial and radial strains are calculated as follows:

[0013] ε v = ε1+ 2ε3 (1)

[0014] Wherein, ε1 and ε3 represent the axial strain and the radial strain respectively, and ε v is the volume strain.

[0015] Preferably, the threshold stress of the rock includes the crack closure stress σ cc , the crack initiation stress σ ci , the crack damage stress σ cd and the peak stress σ p , and according to the four threshold stresses, the crack evolution of the rock is divided into the crack closure stage, the elastic stage, the crack stable growth stage, the crack unstable growth stage and the post-peak stage.

[0016] Preferably, the rock will produce strain under the action of external load, and the strain can be divided into elastic strain and crack strain, and the volume strain is composed of elastic strain εe v and crack strain εc v, which can be expressed as:

[0017]

[0018] When the deviatoric stress reaches σ cc , the natural micro-cracks in the rock are completely closed, and after the deviatoric stress reaches σ ci , the crack continues to expand, so the deviatoric stress is between σ cc and σ cibetween σ cc and σ ci , the slope of the straight line between σ cc and σ ci in the σ cc -σ ci curve can be taken as the elastic modulus E of the rock sample;

[0019] A dimensionless parameter R d , i.e. the ratio of deviatoric stress to peak strength, is introduced for analyzing the test data, which can be expressed as:

[0020]

[0021] where σ1-σ3 is deviatoric stress; σ p is peak strength, i.e. deviatoric stress σ1-σ3 when R d =1;

[0022] The crack closure stress, crack initiation stress, crack damage stress and the ratio of peak stress to peak strength are denoted as Rcc d, Rci d, Rcd d and Rp d, respectively.

[0023] Preferably, the axial and radial elastic strains εe 1 and εe 3 can be expressed as:

[0024]

[0025] where μ is Poisson's ratio;

[0026] The axial and radial crack strains εc 1 and εc 3 can be expressed as:

[0027]

[0028] where εe 1 and εe 3 are axial and radial elastic strains, and εc 1 and εc 3 are axial and radial crack strains;

[0029] The axial and radial elastic strains are calculated by formula (4), and the axial and radial crack strains under different confining pressures are calculated by formula (5) using the deviatoric stress and the axial and radial elastic strains;

[0030] The axial and radial crack strains at Rcc d, Rci d, Rcd d and Rp d, i.e. ε cc 1,ε cc 3,ε ci 1,ε ci 3,ε cd 1,ε cd 3,ε cp 1 and ε cp 3, are calculated.

[0031] The crack strain is preferably in exponential relationship with the confining pressure, the confining pressure can affect the axial crack strain of the rock, and the influence capacity gradually decreases with the increase of the confining pressure; the cracks of the rock gradually close with the increase of the axial stress in the crack closing stage; in order to facilitate the evaluation of the crack closing degree, the axial and radial crack closing degrees C1 and C3 are introduced:

[0032]

[0033] Wherein, ΔR d is the increment of R d , ΔR d >0 in each stage before the peak, and ΔR d <0 in the stage after the peak;

[0034] In the crack stable growth stage (Rcc d<R d <Rcd d), the crack evolution is slow, and the crack closing degree C3 gradually decreases to 0;

[0035] In the crack unstable growth stage (Rcd d<R d <1), the crack expansion speed gradually increases, the crack closing degree C3 rapidly decreases with the increase of R d , and when R d =1, C3=x, the rock starts to be damaged;

[0036] In the softening stage, R d decreases, and C3 continuously decreases to the complete disintegration of the rock.

[0037] Preferably, the optimal supporting opportunity can be calculated as follows:

[0038]

[0039] In the above formula, the optimal supporting opportunity T x (unit: day), the surrounding rock deformation convergence time T c , the strength stress ratio k σ , the strain margin K, the ratio r of the first principal stress σ1 of the surrounding rock after excavation to the uniaxial compressive strength σ c , the supporting confining pressure P, and the time-dependent deformation load coefficient α.

[0040] Preferably, the anchor cable pre-tightening coefficient can be calculated as follows:

[0041]

[0042] Wherein, the anchor cable load sharing coefficient κ=0.5, and the released stress σ nThe anchor cable design tonnage Ns, the anchor cable spacing a×b, the time load factor α, the installation time t (days), and the stable convergence time Tc are 90 days (β=-0.05117), 180 days (β=-0.02558), and 365 days (β=-0.01260), respectively.

[0043] This invention provides a method for determining the timing of underground cavern support. Through systematic testing and calculation based on the rock mass properties of the underground cavern, the crack closure degree in the radial stress direction is used as the basis for time-dependent support of the surrounding rock. There are three cases of crack closure degree changing over time. The surrounding rock of the cavern is treated according to different cases. Under the time-dependent effect, the tangential and radial stresses of the cavern wall will gradually be released. The installation of anchor cables and anchor rods provides radial compressive stress to the surrounding rock, compensating for the radial stress released by the surrounding rock itself. This reduces the difference between tangential and radial stresses compared to the unsupported condition, thereby ensuring that the crack closure degree of the rock mass is in a non-destructive stage, which can ensure the smooth progress of underground cavern operations. Attached Figure Description

[0044] The present invention will be further described below with reference to the accompanying drawings and embodiments:

[0045] Figure 1 It is the stress-strain curve of a granite sample;

[0046] Figure 2 The relationship between fracture closure degree and R under confining pressure of 1 MPa d The relationship between them;

[0047] Figure 3 This is the time-related change curve of C3;

[0048] Figure 4 It is the threshold stress of a granite sample with a confining pressure of 10 MPa. Detailed Implementation

[0049] Example 1

[0050] like Figures 1-4 As shown, the method for determining the timing of support for underground caverns is illustrated. In this example, the rock mass is granite. Based on the degree of fracture closure, the support timing for various parts of the surrounding rock during the aging deformation process is given. The maximum principal stress (tangential stress) is generally parallel to the cavern wall, while the minimum principal stress (radial stress) is perpendicular to the cavern wall. Rock mass failure is dominated by fracture propagation in the radial stress direction. In actual engineering, at locations with obvious compressive failure such as spalling, peeling, and splitting, the tangential stress is the greatest, while the radial stress is very small. For the surrounding rock of an excavated cavern, after the in-situ stress is partially released, the cavern wall surrounding rock can be regarded as being in a uniaxial compression state without confining pressure stress or a triaxial compression state under low confining pressure stress. Figure 1It can be seen that the stress-strain of conventional triaxial test has a close relationship with the confining pressure: with the increase of confining pressure, the failure mode of rock gradually changes from elastic softening to elastic-plastic hardening, which shows that the confining pressure can be used as a basis for rock failure. In addition, according to Figure 2 , the rock with confining pressure of 1 MPa is in the stage of stable growth of fissure (Rcc d<R d <Rcd d), the fissure evolution is slow, and the fissure closure C3 gradually decreases to 0; while in the stage of unstable growth of fissure (Rcd d<Rd<1), the fissure expansion speed gradually increases, and the fissure closure C3 rapidly decreases with the increase of R d ; when R d =1, C3=-17.71, the rock begins to fail; into the softening section, R d decreases, and C3 continuously decreases to-28.0, and the rock completely disintegrates. Under the effect of time, the tangential and radial stresses of the hole wall will gradually release, and the setting of anchor cable and anchor rod provides radial compressive stress to the surrounding rock, compensates for the radial stress released by the surrounding rock itself, reduces the difference between the tangential stress and the radial stress compared with the unsupported working condition, and further makes the fissure closure C3 of the rock mass in the non-destructive stage.

[0051] Therefore, for the surrounding rock of the cavern under the low confining pressure compression state, the fissure closure C3 in the radial stress direction can be used as the time-dependent support basis of the surrounding rock. The change of fissure closure C3 with time has three cases, as shown in Figure 3 . Therefore, the time-dependent support method of the cavern after excavation is:

[0052] (1) The surrounding rock with rock mass fissure closure C3<-17.0 is considered to be damaged, and immediate support is required;

[0053] (2) For the surrounding rock with-17<C3<0, the tangential and radial stresses of the rock mass are allowed to be further released; the inflection point of C3 is determined according to the change curve of C3 value, and is considered as the optimal support opportunity;

[0054] (3) Combined with the actual engineering support method, the surrounding rock is divided into three regions of arch top, upstream side wall and downstream side wall. If the rock mass needs to be supported in a certain level of excavation in a certain region, the surrounding rock in this region at this level is fully supported.

[0055] Example 2

[0056] Based on the time-dependent deformation theory, the calculation formula of the optimal support time of surrounding rock and the pre-tightening coefficient of pre-stressed anchor is derived. The optimal support opportunity can be calculated as follows:

[0057]

[0058] In the above formula: the optimal support opportunity T x (unit: day), the convergence time of surrounding rock deformation Tc , strength stress ratio k σ , strain margin K, first principal stress of surrounding rock after excavation σ1 and uniaxial compressive strength σ c ratio r, supporting confining pressure P, and time-dependent deformation load coefficient α.

[0059] The anchor pretension coefficient can be calculated by the following formula:

[0060]

[0061] Wherein: anchor load sharing coefficient κ = 0.5, stress release σ n , anchor design tonnage Ns, anchor spacing a x b, time-dependent load coefficient α, installation time t (days), stable convergence time Tc is 90 days (β = -0.05117), 180 days (β = -0.02558), 365 days (β = -0.01260) respectively. .

[0062] Example 3

[0063] The stress-strain curve of the granite sample in the test is shown in Figure 1 . ε1 and ε3 represent axial strain and radial strain respectively, and the positive strain value is defined as compression of the sample, and the negative value represents expansion. The volume strain εv can be calculated from ε1 and ε3:

[0064] ε v = ε1 + 2ε3 (1)

[0065] Wherein, ε1 and ε3 represent axial strain and radial strain respectively, and ε v is the volume strain.

[0066] As can be seen from Figure 1 , the peak stress σ p increases with the increase of confining pressure σ3, and when the confining pressure is 1, 3, 5, 10, 20, 30 and 40 MPa, σ p is 114.72, 139.65, 157.22, 182.97, 216.30, 345.73 and 374.63 MPa respectively.

[0067] In order to determine the elastic modulus and Poisson's ratio of granite under different confining pressures, four threshold stresses of granite need to be determined first, i.e. crack closure stress σ cc , crack initiation stress σ ci , crack damage stress σ cd and peak stress σ p ​The four threshold stresses can divide the fracture evolution of rock into five stages: fracture closure stage (stage I), elastic stage (stage II), stable fracture growth stage (stage III), unstable fracture growth stage (stage IV), and post-peak fracture stage (stage V), as shown in FIG. 1. Figure 4

[0068] Under the action of external load, rock will produce strain, which can be divided into elastic strain and fracture strain. The volumetric strain can be composed of elastic volumetric strain εe v and fracture volumetric strain εc v, which can be expressed as:

[0069]

[0070] When the deviatoric stress reaches σ cc , the natural micro-fractures in the rock are completely closed, and after the deviatoric stress reaches σ ci , the fractures begin to expand. Therefore, between σ cc and σ ci , there is no fracture expansion in the rock, and thus no fracture strain is generated. Therefore, the slope value of the straight line between σ cc and σ ci in the rock strain curve can be regarded as the elastic modulus E of the rock sample. At σ3=10MPa, the elastic modulus E of the rock sample is 54.29GPa.

[0071] According to Hooke's law, the axial and radial elastic strains εe 1 and εe 3 can be expressed as:

[0072]

[0073] where μ is the Poisson's ratio.

[0074] Let B=εe 3 / εe 1, then

[0075]

[0076] According to equation (4), the Poisson's ratio μ in the elastic stage is 0.1846 when σ3=10MPa. Therefore, the fracture volumetric strain can be expressed as:

[0077]

[0078] Since there is no fracture strain between σ cc and σ ci , the fracture volumetric strain curve in this interval is a horizontal line. The above method can also be used to calculate different threshold stresses, elastic moduli, and Poisson's ratios under other confining pressures, and the results are shown in Table 1.

[0079] Table 1: Mechanical parameters of granite samples under different confining pressures

[0080]

[0081] For triaxial compression tests, the ratio of threshold stress to peak strength is widely used to analyze the mechanical properties of rocks. In this study, a dimensionless parameter R d , i.e., the ratio of deviatoric stress to peak strength σp, is introduced to analyze the test data, which can be expressed as:

[0082]

[0083] where σ1-σ3 is the deviatoric stress; σ p is the peak strength, i.e., the deviatoric stress σ1-σ3 when R d = 1;

[0084] The crack closure stress, crack initiation stress, crack damage stress, and the ratio of peak stress to peak strength are denoted as Rcc d, Rci d, Rcd d, and Rp d, respectively.

[0085] The axial and radial elastic strains εe 1 and εe 3 can be expressed as:

[0086]

[0087] where μ is the Poisson’s ratio;

[0088] The axial and radial crack strains εc 1 and εc 3 can be expressed as:

[0089]

[0090] where εe 1 and εe 3 are the axial and radial elastic strains, and εc 1 and εc 3 are the axial and radial crack strains;

[0091] The axial and radial elastic strains are calculated by equation (4), and then the deviatoric stress and the axial and radial crack strains under different confining pressures can be calculated by equation (5);

[0092] The axial and radial crack strains at Rcc d, Rci d, Rcd d, and Rp d, i.e., εcc 1, ε cc 3,ε ci 1,ε ci 3,ε cd 1,ε cd 3,ε cp 1, and ε cp 3, are calculated.

[0093] The crack strain is in exponential relationship with the confining pressure, the confining pressure can affect the axial crack strain of the rock, the influence ability thereof is gradually weakened with the increase of the confining pressure, the crack of the rock is gradually closed with the increase of the axial stress in the crack closing stage, in order to facilitate the evaluation of the crack closing degree, the axial and radial crack closing degrees C1 and C3 are introduced:

[0094]

[0095] Wherein, ΔR d is the increment of R d , ΔR d >0 in each stage before the peak, and ΔR d <0 in the stage after the peak;

[0096] In the crack stable growth stage (Rcc d<R d <Rcd d) of the rock, the crack evolution is slow, and the crack closing degree C3 gradually decreases to 0;

[0097] In the crack unstable growth stage (Rcd d<R d <1) of the rock, the crack expansion speed gradually increases, the crack closing degree C3 rapidly decreases with the increase of R d , when R d =1, C3=-17.71, and the rock starts to be damaged;

[0098] In the softening stage, R d decreases, and C3 continuously decreases to the complete disintegration of the rock.

[0099] The above embodiment is only a preferred technical solution of the present application, and should not be regarded as a limitation of the present application, the protection scope of the present application should be the technical solution recorded in the claims, including the equivalent replacement solution of the technical features recorded in the claims as the protection scope. That is, the equivalent replacement improvement in this range is also within the protection scope of the present application.

Claims

1. A method for determining the supporting time of underground caverns, which comprises the following steps: based on the crack closure degree, the supporting time of rock mass at each part of surrounding rock in the time-dependent deformation process is given, for the cavern surrounding rock in the low confining pressure compression state, the crack closure degree C3 in the radial stress direction is taken as the time-dependent supporting basis of the surrounding rock, the change of the crack closure degree C3 with time has three cases, and the time-dependent supporting method of the cavern after excavation is as follows: S1, the surrounding rock with the crack closure degree C3 < x is regarded as damaged, and immediate supporting is required; S2, for the surrounding rock with x < C3 < 0, the tangential stress and the radial stress of the rock mass are allowed to be further released, the inflection point of C3 is determined according to the change curve of the C3 value, and the optimal supporting time is regarded as the inflection point; S3, in combination with the actual engineering supporting method, the surrounding rock is divided into three regions of the arch top, the upstream side wall and the downstream side wall, if the rock mass of a region needs to be supported at a certain level of excavation, the surrounding rock of the region at the level is fully supported; the optimal supporting time is calculated as follows: the maximum principal stress in the surrounding rock is the axial stress which is parallel to the wall, and the minimum principal stress is the radial stress which is perpendicular to the wall; the rock mass failure is dominated by the crack expansion in the radial stress direction, for the surrounding rock of the excavated cavern, after the ground stress is released, the wall surrounding rock is regarded as being in the uniaxial compression state under the condition of no confining pressure stress or the triaxial compression state under the condition of low confining pressure stress; in the conventional triaxial test, with the increase of the confining pressure, the failure mode of the rock gradually changes from elastic softening to elastic plastic hardening, so the increase of the confining pressure is taken as the basis for rock failure; under the time-dependent effect, the axial and radial stresses of the wall gradually release, the corresponding anchor cables and anchor rods provide radial compressive stress for the surrounding rock, compensate for the radial pressure released by the surrounding rock itself, reduce the difference between the axial stress and the radial stress compared with the no-supporting working condition, and further make the crack closure degree C3 of the rock mass in the non-damage stage. The axial and radial strains are calculated as follows: wherein, µ is the Poisson's ratio; the axial and radial elastic strains are calculated by formula (4), and the bias stress and the axial and radial crack strain values under different confining pressures are calculated by formula (5); the crack strain and the confining pressure have an exponential relationship, the confining pressure affects the axial crack strain of the rock, and the influence ability gradually decreases with the increase of the confining pressure; in the crack closure stage of the rock, the crack gradually closes with the increase of the axial stress, in order to facilitate the evaluation of the crack closure degree, the axial and radial crack closure degrees C1 and C3 are introduced; the anchor cable pretightening coefficient is calculated by the following formula: ​ ​ ​ ​ and (7) In the formula: optimal support timing (unit: days), surrounding rock deformation convergence time , strength stress ratio , strain margin , first principal stress of surrounding rock after excavation and uniaxial compressive strength ratio , support confining pressure , and time-dependent deformation load coefficient .

2. The method of claim 1, wherein: ​ ​ ​ ​ 3. The method of claim 2, wherein: the time of the occurrence of the event is determined by the step of: determining the time of the occurrence of the event based on the time of the occurrence of the event in the time domain. ​ （1） where ε1and ε3represent axial and radial strain, respectively, and ε v is the volumetric strain.

4. The method of claim 3, wherein: The threshold stresses of rock include a crack closure stress σ cc , a crack initiation stress σ ci , a crack damage stress σ cd , and a peak stress σ p The crack evolution of rock is divided into a crack closure stage, an elastic stage, a crack stable growth stage, a crack unstable growth stage, and a post-peak stage according to the four threshold stresses.

5. The method of claim 4, wherein: Rock will produce strain under the action of external load, and the strain is divided into elastic strain and fracture strain, and the volume strain is composed of elastic strain and fracture strain , expressed as: （2） When the deviatoric stress reaches σ cc , the natural microcracks in the rock are completely closed, and the cracks start to expand only after the deviatoric stress reaches σ ci . Therefore, there is no crack expansion and no crack strain between σ cc and σ ci . Thus, the slope of the straight line between σ cc and σ ci in the rock strain curve is taken as the elastic modulus E of the rock sample. A dimensionless parameter R d , i.e. the ratio of the deviatoric stress to the peak strength, was introduced to analyze the test data and is expressed as: （3） where σ1-σ3are the principal stresses; σ p is the peak strength, i.e. the principal stress σ1-σ3when R d = 1. The ratio of the fracture closure stress, the fracture initiation stress, the fracture damage stress, and the peak stress to the peak strength are denoted as , , and .

6. The method of claim 5, wherein: axial and radial elastic strain and is represented as: （4） ​ axial fissure strain and radial fissure strain is expressed as: （5） wherein, and are the axial and radial elastic strains, and are the axial and radial crack strains; ​ calculated , , and axial and radial crack strains at , , , , , , and .

7. The method of claim 6, wherein: ​ ​ （5） where ΔR d is the increment of R d , ΔR d > 0 in the pre-peak phase and ΔR d < 0 in the post-peak phase. Rock in the stable growth of the crack phase ( <R d < ), the crack evolution is slow, and the crack closure degree C3 gradually decreases to 0; And the crack unstable growth stage (R <R d <1> crack propagation rate gradually increased, crack closure C3 with R d increased rapidly, in R d = 1, C3 = x, the rock began to damage; Into the softening section, R d decreases, while C3 continuously decreases until the rock is completely disintegrated.

8. The method of claim 1, wherein: ​ ​ （8） Wherein: anchor cable load sharing coefficient = 0.5, release stress , anchor cable design tonnage N s , anchor cable spacing , time load factor respectively α, installation time t (days), surrounding rock deformation convergence time respectively 90 days ( ), 180 days ( ), 365 days ( ).

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