CN111400886A - Displacement calculation method for enclosed pressure arch circular tunnel with unevenly distributed surrounding rock space - Google Patents

Abstract

The invention discloses a displacement calculation method for a closed pressure arch circular tunnel with unevenly distributed surrounding rock space, which comprises the steps of establishing a circumferential statistical analysis method for the unevenly distributed surrounding rock space of the tunnel, establishing a theoretical integral calculation method for the displacement of a deep-buried circular tunnel, and approximately solving an approximate value of the theoretical integral method by adopting a layered summation method idea to obtain the displacement values of the surrounding rock under different reliability degrees. The method introduces a reliability thought, adopts a random theory, considers the statistical rule characteristic of the spatial distribution nonuniformity of the surrounding rock to carry out design calculation, and improves the design scientificity. And establishing a tunnel displacement calculation method capable of considering the spatial nonuniformity of surrounding rocks in the disturbance area.

Description

Displacement calculation method of closed pressure arch circular tunnel with uneven distribution of surrounding rock space

technical field

The invention relates to a tunnel displacement calculation method, in particular to a closed pressure arch circular tunnel displacement calculation method with uneven distribution of surrounding rock space.

Background technique

The initial stress field of the surrounding rock of a deep tunnel usually has the characteristics of a hydrostatic stress field. Therefore, a circular tunnel is a common section form of a deep tunnel. According to the mechanical characteristics of the pressure arch structure, the pressure arch of the deep tunnel is divided into two types: the arch foot type and the closed type, as shown in Figure 1. Generally, under the self-stabilizing condition of the pressure arch in a deep-buried circular tunnel, the surrounding rock disturbance zone can be mainly divided into the following parts: the crushing damage zone (including the residual strength zone), the plastic strengthening zone, and the elastic zone. The surrounding rocks have different mineral compositions and structural and structural characteristics, and are affected by the changing geological processes over time, which make the surrounding rocks show strong heterogeneity. In a deep-buried circular tunnel, not only the surrounding rock of different tunnel sections has inhomogeneity, but also in different positions in the same section, such as three points A, B, and C and points B and D in Figure 2. , E three points, their respective physical and mechanical properties are inhomogeneous. At present, the standard design calculation is mainly based on the classification of the surrounding rock, and the typical section is selected for the calculation of the displacement of the surrounding rock after excavation. However, due to the inhomogeneity of each point on each tunnel section, which section is selected as the typical section for the design calculation becomes the design The key to the calculation, if the selection is unreasonable, often leads to an increase in the error of the predicted reserved deformation, which may lead to over-excavation or under-excavation in the lightest, and unreasonable support design and accidents in severe cases.

SUMMARY OF THE INVENTION

Purpose of the invention: The purpose of the present invention is to provide a displacement calculation method for a closed pressure arch circular tunnel with uneven distribution of surrounding rock space. The idea of reliability is introduced, the random theory is adopted, and the statistical law characteristics of the spatial distribution of the surrounding rock are considered to carry out the design calculation, so as to improve the scientificity of the design. A tunnel displacement calculation method that can consider the spatial inhomogeneity of surrounding rock in the disturbance zone is established.

Technical solution: The present invention provides a closed pressure arch circular tunnel displacement calculation method with uneven distribution of surrounding rock space,

(1) Establish a circumferential statistical analysis method for the spatial distribution of the uneven distribution of the surrounding rock in the tunnel. For a certain section of the tunnel with the same surrounding rock level and similar burial depth, construct a typical cross-section of the reliability of displacement calculation considering the spatial distribution of the surrounding rock. Obtain the probability and statistical function of the physical and mechanical parameters of the surrounding rock at each point on the section along the tunnel axis, and use the truncated normal distribution to fit;

(2) Based on the hoop statistical analysis method of spatial inhomogeneity distribution, a theoretical integral calculation method of displacement for deep-buried circular tunnels is established for the typical cross-section of the reliability of displacement calculation considering the spatial distribution inhomogeneity of surrounding rock;

(3) Circumferential layering is carried out on the surrounding rock along the radial direction, and the strain value is determined according to the stress-strain state of each layer of surrounding rock or according to the stress state and the adopted constitutive model, and the theoretical integral is approximately solved by the layered sum method idea. The approximate value of the method can be used to obtain the displacement value of the surrounding rock under different reliability, and realize the reliability design of the reserved deformation of the deep-buried annular closed pressure arch circular tunnel.

Further, the probability and statistical functions in the step (1) are respectively:

k∈(1，Q)，j∈(1，N)，

k∈(1,Q), j∈(1,N),

是基于随机理论的设计单元段抽象典型断面围岩某一环层j的平均弹性模量、平均应力、平均泊松比、平均粘聚力、平均内摩擦角；g_j、p_j、h_j、k_j、t_j是该典型断面上某一环层j围岩的物理力学参数沿隧道轴向的概率统计函数；其中的μ、σ分别表示物理力学参数在任一断面任一环层上任一点统计的平均值和标准差。In the formula, E _j , σ _j , υ _j , c _j ,

is the average elastic modulus, average stress, average Poisson's ratio, average cohesion, and average internal friction angle of a ring layer j of the surrounding rock at an abstract typical section of the design unit segment based on random theory; g _j , p _j , h _j , k _j , t _j are the probability and statistical functions of the physical and mechanical parameters of the surrounding rock of a certain ring layer j on the typical section along the tunnel axis; where μ and σ represent the physical and mechanical parameters at any point on any ring layer of any section, respectively The mean and standard deviation of the statistics.

Further, in the described step (2), the theoretical integral formula of displacement at any point on the wall of the deep-buried circular tunnel is as follows:

where ω _0,i and ω _N,i are the corresponding displacements at the elastic-plastic boundary of the surrounding rock tunnel and at the tunnel wall along any path i on a typical section constructed based on the spatial inhomogeneity distribution hoop statistical analysis method; ε _j,i is the strain of the corresponding point on the j ring layer on the radial path i; x _0,i , x _N,i , x _j,i are the outer boundary of the first ring layer along the radial path, the The radial distance from the corresponding point on the inner boundary of the ring layer and the inner boundary of the jth ring layer to the center of the tunnel.

Further, the calculation formula of the layered sum method in the step (3) is as follows:

In the formula, ω ₀ and ω _N are respectively the elastic-plastic boundary of a typical cross-section tunnel constructed based on the spatial inhomogeneous distribution hoop statistical analysis method, the corresponding displacement at the tunnel wall, and the strain of ε _j along the radial j hoop; R _j -R _j-1 is the thickness of the jth ring layer.

Further, when N tends to infinity, the formula can be written in integral form as follows:

In the formula, ω ₀ , ω _N , and ε _j have the same meanings as before, and R ₀ , R _N , and R _j are the diameters from the outer boundary of the first ring layer, the inner boundary of the Nth ring layer, and the inner boundary of the jth ring layer to the center of the tunnel, respectively. to distance.

The technical scheme of the present invention achieves the following purposes: 1. For a certain section of deep-buried annular closed pressure arch circular tunnel with the same surrounding rock level and similar burial depth, according to the damage and deformation characteristics of the surrounding rock in the disturbance zone after excavation and the The distance of the center of the circle has a great correlation. The mathematical model of the circumferential statistical method of the spatial inhomogeneity of the surrounding rock of the tunnel is proposed, and an abstract typical cross-section of the reliability of displacement calculation is established. Different regions and different regions adopt different constitutive models to establish the displacement integration method along the radial direction at the cave wall; 3. The idea of layered summation method is adopted, and the layered displacement summation is used to approximate the integral value along the path, and the establishment takes into account the spatial unevenness of surrounding rock. According to the deformation characteristics of the surrounding rock, different constitutive theories are used to establish a tunnel displacement prediction method based on reliability theory, which is a reliable prediction method for tunnel prediction based on reliability theory. The design value of residual deformation provides a theoretical basis.

Beneficial effects: The beneficial effects of the present invention are: the present invention takes into account the uneven spatial distribution of surrounding rocks, and uses random field theory and probability and statistics theory to more scientifically predict the impact of uneven spatial distribution of surrounding rocks on the displacement of surrounding rocks. The influence law provides a theoretical basis for realizing the reliability design of the reserved deformation of the deep-buried annular closed pressure arch circular tunnel, and improves the tunnel design level in my country.

Description of drawings

Fig. 1 is the type diagram of deep buried tunnel pressure arch classified according to the mechanical properties of pressure arch structure in the prior art, wherein, (a) schematic diagram of annular closed pressure arch (b) schematic diagram of arch foot type pressure arch;

Figure 2 is a schematic diagram of the unevenness of surrounding rock at different positions in a certain section of the tunnel;

Figure 3 is a schematic diagram of the design unit section with the same grade of surrounding rock and similar burial depth;

Figure 4 is a schematic diagram of a circumferential statistical analysis method for spatially uneven distribution of physical and mechanical properties of surrounding rocks;

Figure 5 is a schematic diagram of the distribution of the surrounding rock disturbance zone in a circular cavern;

6 is a schematic diagram of a statistical method for the circumferential direction of the surrounding rock in the j-ring layer of the seventh section;

Fig. 7 is a schematic diagram of the statistical method of the surrounding rock circumferential direction of the j-ring layer of the design unit section;

Fig. 8 is the normal distribution curve of the elastic modulus E, wherein (a) the normal distribution curve of the elastic modulus E when N=200 (b) the normal distribution curve of the elastic modulus E when N=5000 ( c) Normal distribution curve of elastic modulus E when N=10000;

Fig. 9 is the probability accumulation curve diagram of elastic modulus E;

Fig. 10 is the probability accumulation curve and normal distribution curve diagram of displacement when N=200, wherein (a) the probability accumulation curve diagram of displacement u (b) the normal distribution curve diagram of displacement u;

Figure 11 is the probability accumulation curve and normal distribution curve of displacement when N=5000, wherein (a) the probability accumulation curve of displacement u (b) the normal distribution curve of displacement u;

Fig. 12 The probability accumulation curve and normal distribution curve of displacement when N=10000, wherein (a) the probability accumulation curve of displacement u (b) the normal distribution curve of displacement u;

Figure 13 is a graph showing the relationship between the mean value of elastic modulus and the number of samples;

Figure 14 is a graph of the relationship between the displacement value corresponding to the reliability of 0.9 calculated by this method and the number of samples.

Detailed ways

The following calculations are routine calculations unless otherwise specified.

The calculation method of this embodiment is specifically as follows:

1. The theoretical calculation method of the displacement of a deep-buried circular tunnel based on the statistical analysis method of the spatially uneven distribution in the circumferential direction

For a tunnel with the same level of surrounding rock and a similar buried depth of length L, it is defined as a design unit section, and the design unit section is divided into Q sections, as shown in Figure 3. The design unit section is introduced as an example. A theoretical calculation method for the displacement of deep-buried circular tunnels considering spatially uneven distribution.

Usually, the displacement calculation of a typical section based on surrounding rock classification is selected as the design value of the design unit section according to the design requirements of traditional codes, but it does not consider the heterogeneity of the surrounding rock in the tunnel disturbance zone. Assuming that the heterogeneity of the surrounding rock is formed by natural conditions such as regular geological movements, the deformation and mechanical properties of the surrounding rock in the same area often have certain statistical laws. According to the research, this kind of inhomogeneity can often be represented by a random function, so random theory is introduced for research, and after the tunnel excavation, the stress state and damage process of the surrounding rock in the disturbed area and the distance from the excavation center point exist. Therefore, according to the characteristics of the surrounding rock disturbance zone, the tunnel section is stratified in the circumferential direction, and the circumferential statistical analysis method of the inhomogeneity of the surrounding rock of the tunnel is proposed. Combined with the random theory, a circumferential statistical analysis method considering the spatial randomness of the surrounding rock is established. The theoretical calculation method of displacement is analyzed, as follows.

In order to effectively study the influence of the spatial uneven distribution of surrounding rock on the displacement, a circumferential statistical analysis method for the spatial uneven distribution of the physical and mechanical properties of the surrounding rock of the rock tunnel is proposed, as shown in Figure 4. It is assumed that there are Q sections along the axial length L of the design unit section, each section is divided into N rings in the radial direction, and the physical and mechanical parameters of the surrounding rock at M points on each ring are used for statistical analysis. Then, the research is carried out on any K-th section in the length direction of the design unit section L, as shown in Figure 4 below, and any j-th ring on this section is taken. The physical and mechanical properties of surrounding rocks at different positions on this ring are often inhomogeneous The properties of the points are not necessarily the same), and when other factors such as self-weight are considered, the stress state is not necessarily the same. Since the physical and mechanical properties of the surrounding rock at the same position of each section along the axial length L are also non-uniform, the physical and mechanical parameters of the surrounding rock at the same relative position c _{j, i} of the Q sections of this design unit section (including fractures etc.) for statistical analysis, assuming that the random distribution function f _{j, i} is satisfied. Therefore, the typical cross-section of the reliability of displacement calculation of the design element section can be abstracted. The physical and mechanical parameters of the surrounding rock at any point c _{j, i} , j∈(1, N), i∈(1, M) on the cross-section satisfy f _{j , i} , j∈(1, N), i∈(1, M) random distribution function, the strain at any point can be calculated according to the balance equation of the force after tunnel excavation and the stress-strain constitutive equation as follows:

是基于随机理论的设计单元段抽象典型断面围岩某一点的应力、弹性模量、泊松比、粘聚力、内摩擦角，它们均是关于环形空间的位置、时间等参数(假设用数组c_j，i综合表示)的统计函数σ_j，i＝p_j，i(C_j，i)、E_j，i＝g_j，i(C_j，i)、υ_j，i＝h_j，i(C_j，i)、c_j，i＝k_j，i(C_j，i)、

δ_j，i是开挖洞室的形状参数。where σ _j,i , E _j,i , υ _j,i , c _j,i ,

It is the stress, elastic modulus, Poisson's ratio, cohesion, and internal friction angle of a certain point of the surrounding rock of an abstract typical section of the design unit segment based on random theory. Statistical function σ _j,i =p _j,i (C _{j ,i} ), E _j,i =g _j,i (C _j,i ),υ _j,i =h _{j, i} (C _{j, i} ), c _{j, i} = k _{j, i} (C _{j, i} ),

δ _{j, i} are the shape parameters of the excavated cavern.

According to the idea of the circumferential layered sum method, the thickness of the ring at each point in Figure 4 is x _{j, i} -x _{j-1, i} , the displacement of any point on the tunnel wall can be expressed as the deformation of each ring along the radial direction The sum, that is, the displacement at the wall of the cave (taking the vault in Figure 4 as an example) can be calculated by the following formula:

When N tends to infinity, the theoretical integral method formula considering the spatial randomness of surrounding rock is obtained as follows:

The displacement calculation formula for any point on the tunnel wall is as follows:

where ε _{i, i} see formula (1).

Formula (4) is the calculation formula of the theoretical integral method for the displacement of tunnels with uneven distribution of surrounding rock space based on random theory. Combined with the reliability idea and the analysis of the safety state of surrounding rock stress and strain, the displacement theory considering the spatial unevenness of surrounding rock can be further established. The calculation and safety prediction method can provide a theoretical basis for establishing a tunnel reliability design method, which has important practical significance and theoretical value.

2. Simplified calculation method for displacement of deep-buried circular tunnels based on the statistical analysis method of spatially uneven distribution in hoop direction

Since the integral function of formula (4) is a random function, it is a stochastic integral problem based on modern martingale theory, which is very difficult to solve theoretically, and can only be realized by numerical simulation at present; usually deep buried tunnels are circular or approximately circular as Therefore, it is proposed to adopt the idea of separating variables, simplify formula (4), and propose a simplified calculation method for the displacement theory of deep-buried circular tunnels based on the spatially uneven distribution hoop statistical analysis method as follows:

Assuming that the surrounding rock adopts the elastic-plastic-damage theory (similar to other rock constitutive theories), and does not consider the residual strength zone, the disturbance zone is mainly divided into the crushing damage zone, the plastic strengthening zone, and the elastic zone. Figure 5 shows the circular cavern Schematic diagram of the distribution of surrounding rock disturbance zones. In the figure, R ₀ , R _c , and R _p are the radius of the circular cavity, the radius of the crushing zone, and the radius of the plastic zone, respectively, _Pi is the support stress, and P ₀ is the initial hydrostatic stress field.

Taking the seventh section of the design unit section as an example, the space is divided into N ring layers along the radial direction, and M measurements are taken from each ring. The layered schematic diagram is shown in Figure 6.

The physical and mechanical parameters of surrounding rock at each point in each ring layer of each section can be obtained by means of radar wave velocity measurement or borehole sampling. For M points in the jth ring layer such as 1, 2..., i...M in Fig. 6, the physical and mechanical parameters of the surrounding rock at these points are obtained.

Since the damage degree of the surrounding rock increases linearly along the radial path, if the number of circumferential layers N is large enough, the damage state of the surrounding rock of each ring layer can be approximately uniform, and its physical and mechanical parameters are set as constants. In order to simplify the calculation, it is recommended to take the parameter average value of M points as the design value of the physical and mechanical parameters of the j-ring layer. Then, taking the elastic modulus as an example, the design value of the elastic modulus of the jth ring layer of the seventh section in Figure 6 (similar to other physical and mechanical parameters) is expressed as:

见图7(以弹性模量为例，其他参数类似)假设满足随机分布函数f_j，在解决工程问题时，根据实测经验，一般它们服从截断式正态分布，即

In the same way, other physical and mechanical parameters of M points at the same position of the same ring layer j (the inner boundary distance from the tunnel center is R _j ) of Q sections can be obtained, and the physical and mechanical parameters of all j ring layers can be calculated according to formula (5). design value

See Figure 7 (take the elastic modulus as an example, other parameters are similar). Assuming that the random distribution function f _j is satisfied, when solving engineering problems, according to the actual measurement experience, generally they obey the truncated normal distribution, namely

j∈(1，N)，抽取Q个断面中同一环层的物理力学参数设计值进行统计，可以得到该设计单元段每个环层参数的分布函数f_j，j∈(1，N)，均服从截断式正态分布。Repeat the above steps to obtain the design value of physical and mechanical parameters of each ring layer of the Q sections of the design unit segment

j∈(1, N), extract the design values of physical and mechanical parameters of the same ring layer in Q sections for statistics, and obtain the distribution function f _j , j∈(1, N) of each ring layer parameter of the design element segment, All obey a truncated normal distribution.

Finally, a section whose physical and mechanical parameters of surrounding rock of each ring layer satisfy its corresponding ring layer space random distribution function f _j , j∈(1, N) is abstracted as the design section of this design unit section (defined as the reliability of displacement calculation According to the balance equation of the force after tunnel excavation and the stress-strain constitutive equation, the strain at any point on the ring layer can be calculated as follows:

是基于随机理论的设计单元段抽象典型断面围岩某一环层中M个点的的平均应力，平均弹性模量，平均泊松比，平均粘聚力，平均内摩擦角，它们均是服从截断式正态分布的函数

k∈(1，Q)，j∈(1，N)。where σ _j , E _j , υ _j , c _j ,

is the average stress, average elastic modulus, average Poisson's ratio, average cohesion, and average internal friction angle of M points in a ring layer of the surrounding rock of an abstract typical section based on random theory. They are all subject to function of truncated normal distribution

k∈(1,Q), j∈(1,N).

Usually in the tunnel design stage, the tunnel has not been excavated, and the statistical values of the deformation and mechanical parameters in the surrounding rock disturbance area after excavation cannot be obtained, but the space for the initial surrounding rock physical and mechanical parameters can be obtained through radar wave measurement technology or drilling technology. The random distribution function, on the basis of the initial random distribution of the surrounding rock space, can obtain the average value of the surrounding rock deformation mechanical parameters of each section and each ring layer.

According to the idea of the circumferential layered summation method, the thickness of each ring in Figure 6 is R _j -R _j-1 , the displacement calculation of any point on the tunnel wall can be expressed as the sum of the deformations of each ring along the radial direction, namely The sum of the deformations of each ring of the abstract design section can be expressed by the following formula:

Therefore, the design value of the displacement of the design unit section can be obtained, so a simplified calculation method of the displacement theory of the deep-buried circular tunnel that can reflect the spatial inhomogeneity of the surrounding rock is obtained.

When N tends to infinity, the formula (7) can be written in the integral form as follows:

where ε _j is shown in formula (6).

Formulas (7) and (8) are based on the stochastic theory based on the spatially uneven distribution hoop statistical analysis method for deep-buried circular tunnel displacement theory to calculate the layered sum method and integral method.

Assuming that only the elastic zone and the plastic zone appear in the surrounding rock (according to the different deformation characteristics of the surrounding rock, different constitutive theories can be selected for calculation, and the calculation method is similar), the calculation example of the displacement theory calculation method using this method is as follows:

For a design unit section of a circular tunnel with an excavation radius R ₀ of 2.5m in an isotropic rock layer, the surrounding rock is grade III, the tunnel burial depth is 100m, the bulk density is 25KN/m ³ , and the initial in-situ stress P _v =P _h =P ₀ =2500KPa, assuming that only the spatial randomness of the elastic modulus is considered as an example, the calculation parameters of the typical section of the abstract reliability design of this design unit segment are shown in Table 1.

Table 1 The values of surrounding rock parameters of typical sections of abstract reliability design

The statistical value of the elastic modulus of the surrounding rock approximately satisfies the truncated normal distribution of formula (9).

Φ(·)为标准正态分布的累积分布函数，

where φ( ) is a standard normal distribution with mean 0 and variance 1,

Φ( ) is the cumulative distribution function of the standard normal distribution,

(1) The traditional Fenner formula displacement theory calculation method

The traditional method is to select the average value of the elastic modulus or the determined value of a certain section as the design parameter, and calculate based on the modified Fenner formulas (10), (11) and (12) of the elastic-plastic theory. The radius of the plastic zone is obtained as R _P =6.24m, and the displacement of the surrounding rock is u = 0.135459cm.

(2) Theoretical calculation method of tunnel displacement considering the spatial inhomogeneity of surrounding rock

According to a large number of theoretical analysis and experiments, it has been proved that the elastic modulus of the surrounding rock physical and mechanical parameters has the most obvious influence on the deformation of the surrounding rock. is 13GPa, the standard deviation is 1GPa, and the upper and lower limits are 9GPa and 17GPa. According to the method of the present invention, if the plastic zone is regarded as one layer (because the farther from the center of the tunnel, the damage to the surrounding rock is relatively small, so the theoretical deformation characteristics of the surrounding rock are different at different positions, so the more layers are divided, the closer to the actual situation. , but the calculation method is the same), then there is only one layer in the ring direction in Figure 6, then the corresponding modified Fenner formula can be directly used to calculate the displacement of the surrounding rock of the tunnel wall. The specific calculation process is as follows:

First, according to the statistical value of the elastic modulus of the surrounding rock, a fitting analysis is performed to obtain its truncated normal distribution function (see formula 1 for this example); secondly, according to the truncated normal distribution function, enough sample values are taken to In this example, 200, 500, 1000, 2000, 5000, and 10000 sample values were taken for calculation and analysis, and the accuracy of the calculation results was compared. Theoretical calculation analysis.

The calculation results of this example are analyzed as follows:

When the number of samples for elastic modulus values is 200, 5000, and 10000, respectively, the corresponding histogram distribution can be calculated by using the truncated normal distribution function as shown in Figure 8.

According to Figure 8 and Figure 9, the generated elastic moduli have the characteristics of a truncated normal distribution, the mean values are: 12.9385GPa, 13.00277GPa, 13.01896GPa, and the standard deviations are: 0.96956GPa, 0.99409GPa, 1.00503GPa, N The probability accumulation curves for 5000 and 1000 are almost identical.

The tunnel displacement results calculated for different generated samples are as follows:

When the number of samples is N=200, the displacement of surrounding rock is approximately normally distributed, with an average value of 0.13687cm. The cumulative curve shows that its distribution range is 0.10866～0.1721em, which is controlled by 90% reliability. The predicted displacement design value can be taken as 0.14893cm. The reliability is 80% controlled, and the predicted displacement design value can be 0.14209cm. The calculated displacement value of the average elastic modulus of 12.9385GPa is 0.136103cm, and its corresponding reliability is 58.065% according to the probability accumulation curve in Figure 10(a).

When the number of samples is N=5000, the displacement of surrounding rock is approximately normally distributed, with an average value of 0.13624cm. The cumulative curve shows that its distribution range is 0.10465-0.19443cm. It is controlled according to the reliability of 90%. The predicted displacement design value can be taken as 0.14799cm. The reliability is 80% controlled, and the predicted displacement design value can be 0.14264cm. The calculated displacement value of the average elastic modulus of 13.00277GPa is 0.13543cm, and its corresponding reliability is 59.423% according to the probability accumulation curve in Figure 11(a).

When the number of samples is N=10000, the displacement of surrounding rock is approximately normally distributed, with an average value of 0.13608cm. The cumulative curve shows that its distribution range is 0.10394-0.18889cm, which is controlled by 90% reliability. The design value of the predicted displacement can be taken as 0.14797cm. The reliability is 80% controlled, and the predicted displacement design value can be 0.1425cm. The calculated displacement value of the average elastic modulus of 13.01896GPa is 0.135262cm, and the corresponding reliability is 59.593% according to the probability accumulation curve in Figure 12(a).

Table 2 Comparative analysis of different sample values:

It can be seen from the calculation results of different sample numbers (see Figures 13 and 14) that when the sample value is greater than 2000, the error of the generated sample is less than 0.2‰, and the displacement value corresponding to the reliability of 0.9 tends to converge, and the error is less than 0.5‰ , so as long as the sample is large enough (this example is greater than 2000), the calculation result of this calculation method tends to converge, and the calculation result is stable and reliable. This method can be used as the theoretical basis for the reliability design method of the reserved displacement in the tunnel design specification.

From the analysis of the calculation results of the case, it can be seen that the method of the present invention can effectively reflect the reliability law of the surrounding rock displacement caused by the spatial distribution of the physical and mechanical properties of the surrounding rock, and can realize the reliability design of the reserved deformation of the tunnel. The result of a certain section or average calculation is more scientific.

Claims (5)

1. a closed-type pressure arch circular tunnel displacement calculation method with uneven distribution of surrounding rock space, is characterized in that: comprise the steps: (1) Establish a circumferential statistical analysis method for the spatial distribution of the uneven distribution of the surrounding rock in the tunnel. For a certain section of the tunnel with the same surrounding rock level and similar burial depth, construct a typical cross-section of the reliability of displacement calculation considering the spatial distribution of the surrounding rock. Obtain the probability and statistical function of the physical and mechanical parameters of the surrounding rock at each point on the section along the tunnel axis, and use the truncated normal distribution to fit; (2) Based on the hoop statistical analysis method of spatial inhomogeneity distribution, a theoretical integral calculation method of displacement for deep-buried circular tunnels is established for the typical cross-section of the reliability of displacement calculation considering the spatial distribution inhomogeneity of surrounding rock; (3) Circumferential layering is carried out on the surrounding rock along the radial direction, and the strain value is determined according to the stress-strain state of each layer of surrounding rock or according to the stress state and the adopted constitutive model, and the theoretical integral is approximately solved by the layered sum method idea. The approximate value of the method can be used to obtain the displacement value of the surrounding rock under different reliability, and realize the reliability design of the reserved deformation of the deep-buried annular closed pressure arch circular tunnel. 2. The closed-type pressure arch circular tunnel displacement calculation method with uneven distribution of surrounding rock space according to claim 1, is characterized in that: in the described step (1), the probability and statistical functions are respectively:

In the formula, E _j , σ _j , υ _j , c _j ,

is the average elastic modulus, average stress, average Poisson's ratio, average cohesion, and average internal friction angle of the surrounding rock j ring layer of the abstract typical section of the design unit segment based on random theory; g _j , p _j , h _j , k _j and t _j are the probability and statistical functions of the physical and mechanical parameters of the surrounding rock of the j ring on the typical section along the tunnel axis; where μ and σ represent the statistical average values of the physical and mechanical parameters at any point on any ring of any section, respectively and standard deviation. 3. The closed pressure arch circular tunnel displacement calculation method with uneven distribution of surrounding rock space according to claim 1, is characterized in that: in described step (2), any point displacement theory integral of deep-buried circular tunnel wall The formula is as follows:

where ω _0,i and ω _N,i are the corresponding displacements at the elastic-plastic boundary of the surrounding rock tunnel and at the tunnel wall along any path i on a typical section constructed based on the spatial inhomogeneity distribution hoop statistical analysis method; ε _j,i is the strain of the corresponding point on the j ring layer on the radial path i; x _0,i , x _N,i , x _j,i are the outer boundary of the first ring layer along the radial path, the The radial distance from the corresponding point on the inner boundary of the ring layer and the inner boundary of the jth ring layer to the center of the tunnel. 4. the preparation method of the closed pressure arch circular tunnel displacement calculation method of the uneven distribution of surrounding rock space according to claim 1, is characterized in that: the calculation formula of layered sum method in described step (3) is as follows:

In the formula, ω ₀ and ω _N are respectively the elastic-plastic boundary of a typical cross-section tunnel constructed based on the spatial inhomogeneous distribution hoop statistical analysis method, the corresponding displacement at the tunnel wall, and the strain of ε _j along the radial j hoop; R _j -R _j-1 is the thickness of the jth ring layer. 5. the preparation method of the closed pressure arch circular tunnel displacement calculation method of the uneven distribution of surrounding rock space according to claim 4, it is characterized in that: when N tends to infinity, then formula can be written as integral form as follows:

In the formula, R ₀ , R _N , and R _j are the radial distances from the outer boundary of the first annular layer, the inner boundary of the N-th annular layer, and the inner boundary of the j-th annular layer to the center of the tunnel, respectively.

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