JP5181272B2 - Tunnel stability evaluation method and program thereof - Google Patents

Description

  The present invention relates to a method and a program for evaluating the stability of a tunnel in advance when constructing a tunnel.

  As a high-level radioactive waste disposal method, “geological disposal” in which a tunnel group is built deep underground and the radioactive waste is buried therein is being studied. As shown in Fig. 13, it is stipulated by law that this geological disposal facility should be an underground facility with a depth of 300m or more. Multiple disposal tunnels (tunnels), main tunnels connecting these tunnels, and these tunnels above the ground It consists of several types of shafts connected to the receiving facility.

  The characteristic curve method is used as a method for evaluating the stability of a mine shaft for such a geological disposal facility. The characteristic curve method has been established as a stability analysis method for the standard method of mountain tunnels since the introduction of the New Austrian Tunneling Method (NATM) as a tunnel construction method. The mechanical behavior at the excavation site (face) of the tunnel is extremely three-dimensional, but the characteristic curve method solves the mechanical behavior of the excavation site by replacing it with a two-dimensional dynamic model.

This characteristic curve method is composed of a ground characteristic curve representing deformation behavior associated with excavation of a natural ground and a support characteristic curve representing deformation behavior of the support after the support is installed. FIG. 14-1 shows an example of a natural ground characteristic curve and a support characteristic curve. Natural ground characteristic curve performs theoretical analysis and the finite element method or the like to the 2-dimensional cross section of the plane strain state, as shown in Figure 14-2, and支保pressure P _i is the pressure支保supports the natural ground It is obtained by the relationship of the wall surface displacement u. Further, as shown in FIG. 14-3, the support characteristic curve is obtained from the relationship between the support reaction force P _i that is the earth pressure acting on the support and the displacement (= wall surface displacement) u of the support outer periphery.

  In the characteristic curve method, a two-dimensional model is used to evaluate the interaction between support internal pressure on ground such as shotcrete and the earth pressure acting on the support. For this reason, the state where both the natural ground and the support are stable is considered to be the balance point because the internal pressure acting on the natural ground and the ground pressure acting on the support (supporting reaction force) are equal. This is the intersection of the support characteristic curves.

  Since the interaction between the ground and the support near the face during tunnel excavation shows a very three-dimensional behavior, it is necessary to predict the behavior closer to the actual situation and to evaluate the stability of the ground and the support. Or examination with a quasi-three-dimensional model is required.

The present inventor has proposed a method for obtaining a support characteristic curve by performing sequential excavation / sequential support analysis using an axially symmetric model with the central axis of the circular mine shaft as a symmetric axis (Non-Patent Document 1 and Japanese Patent Application No. 2006-193280). reference). The outline of a method for obtaining a support characteristic curve by sequential excavation / sequential support analysis using this axisymmetric model will be described below. First, set the excavation section for excavation and support installation of a predetermined length, and the physical properties of surrounding ground and support, and divide the excavation part, support installation and surrounding ground into finite elements and analyze model Create Next, sequential excavation and sequential support analysis is performed using this analysis model. In sequential drilling / sequential support analysis, after installing the support of the i-1th excavation section, excavation of the ith excavation section is performed, and the excavation for which stability is evaluated along with this ith excavation A process of calculating the nodal displacement and the radial stress of the element located at the boundary between the natural ground and the support in the section (evaluation target excavation section) is performed. This process is sequentially repeated until i is incremented by 1 until i reaches the total number of excavation sections. Next, a calculation is performed to average the node displacement and radial stress obtained by the above processing for each excavation section analyzed for excavation. Here, the average value of the nodal displacement corresponding to each excavation section analyzed for excavation is regarded as the wall displacement u ^L of the evaluation excavation section at the time when excavation in each excavation section is completed. Further, the average value of the radial stress corresponding to each excavation section analyzed for excavation is regarded as the support reaction force P _i ^L of the evaluation target excavation section when the excavation of each excavation section is completed. The parietal displacements u and x-axis, the支保reaction force P _i on the u-P _i plane with y-axis, by plotting the values of these parietal displacements u and支保reaction force P _i, obtaining a支保characteristic curve .

International Journal of the JCRM, Volume 3, Number 1, February 2007, pp1-6

  However, the support characteristic curve obtained by performing the sequential excavation / sequential support analysis by the above-mentioned three-dimensional or quasi-three-dimensional model (axisymmetric model) shows the natural ground characteristics when the natural ground is assumed to be an elastic body. When the ground is assumed to be an elasto-plastic body at the point of intersection with the curve, and the yield / fracture behavior of the ground due to excavation is taken into account, the wall displacement and support reaction of the support characteristic curve are considered. The results showed that the force did not converge on the natural ground characteristic curve, and both the wall displacement and the supporting reaction force had large values. That is, when the natural ground model is an elasto-plastic body, the support characteristic curve obtained by the above analysis is not in a balanced state on the natural ground characteristic curve. In particular, under conditions using support by shotcrete that exhibits high rigidity in a short time to prevent the influence of excavation as much as possible at large depths where the earth pressure is large, wall displacement and support obtained from analysis by the conventional characteristic curve method There are reports that these values are clearly greater than reaction forces. For this reason, as in the conventional characteristic curve method, when the support design is performed by using the value of the intersection of the natural ground characteristic curve and the support characteristic curve, it is designed assuming a smaller load (support reaction force) than the actual one. May be done. Similarly, the wall displacement of the natural ground becomes a large value, and the deformation of the natural ground around the tunnel is evaluated small. In other words, it is considered that the stability of the natural ground and the stability of the support may be underestimated, and there is a possibility that the support design is insufficient for the actually required strength.

  Therefore, when applying the results of the above-mentioned sequential excavation / sequential support analysis to the characteristic curve method, this stability index is newly set so that the stability of the ground and the support can be properly determined. There is a need.

  In view of the above points, the present invention stabilizes the ground and the support when the analysis result of the sequential excavation / sequential support analysis by the above-described three-dimensional or quasi-three-dimensional model (axisymmetric model) is applied to the characteristic curve method. It is an object of the present invention to provide a tunnel stability evaluation method and a program thereof that can improve the determination accuracy of sex.

In the tunnel stability evaluation method according to claim 1 of the present invention, the excavation section for excavation and support installation of a predetermined length, the surrounding ground and the physical property values of the support are set, and the excavation part and the support installation are set. The process of creating an analysis model by dividing a part and surrounding natural ground into finite elements, and a circular hole model in a two-dimensional infinite body with the natural ground as an elasto-plastic body, A step of obtaining a curve, and after installing the support of the ( i-1) excavation section, excavation of the i th excavation section, and the ground in the excavation section to evaluate the stability with the i th excavation The process of calculating the node displacement and radial stress of the element located at the boundary between the support and the support is sequentially repeated until i is increased by 1 until i becomes the total number of excavation sections, and excavation in the final excavation section is performed. In the excavation section to assess the stability at the time of completion The average value of the nodal displacement of each element located at the boundary between the natural ground and the support is calculated, and this is used as the wall displacement u ^{L in the} excavation section, and the stability when the excavation in the final excavation section is completed The average value of the radial stress of the natural ground element located at the boundary between the natural ground and the support in the excavation section and the radial stress of the support element is calculated, and this is calculated as the support reaction force P _i ^L in the excavation section. and a step of, strain allowable wall holds for the natural ground epsilon _theta, from the relationship between the permissible wall displacement u _a and支保pressure P _i which is calculated using _a, a step of creating an acceptable land mountains strain curve支保inner edge From the value of the supporting reaction force P _{i, max} when the tangential stress σ _θ is the allowable stress σ _a of the supporting material, and the horizontal axis is the tunnel wall displacement u, the vertical axis in u-P _i plane was支保pressure P _i the axis, the wall Position end point determined by the u ^L and the支保reaction force P _i ^L is the permissible locations Mountain strain curve, the allowable working place pressure curve, and, whether the stable region surrounded by the natural ground characteristic curve And a step of determining.

The tunnel stability evaluation method according to claim 2 of the present invention is characterized in that, in the above-mentioned claim 1, the allowable wall surface displacement u _a is calculated from a state strain of a natural ground.

  A program according to a third aspect of the present invention causes a computer to execute each step in the tunnel stability evaluation method according to the first aspect.

  According to the tunnel stability evaluation method and the program thereof of the present invention, it is possible to appropriately evaluate the support and the stability of surrounding grounds when a tunnel is constructed under a high ground pressure at a deep depth. As a result, when constructing a tunnel with a low construction record, such as a disposal tunnel in a geological disposal facility, it is possible to perform an accurate support design.

  Exemplary embodiments of a tunnel stability evaluation method according to the present invention will be described below in detail with reference to the accompanying drawings.

  FIG. 1 is a block diagram showing a configuration of an analysis apparatus 10 applied in the tunnel stability evaluation method according to the present embodiment. The analysis device 10 exemplified here is realized by reading a program into a numerical computing device such as a personal computer. The analysis device 10 includes a support characteristic curve creating unit 20, a ground characteristic curve creating unit 30, an allowable ground pattern strain. A curve creation means 40, an allowable action ground pressure line creation means 50, and a stability determination means 60 are provided.

  The support characteristic curve creation means 20 includes an analysis model creation means 21, a sequential excavation / support analysis means 22, and a nodal displacement / radial stress average value calculation means 23.

  The analysis model creation means 21 includes analysis conditions input from an input device 70 such as a keyboard, specifically, excavation sections for excavation and support installation of a predetermined length, surrounding natural ground and support physical property values, etc. Based on the data, analysis model data is created by dividing the excavation part, the support installation part, and the surrounding natural ground into elements. Specific analysis conditions will be described later.

  The sequential excavation / support analysis means 22 performs the following sequential excavation / support support analysis using the analysis model created by the analysis model creation means 21. The details of the analysis procedure will be described later. The outline of the analysis will be described below. After installing the support for the i-1th excavation section, the excavation analysis of the ith excavation section is performed, and the analysis result is attached. Then, a process of calculating the nodal displacement and the radial stress of the element located at the boundary between the natural ground and the support in the excavation section for evaluating the stability is performed. This process is sequentially repeated until i is incremented by 1 until i reaches the total number of excavation sections. Note that only excavation analysis is performed for i = 1 (that is, the first excavation section). Here, “an excavation section for evaluating stability” means an excavation section to be evaluated for stability, and a single excavation section at a position behind the face where the influence of the face is almost eliminated is selected. . Hereinafter, this is referred to as “evaluation target excavation section”.

The average value calculation means 23 of the nodal displacement and the radial stress (support reaction force) is calculated by the sequential excavation / support analysis means 22 along with the excavation analysis of each excavation section, and the ground and support in the evaluation target excavation section are calculated. The node displacement and radial stress of each element located at the boundary are averaged for each excavation section analyzed for excavation, and the support characteristic curve is calculated based on the average value of these node displacement and the average value of radial stress. Is to be calculated. In this embodiment, as will be described later, the average value of the nodal displacement corresponding to each excavation section analyzed for excavation is set as the wall displacement u ^L of the evaluation target excavation section at the time when excavation in each excavation section is completed. . Further, the average value of the radial stress for each excavation section excavated analyzed, and支保reaction force P _i ^L evaluated excavation section at the time the excavation is completed for each excavation section. Then, these wall displacement u ^L and支保reaction force P _i ^L, by plotting the horizontal axis parietal displacements u, a vertical axis on支保pressure P _i and the u-P _i plane, the evaluation excavation section Create a support characteristic curve. Here, the support internal pressure P _i is an internal pressure in the tunnel acting on the natural ground (pressure at which the support supports the natural ground).

Natural ground characteristic curve creation unit 30 is adapted to create a natural ground characteristic curve on u-P _i plane. In this embodiment, assuming a natural hole as an elastic-plastic body and assuming a circular hole model in a two-dimensional infinite body, a natural ground characteristic curve is created based on an elastic-plastic theory under a predetermined condition of this model. The relationship between the wall displacement u and the support pressure P _i in the natural mountain characteristic curve is described in, for example, Geoffronte Study Group, New Mountain Tunnel Technology, Civil Engineering Company, p. It can be expressed using a known calculation formula described in No. 43 and the like. An example of a natural ground characteristic curve is shown in FIG. In this embodiment, a natural ground characteristic curve is created by a theoretical solution. In numerical analysis such as a finite element method in which the tunnel is a two-dimensional plane strain model, the tunnel internal pressure P _i is used as a given condition. the calculated wall displacement u and支保pressure P _i, they may be created natural ground characteristic curve by plotting on u-P _i plane.

ここに、ε_θ,a：許容壁面ひずみ，ｑ_u：一軸圧縮強度，ν：ポアソン比，κ：ダイレイタンシー係数，Ｐ_i：支保内圧，η_a：室内三軸試験の軸ひずみε₁と限界ひずみε₀との比である。ここで、限界ひずみとは、図１１で示されるε₀である。なお、η_aは、拘束圧＝０である一軸圧縮試験を含めて室内三軸試験を残留応力状態まで実施した際の応力−ひずみ曲線から、限界ひずみと状態ひずみの定義に基づいて各ひずみε₁、ε₀を求めることにより算出される。 The allowable ground strain curve creating means 40 creates an allowable ground strain curve on the u- _Pi plane. An example of an allowable ground strain curve is shown in FIG. The allowable ground strain curve shows the relationship between the allowable wall displacement u _a and the internal pressure P _i of the ground where the stability of the ground is ensured, and is an index for judging the stability of the ground and rock around the tunnel. It will be. Here, the radius of the tunnel is a. If a strain ε _θ in the tangential direction of the ground wall of the circular tunnel defined by ε _θ ≒ u _a / a is introduced between the allowable wall displacement u _a of the ground strain curve and the supporting internal pressure P _i , The relationship expressed by Equation (1) is established.

Where ε _{θ, a} : allowable wall strain, q _u : uniaxial compressive strength, ν: Poisson's ratio, κ: dilatancy coefficient, P _i : support internal pressure, η _a : axial strain ε _{1 in the} indoor triaxial test It is the ratio to the limit strain ε ₀ . Here, the critical strain is ε ₀ shown in FIG. Note that η _a is a strain ε based on the definition of the limit strain and the state strain from the stress-strain curve when the indoor triaxial test including the uniaxial compression test where the constraint pressure = 0 is performed to the residual stress state. ₁ and ε ₀ are calculated.

ここに、Ｐ₀：初期地圧である。 Further, F in the equation (1) is a stability evaluation index due to the stress of the tunnel wall surface and is given by the following equation.

Here, P _{0 is the} initial ground pressure.

In the present embodiment, the state strain is adopted as the allowable strain of the natural ground, and the allowable wall displacement u _a is calculated from this state strain. That is, the evaluation criteria for the stability of the natural ground are relaxed so that they are consistent with the construction results, compared to the case where the limit strain (constant regardless of the support internal pressure) is adopted as the allowable strain. Here, the reason why the allowable strain of the ground is set as the state strain will be briefly described. FIG. 11 shows the stress-strain relationship obtained in the indoor triaxial test. Epsilon ₁ of the horizontal axis in FIG. 11 is the strain axis, σ ₁ -σ ₃ of ordinate axis difference stress (sigma ₁ is axial pressure, sigma ₃ is confining pressure) it is. Moreover, the straight line in FIG. 11 is a tangent at the origin of three curves. FIG. 11 shows the stress-strain relationship when σ ₃ = 0, σ ₃ = c, and σ ₃ = d. As shown in this figure, in the case of soft rock, the strain at the peak stress (ε ⁰ peak, ε ^c peak, ε ^d peak) increases as the restraining pressure σ ₃ increases. That is, the allowable strain amount can be increased in consideration of the restraint pressure. Therefore, as shown in the relationship between the permissible locations Mountain strain curves and支保pressure P _i in FIG. 10, it is possible to increase the allowable wall displacement u _a near natural ground when支保pressure P _i increases. Therefore, when the support internal pressure P _i is large, it is considered that a design that can ensure the stability of the natural ground is possible even if the allowable strain is increased.

  In addition, (Equation 1) and (Equation 2) are based on a paper by the present inventors ("Study on tunnel stability evaluation based on tunnel construction results and ground strain ratio"). 11 volume 2001 November report pp.257-260).

Allowable working place pressure curve creating means 50 is for calculating the allowable working place pressure curve on u-P _i plane. An example of the allowable action ground pressure line is shown in FIG. Allowable working place pressure line is支保tangential stress sigma _theta of tunnel air side (maximum compressive stress), when equal to allowable stress sigma _a of支保, between the displacement u of支保reaction force P _i and支保periphery The relationship is shown and serves as an index for determining the stability as a support member. Here, the support reaction force is a ground pressure (acting ground pressure) acting on the support. Further, the supporting tangential direction stress σ _θ (maximum compressive stress) on the air side in the tunnel is a stress in the θ direction in FIG. (In FIG. 12, σ _r is the radial stress of the tunnel.) In the present embodiment, the support reaction force P _i at the allowable action ground pressure line is constant regardless of the displacement u of the support outer periphery, This constant value is written as P _{i, max} .

ここに、ａはトンネルの半径、ｔは支保厚である。 The allowable stress σ _a of the support is calculated in advance from the shape, dimensions, thickness, strength, and the like of the support. On the other hand, for example, the thickness and tangential stresses sigma _theta of using the支保inner wall cylinder theory, between the支保reaction force P _i acting on the outer periphery, the following equation (3) relationship with. Accordingly, the support reaction force P _{i, max} can be obtained by substituting the allowable stress σ _a of the support material into the tangential stress σ _θ .

Here, a is the radius of the tunnel, and t is the support thickness.

The stability determination means 60 uses the natural ground characteristic curve calculated by the natural ground characteristic curve creation means 30 and the allowable natural ground strain line creation means 40 at the end point of the support characteristic curve created by the support characteristic curve creation means 20. It is determined whether or not it is within a region surrounded by the calculated allowable ground strain line and the allowable action ground pressure line calculated by the allowable action pressure line creation means 50. As will be described later, the end point of the support characteristic curve is the value of the wall displacement u ^L and the support reaction force P _i ^L in the excavation section in which the support was last installed. Hereinafter, a region surrounded by the natural ground characteristic curve, the allowable natural ground strain curve, and the allowable action pressure line is referred to as a “stable region”. When the end point of the support characteristic curve is within the stable region, the stability determination means 60 determines that both the natural ground and the support are stable. On the other hand, when the end point of the support characteristic curve is outside the stable region, the stability determination means 60 determines that the ground and the support are unstable, or one of the ground and the support is unstable. .

  Note that the above-mentioned support characteristic curve, natural ground characteristic curve, allowable ground strain curve, allowable action ground pressure line, analysis results of sequential excavation / sequential support analysis, stability determination results, etc. It is possible to output through the output means 80.

  Next, an example of creating a support characteristic curve by sequential excavation / sequential support analysis will be described.

(Analysis conditions)
The mine shaft to be analyzed has a circular cross section and an inner diameter of 5 m (excavation diameter of 6 m). The support is only for shotcrete, and the spray thickness is 0.5m. FIG. 4 shows the cross-sectional shape and dimensions of an actual mine shaft to be analyzed. One excavation length (the length of the excavation section) is set to 1.5 m. The analysis area is 100 m × 100 m, and the final face position is 60 m from the boundary so as not to be affected by the excavation start boundary. The element length is set to 0.1 m × 0.25 m. FIG. 5 shows the constraint conditions between the analysis region and the boundary. As shown in FIG. 5, the analysis model of the present embodiment uses an axially symmetric model with the central axis of the circular mine shaft as the symmetric axis by performing axially symmetric analysis.

  FIG. 6 shows a face portion in a mine excavation part of the analysis model shown in FIG. In FIG. 6, i, i-1, i-2,... Each indicate an excavation section having an excavation length of 1.5 m. Although not shown in the figure, 40 excavation sections are set between the mine entrance and the final face position. As shown in FIG. 6, one excavation section is divided into six rows, and the excavation part is subdivided into elements a 'to f' and the shotcrete installation part is subdivided into elements a to f.

  In the present embodiment, excavation and shotcrete installation are performed in one excavation section, and this is repeated starting from the first excavation section 1 until the final excavation in the final excavation section 40 is completed. That is, FIG. 6 shows a situation before excavation up to the excavation section i-1 and installation of shotcrete are completed and excavation of the next excavation section i is performed.

(Physical properties of natural ground)
Natural ground and shotcrete shall be elastic. The physical properties of the rocks are between the softest rock mass data set used for studying the stability of geological disposal facilities, SR-A, which has the maximum strength, and SR-E, which has the minimum strength, at a depth of 500 m. SR-C, which was judged to be the limit ground condition that can be practically disposed of, was used. The initial ground pressure is 10.8 MPa and the depth is 500 m. Table 1 shows various physical property values of the bedrock SR-C.

(Analysis case and shotcrete physical properties and natural model)
Table 2 shows the physical properties of the analysis case, shotcrete, and natural ground model. As shown in Table 2, nine types of analysis are performed according to the elastic modulus of the shotcrete and the natural ground model. Analysis cases 01 to 04 are cases where the natural ground is an elastic body, and analysis cases 11 to 14 are cases where the natural ground is an elasto-plastic body. The analysis case 00 is an excavation analysis in the case of no support without installing shotcrete. In this analysis case 00, the above excavation section is not set, and analysis by collective excavation is performed.

Further, as described above, in this embodiment, the natural ground and the shotcrete are made elastic, and the hardening of the shotcrete with the progress of the face is not considered. As shown in Table 2, the properties of shotcrete were set to 5 GPa from the elastic modulus used when using the characteristic curve method in a general tunnel. Based on this, 10 GPa, 20 GPa, and 40 GPa were set. The elastic modulus 20 GPa is a shotcrete that exhibits high rigidity in a short time (3 hours), and 40 GPa is an elastic coefficient that assumes the elastic modulus of the concrete segment.

(Procedure for sequential excavation and sequential support analysis)
Hereinafter, the procedure of sequential excavation and sequential support analysis will be described with reference to the flowchart of FIG. The sequential excavation / sequential support analysis includes steps S101 for creating an analysis model, steps S102 to S106 for executing the sequential excavation / sequential support analysis, and elements located at the boundary between the natural ground and the support calculated by this analysis. The calculation step S107 for averaging the nodal displacement and the radial stress in the excavation section is sequentially repeated until the final excavation section. The sequential excavation / sequential support analysis uses, for example, a finite difference method FLAC or the like.

  After inputting the above-mentioned analysis conditions, physical properties of the ground, physical properties of the support, natural ground model, etc., and generating the analysis model by the analysis model creation means 21 (step 101), the sequential excavation / support analysis means 22 The excavation of the first excavation section 1 is started (step S102). Excavation in one excavation section is performed 6 times every 0.25 m in the order of a ′ to f ′ as shown in FIG. 6. At this point, no support has been established.

  2 is input to i (step S103), and the support element of the excavation section i-1 is installed (S104). The support elements are installed at the same time from a to f.

  Next, excavation in the excavation section i is started (step S105). The elastic modulus and strength constant of the support (sprayed concrete) in the excavation section i-1 to the excavation section 1 are set to constant values as shown in Table 2. In consideration of the time-lapse characteristics of the shotcrete, that is, the hardening characteristics, the excavation is set according to the elapsed time from the excavation section 1 to the excavation section i based on the relationship between the age and physical properties of the shotcrete. Analysis can also be performed.

At the time when excavation of the a ′ portion of the excavation section i is completed, the nodal displacement and the radial stress in the support element and the natural ground element located at the boundary between the support of the evaluation target excavation section and the natural ground are calculated (step 106). . In addition, the evaluation target excavation section may be any of i-1 to 1 where i is the section where excavation is performed, but when evaluating the stability of natural ground and support in the state after excavation, the influence of the face It is desirable to consider at a position where there is almost no (digging section). As a guide, it is a position 3 to 5 times the tunnel diameter D from the face. In the present embodiment, the excavation section 31 is set as the evaluation target excavation section. As shown in FIG. 6, when the excavation length is 1.5 m, the number of elements located at the boundary between the support and the ground in one excavation section is twelve. FIG. 7 is an enlarged view of the natural ground element and the supporting element at the boundary portion between the natural ground and the support (sprayed concrete). As shown in FIG. 7, the nodal displacements of one element located at the boundary between the natural ground and the support are u _j and u _{j + 1} . Further, σ _s is a radial stress in one support element located at the boundary between the natural ground and the support, and σ _g is a radial stress of a natural element adjacent to the support element.

Next, the value calculated in step S106 is sent to the nodal displacement / radial stress average value calculating means 23, and the radial stresses and nodal points of the twelve elements located at the boundary between the support of the evaluation excavation section 31 and the natural ground. The displacements are averaged within the excavation section (step S107). The process of step S107 is executed through the following two stages. First, the average value of the radial stresses σ _s and σ _g of the elements calculated in step S106 is calculated from the following equation (4).

Similarly, the average value of the nodal displacements u _j and u _{j + 1} of the element calculated in step S106 is calculated by the equation (5).

Here, the average value of the radial stress σ _s in the support element and the radial stress σ _g in the ground element is defined as the stress acting on the boundary between the ground element and the support element, that is, the ground element and the support element The support reaction force P _{av at} the boundary of The average value of the nodal displacements u _j and u _{j + 1} is regarded as the wall surface displacement u _{av at} the boundary between the natural ground element and the supporting element.

Next, the support reaction force P _av and the wall surface displacement u _av at the boundary between the natural ground element and the support element are averaged within the evaluation target excavation section 31 (af). That is, the average value of the six supporting reaction forces P _av of a to f in the evaluation target excavation section 31 is calculated by the equation (6). Similarly, an average value of six wall surface displacements u _av of a to f in the evaluation target excavation section 31 is calculated by the equation (7). Here, the average value of the support reaction force P _av in the evaluation target excavation section 31 is regarded as the support reaction force P _i ^L in the evaluation target excavation section 31 when the excavation of the a ′ portion of the excavation section i is completed. Further, the average value of the wall displacement u _av in the evaluation target excavation section 31 is regarded as the wall displacement u ^L in the evaluation target excavation section 31 at the time when excavation of the a ′ portion of the excavation section i is completed.

The processes in steps S105 to S107 are performed every time the excavation of the b ′ to f ′ portion of the excavation section i is completed.

The processes in steps S104 to S107 are repeated until the final excavation section (step S108). The excavation section 39 is supported, the final excavation section 40 is excavated, and the wall displacement u ^L and the supporting reaction force P _i ^L in the evaluation target excavation section 31 at the time when the excavation of the f ′ portion of the excavation section 40 is completed. Is calculated and the calculation is terminated (step S109).

Using the values of the wall displacement u ^L and the support reaction force P _i ^L of the evaluation target excavation section 31 obtained in step S107, a support characteristic curve is created by the following procedure. The convergence value (final wall displacement) of the wall displacement obtained by the collective excavation analysis in the case of no support in the analysis case 00 is u _0, and the initial ground pressure set in step S101 is P ₀ . The ratio (u / u ₀ ) of wall displacement u to final wall displacement u ₀ obtained by unsupported excavation analysis is x-axis, and the ratio (P / P ₀ ) of support reaction force P _i to initial ground pressure P ₀ is As the y-axis, the values obtained in step S107 are plotted for each analysis case. A support characteristic curve of the wall displacement and the support reaction force in the evaluation target excavation section 31 is obtained by linearly approximating the plotted points by the least square method.

  The graph (b) in FIG. 8 shows support characteristic curves in four types of analysis cases 01 to 04 when the natural ground is an elastic body. In the graph (b), straight lines passing through 1.0 on the x-axis and the y-axis are natural ground characteristic curves. This natural ground characteristic curve is obtained by the theoretical solution of the natural ground physical properties and the circular hole of the elastic natural ground shown in Table 1. In the case of an elastic natural ground, it is known that the natural ground characteristic curve is a straight line. As shown in FIG. 8B, when the natural ground is an elastic body, the end point of the support characteristic curve (final displacement) is on the intersection with the natural ground characteristic curve, and on the intersection with the natural ground characteristic curve. It will be in a balanced state. Therefore, when the natural ground is assumed to be an elastic body, it matches the result obtained by the two-dimensional analysis using the characteristic curve.

  Note that the intersection (x-axis intercept) between each support characteristic curve and the x-axis is the preceding displacement rate. In the case of an elastic natural ground, since the preceding displacement rate and the stress release rate are equal, the intersection of the support characteristic curve and the x axis is the stress release rate. Here, the stress release rate is one of the important parameters for the calculation using the characteristic curve method. The initial reaction pressure at the face or support installation position and the support reaction force acting on the ground from the tunnel wall surface. Or it is the ratio of the difference from the reaction force of the natural ground just before excavation to the initial ground pressure.

  On the other hand, FIG. 9 is a graph showing support characteristic curves in four types of analysis cases 11 to 14 when the natural ground is made of an elastoplastic material. A curve A in the figure is a natural ground characteristic curve created by the natural ground characteristic curve creating means 30. This natural ground characteristic curve is a natural ground characteristic curve obtained by the theoretical solution of the natural ground physical properties and elasto-plastic natural ground shown in Table 1, and is not a straight line as in the case of an elastic natural ground. Become. As shown in FIG. 9, when the natural ground is assumed to be elasto-plastic, unlike the analysis case of the elastic natural ground described above, the wall displacement and the support reaction force of the support characteristic curve do not converge on the natural ground characteristic curve. It can be seen that both the displacement and the supporting reaction force are larger than those of the elastic ground. That is, when the natural ground model is an elasto-plastic body, the support characteristic curve is not balanced on the natural ground characteristic curve.

(Tunnel stability determination procedure)
As described above, when the natural ground model is an elasto-plastic body, the support characteristic curve obtained by the sequential excavation / sequential support analysis is not in a balanced state on the natural ground characteristic curve. Therefore, as in the prior art, when performing adopted by支保designed支保pressure P _i and the wall displacement u at the intersection of the natural ground characteristic curve and支保characteristic curve, to be performed actually designed for smaller loads than Therefore, there is a possibility that the support design is insufficient for the actually required strength. In the present embodiment, a stable region surrounded by the above-described allowable ground strain curve, allowable action ground pressure line, and natural ground characteristic curve is set, and whether or not the end point of the support characteristic curve enters this stable region. By judging, the tunnel stability is evaluated. The procedure in the tunnel stability evaluation method of the present embodiment will be described below with reference to the flowchart of FIG. 2 and the graph of FIG.

First, as explained above, an analysis model in which the natural ground is assumed to be an elasto-plastic body is created, and sequential excavation and sequential support analysis are performed. Along with the excavation analysis of each excavation section, values of the wall displacement u ^L and the supporting reaction force P _i ^L of the evaluation excavation section are calculated. The calculated values are plotted on the u- _Pi plane as shown in FIG. 10, and a support characteristic curve is created (step S100).

Next, the natural ground characteristic curve creating means 30 creates natural ground characteristic curves based on the theoretical solution of the natural ground physical properties and the elasto-plastic natural ground shown in Table 1 (step S111). Next, the allowable ground strain curve creating means 40 creates the above-described allowable ground strain curve on the u- _Pi plane (step S112). Then, the allowable working place pressure curve creating means 50 creates an allowable action land pressure curve mentioned above on u-P _i plane (step S113). By executing steps S111 to S113, as shown in FIG. 10, a stable region surrounded by a natural ground characteristic curve, an allowable natural ground strain curve, and an allowable action ground pressure line is created.

Next, it is determined whether or not the end point of the support characteristic curve is in the stable region (step S114). Here, the end point of the support characteristic curve is the value of the wall displacement u ^L and the support reaction force P _i ^{L in} the evaluation target excavation section 31 when excavation of the f ′ portion of the excavation section 40 is completed. As shown in FIG. 10, when the end point of the support characteristic curve is in the stable region (step S114: Yes), the stability determination means 60 determines that both the ground and the support are stable, and adopts the analysis model ( Step S115). When it is determined that the stability determination means 60 is stable, the support design is performed based on the end point value of the support characteristic curve.

On the other hand, although illustration is omitted, when the end point of the support characteristic curve is outside the stable region (step S114: No), the stability determination means 60 determines that the support and the surrounding ground are unstable, Judge that the tunnel is not stable. For example, when the end point of the support characteristic curve is located on the right side of the allowable ground strain curve, the stability determination unit 60 determines that the surrounding ground is unstable. That is, in this state, since the wall surface displacement exceeds the allowable wall surface displacement u _a , it can be said that there is a possibility that the natural ground may be greatly deformed compared to the case where it is in the stable region.

In addition, when the end point of the support characteristic curve is located above the allowable action pressure line, the stability determination unit 60 determines that the support is unstable. That is, in this state, since the support reaction force exceeds the allowable working ground pressure _{Pi, max} , there is a possibility that a greater load may be applied to the support than in the stable region. It is judged that the stability of the system cannot be secured.

In addition, when the end point of the support characteristic curve is at a position satisfying the right side of the allowable ground pressure strain curve and the upper side of the allowable action ground pressure line , the stability determination means 60 is unstable in both the surrounding ground and the support. Is determined. That is, in this state, the wall displacement and the support reaction force both exceed the allowable values, so that the natural ground may be greatly deformed and a large ground pressure may be applied to the support as compared to the stable region. It can be said that there is.

  In addition, when the end point of the support characteristic curve is at a position satisfying the left side of the natural ground characteristic curve and the upper side of the allowable action pressure line, the stability determination means 60 determines that an excessive ground pressure is acting on the support. To do. In addition, when the end point of the support characteristic curve is located below the natural ground characteristic curve, it is considered to be a stable region as a judgment, but for the analysis, the end point of the support characteristic curve comes here. Since it does not exist in the case, it is unlikely to actually occur.

  In addition, when it becomes No in step S114, the determination result of stability is fed back, for example, the analysis model is set again and the analysis is performed again.

  The above steps S100 to S115 can be realized by a computer and a program executed by the computer, and the program can be stored in a computer-readable recording medium such as a magnetic disk, an optical disk, or a semiconductor memory. . In this case, the analysis apparatus 10 executes steps S100 to S115 by a program read from the recording medium.

  As described above, according to the tunnel stability evaluation method and the program thereof according to the present embodiment, the support and the stability of surrounding ground are appropriately evaluated when a tunnel is constructed under a deep deep ground pressure. It becomes possible. As a result, it is possible to carry out a highly accurate support design when constructing a tunnel with few construction results, such as a disposal tunnel in a geological disposal facility.

  In addition, since the tunnel stability evaluation method and the program according to the present embodiment apply the evaluation method based on the conventional characteristic curve method, the support designer who has evaluated the tunnel stability by the characteristic curve method. The effect is easy to understand.

Moreover, in the tunnel stability evaluation method which is the embodiment calculates the allowable wall displacement u _a from strain state of the natural ground, the strain allowable locations mountain relationship between the allowable wall displacement u _a and支保pressure P _i A curve was created. As described above, when the support internal pressure increases (that is, when the support effect increases), the allowable wall surface displacement u _a of the surrounding natural ground also increases. That is, compared to the case where the allowable strain is the limit strain (constant regardless of the support internal pressure), the difference in support performance of the support can be evaluated in a form closer to the actual situation. As a result, when支保internal pressure P _i is large, it is possible to reflect the effect that even by increasing the permissible wall displacement u _a can be ensured stability in支保design.

  The number of elements, the number of excavation sections, the number of excavation rows (a ′ to f ′) in the excavation sections, etc. are examples, and are not limited to these. It is. Further, in the above-described sequential excavation / sequential support analysis, the evaluation target excavation section is the excavation section 31, but the present invention is not limited to this, and other excavation sections may be evaluated if the position is sufficiently away from the face. It may be a digging section. Further, in the above embodiment, a procedure for sequentially repeating the calculation process of averaging the ground displacement element and the nodal displacement and the radial stress of the support element calculated in the sequential excavation / support analysis means 22 in the excavation section until the final excavation section. In other words, although the procedure from step S104 to step S109 is sequentially repeated and then the procedure proceeds to step S110, the flow of this process is an example, and the following procedure may be used.

  For example, after the sequential excavation / support analysis is executed up to the final excavation section, the calculated nodal displacement and radial stress values of each element are collectively sent to the nodal displacement / radial stress average value calculation means 23, and the excavation section It is good also as a procedure which calculates each average value in 1-digging section 39. That is, after repeating step S104 to step S106 to the last excavation section, it is good also as a procedure which progresses to step S107 and calculates the average value of each excavation section.

  Further, the sequential excavation / support analysis, the calculation process of the average value in the excavation section and the plot processing of the average value may be sequentially repeated until the final excavation section. In other words, steps S104 to S110 may be sequentially repeated until the final excavation section.

In the tunnel stability determination in the above embodiment, it is determined whether or not the end point of the support characteristic curve is in the stable region. That is, for the stability determination, only the values of the wall displacement u ^L and the support reaction force P _i ^L in the excavation section 39 where the support was last installed are used. Therefore, it is not always necessary to create a support characteristic curve, and only the end point may be plotted on the u- _Pi plane.

  Furthermore, in the above embodiment, the support characteristic curve is created by the sequential excavation / sequential support analysis, and then the natural ground characteristic curve, the allowable natural ground strain curve, and the allowable action ground pressure line are created. Curves, allowable ground strain curves, and allowable action pressure lines are obtained independently of sequential excavation and sequential support analysis. Therefore, it is good also as a procedure which produces these three lines beforehand, before performing sequential excavation and sequential support analysis.

It is a block diagram which shows the structure of the analyzer applied in this Embodiment. It is the flowchart which showed the procedure of the process which the analyzer shown in FIG. 1 implements. It is the flowchart which showed the procedure of the process which the analyzer shown in FIG. 1 implements. It is sectional drawing of the mine shaft of the analysis model applied in this Embodiment. It is a conceptual diagram which shows the analysis area | region of the analysis model applied in this Embodiment. It is a conceptual diagram which shows the element division | segmentation condition of the analysis model applied in this Embodiment. It is the figure which expanded and showed the boundary of the natural ground and support of the analysis model applied in this Embodiment. In sequential excavation and sequential support analysis, it is a graph which shows the relationship between the distance from a face and a wall surface displacement ratio when a natural ground is made into an elastic body, and a graph which shows a natural ground characteristic curve and a support characteristic curve. It is a graph which shows a natural ground characteristic curve and a supporting characteristic curve when a natural ground is made into an elasto-plastic body in sequential excavation and sequential support analysis. It is a graph for demonstrating determination of the tunnel stability in this Embodiment. It is a graph which shows the relationship between the stress obtained by an indoor triaxial test, and distortion. It is a figure for demonstrating the support tangential direction stress of the sky side in a tunnel. It is the schematic of a geological disposal facility. It is a graph which shows an example of the natural ground characteristic curve and support characteristic curve in the conventional characteristic curve method. It is a figure for demonstrating support internal pressure and wall surface displacement. It is a figure for demonstrating support reaction force and wall surface displacement.

Explanation of symbols

DESCRIPTION OF SYMBOLS 10 Analyzing device 20 Support characteristic curve creation means 21 Analytical model creation means 22 Sequential excavation / support analysis means 23 Nodal displacement / radial direction stress average calculation means 30 Ground rock characteristic curve creation means 40 Allowable ground strain curve creation means 50 Allowable action Ground pressure line creation means 60 Stability judgment means 70 Input device 80 Output device

Claims (3)

Set the excavation section for excavation and support installation of a predetermined length, and the physical properties of surrounding ground and support, and divide the excavation part, support installation and surrounding ground into finite elements to create an analysis model And a process of
Assuming a circular hole model in a two-dimensional infinite body with the natural ground as an elasto-plastic body, obtaining a natural ground characteristic curve from the physical values of the surrounding natural ground,
After installing the support for the i-1 th excavation section, excavation for the i th excavation section, and with the i th excavation, at the boundary between the natural ground and the support in the excavation section to evaluate the stability Repeating the process of calculating the nodal displacement and the radial stress of the located element by increasing i by 1 until i becomes the total number of excavation sections;
Calculate the average value of the nodal displacement of each element located at the boundary between the natural ground and the support in the excavation section to evaluate the stability at the time when excavation in the final excavation section is completed, and calculate the wall displacement in the excavation section u ^L and the radial stress of the ground element and the radial stress of the support element at the boundary between the natural ground and the support in the excavation section to evaluate the stability when the excavation of the final excavation section is completed And calculating this average value as the support reaction force P _i ^L in the excavation section,
Creating a permissible ground strain curve from the relationship between the permissible wall displacement u _a calculated using the permissible wall strain ε _{θ, a established} for the natural ground and the support internal pressure Pi;
Creating an allowable working pressure line from the value of the supporting reaction force P _{i, max} when the tangential stress σ _θ of the supporting inner edge becomes the allowable stress σ _a of the supporting material;
The horizontal axis tunnel wall displacement u, a vertical axis u- P _i plane was支保pressure P _i, the end point determined by said wall displacement u ^L and the支保reaction force P _i ^L is the permissible locations Mountain strain curve, Determining whether it is in a stable region surrounded by the allowable action ground pressure line and the natural ground characteristic curve;
A method for evaluating tunnel stability, comprising: The tunnel stability evaluation method according to claim 1, wherein the allowable wall displacement u _a is calculated from a state strain of a natural ground.   A program for causing a computer to execute each step in the tunnel stability evaluation method according to claim 1.

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