Principal stress calculation program and principal stress calculation method

Abstract

To provide a principal stress calculation program capable of solving problems of conventional arts, that is, relatively easily obtaining principal stress of anisotropic rock mass from a result of an original position test, and a principal stress calculation method using the program.SOLUTION: A principal stress calculation program is a program for causing a computer to execute a function for obtaining a maximum principal stress σ1∞, a minimum principal stress σ2∞, and a working angle α of principal stress of rock mass, based on a first deformation coefficient E1, a second deformation coefficient E2 and an initial loading pressure p0 for N times, which are obtained by performing a loading test, in which a wall surface of a borehole provided in anisotropic rock mass is pressurized by a uniform displacement loading method, while changing a loading direction. The principal stress calculation program comprises a function that causes a computer to execute condition value acquisition processing, working angle setting processing, provisional principal stress calculation processing, sensitivity coefficient calculation processing, difference sum square calculation processing, working angle determination processing, and principal stress determination processing.SELECTED DRAWING: Figure 7

Description

Technical Field

[0001] The present invention relates to a technique for the principal stress of rock masses exhibiting anisotropy in deformation characteristics. More specifically, it relates to a technique for obtaining the two-dimensional initial principal stress of a rock mass by performing an analysis based on the anisotropic elasticity theory on the results obtained from an in-hole loading test using the equal-displacement loading method.

Background Art

[0002] When planning the design of a structure constructed on or within a rock mass, it is extremely important to understand the mechanical properties of the rock mass. Examples of the mechanical properties of the rock mass include, for example, the stress state and deformation coefficient of the rock mass. Among these, the stress state of the rock mass is indispensable information for the design of new tunnels or large-depth underground cavities, or for the design of reinforcing existing tunnels showing deformations beyond expectations or aging tunnels with significant deterioration over time.

[0003] To understand the stress state of a rock mass, in-situ tests, that is, actually measuring the stress at the site, are generally performed. In particular, it can be broadly classified into the "hydraulic fracturing method" shown in Patent Document 1 and the "stress relief method" shown in Patent Documents 2 and 3. In addition, the applicant of the present application has disclosed in Patent Document 4 a suitable invention capable of obtaining the initial stress of a rock mass based only on the results obtained from a borehole jack test.

Prior Art Documents

Patent Documents

[0004]

Patent Document 1

Patent Document 2

Patent Document 3

Patent Document 4

Summary of the Invention

Problems to be Solved by the Invention

[0005] The hydraulic fracturing method as shown in Patent Document 1 is a method of generating an artificial crack by plugging a predetermined section in a borehole with a packer and applying hydraulic pressure to this part, and obtaining the stress of the rock mass from the relationship between the hydraulic pressure and the crack. Therefore, in order to perform the hydraulic fracturing method, it is necessary to prepare various devices such as a packer, a high-pressure pump, a water tank, and a cable winch, that is, the entire device becomes large-scale.

[0006] On the other hand, the stress relief method as shown in Patent Document 2 and Patent Document 3 is a method of obtaining the stress of the rock mass by fixing a rock pressure detector (or a specially processed strain gauge) in a borehole with cement milk or an adhesive and then performing overcoring, and continuously measuring the released strain before and after this overcoring for a certain period of time. Therefore, in order to perform the stress relief method, an operation of constructing an overcoring is required, and moreover, an operation of fixing the rock pressure detector or the special strain gauge in the borehole using grout or the like is also required.

[0007] Among these, the method shown in Patent Document 2 is a method particularly called the "Denchuken-type embedded strain method" among the stress relief methods, and it is considered unsuitable because it is difficult to grout-fix the rock pressure detector in the case of a large amount of water inflow. In addition, since an overcoring with a large bore diameter (usually about φ200 mm) is required, it requires a great deal of labor and time, and an indoor test using the core collected by overcoring must be carried out in order to obtain the sensitivity coefficient of each strain gauge used. The method shown in Patent Document 3 is a method particularly called the "conical hole bottom strain method" among the stress relief methods, and it is considered unsuitable because it is difficult to adhesively fix the strain gauge in the case of even a little water inflow or in the case of porous soft rock. In addition, an indoor test must also be carried out in order to obtain the deformation coefficient and Poisson's ratio.

[0008] By the way, since the stress distribution in rock masses generally has significant variations, it is considered desirable to perform measurements at multiple points instead of just at one point (one borehole). However, in the method of Patent Document 1, the entire apparatus is large-scale, so it takes time for preliminary preparation. In the method of Patent Document 2, it requires a great deal of labor and time. Also, in the method of Patent Document 3, there are the above-mentioned restrictive conditions for strain gauge installation. Thus, it is by no means realistic to perform measurements at a large number of points (boreholes) by conventional methods, such as requiring construction work for overcoring and grouting fixation work.

[0009] In this regard, the invention disclosed in Patent Document 4 only requires performing a normal borehole jack test, that is, it can perform the test at low cost and easily, so it can realize measurement at multiple points without difficulty. However, this invention is an analysis technique based on the premise of an isotropic rock mass, and sufficient results cannot be obtained when applied to a rock mass showing anisotropy.

[0010] The problem of the present invention is to solve the problems of the prior art, that is, to provide a principal stress calculation program that can relatively easily obtain the principal stresses of an anisotropic rock mass from the results of in-situ tests, and a principal stress calculation method using the same.

Means for Solving the Problem

[0011] The present invention focuses on the fact that since there is a linear relationship between the initial loading pressure p0 in an in-situ test and the principal stresses (the maximum principal stress σ1 ∞ and the minimum principal stress σ2 ∞ ), respectively, it is possible to convert a complex implicit function for calculating the initial loading pressure p0 into a relatively simple explicit function. It is an invention made based on an unprecedented idea.

[0012] Based on the first deformation coefficient E1, the second deformation coefficient E2, and the initial loading pressure p0 obtained from N (N is a natural number of 3 or more) times of loading tests in which a loading test for pressurizing the wall surface of a borehole provided in an anisotropic rock mass by an equal-displacement loading method is performed while changing the loading direction, the maximum principal stress σ1 of the rock mass∞ , the minimum principal stress σ2 ∞ , and the maximum principal stress σ1 ∞ A program that causes a computer to execute a function for obtaining the angle of action α, which has functions for causing the computer to execute a condition value input process, an action angle setting process, a provisional principal stress calculation process, a sensitivity coefficient calculation process, a sum of squared differences calculation process, an action angle determination process, and a principal stress determination process. Note that the first deformation coefficient E1 is the deformation coefficient in the direction of the first axis among three orthogonal axes (the first axis, the second axis, and the third axis), and the second deformation coefficient E2 is the deformation coefficient in the direction of the second axis. Among these, the condition value input process is the test hole radius r and the loading surface curvature β in the loading test, the first Poisson's ratio ν 12 (however, within the plane including the first axis and the second axis), the second Poisson's ratio ν 13 (however, within the plane including the first axis and the third axis), the first deformation coefficient E1, the second deformation coefficient E2, and the initial loading pressure p0 are processes for taking in. The action angle setting process is a process for setting a plurality of types of candidate action angles α(i) that are candidates for the action angle α, and the sensitivity coefficient calculation process is a process for calculating a first sensitivity coefficient Ω1 and a second sensitivity coefficient Ω2 given by the following formula for each candidate action angle α(i). p0 = Ω1×σ1 ∞ (i) + Ω2×σ2 ∞ (i) The provisional principal stress calculation process is a process for calculating a provisional maximum principal stress σ1 ∞ (i) and a provisional minimum principal stress σ2 ∞ (i) for each candidate action angle α(i), and the sum of squared differences calculation process is a process for calculating a squared difference s given by the following formula for each of the N tests for each candidate action angle α(i), and calculating a sum of squared differences that is the sum of the squared differences for N times. s = [p0 - Ω1×σ1 ∞ (i) + Ω2×σ2 ∞ (i)] 2 The action angle determination process is a process for selecting the minimum sum of squared differences among the sums of squared differences obtained for each candidate action angle α(i), and determining the candidate action angle α(i) corresponding to the minimum sum of squared differences as the action angle α. The principal stress determination process is the provisional maximum principal stress σ1 ∞ (i) and the provisional minimum principal stress σ2∞ (i) is a process of determining each as the maximum principal stress σ1 ∞ and the minimum principal stress σ2 ∞ respectively.

[0013] The principal stress calculation program of the present invention can also be such that the provisional principal stress calculation process calculates the provisional maximum principal stress σ1 ∞ (i) and the provisional minimum principal stress σ2 ∞ (i) by using the least squares method with the following formula.

Equation

[0014] The principal stress calculation method of the present invention is a method of obtaining the maximum principal stress σ1 ∞ and the minimum principal stress σ2 ∞ of a rock mass showing anisotropy, and the acting angle α of the maximum principal stress σ1 ∞ . It is a method having a loading test process and an analysis process. In the loading test process, N (N is a natural number of 3 or more) loading tests are performed on the rock mass while changing the loading direction. In the analysis process, the principal stress calculation program of the present invention is used, and based on the test results for N times, the maximum principal stress σ1 ∞ and the minimum principal stress σ2 ∞ and the acting angle α of the principal stress are obtained.

Advantages of the Invention

[0015] The principal stress calculation program and the principal stress calculation method of the present invention have the following effects. (1) Based on the results of in-situ tests, the principal stress of an anisotropic rock mass can be obtained relatively easily. (2) By considering anisotropy, the variation in the measurement results of the principal stress can be reduced. (3) When performing numerical analysis of cavities, structures, etc. in a rock mass, input values considering the anisotropy of the principal stress of the rock mass can be adopted, and cavities, structures, etc. can be evaluated more accurately than before.

Brief Description of the Drawings

[0016]

Figure 1

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Figure 4

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Figure 10

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Figure 12

Embodiments for Carrying Out the Invention

[0017] Examples of embodiments of the principal stress calculation program and the principal stress calculation method of the present invention will be described based on the drawings.

[0018] 1. Definitions In explaining examples of embodiments of the principal stress calculation program and the principal stress calculation method of the present invention, first, definitions of terms used here will be shown.

[0019] (Borehole Jack Test) One of the technical features of the present invention is to obtain the principal stress, which is a mechanical property of rock mass, using the results of in-situ tests. As this in-situ test, a loading test in which the borehole wall surface is pressurized by an equal-displacement loading method may be adopted. For convenience, here this loading test method will be referred to as the "borehole jack test". Hereinafter, the method of the borehole jack test in the present invention will be described.

[0020] FIG. 1 is a diagram for explaining the borehole jack test, where (a) is a cross-sectional view cut along the vertical plane and (b) is a cross-sectional view of the borehole BH cut along the horizontal plane. As shown in this figure, in conducting the borehole jack test, a loading device (hereinafter referred to as the "borehole jack JB") is arranged at a predetermined position in a previously constructed borehole BH. This borehole jack JB is composed of a piston jack and a loading plate LB, and has a structure in which the piston jack operated by hydraulic pressure presses the loading plate LB in the direction of the hole wall. A pressure gauge and a displacement gauge are built into the borehole jack JB. This hydraulic pressure is transmitted from a pressure source CP installed on the ground through a hose HS. And through a communication cable SC connected to the borehole jack JB, a data logger DL records the values of pressure (hydraulic pressure) and displacement. As shown in FIG. 1(b), the loading plate LB has a predetermined width, that is, the hole wall can be pressurized by the width dimension of the loading plate LB. For convenience, here, half of the central angle extending from the center of the borehole jack JB to both ends of the loading plate LB will be referred to as the "loading surface curvature β", and the radius of the borehole BH (test hole) will be referred to as the "test hole radius r" (FIG. 1(b)).

[0021] In the borehole jack test according to the present invention, the test is performed N times (N is a natural number of 3 or more) while changing the loading direction, and the test results for N times are used for analysis. FIG. 2 is a cross-sectional view obtained by horizontally cutting the boring hole BH, similar to FIG. 1(b), showing the relationship between the loading direction θ and the maximum principal stress σ1 ∞ (or the minimum principal stress σ2 ∞ ) and the acting direction (hereinafter referred to as "acting angle α"). FIG. 4(a) shows the maximum principal stress σ1 ∞ and the minimum principal stress σ2 ∞ when the loading direction θ is 0°, and FIG. 4(b) shows the maximum principal stress σ1 ∞ and the minimum principal stress σ2 ∞ when the loading direction θ is -45°. Here, the loading direction θ is the direction in which the loading plate LB presses the hole wall. When a two-dimensional orthogonal coordinate system consisting of the X-axis and the Y-axis is set on the horizontal plane, the positive direction of the X-axis is defined as 0°, and the rotation angle is positive in the counterclockwise direction. Of course, the X-axis - Y-axis can be set arbitrarily, and the 0° direction of the rotation angle can also be set arbitrarily, for example, as the positive direction of the Y-axis. The positive direction of the rotation angle can also be set clockwise instead of counterclockwise. In this figure, an example of the borehole jack test for two times with different loading directions is shown. However, as described above, in the present invention, it is necessary to perform at least 3 times (for example, 4 times) of the borehole jack test while changing the loading direction θ.

[0022] (First deformation coefficient and second deformation coefficient) The present invention is for obtaining the principal stress of "anisotropic rock masses" that exhibit anisotropy in deformation characteristics, such as sedimentary rocks with developed bedding, metamorphic rocks with developed schistosity, and igneous rocks with developed joints. FIG. 3 is a diagram schematically showing the deformation coefficients in three axial directions of this anisotropic rock mass. FIG. 3(a) shows a case where the layer direction (the direction of bedding, schistosity, or joints) of the anisotropic rock mass is the horizontal plane (in this case, the plane including the x-axis and the z-axis), and FIG. 3(b) shows a case where the layer direction of the anisotropic rock mass is inclined with respect to the horizontal plane.

[0023] As shown in Fig. 3, the anisotropic rock mass has deformation coefficients in three orthogonal axis directions set along the strike and dip of the rock mass. For convenience, here the three orthogonal axis directions set in the rock mass are respectively referred to as the "first axis", "second axis", and "third axis", and further, the deformation coefficient in the first axis direction is the "first deformation coefficient E1", the deformation coefficient in the second axis direction is the "second deformation coefficient E2", and the deformation coefficient in the third axis direction is the "third deformation coefficient E3". For example, in the case of Fig. 3(a), since the layer direction of the anisotropic rock mass is horizontal, the first deformation coefficient E1 can be set in the x-axis direction, the second deformation coefficient E2 in the y-axis direction, and the third deformation coefficient E3 in the z-axis direction. On the other hand, in the case of Fig. 3(b), since the layer direction of the anisotropic rock mass is inclined by a predetermined angle (hereinafter referred to as the "inclination angle φ") from the horizontal plane, the first deformation coefficient E1 can be set in the direction inclined by the inclination angle φ from the x-axis, the second deformation coefficient E2 in the direction inclined by the inclination angle φ from the y-axis, and the third deformation coefficient E3 in the z-axis direction.

[0024] Normally, for the anisotropic rock mass, the two deformation coefficients (in this case, the first deformation coefficient E1 and the third deformation coefficient E3 in the z-axis direction) parallel to the plane of each layer can be treated as having substantially the same magnitude only with different directions. On the other hand, the deformation coefficient (in this case, the second deformation coefficient E2) perpendicular to the plane of each layer is quite different in magnitude from the deformation coefficients in the other two directions (in this case, the first deformation coefficient E1 and the third deformation coefficient E3 in the z-axis direction). Therefore, for convenience, an example using the first deformation coefficient E1, the second deformation coefficient E2, and the inclination angle φ will be described here.

[0025] (Poisson's ratio and shear modulus) Since the anisotropic rock mass has Poisson's ratios in three mutually perpendicular planes, for convenience, here the Poisson's ratio in the plane containing the first axis (x-axis in Fig. 3) and the second axis (y-axis in Fig. 3) is the "first Poisson's ratio ν 12 ", the Poisson's ratio in the plane containing the first axis (x-axis in Fig. 3) and the third axis (z-axis in Fig. 3) is the "second Poisson's ratio ν 13 ", and the Poisson's ratio in the plane containing the second axis (y-axis in Fig. 3) and the third axis (z-axis in Fig. 3) is the "third Poisson's ratio ν 23shall be defined as such. Also, the shear modulus of the rock mass in the plane containing the first axis and the second axis shall be defined as the "first shear modulus G 12 ", and the shear modulus of the rock mass in the plane containing the first axis and the third axis shall be defined as the "second shear modulus G 13 "). For the reasons stated above, the shear modulus of the rock mass in the plane containing the second axis and the third axis (the third shear modulus G 23 ) can be treated as approximately the same value as the first shear modulus G 12 .

[0026] (Initial loading pressure and coefficient of subgrade reaction) When a borehole jack test is conducted, the loading pressure and the displacement of the hole wall can be plotted on a graph of two orthogonal axes. As shown in FIG. 4, the initial loading pressure p0 can be obtained, and further, the slope of the straight line portion showing the relationship between the loading pressure and the displacement (i.e., the ratio of the increment of the loading pressure to the increment of the displacement) can be obtained as the "coefficient of subgrade reaction K".

[0027] 2. Principal stress calculation program The principal stress calculation program of the present invention will be described in detail with reference to the drawings. The principal stress calculation method of the present invention is a method for obtaining the principal stress of a rock mass by using the principal stress calculation program of the present invention. Therefore, first, the principal stress calculation program of the present invention will be described, and then the principal stress calculation method of the present invention will be described.

[0028] The principal stress calculation program of the present invention uses the "Lekhnitskii's theory of anisotropic elasticity (S.G. Lekhnitskii: Theory of Elasticity of an Anisotropic Body, Mir Publishers)" to theoretically handle anisotropic rock masses, and uses the "theory of the Kamata paper (Takeshi Kamata: Two-dimensional mixed boundary value problem of an anisotropic infinite plate with a circular hole (Transactions of the Japan Society of Mechanical Engineers))" to derive various numerical values. Therefore, the "Lekhnitskii's theory of anisotropic elasticity" and the "theory of the Kamata paper" will be briefly described.

[0029] (Lekhnitskii's theory of anisotropic elasticity) Figure 5 is a mathematical formula diagram for explaining Lekhnitskii's anisotropic elasticity theory. Among these, formula (1) is a constitutive equation showing the relationship between strain and stress in an anisotropic elastic body. In the formula, σ x is the direct stress in the x-axis direction. Similarly, σ y is the direct stress in the y-axis direction, σ z is the direct stress in the z-axis direction, τ xy is the shear stress in the plane containing the x-axis and the y-axis, ε x is the direct strain in the x-axis direction, ε y is the direct strain in the y-axis direction, γ xy is the shear strain in the plane containing the x-axis and the y-axis. Among these constitutive equations, the coefficients (b 11 ~b 66 ) of each stress component are referred to as "elastic compliances".

[0030] The elastic compliances (b 11 ~b 66 ) can be expressed by the elastic compliances (a 11 ~a 66 ) as shown in formula (4) of Figure 5. And these elastic compliances (a 11 ~a 66 ) can be expressed using the first Poisson's ratio ν 12 , the second Poisson's ratio ν 13 , the third Poisson's ratio ν 23 , the first shear modulus G 12 , furthermore, the first modulus of deformation E1, the second modulus of deformation E2, and the inclination angle φ as shown in formula (2) of Figure 5. Also, as shown in formula (3) of Figure 5, the first shear modulus G 12 can be expressed using the first Poisson's ratio ν 12 , the first modulus of deformation E1, and the second modulus of deformation E2. The second shear modulus G 13 can be expressed using the second Poisson's ratio ν 13 and the first modulus of deformation E1. Since the elastic compliances are symmetric, a ij =a ji and b ij =b ji hold.

[0031] (Theory of Kamata's paper) Figure 6 is a mathematical formula diagram for explaining the theory of Kamata's paper. Among these, formula (5) is a quartic algebraic equation for obtaining characteristic values μ j (j = 1, 2). In the theory of Kamata's paper, the characteristic values μ j (j = 1, 2) are defined as two solutions that satisfy |μ j | < 1 among the four solutions of formula (5). Note that A1 to A4 in the formula are complex constants represented by formula (6) in Figure 6, the bar attached to the letter indicates conjugation, and i indicates the imaginary unit.

[0032] Complex constant δ j and ρ j (j = 1, 2) are defined by formula (7) in Figure 6. After that, when P, Q, and R are defined by formula (8) in Figure 6, the solutions λ j of the quadratic equation shown in formula (9) of Figure 6 are obtained. Then, real constants κ j (j = 1, 2) and real number κ are set so as to satisfy formula (10) in Figure 6. Also, using this real number κ, γ and γ j , γ j ’ can be defined as shown in formula (11) of Figure 6.

[0033] (Negative function and positive function) The maximum principal stress σ1 ∞ and the minimum principal stress σ2 ∞ , and the acting angle α can be obtained by formula (12) in Figure 7 using various numerical values (hereinafter, for convenience, referred to as "Kamata constants" here) and complex constants B1, B2 (the bar indicates conjugation) explained so far. In other words, if the maximum principal stress σ1 ∞ and the minimum principal stress σ2 ∞ , and the acting angle α are known, the complex constants B1, B2 can be obtained by the Kamata constants and formula (12). Then, formula (16) in Figure 7 can be derived by formulas (13) to (15) in Figure 7 using the Kamata constants and the complex constants B1, B2. Note that r0 in formula (13) is the test hole radius r, β in formulas (14) to (16) is the loading surface curvature β, θ in formula (15) and σ in formula (16) are integral constants respectively, and Λ’ in formula (16) is the loading range shown in Figure 1(b) (4β, unit is radian).

[0034] When the mathematical formula (16) is obtained, the initial loading pressure p0 can be expressed by the mathematical formula (17) in FIG. 8. Here, r0 in the mathematical formula (16) is the test hole radius r, β is the curvature of the loading surface, Re[] represents the real part inside the brackets, and Im[] represents the imaginary part inside the brackets. Here, the right side of the second formula in the mathematical formula (17) (that is, X) is the first deformation coefficient E1, the second deformation coefficient E2, the inclination angle φ, the action angle α, and the maximum principal stress σ1 ∞ and the minimum principal stress σ2 ∞ is an implicit function with respect to, and since the initial loading pressure p0 has a linear relationship with the initial principal stresses (the maximum principal stress σ1 ∞ , the minimum principal stress σ2 ∞ ), the mathematical formula (17) can be rewritten in the explicit form (hereinafter referred to as the "explicit function") shown in the mathematical formula (18) of FIG. 8. Here, Ω1 and Ω2 in the mathematical formula (18) represent the initial loading pressure p0 when the unit maximum principal stress σ1 ∞ , the minimum principal stress σ2 ∞ acts. For convenience, here Ω1 and Ω2 are referred to as sensitivity coefficients. These sensitivity coefficients Ω1 and Ω2 are calculated by the mathematical formula (19) in FIG. 8 in the mathematical formula (17) and the mathematical formula (18).

[0035] (Initial loading pressure) When N borehole jack tests are performed, the initial principal stresses (the maximum principal stress σ1 ∞ , the minimum principal stress σ2 ∞ ) can be obtained by the mathematical formula (20) in FIG. 8 using the sensitivity coefficients Ω1, Ω2 and the initial loading pressure p0. More specifically, by solving the mathematical formula (20) using the least squares method, the initial principal stresses (the maximum principal stress σ1 ∞ , the minimum principal stress σ2 ∞ ) are obtained. In the mathematical formula (18), the sensitivity coefficients Ω1, Ω2 and the initial loading pressure p0 for each borehole jack test are shown. For convenience, here the test number is represented by i (i = 1 to N) shown in the upper brackets.

[0036] The initial principal stresses (the maximum principal stress σ1 ∞ , the minimum principal stress σ2 ∞is a so-called provisional value in the analysis for each borehole jack test and is not the initial principal stress that is finally determined. Therefore, this maximum principal stress σ1 ∞ and the minimum principal stress σ2 ∞ shall be referred to as the "provisional maximum principal stress" and the "provisional minimum principal stress", respectively. Also, when the provisional maximum principal stress and the provisional minimum principal stress are obtained, the initial loading pressure p0 (hereinafter referred to as the "analytical loading initial pressure p 0c ") for each borehole jack test by these initial principal stresses can be obtained by the formula (22) in FIG. 8. Furthermore, the square of the difference (hereinafter referred to as the "square difference S") between the actual initial loading pressure p0 (hereinafter referred to as the "measured initial loading pressure p0" for convenience) obtained in each borehole jack test and the analytical loading initial pressure p 0c can be obtained, and the sum of the square differences S for N times of the borehole jack test (hereinafter referred to as the "sum of square differences ΣS") can be obtained by the formula (21) in FIG. 8.

[0037] (Determination of initial principal stress) As described above, the formula (18) in FIG. 8 is a positive function with the action angle α as a variable. Therefore, the values of the sensitivity coefficients Ω1 and Ω2 change depending on the action angle α, and the values of the provisional maximum principal stress, the provisional minimum principal stress, the analytical loading initial pressure p 0c , and the sum of square differences ΣS are also different from each other. Therefore, the sum of square differences ΣS is obtained while changing the value of the action angle α, and the sum of square differences ΣS (hereinafter particularly referred to as the "minimum sum of square differences") showing the minimum value among them is selected. For convenience, here, the action angle α set with various values is particularly referred to as the "candidate action angle". Then, the candidate action angle when the minimum sum of square differences is obtained is determined as the final "action angle α", and the provisional maximum principal stress and the provisional minimum principal stress related to the action angle α are determined as the final maximum principal stress σ1 ∞ and the minimum principal stress σ2 ∞ , respectively.

[0038] (Flow of processing) Next, the main processing flow of the principal stress calculation program of the present invention will be described with reference to FIG. 9. FIG. 9 is a flowchart showing the main processing flow of the principal stress calculation program of the present invention. The processing to be performed is shown in the central column, the information necessary for the processing is shown in the left column, and the information generated from the processing is shown in the right column.

[0039] When N borehole jack tests are performed on the borehole BH (FIG. 1) provided in the anisotropic rock mass and test results are obtained respectively, a computer is made to execute a series of processes shown in FIG. 9 using the principal stress calculation program of the present invention. At the start of the process, first, various condition values (test hole radius r, loading surface curvature β, first Poisson's ratio ν 12 , second Poisson's ratio ν 13 , first deformation coefficient E1, second deformation coefficient E2, inclination angle φ, measured loading initial pressure p0) including the test results for N times obtained by the test are taken in (Step 101 in FIG. 9). Specifically, the test results are taken in by reading the stored condition values or having the operator input the condition values.

[0040] After taking in the condition values, a candidate action angle is set while changing the values (Step 102 in FIG. 9). For convenience, here, M (a natural number of 2 or more) types of candidate action angles are set, and the j-th (j = 1 to M) type of candidate action angle is expressed as "candidate action angle α(j)". When the candidate action angle α(j) is set, elastic compliances (b 11 ~b 66 ) are calculated (Step 103 in FIG. 9), and complex constants B1(j) and B2(j) are calculated (Step 104 in FIG. 9). Then, an implicit function (formula (17) in FIG. 8) representing the analytical loading initial pressure p 0c is set (Step 105 in FIG. 9), and by rewriting this implicit function, the analytical loading initial pressure p 0cSet a positive function (Equation (18) in Figure 8) representing it, and obtain two sensitivity coefficients (hereinafter referred to as "first sensitivity coefficient Ω1(i,j)" and "second sensitivity coefficient Ω2(i,j)"). (Step 106 in Figure 9). Here, (j) attached to each value means that the value changes for each candidate action angle α(j), and (i,j) means that the value changes for each test and for each candidate action angle α(j).

[0041] When the first sensitivity coefficient Ω1(i,j) and the second sensitivity coefficient Ω2(i,j) are obtained, the provisional maximum principal stress σ1 ∞ (i,j) and the provisional minimum principal stress σ2 ∞ (i,j) are calculated, and the analytical load initial pressure p 0c is obtained (Step 107 in Figure 9), and further the sum of squares difference ΣS(j) is obtained by Equation (21) in Figure 8. (Step 108 in Figure 9).

[0042] When the sum of squares difference ΣS(j) is obtained, after setting different candidate action angles α(j) (Step 102 in Figure 9), a series of processes (Step 102 to Step 108 in Figure 9) are repeatedly executed. And when M times of repeated processes are executed, the sum of squares difference ΣS(j) showing the minimum value is selected as the "minimum sum of squares difference" (Step 109 in Figure 9), and the candidate action angle α(j) when the minimum sum of squares difference is obtained is determined as the "action angle α", and further the provisional maximum principal stress σ1 ∞ (i,j) and the provisional minimum principal stress σ2 ∞ (i,j) are determined as the final maximum principal stress σ1 ∞ and the minimum principal stress σ2 ∞ and determined as such. (Step 110 in Figure 9).

[0043] (Verification of validity) The inventor is verifying the validity of the analysis method by the principal stress calculation program of the present invention. The content will be described below.

[0044] In this verification, as shown in Fig. 10(a), four borehole jack tests were carried out while changing the loading direction (θ = 90°, 45°, 0°, -45°), and as shown in Fig. 11, after setting 90 types (-88° to 90°) of candidate action angles α(j), analysis was performed using the principal stress calculation program. As a result, as shown in Fig. 10(c) and Fig. 11, when the candidate action angle α(j) was 90°, the sum of squares difference ΣS(j) showed the minimum value. Note that since the action angle α(j) = 0° and the action angle α(j) = 90° are in the same mechanical state, either can be adopted, and since the -28th power in double-precision calculation indicates 0, the sum of squares difference ΣS(j) between the two can be treated as the same value. Therefore, here, the action angle α(j) = 90° was adopted. That is, in this case, the action angle α at which the minimum sum of squares difference is obtained is 90°, and furthermore, the maximum principal stress σ1 ∞ = 5.0 MPa and the minimum principal stress σ2 ∞ = 3.0 MPa are determined. And the inventor has performed isotropic analysis in this verification for comparison, and the result is shown in Fig. 10(b). According to this, the anisotropic analysis using the principal stress calculation program of the present invention has obtained the same value as the actual result (set value), while the isotropic analysis result on the other hand has calculated different values (the maximum principal stress σ1 ∞ is 5.0 MPa ≠ 5.5 MPa, the action angle α is 90° ≠ 106°). That is, it can be said that the anisotropic analysis using the principal stress calculation program of the present invention is reasonable.

[0045] 3. Deformation coefficient calculation method Next, the principal stress calculation method of the present invention will be described with reference to the drawings. The principal stress calculation method of the present invention is a method for obtaining the principal stress of a rock mass using the principal stress calculation program of the present invention described so far. Therefore, descriptions that overlap with the content described in the principal stress calculation program of the present invention will be avoided, and only the content specific to the principal stress calculation method of the present invention will be described. That is, the content not described here is the same as that described in "2. Principal stress calculation program" and "1. Definition".

[0046] Figure 12 is a flowchart showing the main steps of the principal stress calculation method of the present invention. As shown in this figure, first, an anisotropic rock mass is drilled (excavated) using a boring machine or the like to construct a boring hole BH (Step 201). After constructing the boring hole BH, a borehole jack test as shown in FIG. 1 is carried out (Step 202). At this time, as described above, while changing the loading direction θ the borehole jack test is repeated N times (a natural number of 3 or more) as planned.

[0047] When the borehole jack test is carried out and test results for N times are obtained, by causing a computer to execute a series of processes shown in FIG. 9 using the principal stress calculation program of the present invention, the maximum principal stress σ1 ∞ and the minimum principal stress σ2 ∞ of the anisotropic rock mass and the acting angle α of the principal stress are obtained (Step 203).

Industrial Applicability

[0048] The principal stress calculation program and the principal stress calculation method of the present invention can be used for various structure designs and stability studies such as pile foundations, designs for constructing new tunnels and underground cavities, stability studies of underground cavities during construction, or reinforced designs for deformed tunnels. According to the present invention, on the premise of its anisotropy, the principal stress of the rock mass can be appropriately evaluated, thereby enabling more accurate design of structures and the like. As a result, considering that it leads to higher quality of the construction infrastructure in our country, it can be said that the present invention is not only industrially applicable but also an invention that can be expected to make a great social contribution.

Explanation of Reference Numerals

[0049] BH Boring hole CP Pressure source HS Hose JB Borehole jack LB Loading plate DL Data logger SC Communication cable

Claims

1. A loading test for pressurizing the wall surface of a borehole provided in an anisotropic rock mass by an equal-displacement loading method is carried out while changing the loading direction, and the first deformation coefficient E for N (N is a natural number of 3 or more) times １ , the second deformation coefficient E ２ , and the initial loading pressure p ０ . Based on these, a program that causes a computer to execute a function of obtaining the maximum principal stress σ １ ∞ , the minimum principal stress σ ２ ∞ , and the action angle α of the maximum principal stress σ １ ∞ is as follows: the first deformation coefficient E １ is the deformation coefficient in the direction of the first axis among the first, second, and third orthogonal axes, and the second deformation coefficient E ２ is the deformation coefficient in the direction of the second axis, The test hole radius r and the loading surface curvature β in the load test, the first Poisson's ratio ν in the plane including the first axis and the second axis １２ , the second Poisson's ratio ν in the plane including the first axis and the third axis １３ , the first deformation coefficient E １ , the second deformation coefficient E ２ , the inclination angle φ between the horizontal plane and the first axis, and the initial loading pressure p ０ A conditional value acquisition process for acquiring them, and An action angle setting process for setting a plurality of candidate action angles α(j) that are candidates for the action angle α, For each of the candidate action angles α(j), it is given by the following formula, and the first deformation coefficient E １ , the second deformation coefficient E ２ , the inclination angle φ, and the first sensitivity coefficient Ω １ (i, j) and the second sensitivity coefficient Ω ２ (i, j) are calculated by a sensitivity coefficient calculation process, p ０ = Ω １ (i, j) × σ １ ∞ (i, j) + Ω ２ (i, j) × σ ２ ∞ (i, j) For each candidate action angle α(j), the provisional maximum principal stress σ １ ∞ (i, j) and the provisional minimum principal stress σ ２ ∞ (i, j) are calculated by a provisional principal stress calculation process, For each of the candidate action angles α(j), a difference square sum calculation process for calculating a square difference s(i, j) given by the following formula for each of N tests and calculating a sum of square differences that is the sum of the square differences for N times, s(i,j) = [p ０ −Ω １ (i,j)×σ １ ∞ (i,j)+Ω ２ (i,j)×σ ２ ∞ (i,j)] ２ An action angle determination process for selecting the minimum sum of square differences among the sums of square differences obtained for each candidate action angle α(j) and determining the candidate action angle α(j) corresponding to the minimum sum of square differences as the action angle α, The provisional maximum principal stress σ related to the action angle α determined by the action angle determination process １ ∞ at (i, j) and the provisional minimum principal stress σ ２ ∞ at (i, j) are determined as the provisional maximum principal stress σ １ ∞ and the minimum principal stress σ ２ ∞ The computer is provided with a function of executing a principal stress determination process for determination, A principal stress calculation program characterized by the above.

2. The tentative principal stress calculation process calculates the tentative maximum principal stress σ １ ∞ (i, j) and the tentative minimum principal stress σ ２ ∞ (i, j) by using the least squares method with the following formula: The principal stress calculation program according to Claim 1, characterized by the above.

3. By performing a loading test in which the wall surface of the boring hole is pressurized by an equal-displacement loading method, the maximum principal stress σ of the rock mass showing anisotropy １ ∞ , the minimum principal stress σ ２ ∞ , and the acting angle α of the maximum principal stress σ １ ∞ are obtained, which is a method for A loading test step of performing the N (N is a natural number of 3 or more) loading tests on the rock mass while changing the loading direction, Based on the test results for N times, the maximum principal stress σ of the rock mass １ ∞ , the minimum principal stress σ ２ ∞ , and an analysis step of obtaining the action angle α, are provided In the analysis step, the maximum principal stress σ is obtained using the principal stress calculation program according to claim 1 or claim 2. １ ∞ , the minimum principal stress σ ２ ∞ , and the acting angle α of the principal stress are determined. A principal stress calculation method characterized by the above.

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