CN111794732A - A method for estimating in-situ stress of soft rock in fault fracture zone - Google Patents

A method for estimating in-situ stress of soft rock in fault fracture zone Download PDF

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CN111794732A
CN111794732A CN202010439581.4A CN202010439581A CN111794732A CN 111794732 A CN111794732 A CN 111794732A CN 202010439581 A CN202010439581 A CN 202010439581A CN 111794732 A CN111794732 A CN 111794732A
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陈卫忠
李喆
田洪铭
张广泽
王栋
杨建平
田云
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Wuhan Institute of Rock and Soil Mechanics of CAS
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Abstract

本发明涉及一种断层破碎带软岩地应力估算方法，包括：获得硬岩地区的三个主应力的地应力测试结果，以确定硬岩地区的原始坐标系的应力矩阵；将硬岩地区的原始坐标系的应力矩阵转换成硬岩地区的大地坐标系的应力矩阵；将硬岩地区的大地坐标系的应力矩阵转换成硬岩地区的断层坐标系的应力矩阵；将硬岩地区的断层坐标系的应力矩阵转换成软岩地区的断层坐标系的应力矩阵；将软岩地区的断层坐标系的应力矩阵转换成软岩地区的大地坐标系的应力矩阵；将软岩地区的大地坐标系的应力矩阵转换成软岩地区的隧道坐标系的应力矩阵。该应力估算方法基于完整岩体地应力测试结果进行断层破碎带软岩地应力的估算，使大变形预测结果能良好符合实测结果。

Figure 202010439581

The invention relates to a method for estimating in-situ stress of soft rock in a fault fracture zone, comprising: obtaining in-situ stress test results of three principal stresses in a hard rock area to determine a stress matrix of an original coordinate system in the hard rock area; The stress matrix of the coordinate system is converted into the stress matrix of the geodetic coordinate system in the hard rock area; the stress matrix of the geodetic coordinate system in the hard rock area is converted into the stress matrix of the fault coordinate system in the hard rock area; the fault coordinate system in the hard rock area is converted. Convert the stress matrix of the soft rock area into the stress matrix of the fault coordinate system in the soft rock area; convert the stress matrix of the fault coordinate system in the soft rock area into the stress matrix of the geodetic coordinate system in the soft rock area; convert the stress matrix of the geodetic coordinate system in the soft rock area The matrix is transformed into the stress matrix of the tunnel coordinate system in the soft rock region. This stress estimation method estimates the in-situ stress of the soft rock in the fault fracture zone based on the in-situ stress test results of the intact rock mass, so that the large deformation prediction results can be well in line with the measured results.

Figure 202010439581

Description

一种断层破碎带软岩地应力估算方法A method for estimating in-situ stress of soft rock in fault fracture zone

技术领域technical field

本发明涉及土木工程技术领域，特别涉及一种断层破碎带软岩地应力估算方法。The invention relates to the technical field of civil engineering, in particular to a method for estimating in-situ stress of soft rock in a fault fracture zone.

背景技术Background technique

深埋长大隧道断层破碎带软岩容易产生大变形灾害，地应力是大变形灾害分级和预测的重要参数，其合理取值至关重要。目前常用的地应力测试方法包括水压致裂法和应力解除法，上述两种方法的地应力测试均要求岩石相对完整，尤其是应力解除法还需要钻孔取芯对岩体完整性的要求更高。The soft rock in the fault fracture zone of the deep and long tunnel is prone to large deformation disasters. In-situ stress is an important parameter for the classification and prediction of large deformation disasters, and its reasonable value is very important. At present, the commonly used in-situ stress testing methods include hydraulic fracturing method and stress relief method. The in-situ stress testing of the above two methods requires the rock to be relatively intact, especially the stress relief method also requires drilling cores for the integrity of the rock mass. higher.

因此现有的地应力测试多在完整岩体中开展，其地应力测试结果难以反映断层破碎带软岩的真实地应力状况，导致大变形预测结果与实测结果间存在较大差异，需要提出一种基于完整岩体地应力测试结果，估算断层破碎带软岩地应力的方法。Therefore, the existing in-situ stress tests are mostly carried out in the complete rock mass, and the in-situ stress test results cannot reflect the real in-situ stress condition of the soft rock in the fault fracture zone, resulting in a large difference between the large deformation prediction results and the measured results. A method for estimating the in-situ stress of soft rock in the fault fracture zone based on the in-situ stress test results of the intact rock mass.

发明内容SUMMARY OF THE INVENTION

本申请提供了一种断层破碎带软岩地应力估算方法，解决了现有深埋长大隧道的地应力测试多在完整岩体中开展，其地应力测试结果难以反映断层破碎带软岩的真实地应力状况，导致大变形预测结果与实测结果间存在较大差异的技术问题，实现了基于完整岩体地应力测试结果，估算断层破碎带软岩地应力的技术效果。The present application provides a method for estimating the in-situ stress of soft rock in the fault-fractured zone, which solves the problem that the in-situ stress test of the existing deep-buried and long tunnels is mostly carried out in the complete rock mass, and the in-situ stress test results cannot reflect the true nature of the soft rock in the fault-fractured zone. The in-situ stress condition leads to the technical problem that there is a big difference between the prediction results of large deformation and the measured results, and realizes the technical effect of estimating the in-situ stress of soft rock in the fault fracture zone based on the in-situ stress test results of the intact rock mass.

本申请所提供的一种断层破碎带软岩地应力估算方法，包括：A method for estimating in-situ stress of soft rock in a fault fracture zone provided by this application includes:

步骤1：获得硬岩地区的三个主应力的地应力测试结果，所述三个主应力包括：水平大主应力、水平小主应力及竖直应力；以水平大主应力方向为X轴，水平小主应力方向为Y轴，竖直应力方向为Z轴建立原始坐标系，以确定所述硬岩地区的原始坐标系的应力矩阵；Step 1: Obtain in-situ stress test results of three principal stresses in the hard rock area, where the three principal stresses include: horizontal large principal stress, horizontal small principal stress and vertical stress; taking the direction of the horizontal large principal stress as the X-axis, The horizontal small principal stress direction is the Y axis, and the vertical stress direction is the Z axis to establish an original coordinate system to determine the stress matrix of the original coordinate system of the hard rock area;

步骤2：根据转换矩阵公式确定坐标转换的第一转换矩阵，并根据所述第一转换矩阵及应力分量转换公式，将所述硬岩地区的原始坐标系的应力矩阵转换成所述硬岩地区的大地坐标系的应力矩阵；Step 2: Determine the first transformation matrix of coordinate transformation according to the transformation matrix formula, and transform the stress matrix of the original coordinate system of the hard rock area into the hard rock area according to the first transformation matrix and the stress component transformation formula The stress matrix of the geodetic coordinate system;

步骤3：根据转换矩阵公式确定坐标转换的第二转换矩阵，并根据所述第二转换矩阵及所述应力分量转换公式，将所述硬岩地区的大地坐标系的应力矩阵转换成所述硬岩地区的断层坐标系的应力矩阵；再根据广义胡克定律，将所述硬岩地区的断层坐标系的应力矩阵转换成软岩地区的断层坐标系的应力矩阵；Step 3: Determine the second transformation matrix of coordinate transformation according to the transformation matrix formula, and according to the second transformation matrix and the stress component transformation formula, transform the stress matrix of the geodetic coordinate system in the hard rock area into the hard rock area. The stress matrix of the fault coordinate system in the rock area; and then according to the generalized Hooke's law, the stress matrix of the fault coordinate system in the hard rock area is converted into the stress matrix of the fault coordinate system in the soft rock area;

步骤4：通过第三转换矩阵运用所述应力分量转换公式的反运算，所述第三转换矩阵为所述第二转换矩阵的转置矩阵，将所述软岩地区的断层坐标系的应力矩阵转换成软岩地区的大地坐标系的应力矩阵；Step 4: Using the inverse operation of the stress component transformation formula through a third transformation matrix, the third transformation matrix is the transposed matrix of the second transformation matrix, and the stress matrix of the fault coordinate system in the soft rock area is converted into The stress matrix converted to the geodetic coordinate system of the soft rock area;

步骤5：通过第四转换矩阵运用所述应力分量转换公式的反运算，所述第四转换矩阵为所述第一转换矩阵的转置矩阵，将所述软岩地区的大地坐标系的应力矩阵转换成软岩地区的隧道坐标系的应力矩阵。Step 5: Using the inverse operation of the stress component conversion formula through a fourth transformation matrix, the fourth transformation matrix is the transpose matrix of the first transformation matrix, and the stress matrix of the geodetic coordinate system in the soft rock area is converted into The stress matrix converted to the tunnel coordinate system in the soft rock region.

作为优选，还包括步骤6：Preferably, it also includes step 6:

根据所述第四转换矩阵及所述应力分量转换公式，将所述硬岩地区的大地坐标系的应力矩阵转换成所述硬岩地区的隧道坐标系的应力矩阵。According to the fourth conversion matrix and the stress component conversion formula, the stress matrix of the geodetic coordinate system of the hard rock area is converted into the stress matrix of the tunnel coordinate system of the hard rock area.

作为优选，所述断层破碎带软岩地应力估算方法具有假定前提条件，所述假定前提条件为：Preferably, the method for estimating the in-situ stress of the soft rock in the fractured zone of the fault has assumed preconditions, and the assumed preconditions are:

平行于xoy面的岩层的水平方向的尺寸比竖直方向的尺寸大；The horizontal dimension of the rock formation parallel to the xoy plane is larger than the vertical dimension;

岩层各向同性；isotropic rock formation;

材料满足弹性假设。The material satisfies the elasticity assumption.

作为优选，对于同一点在不同坐标系下的所述应力分量转换公式的矩阵表达式为为：Preferably, the matrix expression of the stress component conversion formula for the same point in different coordinate systems is:

[σ']＝[β][σ][β]T；[σ']=[β][σ][β] T ;

Figure BDA0002503583020000031
Figure BDA0002503583020000031

其中，[σ′]为新坐标系的应力矩阵，[β]为转换矩阵，[σ]为原坐标系的应力矩阵。Among them, [σ′] is the stress matrix of the new coordinate system, [β] is the transformation matrix, and [σ] is the stress matrix of the original coordinate system.

作为优选，对于同一点在不同坐标系下的转换矩阵公式为：As an option, the transformation matrix formula for the same point in different coordinate systems is:

Figure BDA0002503583020000032
Figure BDA0002503583020000032

其中，设x，y，z为原坐标系的坐标轴，x′，y′，z′为新坐标系的坐标轴，lij＝cos(Ai，Bj)，i＝1～3，j＝1～3，所述A1～A3分别为x′、y′、z′，所述B1～B3分别为x、y、z，即所述lij为Ai轴与Bj轴夹角的余弦。Among them, let x, y, z be the coordinate axes of the original coordinate system, x', y', z' are the coordinate axes of the new coordinate system, lij=cos(Ai, Bj), i=1～3, j=1 ~3, the A1-A3 are respectively x', y', and z', and the B1-B3 are respectively x, y, and z, that is, the lij is the cosine of the angle between the Ai axis and the Bj axis.

作为优选，设定所述硬岩地区的大地坐标系的最大水平主应力方向为X′轴向北，最小水平主应力方向为Y′轴向东，竖直应力为Z′轴向下；所述大地坐标系的最大水平主应力的方位角为α；Preferably, the direction of the maximum horizontal principal stress of the geodetic coordinate system in the hard rock area is set as the north of the X' axis, the direction of the minimum horizontal principal stress is the east of the Y' axis, and the vertical stress is set as the downward of the Z' axis; The azimuth angle of the maximum horizontal principal stress of the geodetic coordinate system is α;

所述步骤2中的所述第一转换矩阵公式为：The first conversion matrix formula in the step 2 is:

Figure BDA0002503583020000033
Figure BDA0002503583020000033

作为优选，所述硬岩地区的断层坐标系的垂直断层面为z′轴，所述大地坐标系中断层面交水平面的方向设为x′轴，垂直于x′轴和z′轴的方向设为y′轴；设定所述硬岩地区的断层的倾向为α，倾角为β；Preferably, the vertical fault plane of the fault coordinate system in the hard rock area is the z' axis, the direction of the fault plane crossing the horizontal plane of the geodetic coordinate system is set as the x' axis, and the direction perpendicular to the x' axis and the z' axis is set as the x' axis. is the y′ axis; set the inclination of the fault in the hard rock area as α and the dip angle as β;

则z′轴单位向量方向为(cosαsinβ，sinαsinβ，cosβ)；x′轴单位向量方向为(sinα，-cosα，0)；y′轴单位向量方向为(cosαcosβ，sinαcosβ，-sinβ)；所述大地坐标系x轴、y轴、z轴的单位向量方向分别为(1，0，0)、(0，1，0)、(0，0，1)；Then the direction of the unit vector of the z' axis is (cosαsinβ, sinαsinβ, cosβ); the direction of the unit vector of the x' axis is (sinα, -cosα, 0); the direction of the unit vector of the y' axis is (cosαcosβ, sinαcosβ, -sinβ); the The unit vector directions of the x-axis, y-axis, and z-axis of the geodetic coordinate system are (1, 0, 0), (0, 1, 0), (0, 0, 1) respectively;

所述步骤3中的所述第二转换矩阵公式为：The second conversion matrix formula in the step 3 is:

Figure BDA0002503583020000041
Figure BDA0002503583020000041

作为优选，所述广义胡克定律进行解析解的求解公式为：Preferably, the solution formula for the analytical solution of the generalized Hooke's law is:

Figure BDA0002503583020000042
Figure BDA0002503583020000042

Figure BDA0002503583020000043
Figure BDA0002503583020000043

Figure BDA0002503583020000044
Figure BDA0002503583020000044

所述软岩地区的应力为

Figure BDA0002503583020000045
所述硬岩地区的应力为
Figure BDA0002503583020000046
将软岩地区和硬岩地区的应变相等代入所述广义胡克定律可得：The stress in the soft rock region is
Figure BDA0002503583020000045
The stress in the hard rock region is
Figure BDA0002503583020000046
Substituting equal strains in the soft-rock region and hard-rock region into the generalized Hooke's law yields:

Figure BDA0002503583020000047
Figure BDA0002503583020000047

Figure BDA0002503583020000048
Figure BDA0002503583020000048

Figure BDA0002503583020000049
Figure BDA0002503583020000049

本申请实施例中提供的一个或多个技术方案，至少具有如下技术效果或优点：One or more technical solutions provided in the embodiments of this application have at least the following technical effects or advantages:

本申请基于完整岩体地应力测试结果进行断层破碎带软岩地应力的估算，使大变形预测结果能良好符合实测结果。The present application estimates the in-situ stress of the soft rock in the fault fracture zone based on the in-situ stress test results of the complete rock mass, so that the large deformation prediction results can be well in line with the actual measurement results.

附图说明Description of drawings

为了更清楚地说明本申请实施例或现有技术中的技术方案，下面将对实施例或现有技术描述中所需要使用的附图作简单地介绍。In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, the following briefly introduces the accompanying drawings that are required to be used in the description of the embodiments or the prior art.

图1为本申请实施例提供的断层破碎带软岩地应力估算方法的流程示意图；1 is a schematic flowchart of a method for estimating in-situ stress of soft rock in a fault fracture zone provided by an embodiment of the present application;

图2为本申请实施例提供的原始坐标系到大地坐标系的坐标转化示意图；2 is a schematic diagram of coordinate transformation from an original coordinate system to a geodetic coordinate system provided by an embodiment of the present application;

图3为本申请实施例提供的大地坐标系到断层坐标系的坐标转化示意图。FIG. 3 is a schematic diagram of coordinate transformation from a geodetic coordinate system to a fault coordinate system according to an embodiment of the present application.

具体实施方式Detailed ways

为使本申请实施例的目的、技术方案和优点更加清楚，下面将结合本申请实施例中的附图，对本申请实施例中的技术方案进行清楚、完整地描述，显然，所描述的实施例是本申请一部分实施例，而不是全部的实施例。基于本申请中的实施例，本领域普通技术人员在没有作出创造性劳动前提下所获得的所有其他实施例，都属于本申请保护的范围。In order to make the purposes, technical solutions and advantages of the embodiments of the present application clearer, the technical solutions in the embodiments of the present application will be described clearly and completely below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments It is a part of the embodiments of the present application, but not all of the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those of ordinary skill in the art without creative work fall within the protection scope of the present application.

参见附图1，本申请所提供的一种断层破碎带软岩地应力估算方法，包括：Referring to accompanying drawing 1, a method for estimating the in-situ stress of soft rock in a fault fracture zone provided by the application includes:

S1：获得硬岩地区的三个主应力的地应力测试结果，三个主应力包括：水平大主应力、水平小主应力及竖直应力；以水平大主应力方向为X轴，水平小主应力方向为Y轴，竖直应力方向为Z轴建立原始坐标系，以确定硬岩地区的原始坐标系的应力矩阵。S1: Obtain the in-situ stress test results of the three principal stresses in the hard rock area. The three principal stresses include: horizontal large principal stress, horizontal small principal stress and vertical stress; The stress direction is the Y axis, and the vertical stress direction is the Z axis to establish the original coordinate system to determine the stress matrix of the original coordinate system in the hard rock area.

S2：根据转换矩阵公式确定坐标转换的第一转换矩阵，并根据第一转换矩阵及应力分量转换公式，将硬岩地区的原始坐标系的应力矩阵转换成硬岩地区的大地坐标系的应力矩阵。S2: Determine the first transformation matrix of coordinate transformation according to the transformation matrix formula, and convert the stress matrix of the original coordinate system in the hard rock area into the stress matrix of the geodetic coordinate system in the hard rock area according to the first transformation matrix and the stress component transformation formula .

S3：根据转换矩阵公式确定坐标转换的第二转换矩阵，并根据第二转换矩阵及应力分量转换公式，将硬岩地区的大地坐标系的应力矩阵转换成硬岩地区的断层坐标系的应力矩阵；再根据广义胡克定律，将硬岩地区的断层坐标系的应力矩阵转换成软岩地区的断层坐标系的应力矩阵。S3: Determine the second transformation matrix for coordinate transformation according to the transformation matrix formula, and convert the stress matrix of the geodetic coordinate system in the hard rock area into the stress matrix of the fault coordinate system in the hard rock area according to the second transformation matrix and the stress component transformation formula ; Then according to the generalized Hooke's law, the stress matrix of the fault coordinate system in the hard rock area is transformed into the stress matrix of the fault coordinate system in the soft rock area.

S4：通过第三转换矩阵运用应力分量转换公式的反运算，第三转换矩阵为第二转换矩阵的转置矩阵，将软岩地区的断层坐标系的应力矩阵转换成软岩地区的大地坐标系的应力矩阵；即此步骤S4为步骤S3的反运算，故本次的转换矩阵即为步骤3的转换矩阵的转置矩阵。S4: Using the inverse operation of the stress component conversion formula through the third transformation matrix, the third transformation matrix is the transpose matrix of the second transformation matrix, and the stress matrix of the fault coordinate system in the soft rock area is converted into the geodetic coordinate system in the soft rock area. That is, this step S4 is the inverse operation of step S3, so the transformation matrix this time is the transpose matrix of the transformation matrix in step 3.

S5：通过第四转换矩阵运用应力分量转换公式的反运算，第四转换矩阵为第一转换矩阵的转置矩阵，将软岩地区的大地坐标系的应力矩阵转换成软岩地区的隧道坐标系的应力矩阵；若将隧道方位角看做最大水平主应力方向角，则步骤S5是步骤2的反运算，故本次的转换矩阵即为步骤2的转换矩阵的转置矩阵。S5: Using the inverse operation of the stress component conversion formula through the fourth transformation matrix, the fourth transformation matrix is the transpose matrix of the first transformation matrix, and the stress matrix of the geodetic coordinate system in the soft rock area is converted into the tunnel coordinate system in the soft rock area If the tunnel azimuth is regarded as the maximum horizontal principal stress direction angle, then step S5 is the inverse operation of step 2, so the transformation matrix this time is the transpose matrix of the transformation matrix of step 2.

进一步的，还包括步骤6：根据第四转换矩阵及应力分量转换公式，将硬岩地区的大地坐标系的应力矩阵转换成硬岩地区的隧道坐标系的应力矩阵。Further, it also includes step 6: according to the fourth transformation matrix and the stress component transformation formula, transform the stress matrix of the geodetic coordinate system in the hard rock area into the stress matrix of the tunnel coordinate system in the hard rock area.

进一步的，断层破碎带软岩地应力估算方法具有假定前提条件，假定前提条件为：Further, the method for estimating the in-situ stress of the soft rock in the fault fracture zone has assumed preconditions. The assumed preconditions are:

1)、平行于xoy面的岩层的水平方向的尺寸比竖直方向的尺寸大；1) The horizontal dimension of the rock formation parallel to the xoy plane is larger than the vertical dimension;

2)、岩层各向同性；2), the rock formation is isotropic;

3)、材料满足弹性假设。3) The material satisfies the elasticity assumption.

进一步的，对于同一点在不同坐标系下的应力分量转换公式的矩阵表达式为为：Further, the matrix expression of the stress component conversion formula for the same point in different coordinate systems is:

[σ']＝[β][σ][β]T；[σ']=[β][σ][β] T ;

Figure BDA0002503583020000071
Figure BDA0002503583020000071

其中，[σ′]为新坐标系的应力矩阵，[β]为转换矩阵，[σ]为原坐标系的应力矩阵。Among them, [σ′] is the stress matrix of the new coordinate system, [β] is the transformation matrix, and [σ] is the stress matrix of the original coordinate system.

进一步的，对于同一点在不同坐标系下的转换矩阵公式为：Further, the transformation matrix formula for the same point in different coordinate systems is:

Figure BDA0002503583020000072
Figure BDA0002503583020000072

其中，设x，y，z为原坐标系的坐标轴，x′，y′，z′为新坐标系的坐标轴，lij＝cos(Ai，Bj)，i＝1～3，j＝1～3，所述A1～A3分别为x′、y′、z′，所述B1～B3分别为x、y、z，即所述lij为Ai轴与Bj轴夹角的余弦；比如l12＝cos(x′，y)，l32＝cos(z′，y)。Among them, let x, y, z be the coordinate axes of the original coordinate system, x', y', z' are the coordinate axes of the new coordinate system, lij=cos(Ai, Bj), i=1～3, j=1 ~3, the A1 to A3 are respectively x', y', z', and the B1 to B3 are respectively x, y, z, that is, the lij is the cosine of the angle between the Ai axis and the Bj axis; for example, l 12 =cos(x',y), l 32 =cos(z',y).

进一步的，设定所述硬岩地区的大地坐标系的最大水平主应力方向为X′轴向北，最小水平主应力方向为Y′轴向东，竖直应力为Z′轴向下；大地坐标系的最大水平主应力的方位角为α(方位角：北为0°，东为90°)，如图2所示；Further, the maximum horizontal principal stress direction of the geodetic coordinate system in the hard rock area is set as the north of the X' axis, the minimum horizontal principal stress direction is the east of the Y' axis, and the vertical stress is the downward of the Z' axis; The azimuth angle of the maximum horizontal principal stress of the coordinate system is α (azimuth angle: north is 0°, east is 90°), as shown in Figure 2;

S2中的第一转换矩阵公式为：The first transformation matrix formula in S2 is:

Figure BDA0002503583020000073
Figure BDA0002503583020000073

进一步的，硬岩地区的断层坐标系的垂直断层面为z′轴，所述大地坐标系中断层面交水平面的方向设为x′轴，垂直于x′轴和z′轴的方向设为y′轴；设定所述硬岩地区的断层的倾向为α，倾角为β；如图3所示，某断层面BCD，交水平面XOY于CD，CD即为断层层面走向，设为x′轴方向；过B做BA⊥CD，AB即为y′轴方向；其在水平面的投影AO为倾向，∠BAO为倾角，z′轴⊥层面BCD。Further, the vertical fault plane of the fault coordinate system in the hard rock area is the z' axis, the direction of the fault plane intersecting the horizontal plane of the geodetic coordinate system is set as the x' axis, and the direction perpendicular to the x' axis and the z' axis is set as the y axis. ' axis; set the inclination of the fault in the hard rock area as α and the dip angle as β; as shown in Figure 3, a certain fault plane is BCD, and the intersecting horizontal plane is XOY at CD, and CD is the strike of the fault plane, which is set as the x' axis direction; do BA⊥CD through B, AB is the y′ axis direction; its projection on the horizontal plane AO is the inclination, ∠BAO is the inclination angle, and the z′ axis⊥ plane BCD.

则z′轴单位向量方向为(cosαsinβ，sinαsinβ，cosβ)；x′轴单位向量方向为(sinα，-cosα，0)；y′轴单位向量方向为(cosαcosβ，sinαcosβ，-sinβ)；所述大地坐标系x轴、y轴、z轴的单位向量方向分别为(1，0，0)、(0，1，0)、(0，0，1)；Then the direction of the unit vector of the z' axis is (cosαsinβ, sinαsinβ, cosβ); the direction of the unit vector of the x' axis is (sinα, -cosα, 0); the direction of the unit vector of the y' axis is (cosαcosβ, sinαcosβ, -sinβ); the The unit vector directions of the x-axis, y-axis, and z-axis of the geodetic coordinate system are (1, 0, 0), (0, 1, 0), (0, 0, 1) respectively;

S3中的第二转换矩阵公式为：The second transformation matrix formula in S3 is:

Figure BDA0002503583020000081
Figure BDA0002503583020000081

进一步的，由于已经将坐标系转换为断层坐标系，此时，x′oy′平面与层面平行。而无论硬岩地区还是软岩地区任意平行于水平面的单元体其三个方向所受的力FX、FY、FZ是相等的。因此τXZ，τYZ和σZZ是相等的。而τXY，σXX和σYY是不相等的。但是由于其在XOY面的应变即εXX、εXY、εYY相等，所以可以根据广义胡克定律进行解析解的求解：Further, since the coordinate system has been converted into a fault coordinate system, at this time, the x'oy' plane is parallel to the slice. The forces F X , F Y , and F Z in the three directions of any unit body parallel to the horizontal plane in the hard rock area or the soft rock area are equal. Therefore τ XZ , τ YZ and σ ZZ are equal. And τ XY , σ XX and σ YY are not equal. However, since the strains on the XOY plane, that is, ε XX , ε XY , and ε YY are equal, the analytical solution can be solved according to the generalized Hooke's law:

Figure BDA0002503583020000082
Figure BDA0002503583020000082

Figure BDA0002503583020000083
Figure BDA0002503583020000083

Figure BDA0002503583020000084
Figure BDA0002503583020000084

软岩地区的应力为

Figure BDA0002503583020000085
所述硬岩地区的应力为
Figure BDA0002503583020000086
将软岩地区和硬岩地区的应变相等代入所述广义胡克定律可得：The stress in the soft rock region is
Figure BDA0002503583020000085
The stress in the hard rock region is
Figure BDA0002503583020000086
Substituting equal strains in the soft-rock region and hard-rock region into the generalized Hooke's law yields:

Figure BDA0002503583020000091
Figure BDA0002503583020000091

Figure BDA0002503583020000092
Figure BDA0002503583020000092

Figure BDA0002503583020000093
Figure BDA0002503583020000093

通过以上估算方法，使深埋长大隧道的地应力测试无需在完整岩体中开展，基于完整岩体地应力测试结果，能准确估算断层破碎带软岩地应力。Through the above estimation methods, the in-situ stress test of deep and long tunnels does not need to be carried out in the complete rock mass. Based on the in-situ stress test results of the complete rock mass, the in-situ stress of soft rock in the fault fracture zone can be accurately estimated.

下面通过具体实施例(川藏铁路某隧道断层破碎带应力估算)来详细介绍本申请的估算方法：The estimation method of the present application will be introduced in detail below through a specific embodiment (estimation of the stress of the fractured zone of a certain tunnel of the Sichuan-Tibet Railway):

拟建铁路隧道采用水压致裂法在完整砂岩中开展了地应力测试，地应力测试结果如表1所示。In-situ stress test was carried out in intact sandstone by hydraulic fracturing method for the proposed railway tunnel. The in-situ stress test results are shown in Table 1.

表1压裂地应力测试结果总结Table 1 Summary of fracturing in-situ stress test results

Figure BDA0002503583020000094
Figure BDA0002503583020000094

其中，Shmin：地层最小水平主应力；Shmax：地层最大水平主应力；Sv：竖向应力(岩石容重2.60g/cm3)。Among them, Shmin: minimum horizontal principal stress of formation; Shmax: maximum horizontal principal stress of formation; Sv: vertical stress (rock bulk density 2.60g/cm3).

拟估算的某断层破碎带的具体情况如表2所示，The specific conditions of a fault fracture zone to be estimated are shown in Table 2.

表2断层破碎带具体信息Table 2 Specific information of fault fracture zone

Figure BDA0002503583020000095
Figure BDA0002503583020000095

断层破碎带应力估算的具体过程如下：The specific process of estimating the stress of the fault fracture zone is as follows:

(1)根据完整砂岩地区地应力测试结果，以水平大主应力方向为x轴，水平小主应力方向为y轴，竖直应力方向为z轴建立坐标系。故x轴，y轴，z轴的应力分别为8.40MPa，5.58MPa，5.30MPa。(1) According to the test results of in-situ stress in the intact sandstone area, a coordinate system is established with the direction of the horizontal major principal stress as the x-axis, the direction of the horizontal minor principal stress as the y-axis, and the vertical stress direction as the z-axis. Therefore, the stresses on the x-axis, y-axis, and z-axis are 8.40MPa, 5.58MPa, and 5.30MPa, respectively.

(2)已知最大地应力方向为N55°W，从而原始坐标系到硬岩地区大地坐标系的转换矩阵的角度α为305°。从而得到硬岩地区大地坐标系的应力状态为：(2) It is known that the maximum in-situ stress direction is N55°W, so the angle α of the transformation matrix from the original coordinate system to the geodetic coordinate system in the hard rock area is 305°. Thus, the stress state of the geodetic coordinate system in the hard rock area is obtained as:

Figure BDA0002503583020000101
Figure BDA0002503583020000101

(3)根据F27断层的产状为N52°W∠55°SW，大地坐标系到断层坐标系的转换矩阵的角度α和β分别为308°，55°。代入转换矩阵得到硬岩地区断层坐标系的应力状态：(3) According to the occurrence of the F27 fault N52°W∠55°SW, the angles α and β of the transformation matrix from the geodetic coordinate system to the fault coordinate system are 308° and 55°, respectively. Substitute into the transformation matrix to obtain the stress state of the fault coordinate system in the hard rock area:

Figure BDA0002503583020000102
Figure BDA0002503583020000102

(4)将软硬岩地区的岩体参数代入求得软岩地区断层坐标系的应力状态为：(4) Substitute the parameters of the rock mass in the soft and hard rock area to obtain the stress state of the fault coordinate system in the soft rock area:

Figure BDA0002503583020000103
Figure BDA0002503583020000103

(5)将软岩地区断层坐标系转换为大地坐标系，此步骤为步骤(3)的反运算，转换矩阵为步骤(3)的逆矩阵，得到的软岩地区的断层坐标系：(5) Convert the fault coordinate system in the soft rock area to the geodetic coordinate system, this step is the inverse operation of step (3), the conversion matrix is the inverse matrix of step (3), and the obtained fault coordinate system in the soft rock area:

Figure BDA0002503583020000104
Figure BDA0002503583020000104

(6)由于隧道轴线走向约为N15°E，从而软岩地区断层坐标系到软岩地区大地坐标系的转换矩阵的角度α为105°(6) Since the axis of the tunnel is about N15°E, the angle α of the transformation matrix from the fault coordinate system in the soft rock area to the geodetic coordinate system in the soft rock area is 105°

得到软岩地区隧道坐标系的应力状态为：The stress state of the tunnel coordinate system in the soft rock area is obtained as:

Figure BDA0002503583020000111
Figure BDA0002503583020000111

(7)由步骤(6)的转换矩阵和步骤(3)得到的硬岩地区大地坐标系的应力状态也可以得到硬岩地区的隧道坐标系的应力状态：(7) The stress state of the geodetic coordinate system in the hard rock area can also be obtained from the transformation matrix of step (6) and the stress state of the geodetic coordinate system in the hard rock area:

Figure BDA0002503583020000112
Figure BDA0002503583020000112

软硬岩地区的隧道坐标系应力状态主应力的值见下表3The values of principal stress in the stress state of the tunnel coordinate system in the soft and hard rock area are shown in Table 3 below

Figure BDA0002503583020000113
Figure BDA0002503583020000113

可以看出同地区的软岩地区的应力要小于硬岩地区的应力。It can be seen that the stress in the soft rock area in the same area is smaller than that in the hard rock area.

以上所述的具体实施方式，对本发明的目的、技术方案和有益效果进行了进一步详细说明，所应理解的是，以上所述仅为本发明的具体实施方式而已，并不用于限制本发明，凡在本发明的精神和原则之内，所做的任何修改、等同替换、改进等，均应包含在本发明的保护范围之内。The specific embodiments described above further describe the objectives, technical solutions and beneficial effects of the present invention in detail. It should be understood that the above descriptions are only specific embodiments of the present invention, and are not intended to limit the present invention. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included within the protection scope of the present invention.

Claims (8)

1. A method for estimating the geostress of soft rock in a fault fracture zone is characterized by comprising the following steps:
step 1: obtaining geostress test results for three principal stresses in a hard rock region, the three principal stresses comprising: horizontal large main stress, horizontal small main stress and vertical stress; establishing an original coordinate system by taking the horizontal large principal stress direction as an X axis, the horizontal small principal stress direction as a Y axis and the vertical stress direction as a Z axis so as to determine a stress matrix of the original coordinate system of the hard rock area;
step 2: determining a first conversion matrix of coordinate conversion according to a conversion matrix formula, and converting a stress matrix of an original coordinate system of the hard rock area into a stress matrix of a geodetic coordinate system of the hard rock area according to the first conversion matrix and a stress component conversion formula;
and step 3: determining a second conversion matrix of coordinate conversion according to the conversion matrix formula, and converting the stress matrix of the geodetic coordinate system of the hard rock area into the stress matrix of the fault coordinate system of the hard rock area according to the second conversion matrix and the stress component conversion formula; converting the stress matrix of the fault coordinate system of the hard rock area into the stress matrix of the fault coordinate system of the soft rock area according to the generalized Hooke's law;
and 4, step 4: applying the inverse operation of the stress component conversion formula through a third conversion matrix, wherein the third conversion matrix is a transposed matrix of the second conversion matrix, and converting the stress matrix of the fault coordinate system of the soft rock area into the stress matrix of the geodetic coordinate system of the soft rock area;
and 5: and applying the inverse operation of the stress component conversion formula through a fourth conversion matrix, wherein the fourth conversion matrix is a transposed matrix of the first conversion matrix, and converting the stress matrix of the geodetic coordinate system of the soft rock area into the stress matrix of the tunnel coordinate system of the soft rock area.
2. The method for estimating the geostress of soft rocks in a fractured zone of claim 1, further comprising the step 6 of:
and converting the stress matrix of the geodetic coordinate system of the hard rock area into the stress matrix of the tunnel coordinate system of the hard rock area according to the fourth conversion matrix and the stress component conversion formula.
3. The method for estimating the geostress of the soft rock of the fractured zone of claim 1, wherein the method for estimating the geostress of the soft rock of the fractured zone has the following assumed preconditions:
the dimension of the rock layer parallel to the xoy plane in the horizontal direction is larger than the dimension in the vertical direction;
the rock stratum is isotropic;
the material satisfies the elastic assumption.
4. The method of estimating geostress of soft rock in a fractured zone of claim 1,
the matrix expression of the stress component conversion formula for the same point in different coordinate systems is as follows:
[σ']＝[β][σ][β]T；
Figure FDA0002503583010000021
wherein [ sigma' ] is the stress matrix of the new coordinate system, [ beta ] is the transformation matrix, and [ sigma ] is the stress matrix of the original coordinate system.
5. The method of estimating geostress of soft rock in a fractured zone of claim 1,
the transformation matrix formula under different coordinate systems for the same point is as follows:
Figure FDA0002503583010000022
the method comprises the following steps of setting x, y and z as coordinate axes of an original coordinate system, setting x ', y' and z 'as coordinate axes of a new coordinate system, setting lij to cos (Ai, Bj), i to 1-3, and j to 1-3, setting A1-A3 to be x', y 'and z', setting B1-B3 to be x, y and z, and setting lij to be cosine of an included angle between an Ai axis and a Bj axis.
6. The method of estimating geostress of soft rock in a fractured zone of claim 5,
setting the maximum horizontal principal stress direction of the geodetic coordinate system of the hard rock area as an X ' axial north direction, the minimum horizontal principal stress direction as a Y ' axial east direction, and the vertical stress as a Z ' axial down direction; the azimuth angle of the maximum horizontal principal stress of the geodetic coordinate system is alpha;
the first conversion matrix formula in step 2 is:
Figure FDA0002503583010000031
7. the method of estimating geostress of soft rock in a fractured zone of claim 5,
the vertical fault plane of the fault coordinate system of the hard rock region is a z ' axis, the direction of the fault plane intersection horizontal plane in the geodetic coordinate system is an x ' axis, and the direction vertical to the x ' axis and the z ' axis is a y ' axis; setting the tendency of the fault of the hard rock area as alpha and the inclination angle as beta;
then the z' axis unit vector direction is (cos α sin β, sin α sin β, cos β); the unit vector direction of the x' axis is (sin α, -cos α, 0); the y' axis unit vector direction is (cos α cos β, sin α cos β, -sin β); the unit vector directions of the x axis, the y axis and the z axis of the geodetic coordinate system are (1, 0, 0), (0, 1, 0) and (0, 0, 1) respectively;
the second conversion matrix formula in step 3 is:
Figure FDA0002503583010000032
8. the method for estimating the crustal stress of the soft rock in the fault fracture zone according to claim 7, wherein the analytic solution of the generalized hooke's law is solved by the following formula:
Figure FDA0002503583010000033
the stress in the soft rock area is
Figure FDA0002503583010000034
The stress of the hard rock area is
Figure FDA0002503583010000035
The strain of the soft rock area and the strain of the hard rock area are equally substituted into the generalized Hooke's law to obtain:
Figure FDA0002503583010000041
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