Coulomb stress calculation method considering fluid action

Abstract

The invention discloses a coulomb stress calculation method considering a fluid effect. The method comprises the following steps: determining a fault plane trend and a fault plane inclination angle of a seismic part; calculating the pore water pressure of the fault plane; the normal stress of the fault plane is calculated; the fault plane friction force is calculated; calculating the shear stress of the fault surface; and calculating the effective coulomb stress of the fault plane based on the following formula. According to the method, the change of medium structure parameters caused by reservoir water permeation is considered on the basis of the elastic homogeneous medium model, and the accuracy of effective coulomb stress calculation can be effectively improved.

Description

Technical Field

[0001] The invention belongs to the field of earthquake triggering and fault interaction analysis, and specifically relates to a Coulomb stress calculation method considering fluid action. Background Art

[0002] According to the Coulomb fracture criterion, when a rock breaks, the shear stress τ that causes it to break is determined by the material's cohesive stress S (cohesive strength or shear strength) and the plane normal stress σ multiplied by a constant. n (opening is positive) and the resistance of pore pressure p, that is, the shear strength in the plane is S-μ(σ n +p). Therefore, the Coulomb stress (CFS) on the fracture surface can be defined as the difference between the shear stress and the shear strength.

[0003] In recent years, the temporal and spatial relationship between the Coulomb failure stress changes caused by earthquakes and the occurrence of subsequent earthquakes has attracted widespread attention from seismologists at home and abroad. Calculating the Coulomb stress changes on the faults in the area around the earthquake event after the earthquake can help evaluate the stress state on the faults in the earthquake-prone area, thereby determining the strong earthquake trend in the region. Studies have shown that very small static Coulomb stress changes (threshold of 0.1 bar) may trigger earthquakes, leading to changes in regional seismic activity in the future. Therefore, exploring the relationship between Coulomb stress changes and earthquake triggering is of great significance for studying the medium- and long-term prediction of earthquakes and whether static stress changes trigger subsequent earthquake events. It also provides a theoretical basis for the analysis of regional earthquake hazards in the future. Moreover, Coulomb stress plays an important role in the triggering effect of strong earthquakes on aftershocks, the triggering of strong earthquakes on subsequent earthquake sequences, the inhibitory effect of stress shadows on earthquakes, and the analysis of seismic activity.

[0004] The existing technology uses a uniform and completely elastic earth medium model to calculate the coseismic stress field, and the input is the slip distribution of the earthquake fault plane, the various parameters of the underground medium and the reservoir. The most widely used model is the dislocation model of elastic half-space proposed by Okada et al. in their paper "Surface deformation due to shear and tensile faults in a half-space (1985)". The coseismic Coulomb failure stress change on the fault is calculated based on the Coulomb failure criterion, which is the Coulomb stress change of a certain point, a certain depth plane or a certain section of the fault caused by the earthquake fault.

[0005] However, when calculating coseismic stress, the influence of fluid is generally not considered when setting the parameters of the medium structure, and the values ​​of Poisson's ratio and elastic modulus may not be consistent with the situation of water-containing media. But in fact, fluid plays a very important role in solid deformation. In addition, since the influence of the pore water pressure component of the water-containing fault surface is not considered, the calculated value of Coulomb stress value may be too high. Summary of the invention

[0006] The present invention aims at the problem of calculating the Coulomb stress of a fault when the effect of fluid cannot be ignored, and provides a method for calculating the effective Coulomb stress taking into account the pore water pressure of the fault surface.

[0007] The above-mentioned object of the present invention is achieved by the following technical solutions:

[0008] A Coulomb stress calculation method considering fluid action comprises the following steps:

[0009] Step 1: Confirm the fault plane strike S and fault plane dip D at the earthquake location;

[0010] Step 2: Calculate the pore water pressure p on the fault surface;

[0011] Step 3: Calculate the normal stress σ on the fault plane n ;

[0012] Step 4: Calculate the fault plane friction force f;

[0013] Step 5: Calculate the fault plane shear stress τ;

[0014] Step 6: Calculate the effective Coulomb stress Δσ on the fault plane based on the following formula e

[0015] Δσ e =τ-μ(σ n -p)

[0016] Where μ is the friction coefficient of the fault surface.

[0017] As mentioned above, the pore water pressure p on the fault plane is based on the following formula;

[0018] p=γ l ×h

[0019] Among them, γ l is the density of water, h is the actual hydraulic head of the pore water at the earthquake site, h = ξ(d+H), ξ is the hydraulic head coefficient, D is the burial depth of the earthquake site, and H is the reservoir water depth.

[0020] As mentioned above, the normal stress σ n Based on the following formula:

[0021] σ n =h1×ρ r ×g

[0022] Among them, h1 is the vertical height from the earthquake source to the reservoir surface, ρ r is the average density of the medium from the earthquake source to the reservoir surface, g is the gravitational acceleration, σ n is the normal stress on the fault plane.

[0023] As mentioned above, the fault plane friction force f is based on the following formula:

[0024] f=μσ n .

[0025] The calculation of the fault plane shear stress τ as described above is based on the following formula:

[0026]

[0027] Among them, the principal stress σ 11 =0.0216d+6.7808, principal stress σ 22 =0.0182d+2.2328, d is the earthquake burial depth.

[0028] A computer device comprises a memory and a processor, wherein the memory stores a computer program, and the processor implements the steps of the above-mentioned calculation method when executing the computer program.

[0029] A computer-readable storage medium stores a computer program, which implements the steps of the above-mentioned calculation method when executed by a processor.

[0030] A computer program product comprises a computer program, which implements the steps of the above-mentioned calculation method when executed by a processor.

[0031] Compared with the prior art, the present invention has the following beneficial effects:

[0032] (1) Since the traditional Coulomb stress calculation is based on a uniform and completely elastic earth medium model, the present invention takes into account the changes in medium structure parameters caused by the infiltration of reservoir water on the basis of the elastic uniform medium model, and the effective Coulomb stress calculation is more reasonable;

[0033] (2) Since the influence of the normal stress on the fault surface in a water-containing medium needs to be calculated by taking the effect of the fluid into consideration, the present invention can effectively improve the accuracy of the calculation of the effective Coulomb stress. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] Figure 1 It is a flow chart of the present invention. DETAILED DESCRIPTION

[0035] In order to facilitate those skilled in the art to understand and implement the present invention, the present invention is further described in detail below in conjunction with embodiments. It should be understood that the implementation examples described herein are only used to illustrate and explain the present invention and are not used to limit the present invention.

[0036] Embodiment 1:

[0037] The present invention provides a Coulomb stress calculation method taking into account the effect of fluid, which can take into account the influence of the participation of fluid in the medium on the calculation of the Coulomb stress field, and realize the function of quantitatively calculating the stress changes of the reservoir medium and faults caused by the water storage of the reservoir.

[0038] like Figure 1 As shown in the figure, a method for calculating Coulomb stress taking into account the effect of fluid is used to calculate the effective Coulomb stress on the fault plane based on the burial depth d of the earthquake site, the reservoir water depth H, the fault plane strike S and the dip angle D.

[0039] like Figure 1 As shown, the following steps are included:

[0040] Step 1: Confirm the fault plane strike S and fault plane dip D at the earthquake location;

[0041] Step 1 specifically includes the following steps:

[0042] Before calculating the Coulomb stress, it is necessary to point out which fault plane the required Coulomb stress corresponds to. There are two situations. The first is that when the surface data reveals the fault plane strike S and the fault plane dip D of the fault, the fault plane dip can be used to calculate the Coulomb stress on the fault plane; the second is that when there is no surface data, the fault plane strike and the fault plane dip of the earthquake fault plane are inferred through the monitored earthquake data and the source mechanism of deep aftershocks. The above-mentioned inference of the fault plane strike and the fault plane dip of the earthquake fault plane is a prior art, which will not be described in detail in the present invention, thereby calculating the Coulomb stress of the fault plane;

[0043] Assume that the pre-seismic stress on the fault plane is Shortly after an earthquake occurs, the focal mechanism solution of the earthquake (i.e., the three parameters of fault plane strike, fault plane dip, and fault plane slip angle) can be obtained by combining field geological survey data, and then the occurrence of the earthquake fault can be determined, including the fault plane strike and fault plane dip. After a simple deduction, the fault plane normal vector (n 1 ,n 2 ,n 3 ), where n 1 =cosa 1 , n 2 =cosa 2 , n 3 =cosa 3 , a 1 ,a 2 ,a 3 are the angles between the fault plane normal vector and the x-axis, y-axis, and z-axis respectively. The x-axis and y-axis are perpendicular to each other and are both located in the horizontal plane. The z-axis is perpendicular to the x-axis and y-axis respectively. Then the fault plane normal vector is:

[0044]

[0045] If the effect of fluid is not considered in this area, and a fault plane strike S and a fault plane dip angle D are given arbitrarily, the initial stress vector along each axial direction (x-axis, y-axis, and z-axis) on the fault plane can be calculated. Initial normal stress and the initial shear stress τ 0 :

[0046]

[0047] in, is the intermediate parameter, i and j are both direction numbers, i, j = 1, 2, 3, 1, 2, 3 represent the x-axis, y-axis, and z-axis directions respectively, is the pre-seismic stress on the fault plane, The first subscript indicates the normal direction of the fault plane, and the second subscript indicates the direction of stress on the fault plane. 0 is the magnitude of the initial stress vector.

[0048] On this basis, considering the influence of fluid, the pore water stress is calculated, and step 2 is as follows:

[0049] Step 2: Calculate the pore water pressure p on the fault surface:

[0050] p=γ l ×h (3)

[0051] In the formula, γ l is the density of water (KN / n 3 ), the actual water head of the pore water at the earthquake location h = ξ(d+H); ξ is the water head coefficient, which ranges from 0 to 1; d is the burial depth of the earthquake location (m); H is the reservoir water depth (m);

[0052] Step 3: Given the known geometric shape of the seismogenic fault determined in step 1 (i.e., the fault plane strike S and the fault plane dip D), combined with the earthquake magnitude announced by the seismic network center, the earthquake rupture surface size and displacement amount are estimated based on the earthquake magnitude according to the empirical estimation formula (the calculation process of the earthquake rupture surface size and displacement amount is prior art and will not be described in detail in this application), and then the Okada elastic dislocation model is used to calculate the disturbance stress field Δσ caused by the earthquake ij , fault plane normal stress σ n The overburden pressure can be selected and calculated based on the following formula:

[0053] σ n =h1×ρ r ×g(Mpa) (4)

[0054] Where h1 is the vertical height from the earthquake source to the reservoir surface, h1 = H + d, ρ ris the average density of the medium from the earthquake source to the reservoir surface, g is the gravitational acceleration, σ n is the normal stress on the fault plane, and MPa is the unit of normal stress.

[0055] Among them, we get ρ r It is necessary to consider the changes in Young's modulus and Poisson's ratio caused by the infiltration of reservoir water, and calculate based on the following formula:

[0056]

[0057] In the formula, γ l is the density of water, here we take 1.0×10 3 kg / m 3 , γ s It is the average density of the medium from the earthquake source to the ground, which can be obtained based on the one-dimensional crust velocity model and is related to the earthquake source depth. k is the equivalent permeability of reservoir water, which is related to the type of rock mass and can be found in the table of mechanical parameters and physical parameters of geological bodies.

[0058] Step 4: Assume that the principal compressive stress near the epicenter remains unchanged for a short period of time after an earthquake. The specific time depends on the scale of the earthquake, the nature of the fault, crustal conditions, etc., and generally ranges from 5 minutes to 2 days.

[0059] Calculation of fault plane friction force f:

[0060] f=μσ n (5)

[0061] Where μ is the friction coefficient of the fault surface, σ n is the normal stress on the fault plane calculated based on step 4, and f is the friction force on the fault plane;

[0062] Step 5: Calculation of fault plane shear stress τ:

[0063]

[0064] In the formula, σ ij is the stress field of the fault plane after the earthquake. Among them, the shear stress τ of the fault plane is positive in the direction of fault slip; the normal stress σ of the fault plane n Take tension as positive and compression as negative; principal stress σ 11 is ij i and j are 1 respectively, and the principal stress σ 11 The value is equal to the horizontal principal stress σ x , principal stress σ 22 is ij i and j are 2 respectively, and the principal stress σ 22 The value is equal to the horizontal minor principal stress σ y (Mpa).

[0065]

[0066] Where d is the earthquake burial depth. The additional shear stress generated by reservoir water on deep rock mass is relatively weak, so it is not considered here.

[0067] Step 6: Combining all the above calculation results, calculate the effective Coulomb stress Δσ on the fault plane e Calculation:

[0068] Δσ e =τ-μ(σ n -p) (8)

[0069] In the formula, τ is the shear stress on the fault plane, μ is the friction coefficient on the fault plane, and σ n is the normal stress on the fault plane, p is the pore water pressure on the fault plane, Δσ e It is the effective Coulomb stress on the fault plane, that is, the Coulomb stress on the fault plane obtained by deducting the pore water pressure from the normal stress on the fault plane.

[0070] In one embodiment, a computer device is further provided, including a memory and a processor, wherein a computer program is stored in the memory, and the processor implements the steps in the above method embodiments when executing the computer program.

[0071] In one embodiment, a computer-readable storage medium is provided, on which a computer program is stored. When the computer program is executed by a processor, the steps in the above-mentioned method embodiments are implemented.

[0072] In one embodiment, a computer program product is provided, including a computer program, which implements the steps in the above method embodiments when executed by a processor.

[0073] Embodiment 2:

[0074] The Coulomb stress calculation method considering the fluid effect proposed in Example 1 is applied to the following example. Assume a river-type reservoir. The water surface width of the river in the dam site area is 5 km after the river is filled with water, and the maximum water depth is 200 m. The lithology of the dam site area is mainly granodiorite. There is a fault plane at the bottom of the reservoir. The fault plane dip angle D = 80° and the fault plane strike S = ∠60°. The average density γ from the earthquake source to the ground medium is s Take 2700kg / m 3 , the elastic modulus is 30 GPa, the Poisson's ratio is 0.26, the friction coefficient of the fault plane is 1.2, and the earthquake site is 5 km below the reservoir. Now calculate the stress value on the fault.

[0075] Step 1: Confirm that the fault plane strike S at the earthquake location is ∠60° and the fault plane dip angle D is 80°;

[0076] Step 2: Calculation of pore water pressure on the fault plane:

[0077] p=9.8×h=9.8×ξ×(d+H)

[0078] Among them, d+H is taken as 5200n, the head coefficient ξ is taken as 0.96, and the pore water pressure p on the fault surface is obtained as 48.92Mpa.

[0079] Step 3: Calculate the normal stress σ on the fault plane n ;

[0080]

[0081] σ n =hρ r g=1600×9.8×5200=81.54Mpa;

[0082] where ρ r is the calculated average density of the medium from the earthquake source to the reservoir surface, h1 is 5200m, and g is the gravity constant of 9.8m / s 2 , the equivalent permeability of the reservoir is taken as 0.8.

[0083] Step 4: Calculate the fault plane friction force f:

[0084] f=μσ n =1.2×81.54

[0085] In this embodiment, the friction coefficient of the fault surface μ=1.2.

[0086] Step 5: Calculation of fault plane shear stress τ:

[0087]

[0088] Using the relatively simple elastic semi-infinite space theoretical dislocation model (Okada dislocation model), the strain on the fault plane can be calculated. Then, the corresponding stress value is calculated according to formula (7) to obtain the corresponding σ 11 and σ 22 :

[0089] σ 11 =0.0216d+6.7808

[0090] σ 22 =0.0182d+2.2328

[0091] Where d is the depth of the earthquake location (m), and d = 5000m. 11 =σ x , σ 22 =σ yare the major and minor horizontal principal stresses (Mpa) at the earthquake location. x =114.78Mpa,σ y =93.23Mpa.

[0092] Step 6: Calculate the effective Coulomb stress Δσ on the fault plane e Calculation:

[0093]

[0094] It should be noted that the embodiments described in the present invention are merely examples of the spirit of the present invention. Those skilled in the art may make various modifications or additions to the described embodiments or replace them in similar ways, but they will not deviate from the spirit of the present invention or exceed the scope defined by the attached claims.

Claims

1. A Coulomb stress calculation method considering fluid action, characterized in that: The following steps are involved: Step 1: Confirm the fault plane strike S and fault plane dip D at the earthquake location; Step 2: Calculate the pore water pressure p on the fault surface; Step 3: Calculate the normal stress σ on the fault plane n ; Step 4: Calculate the fault plane friction force f; Step 5: Calculate the fault plane shear stress τ; Step 6: Calculate the effective Coulomb stress Δσ on the fault plane based on the following formula e Board e =τ-μ(σ n -p) Where μ is the friction coefficient of the fault surface.

2. A Coulomb stress calculation method considering fluid action according to claim 1, characterized in that: The pore water pressure p of the fault plane is based on the following formula; p=γ l ×h Among them, γ l is the density of water, h is the actual hydraulic head of the pore water at the earthquake site, h = ξ(d+H), ξ is the hydraulic head coefficient, D is the burial depth of the earthquake site, and H is the reservoir water depth.

3. A Coulomb stress calculation method considering fluid action according to claim 1, characterized in that: The fault plane normal stress σ n Based on the following formula: s n =h1×ρ r ×g Among them, h1 is the vertical height from the earthquake source to the reservoir surface, ρ r is the average density of the medium from the earthquake source to the reservoir surface, g is the gravitational acceleration, σ n is the normal stress on the fault plane.

4. A Coulomb stress calculation method considering fluid action according to claim 1, characterized in that: The fault plane friction force f is based on the following formula: f=μσ n 。 5. The Coulomb stress calculation method considering fluid action according to claim 1, characterized in that: The calculation of the fault plane shear stress τ is based on the following formula: Among them, the principal stress σ 11 =0.0216d+6.7808, principal stress σ 22 =0.0182d+2.2328, d is the earthquake burial depth.

6. A computer device comprising a memory and a processor, wherein the memory stores a computer program, characterized in that: When the processor executes the computer program, the steps of the computing method according to any one of claims 1 to 5 are implemented.

7. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the computing method according to any one of claims 1 to 5 are implemented.

8. A computer program product, comprising a computer program, characterized in that When the computer program is executed by a processor, the steps of the computing method according to any one of claims 1 to 5 are implemented.

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