A method for predicting the rupture trace of overburden soil under the action of a seismic reverse fault
Patent Information
- Application Number
- CN202611169661.6
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2026-08-04
- Publication Date
- 2026-10-23
AI Technical Summary
但该类方法本质上反映的是历史震例的宏观统计规律，难以描述某一具体场地中破裂迹线从基岩面到地表的空间传播路径
[0071]（2）从断层运动学与土体力学本质出发，以对数螺旋线为核心构建了具有明确物理意义的理论预测模型。该模型不仅能准确描述断层错动在土体中的传播与偏转过程，更通过等效剪胀判据与分层修正机制的深度融合，显著提升了对破裂迹线空间展布形态的预测精度。相较于现有的纯几何拟合或经验统计方法，本模型具有更强的理论基础和更广的适用范围。
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Figure CN122962650A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the interdisciplinary field of geotechnical engineering investigation technology and earthquake engineering safety evaluation. Specifically, it relates to a method for predicting the fracture trace of overburden soil under earthquake reverse faulting, which is applicable to the determination of fault avoidance distance and fracture resistance design in engineering sites. Technical Background
[0002] Earthquake damage case studies show that earthquakes of magnitude 6 or higher often trigger significant surface rupture. This surface rupture gradually forms shear zones, compressional uplift zones, or bending deformation zones within the overburden soil, ultimately manifesting at the surface as fault scarps, cracks, or rupture zones of varying widths. Unlike typical seismic inertial loads, permanent displacement caused by fault slippage is sudden, concentrated, and irreversible. Once an engineering structure crosses or is adjacent to a rupture zone, foundations, underground structures, roads, pipelines, and bridges may suffer severe damage due to differential displacement and strong shear deformation. Therefore, in the site selection and seismic design of major engineering projects, accurately predicting the location, distribution, and impact range of fault rupture lines, and thus designing targeted fracture resistance or taking reasonable avoidance measures, is a crucial step in ensuring project safety.
[0003] In current engineering practice, the determination of fault rupture traces mainly relies on two methods: field exploration and empirical statistics.
[0004] Field exploration methods typically include geological surveys, remote sensing interpretation, trench excavation, borehole exposure, and geophysical exploration techniques such as shallow seismic surveys, high-density electrical resistivity tomography (EDS), and transient surface wave detection. These methods can directly or indirectly obtain information on fault location, attitude, and some stratigraphic deformation, serving as a crucial foundation for active fault investigation. However, these methods usually only reveal fault morphology in limited profiles or localized areas, making it difficult to continuously track the propagation of fault dislocations from deep to shallow within the overburden. For engineering sites with thick overburden, indistinct surface ruptures, limited site conditions, or concealed faults, relying solely on trenches, boreholes, or geophysical anomalies to infer rupture trajectories is easily affected by detection resolution, profile layout, and interpretation experience. Furthermore, trench excavation and intensive drilling are costly and time-consuming, making it difficult to meet the timeliness requirements for large-scale site comparison, scheme optimization, and post-earthquake emergency assessment.
[0005] Empirical statistical methods, primarily based on historical earthquake data and seismic damage surveys, establish empirical relationships between earthquake magnitude, fault type, and surface rupture length, dislocation amount, or rupture zone width. These methods offer advantages such as fewer input parameters and ease of use, making them suitable for regional or preliminary fault hazard assessments. However, these methods essentially reflect macroscopic statistical patterns from historical earthquakes and struggle to describe the spatial propagation path of rupture traces from the bedrock surface to the surface in a specific site. Especially in reverse fault overburden rupture problems, parameters such as fault dip angle, overburden thickness, soil internal friction angle, dilatation angle, and dislocation amount collectively influence the curvature of the rupture path and its surface exposure location. Existing empirical formulas cannot fully reflect the coupling effects between these parameters, thus failing to provide directly applicable rupture traces for refined fault-resistant design.
[0006] In summary, the two methods mentioned above have limitations in terms of prediction accuracy, parameter coupling, and engineering applicability. There is an urgent need to establish a rupture trajectory prediction method that can comprehensively consider fault geometric parameters and soil mechanical properties, is computationally simple, and has strong applicability. This invention, based on logarithmic spiral theory and integrating extensive physical simulation experimental results of overburden soil with measured data from trenches in seismogenic rupture zones, proposes a refined quantitative prediction method for reverse fault rupture trajectories. Summary of the Invention
[0007] To address the aforementioned problems and shortcomings in existing technologies, the present invention aims to provide a method for predicting the fracture trajectory of overburden soil under earthquake reverse faulting. This method, based on logarithmic spiral theory, comprehensively considers the coupling effect of fault geometric parameters (dip angle, bedrock dislocation) and soil mechanical parameters (internal friction angle, dilatation angle). Through piecewise rotation correction technology, it achieves refined quantitative prediction of the entire reverse fault fracture path from the deep bedrock surface to the land surface. The present invention integrates fault geometric parameters and soil mechanical parameters, constructs a logarithmic spiral model, and performs piecewise rotation correction to predict the fracture trajectory of reverse faults in the overburden layer. The specific technical solution is as follows:
[0008] Step S1: Obtain key parameters of the seismogenic fault zone and overburden; the key parameters include fault dip angle α and bedrock vertical dislocation D. j The thickness H of the overburden layer, the internal friction angle φ and dilatation angle ψ of each soil layer, and the equivalent dilatation angle ψ are calculated. eq ;
[0009] Specifically:
[0010] Using engineering geophysical exploration methods such as shallow seismic exploration and indoor geotechnical tests, the fault dip angle α and the vertical dislocation D of the bedrock were obtained. j The five basic parameters are: the thickness of the overburden layer (H), the internal friction angle of the soil (φ), and the soil dilatation angle (ψ).
[0011] The fault dip angle α is usually determined by combining shallow high-resolution seismic exploration technology with stratigraphic comparison analysis of multi-hole drilling data. It is recommended to arrange no less than 3 boreholes in the same site for comparison and verification.
[0012] Bedrock vertical dislocation D j This refers to the vertical displacement caused by fault movement at the bedrock surface. The fault plane can be directly exposed by drilling, and the vertical distance difference between the same marker layer on both sides of the fault can be measured. This method has high accuracy but requires deep drilling.
[0013] The thickness H of the overburden refers to the total thickness of loose sediments above the bedrock surface. It is usually detected by geophysical methods such as high-density electrical resistivity tomography, transient surface wave exploration, or micromotion detection, and verified by borehole data.
[0014] soil internal friction angle The shear strength is a key indicator that characterizes the shear strength of soil and is determined by indoor triaxial compression test. The soil dilatation angle ψ is an indicator that characterizes the volume change characteristics of soil during shearing and is also determined by indoor triaxial compression test. Its value is usually smaller than the internal friction angle, and for dense sand, it is generally 20% to 40% of the internal friction angle.
[0015] Taking the equivalent cumulative shear resistance of layered soil and homogeneous soil as the condition of equivalence, and using the soil dilatation angle ψ as the basic equivalent quantity, the equivalent dilatation angle ψ is calculated by weighting the soil layer thickness. eq Calculation formula:
[0016] , where h i Let ψ be the thickness of the i-th soil layer. i Let be the shear dilatation angle of the i-th soil layer.
[0017] Step S2, dislocation quantity conversion and soil layer stratification; based on the vertical dislocation quantity D of the bedrock j Starting from the soil layer dislocation point F, draw an auxiliary line L1 along the fault dip direction, and then calculate the vertical dislocation D of the bedrock. j Reference lines D0, D1, D2, D3 and centerline L2 are constructed in the soil layer along with the thickness H of the overburden layer, and the soil layer is divided into layers.
[0018] Specifically:
[0019] In obtaining the vertical dislocation D of the bedrock j Then, taking the soil layer dislocation point F (i.e., the intersection of the fault plane and the bedrock plane) as the origin, a ray is drawn along the fault dip direction, defined as line L1. Based on this, the positions of the reference lines for each layer are determined according to the following rules:
[0020] (a) Measure the distance D upwards from the bottom of the soil layer (i.e., the bedrock surface). j Let the horizontal line be D0;
[0021] (b) Measure a distance of 2D from the bottom of the soil layer upwards. j Draw a horizontal line as D1;
[0022] (c) Measure a distance of 2D downwards from the top of the soil layer. j Draw a horizontal line as D2;
[0023] (d) Measure the distance D from the top of the soil layer downwards. j Draw a horizontal line as D3;
[0024] (e) Draw a horizontal line at 1 / 2 of the thickness H of the cover layer, and define it as the center line L2.
[0025] Based on this, the soil layers are non-uniformly stratified according to the following rules:
[0026] (a) Deep stratification: Starting from the bottom of the soil layer upwards, according to the thickness of the first layer Δh1=D j / 2 is divided into equally spaced layers until the depth of D2 is reached;
[0027] (b) Shallow densification stratification: From D2 upwards to the surface, according to the second stratification thickness Δh2=D j / 4 is used for equally spaced encrypted layering.
[0028] Step S3: Draw the logarithmic spiral model and preliminary prediction path; based on the fault dip angle α and the bedrock vertical dislocation D... j , thickness H of the overburden layer, and internal friction angle of the soil layer Shear dilatation angle ψ and equivalent shear dilatation angle ψ eq First, based on the fault dip angle α and the equivalent dilatation angle ψ eq First, determine the type of logarithmic spiral model, then calculate the polar angle θ0, angle Ws, and auxiliary angle using the formula. Using β and γ, a logarithmic spiral physical model is constructed, and the initial fracture path S0 in the homogeneous soil layer is plotted.
[0029] The parameters not otherwise marked are controlled by the soil parameters at the bottom layer of the overburden.
[0030] First, based on the fault dip angle α and the equivalent dilatancy angle ψ of the overlying soil layer... eq The sum of values is used to determine the model branch:
[0031] When α+ψ eq When the angle is less than 90°, choose model ①; when α + ψ eq When the angle is ≥90°, select model ②.
[0032] The physical meaning of this criterion is: α + ψeq This comprehensively reflects the coupled effect of fault dip angle and soil dilatation. When this value is less than 90°, shear slip is the dominant mechanism for rupture propagation; when this value is greater than or equal to 90°, the compression heave effect in rupture propagation is significantly enhanced, and the rupture mechanism undergoes a fundamental change, requiring different model branches to describe it.
[0033] Model ① When the site α+ψ eq When <90°:
[0034] First, calculate the auxiliary angle. : ;
[0035] Among them, auxiliary The direction of line r1 is determined by the control of the bedrock dislocation point F and the bottom surface of the soil layer D, and obtained in a clockwise direction.
[0036] In reverse faults, the maximum principal stress is distributed horizontally, and the angle between the fracture surface and the line of action of the maximum principal stress is: φ1 is controlled by the surface soil parameters, and the angle Ws is the angle between the tangent of the initial rupture trace and the ground surface.
[0037] Next, calculate the angle between line r1 and line r0, which is the polar angle θ0: ;
[0038] By combining the polar angle θ0 with point B and line r1, point O is determined; then, a perpendicular line from point B to line r1 is drawn, intersecting at point D, thus constructing triangle OBD.
[0039] Obtain the auxiliary angle γ, which is the angle between line r1 and line x: ;
[0040] The exposed point B of the fractured surface is determined based on the r1 line and the auxiliary angle γ. Point B is connected to the bedrock dislocation point F to determine the x-line.
[0041] Calculate the auxiliary angle β: ;
[0042] Draw a perpendicular line H from the bedrock dislocation point to the surface W of the footwall; the length of the X-ray can be obtained in ΔABE:
[0043] ;
[0044] Calculate the parameters of line r0 and line r1: , ;
[0045] Complete the construction and parameter acquisition of the auxiliary triangle in the logarithmic spiral, and combine the auxiliary triangle with the angle Ws to draw the preliminary predicted rupture trajectory S0.
[0046] Model ② When the site α+ψ eqWhen ≥90°:
[0047] First, calculate the auxiliary angle. : The direction of line r1 is determined by the control of the bedrock dislocation point F and the bottom surface of the soil layer D, and is obtained in a counterclockwise direction.
[0048] In reverse faults, the maximum principal stress is distributed horizontally, and the angle between the fracture surface and the line of action of the maximum principal stress is [value missing]. , The angle Ws is the angle between the tangent of the initial rupture trace and the ground surface.
[0049] Calculate the angle θ between line r1 and line r0. 0， : Using the polar angle θ0 and the line r1, we can determine point O; then, we draw a perpendicular line from point B to the line r1, intersecting at point D, thus constructing triangle OBD.
[0050] Obtain the auxiliary angle γ, which is the angle between line r1 and line X: ;
[0051] The exposed point B on the fractured surface is determined based on the r1 line and the auxiliary angle γ. Point B is then connected to the bedrock dislocation point F to determine the X-line.
[0052] Calculate the auxiliary angle β using the following formula. Draw a perpendicular line H from the bedrock dislocation point to the surface W of the footwall; the length of the X-ray can be obtained in ΔABE. ;
[0053] Calculate the parameters of line r0 and line r1: , .
[0054] Complete the construction and parameter acquisition of the auxiliary triangle in the logarithmic spiral, and combine the auxiliary triangle with the Ws angle to draw the preliminary predicted rupture trajectory S0.
[0055] Step S4: Segmented rotation correction of the logarithmic spiral model; Taking the intersection of the initial rupture path and each soil layer as the reference point, the logarithmic spiral model in each soil layer interval is segmented and rotated and combined from bottom to top to obtain the corrected continuous logarithmic spiral combined model.
[0056] Specifically: taking the intersection of the preliminary predicted rupture path S0 with each layer boundary as a reference, the rupture path in each depth segment is differentially rotated and corrected according to a preset rotation rule to form a corrected combined path.
[0057] Piecewise rotation correction is performed according to the following rules:
[0058] (a) At line D0 (above the bottom of the soil layer D) j(location) and line D1 (2D above the bottom of the soil layer) j The section between (points) retains the original state of the initial fracture path S0 without applying any rotational correction.
[0059] (b) In the section between D1 and the centerline L2 (at the thickness of the overburden layer H / 2), the path in the section is rotated clockwise by an angle θ0 / 3 around the rotation center, with the intersection of the section and the initial rupture path S0 as the rotation center.
[0060] (c) At the centerline L2 and line D3 (below the top surface of the soil layer D) j The section between (points) retains the original state of the initial fracture path S0 without applying any rotational correction.
[0061] (d) In the section between D3 and the surface, take the intersection of the section and the initial rupture path S0 as the rotation center, and rotate the path in the section counterclockwise around the rotation center by an angle θ0 / 2.
[0062] The physical basis of this segmented rotation correction strategy lies in the significant differences in the mechanical constraints on the soil at different depths during the propagation of reverse fault rupture from deep to the surface. In the deep region (between D0 and D1), the soil is subject to strong confining pressure, and the deflection effect of the rupture path is weak, thus maintaining the original state of the initial path. In the mid-deep region (between D1 and L2), the confining pressure gradually decreases, and the rupture path begins to deflect clockwise, thus applying clockwise rotation correction. In the middle region (between L2 and D3), the rupture path is in a transitional state and remains unchanged. In the shallow surface region (between D3 and the surface), due to the significant decrease in confining pressure and the influence of the free surface effect, the rupture path shows a significant upward tilt (counterclockwise deflection), thus applying a larger counterclockwise rotation correction.
[0063] After the above segmented rotation correction, the corrected segment paths are spliced together to form a continuous correction prediction model from bedrock dislocation point F to the surface.
[0064] Step S5: Fit the rupture path; extract the midpoint of the logarithmic spiral arc segment in each soil layer as the control point, take the rupture initiation point F at the bottom of the soil layer as the starting point, extend upward along the preliminary rupture path, and combine the control points to perform curve fitting to obtain the predicted rupture trace of the reverse fault in the overlying soil layer.
[0065] First, extract the midpoints of the arc segments of the corrected path within each layer segment, and label them sequentially as O1, O2, O3, ..., O n (where n is the total number of layers). These midpoints are key control points describing the geometric characteristics of the fracture surface within each layer segment, and can effectively reflect the dip and curvature changes of the fracture surface within the corresponding depth range.
[0066] Then, starting from the fracture initiation point at the bottom of the soil layer (bedrock dislocation point F), extend upward along the corrected path until it intersects with line D0.
[0067] Finally, using the intersection of point F and D0, and the midpoints O1, O2, O3, ..., O of all arc segments as examples... n As control nodes, curve fitting methods (such as least squares polynomial fitting) are used to fit the data and generate a continuous and smooth final rupture path. This path is the rupture trace of the overburden soil under earthquake reverse faulting predicted by the method of this invention.
[0068] The above are the specific steps of this patent, "A method for predicting the fracture traces of overburden soil under earthquake reverse faulting".
[0069] The innovation of this patent, which differs from existing technologies, is as follows:
[0070] (1) By extensively collecting earthquake damage examples and numerous physical model experimental data of overburden soil, key parameters such as fault dip angle, dislocation amount, soil internal friction angle, and dilatation angle were systematically integrated. Based on the fault dip angle α and the equivalent dilatation angle ψ... eq By constructing different model branches, and taking into account the non-uniform deformation characteristics of soil layers at different depths, a segmented rotation correction technique was innovatively adopted for layered fine correction, which achieved high-precision simulation of the reverse fault rupture path from deep to the surface.
[0071] (2) Based on the fundamental principles of fault kinematics and soil mechanics, a theoretical prediction model with clear physical meaning was constructed using a logarithmic spiral as its core. This model not only accurately describes the propagation and deflection process of fault displacement in the soil, but also significantly improves the prediction accuracy of the spatial distribution morphology of the rupture trace through the deep integration of the equivalent dilatation criterion and the layered correction mechanism. Compared with existing pure geometric fitting or empirical statistical methods, this model has a stronger theoretical foundation and a wider range of applicability.
[0072] (3) The experimental results and theoretical models were transformed into engineering models, forming a quantitative prediction method for reverse fault rupture traces with bedrock surface burial depth, bedrock vertical dislocation, and fault dip angle as core parameters. This method covers the entire process from the initiation of bedrock displacement to the formation of surface rupture, achieving accurate quantitative assessment of the fault's influence range. The required input parameters can all be obtained through conventional engineering survey methods, the calculation process is simple, and it is easy to promote and apply in engineering, providing an efficient and reliable solution for seismic fracture resistance design of engineering sites. Attached Figure Description
[0073] Figure 1 Flowchart of a method for predicting fracture traces of overburden soil under earthquake reverse faulting
[0074] Figure 2This is a schematic diagram illustrating the acquisition of fault and site soil layer parameters according to an embodiment of the present invention.
[0075] Figure 3 This is a schematic diagram of soil layering drawn using auxiliary lines according to an embodiment of the present invention.
[0076] Figure 4 This is the logarithmic spiral physical model and preliminary fracture path diagram constructed in the embodiment of the present invention.
[0077] Figure 5 This is a schematic diagram of the segmentation, combination, and correction process according to an embodiment of the present invention.
[0078] Figure 6 This is a schematic diagram of the final fitted rupture path in an embodiment of the present invention. Detailed Implementation
[0079] To make the specific implementation steps and technical solutions of this invention clearer and more explicit, the specific steps of this invention will be further explained below with reference to the accompanying drawings, taking a typical sandy soil site as an example. It should be noted that the embodiments described herein are for illustrative purposes only and do not constitute a limitation on this invention.
[0080] according to Figure 1 The process shown includes the following steps:
[0081] Step S1: Obtain fault and site soil layer parameters
[0082] like Figure 2 As shown, key parameters of the seismogenic fault zone and overburden were obtained through engineering geophysical exploration, borehole survey, and geotechnical testing:
[0083] Fault dip angle α = 60°, bedrock vertical dislocation D j =5.81m (D is taken according to safety principles) j =6m);
[0084] Soil layer 1: Sandy soil, with an internal friction angle φ1 of 37.6° and a soil shear dilatation angle ψ1 of 5°;
[0085] Soil layer 2: Sandy soil, with an internal friction angle φ2 of 40° and a soil shear dilatation angle ψ2 of 7°;
[0086] Soil layer three: clay, with an internal friction angle φ3 of 26°; soil shear dilatation angle ψ3 of 2°;
[0087] Soil layer four: sandy soil, with an internal friction angle φ4 of 35.9° and a soil shear dilatation angle ψ4 of 7°.
[0088] Calculated .
[0089] Step S2: Drawing auxiliary lines and soil layering
[0090] Taking the soil layer dislocation point F as the origin, a ray is drawn along the fault dip angle (60°) as line L1. According to D... j =6m, determine the position of each layer reference line;
[0091] (a) Line D0: Above the bottom of the soil layer (bedrock surface) D j =6m;
[0092] (b) Line D1: 2D above the bottom of the soil layer j =12m;
[0093] (c) Line D2: 2D below the top surface of the soil layer j =12m;
[0094] (d) Line D3: D below the top surface of the soil layer j =6m;
[0095] (e) Centerline L2: at a point where the cover layer thickness H / 2 = 30m.
[0096] Layering is performed according to the non-uniform stratification rule:
[0097] (a) Deep layering: Starting from the bottom of the soil layer and moving upwards, according to Δh1=D j The thickness of the layer is 3m, forming a layered layer with a thickness of 3m within the layered range of D2 to D (12 to 60m);
[0098] (b) Shallow densification stratification: From line D2 (12m below the surface) to the surface, according to Δh2=D j A 1.5m thick layer of densified material is formed by adding 4 layers.
[0099] Stratification results as follows Figure 3 As shown, the entire soil layer is divided into 22 sub-units, numbered from 1 to 22 from bottom to top.
[0100] Step S3: Construct a logarithmic spiral physical model and generate a preliminary path.
[0101] Due to α+ψ eq =65.07°<90°, therefore the logarithmic spiral model① is chosen.
[0102] Calculate auxiliary angles Calculated ;
[0103] Among them, auxiliary The direction of line r1 is determined by controlling the clockwise direction between the bedrock dislocation point F and the bottom surface of the soil layer D.
[0104] In reverse faults, the maximum principal stress is distributed horizontally, and the angle between the rupture surface and the line of action of the maximum principal stress is calculated. ;
[0105] The angle between line r1 and line r0 is calculated as the polar angle θ0. ;
[0106] By combining the polar angle θ0 with point B and line r1, point O is determined. Then, a perpendicular line from point B to line r1 is drawn, intersecting at point D, thus constructing triangle OBD.
[0107] Next, the auxiliary angle γ is obtained as the angle between line r1 and the X-ray;
[0108] In ΔABD, the calculation is as follows: , =70.64°;
[0109] The exposed point B of the fractured surface is determined based on the r1 line and the auxiliary angle γ. Point B is connected to the bedrock dislocation point F to determine the x-line.
[0110] Calculate the auxiliary angle β, and get ;
[0111] Draw a perpendicular line H from the bedrock dislocation point to the surface W of the footwall.
[0112] The result calculated in ΔABE is... ;
[0113] Calculate the parameters of line r0 and line r1:
[0114] Calculated ;
[0115] Calculated 145.92m.
[0116] By obtaining the parameters of the auxiliary triangle in the logarithmic spiral, a physical model of the logarithmic spiral can be constructed, and based on this, a preliminary predicted rupture path S0 within the homogeneous soil layer can be plotted, such as... Figure 4 As shown.
[0117] Step S4: Piecewise Combination and Modified Logarithmic Spiral Model
[0118] like Figure 5 As shown, with the intersection of the initial fracture path S0 and each layer boundary as the rotation center, segmented rotation correction is performed according to preset rules:
[0119] (a) Section D0 to D1 (54m to 48m): Remain unchanged;
[0120] (b) Between D1 and L2 (48m to 30m): Rotate clockwise around the intersection by θ0 / 3 = 33.8° / 3 = 11.3°;
[0121] (c) Section L2 to D3 (30m to 6m): Remain unchanged;
[0122] (d) D3 to the ground surface section (6m to 0m): rotate counterclockwise around the intersection point by θ0 / 2=33.8° / 2=16.9°.
[0123] After the above segmented rotation correction, the corrected segment paths are spliced together to form a continuously corrected prediction model from bedrock dislocation point F to surface exposure point B.
[0124] Step S5: Fit the final rupture path
[0125] like Figure 6 As shown, extract the midpoints O1, O2, O3, ..., O of the arc segments of the corrected path within each layer segment. 22 There are a total of 22 control nodes.
[0126] Starting from bedrock dislocation point F, the modified path is extended upwards to intersect with line D0. Using the intersection of point F and D0, as well as the midpoints of 22 arc segments, as control nodes, the least squares method is used for curve fitting to generate a continuous and smooth final predicted fracture trajectory.
[0127] The final fitted predicted rupture trajectory is as follows: Figure 6 As shown by the S-line, this trajectory originates from bedrock dislocation point F, ascends through the overburden soil, and emerges at the surface at point B. In summary, the final fitted fault rupture path is the predicted rupture trajectory under seismic reverse faulting, which can be used for determining fault avoidance distances and fracture-resistant design in engineering sites.
[0128] The above description is merely to illustrate the specific implementation of the technical solution of this invention, and its description does not constitute any limitation on the scope of patent rights. Any obvious changes, functionally equivalent substitutions, or substantial improvements made based on the core technical concept and basic principles of this invention shall be deemed to fall within the legal protection scope defined by the claims.
Claims
1. A method for predicting fracture traces of overburden soil under earthquake reverse faulting, characterized in that, By integrating fault geometry parameters and soil mechanics parameters, and constructing a logarithmic spiral model combined with piecewise rotation correction using the layered summation method, the rupture trajectory of the reverse fault in the overlying soil layer is predicted. The specific steps include: Step S1: Obtain key parameters of the seismogenic fault zone and overburden; the key parameters include fault dip angle α and bedrock vertical dislocation D. j Calculate the thickness H of the overburden layer, the internal friction angle φ and dilatation angle ψ of each soil layer, and calculate the equivalent dilatation angle ψ of the overburden layer. eq ; Step S2, based on the vertical dislocation amount D of the bedrock j Starting from the soil layer dislocation point F, draw an auxiliary line L1 along the fault dip direction, and then calculate the vertical dislocation D of the bedrock. j Reference lines D0, D1, D2, D3 and centerline L2 are constructed in the soil layer along with the thickness H of the overburden layer, and the soil layer is divided into layers. Step S3, based on the fault dip angle α and the bedrock vertical dislocation D j The thickness of the overburden layer H, the internal friction angle φ of the soil layer, the dilatation angle ψ, and the equivalent dilatation angle ψ of the overburden layer. eq First, based on the fault dip angle α and the equivalent dilatation angle ψ eq First, determine the type of logarithmic spiral model, then calculate the polar angle θ0, angle Ws, and auxiliary angle using the formula. Using β and γ, construct a logarithmic spiral physical model and plot the initial fracture path S0 within the homogeneous soil layer; Step S4: Using the intersection of the initial rupture path and each soil layer as the reference point, the logarithmic spiral model in each soil layer interval is segmented, rotated and combined from bottom to top to obtain the corrected continuous logarithmic spiral combined model. Step S5: Extract the midpoint of the logarithmic spiral arc segment in each soil layer as the control point. Starting from the fracture initiation point F at the bottom of the soil layer, extend upward along the preliminary fracture path. Combine the control points to perform curve fitting to obtain the predicted fracture trace of the reverse fault in the overlying soil layer.
2. The method for predicting fracture traces of overburden soil under earthquake reverse faulting as described in claim 1, characterized in that, The equivalent dilatation angle ψ eq Weighted calculation method: The calculation formula is obtained by weighting the soil layers according to their thickness, assuming that the layered soil and homogeneous soil have the same cumulative shear resistance. , where h i Let ψ be the thickness of the i-th soil layer. i Let be the shear dilatation angle of the i-th soil layer.
3. The method for predicting the fracture traces of overburden soil under earthquake reverse faulting as described in claim 1, characterized in that, The specific method for determining the layered reference line in step S2 is as follows: Measure D from the bottom of the soil layer upwards. j and 2D j Determine the distances to reference lines D0 and D1 respectively; measure D downwards from the top of the soil layer. j and 2D j Determine reference lines D3 and D2 based on the distance; draw center line L2 at the midpoint of the overburden thickness H; arrange the soil layers from bottom to top according to D... j The thickness is divided into equal-interval layers, and within the interval from the D2 reference line to the ground surface, according to D... j / 4 thickness for encrypted layering.
4. The method for predicting fracture traces of overburden soil under earthquake reverse faulting according to claim 1, characterized in that, The specific method for selecting the logarithmic spiral model in step S3 is as follows: Model ①, when the site α+ψ eq When <90°: First, calculate the auxiliary angle. : ; Among them, auxiliary The direction of line r1 is determined by the bedrock dislocation point F and the bottom surface of the soil layer D, and obtained in a clockwise direction. In reverse faults, the maximum principal stress is distributed horizontally, and the angle between the fracture surface and the line of action of the maximum principal stress is: φ1 is controlled by the surface soil parameters, and the angle Ws is the angle between the tangent of the initial rupture trace and the ground surface. Next, calculate the angle between line r1 and line r0, which is the polar angle θ0: ; By combining the polar angle θ0 with point B and line r1, point O is determined; then, a perpendicular line from point B to line r1 is drawn, intersecting at point D, thus constructing triangle OBD. Obtain the auxiliary angle γ, which is the angle between line r1 and line x: ; Based on the r1 line and the auxiliary angle γ, determine the surface outcrop point B of the fracture, and connect point B with the bedrock dislocation point F to determine the x-line; Calculate the auxiliary angle β: ; Draw a perpendicular line H from the bedrock dislocation point to the surface W of the footwall; find the length of the X-ray in ΔABE: ; Calculate the parameters of line r0 and line r1: , ; Complete the construction and parameter acquisition of the auxiliary triangle in the logarithmic spiral, and draw the preliminary predicted rupture trajectory S0 by combining the auxiliary triangle and angle Ws; Model ②, when the site α+ψ eq When ≥90°: First, calculate the auxiliary angle. : The direction of line r1 is determined by the bedrock dislocation point F and the bottom surface of the soil layer D, and is obtained in a counterclockwise direction. In reverse faults, the maximum principal stress is distributed horizontally, and the angle between the fracture surface and the line of action of the maximum principal stress is [value missing]. , The angle Ws is the angle between the tangent of the initial rupture trace and the ground surface; Calculate the angle θ between line r1 and line r0. 0， : Using the polar angle θ0 and the line r1, we can determine point O; then, we draw a perpendicular line from point B to the line r1, intersecting at point D, thus constructing triangle OBD. Obtain the auxiliary angle γ, which is the angle between line r1 and line X: ; Based on the r1 line and the auxiliary angle γ, determine the surface outcrop point B of the fracture, and connect point B with the bedrock dislocation point F to determine the X-line; Calculate the auxiliary angle β. Draw a perpendicular line H from the bedrock dislocation point to the surface W of the footwall; find the length of the X-line in ΔABE. ; Calculate the parameters of line r0 and line r1: , ; Complete the construction and parameter acquisition of the auxiliary triangle in the logarithmic spiral, and draw the preliminary predicted rupture trajectory S0 by combining the auxiliary triangle and the Ws angle.
5. The method for predicting fracture traces of overburden soil under earthquake reverse faulting according to claim 1, characterized in that, The specific method of segmented rotation and combination in step S4 is as follows: Using the intersection of line D0 and the preliminary predicted rupture path S0 as the reference point, the model is directly combined in its original state within the interval from D0 to D1; the model is combined after rotating clockwise by θ0 / 3 around the reference point within the interval from D1 to the center line L2; the model is directly combined in its original state within the interval from L2 to D3; and the model is combined after rotating counterclockwise by θ0 / 2 around the reference point within the interval from D3 to the top surface of the soil layer.
6. The method for predicting fracture traces of overburden soil under earthquake reverse faulting according to claim 1, characterized in that, The specific method for fitting the rupture trajectory under the action of the reverse fault in step S5 is as follows: Extract the midpoints of the logarithmic spiral arc segments constructed in each soil layer and label them sequentially as O1, O2, O3, ... O n Starting from the rupture initiation point F at the bottom of the soil layer, extend upward along the initial predicted rupture path until it intersects with the auxiliary control line D0. The rupture initiation point F, the intersection with line D0, and the midpoints O1, O2, O3, ... O of each arc segment are used as the reference. n Using control points, a curve fitting method is employed to fit the path, resulting in the final predicted rupture trajectory.