Method for correlating accumulated strain damage and energy of accumulation body under rainfall-earthquake coupling

Abstract

The application discloses a method for analyzing the correlation between the accumulated strain damage and energy of a deposit under rainfall and earthquake coupling, and belongs to the technical field of geotechnical engineering geological disaster prevention. The method for analyzing the correlation between the accumulated strain damage and energy of a deposit under rainfall and earthquake coupling relies on a shaking table test, first constructs a deposit slope model, lays out monitoring components, and collects time history data under multi-stage seismic loading; then calculates accumulated strain damage parameters and performs plastic correction, simultaneously calculates hysteresis dissipated energy and accumulated dissipated energy; further establishes a quantitative mapping relationship between the accumulated strain damage and energy dissipation, divides damage evolution stages and identifies energy driving rules; finally, based on the mapping curve inflection point, the slope failure trend is predicted. The application reveals the cause of the differentiated response from the energy essence, reflects the plastic damage nature with the accumulated strain, and can significantly improve the accuracy of slope dynamic damage evaluation and failure prediction, and is suitable for seismic research and disaster prevention and control of mountainous deposit slopes.

Description

Technical Field

[0001] This invention belongs to the field of geotechnical engineering earthquake resistance and slope dynamic response analysis technology, specifically involving a method for analyzing the correlation between cumulative strain damage and energy of accumulated bodies under rainfall-earthquake coupling. Background Technology

[0002] Accumulated slopes are common geological formations in mountainous engineering projects. Under the coupled effects of rainfall infiltration and seismic loads, progressive cumulative damage occurs within the soil, eventually leading to slope instability and failure. These slopes are a key target for geological disaster prevention and control in mountainous areas. Shaking table model tests are a core method for studying the dynamic response and damage evolution of slopes, allowing for the acquisition of dynamic response data throughout the soil's life cycle through multi-stage loading.

[0003] Current research on dynamic damage of embankment slopes still suffers from three significant shortcomings: First, most existing studies analyze dynamic response characteristics from a macroscopic stress-strain perspective, lacking mechanistic analysis at the energy level. This makes it difficult to explain the intrinsic causes of differentiated responses at different locations within the embankment from the perspective of energy dissipation. Second, existing soil damage quantification relies heavily on single strain amplitude indicators, neglecting the cumulative strain damage mechanism caused by the soil's plasticity. This does not align with the gradual failure process induced by continuous strain accumulation in actual engineering. Third, existing technologies have failed to establish a quantitative correlation between cumulative soil damage parameters and seismic energy absorption and dissipation behavior. They cannot reflect the degree of soil damage development through seismic energy evolution patterns, hindering the accurate evaluation of the damage evolution state of embankment soils under seismic loading from the perspective of energy-cumulative strain coupling, and making it difficult to predict slope failure trends based on energy characteristics.

[0004] It should be noted that the analysis of the above technical information is the result of creative labor. The detailed description of it in the background section is only intended to deepen the understanding of the non-obviousness of the overall background technology of this application by those skilled in the art, and should not be regarded as an admission or in any form an implication that the above technical information constitutes prior art known to those skilled in the art. Summary of the Invention

[0005] To address the shortcomings of existing technologies, the present invention aims to provide a method for analyzing the correlation between cumulative strain damage and energy in aggregates under rainfall-earthquake coupling. The technical problem to be solved is: how to accurately characterize the plastic cumulative damage process of unsaturated aggregates under rainfall-earthquake coupling, reveal the causes of differential dynamic responses of slopes from the perspective of energy dissipation, and establish a quantitative correlation between energy and damage to improve the accuracy of slope dynamic damage assessment and failure prediction.

[0006] To solve the above-mentioned technical problems, the present invention adopts the following technical solution:

[0007] A method for analyzing the correlation between cumulative strain, damage, and energy in an accumulation body under rainfall-seismic coupling includes the following steps:

[0008] A shaking table test model of an accumulated slope under rainfall-seismic coupled action was constructed, and acceleration monitoring components and pore water pressure monitoring components were deployed. A graded and progressive seismic loading scheme was designed, and multiple levels of seismic loads were applied after rainfall infiltration and settling, while time history data of each monitoring point were collected simultaneously. Shear strain time history was calculated based on adjacent elevation acceleration data, and cumulative strain damage parameters were calculated in combination with shear wave velocity. The single-stage hysteretic dissipation energy was calculated and accumulated step by step to obtain the cumulative dissipation energy. The damage development sequence and energy dissipation sequence were matched point by point to establish a quantitative energy-damage mapping relationship. The damage evolution stages were divided, and the energy driving law of damage development was identified. Based on the mapping relationship and stage characteristics, the dynamic failure trend of the slope was predicted.

[0009] The beneficial effects of this technical solution are as follows: it breaks through the limitation of existing technologies that evaluate damage based solely on a single strain amplitude, and adopts cumulative strain parameters to truly reflect the essence of cumulative plastic damage in soil; at the same time, it takes an energy dissipation perspective, establishes a quantitative correlation between cumulative damage and energy dissipation, and achieves the technical effect of explaining differentiated responses and predicting damage development from the perspective of energy migration, providing a brand-new analytical framework for the evaluation of dynamic damage on embankment slopes.

[0010] Furthermore, by performing time-domain integration on the absolute value of the shear strain time history, combined with soil shear wave velocity normalization, and using a sliding time window to update the damage index point by point, a continuous damage evolution time history curve is obtained.

[0011] Beneficial effects: It realizes continuous and temporal characterization of cumulative strain damage, can accurately capture the dynamic development process of damage, avoids the defect of losing strain accumulation information in single-panel index, and significantly improves the continuity and accuracy of damage characterization.

[0012] Furthermore: the hysteretic dissipation energy per unit volume is calculated by using the area enclosed by the shear stress-shear strain hysteresis loop under a single load, and the cumulative dissipation energy is obtained by accumulating it step by step according to the loading sequence.

[0013] Beneficial effects: The energy dissipation level of soil under cyclic loading was accurately quantified by the hysteresis loop area method. The cumulative dissipated energy can comprehensively reflect the combined effects of earthquake amplitude, duration and frequency, providing a standardized quantitative indicator for energy-level mechanism analysis.

[0014] Furthermore, the elastic strain component and the plastic strain component are separated from the total shear strain, and the damage index is modified based on the cumulative plastic strain to eliminate the interference of the reversible component of elastic strain.

[0015] Beneficial effects: It eliminates the interference of reversible elastic strain on damage evaluation, so that the damage index only reflects the irreversible plastic cumulative damage of soil, which is more in line with the physical nature of soil dynamic damage. The physical meaning of the damage quantification results is clearer and the reliability is higher.

[0016] Furthermore, based on the growth rate, the cumulative energy dissipation is divided into three stages: rapid growth, slow growth, and stabilization. The energy dissipation rate and dissipation ratio of each stage are calculated respectively.

[0017] Beneficial effects: It enables a refined segmentation of the energy dissipation process, clearly distinguishing the energy input and dissipation characteristics of different loading stages, and providing a segmented analysis basis for subsequent matching of damage development stages and identification of energy-driven laws.

[0018] Furthermore, based on the characteristics of the first derivative change of the damage index, the entire loading process is divided into three characteristic stages: the initial damage stage, the stable development stage, and the rapid deterioration stage.

[0019] Beneficial effects: It clarifies the stage-by-stage evolution law of cumulative soil damage, and can accurately identify the critical turning point when damage changes from gradual to dramatic, providing a clear stage division basis for the graded early warning of slope dynamic damage.

[0020] Furthermore: calculate the damage increment corresponding to a unit energy input to obtain the energy-damage conversion efficiency coefficient, match the dissipation rate and damage development rate at each stage, and form a staged energy-damage correspondence rule.

[0021] Beneficial effects: A quantitative energy-damage conversion relationship was established, the damage increment induced by unit energy at different stages was clarified, and the technical effect of directly estimating the degree of damage development from the energy dissipation level was realized, providing a quantitative basis for damage prediction in the energy dimension.

[0022] Furthermore, by comparing the damage development process and energy dissipation characteristics at different elevation locations and with different initial compaction points, the spatial differences in the dynamic response of the accumulation body can be explained from the perspective of the differences in the energy absorption and dissipation capacity of the soil.

[0023] Beneficial effects: It systematically elucidates the intrinsic mechanism of the differences in dynamic response at different locations and densities of the accumulation body from the perspective of energy essence, making up for the shortcomings of existing technologies that only describe phenomena without revealing the essence, and significantly improving the theoretical depth and engineering guidance value of the analysis conclusions.

[0024] Furthermore, based on the inflection point characteristics of the energy-damage mapping curve, the critical energy threshold for the transition from stable development to rapid deterioration of damage is identified, and the dynamic failure development trend of the slope is predicted in combination with the current cumulative dissipated energy level.

[0025] Beneficial effects: It enables the prediction of slope failure trends based on energy indicators, and can assess damage status and failure risk through energy levels without monitoring strain data throughout the process. This expands the engineering application scenarios of the method and provides a feasible path for the rapid assessment of slope seismic dynamic stability.

[0026] Furthermore, this method was applied to the seismic dynamic damage assessment and stability prediction of unsaturated deposit slopes with a broken bedrock surface.

[0027] Beneficial effects: The method clarifies typical application scenarios and has good adaptability to the widely distributed broken bedrock accumulation slopes in mountainous areas. It can directly serve the seismic design and disaster prevention of engineering slopes in mountainous areas.

[0028] This invention represents a significant technological advancement over existing technologies and is applicable to the damage evolution characterization and failure trend prediction of unsaturated aggregate slopes under multi-field coupling. Its beneficial effects are mainly reflected in the following three core aspects:

[0029] First, the damage characterization is made more essential. Based on the physical nature of plastic cumulative failure of soil, this invention uses cumulative strain parameters to replace the traditional single strain amplitude index. Combined with plastic strain separation correction, it truly restores the process of progressive failure induced by continuous strain accumulation under cyclic loading. The damage quantification results are more in line with engineering practice, greatly improving the rationality and accuracy of damage assessment.

[0030] Second, the explanation of the mechanism is more in-depth. This invention breaks through the limitations of existing technologies that only analyze from the macroscopic stress-strain level. It systematically elucidates the intrinsic mechanism of differentiated responses at different locations within the accumulation body from the perspective of seismic energy input, absorption and dissipation, and establishes a quantitative correlation between energy dissipation and damage development. This provides a brand-new theoretical perspective and support for accurately predicting the overall instability evolution of the accumulation body.

[0031] Third, practical engineering applications. This invention successfully established a quantitative relationship between cumulative strain and the process of seismic energy absorption and dissipation, making it possible to predict soil failure dominated by cumulative strain from the perspective of energy migration. It can quickly assess slope damage status and failure risk based on energy indicators, significantly improving the accuracy and efficiency of stability assessment of deposits under seismic action, and providing more scientific technical support for disaster prevention and mitigation in mountainous areas. Attached Figure Description

[0032] To more clearly illustrate the embodiments of this technical solution, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of this technical solution. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0033] Figure 1 This is a schematic diagram of the planar layout of the accelerometer and the pore water pressure sensor in an embodiment of the present invention. The units of dimensioning are cm.

[0034] Figure 2 This is a typical shear stress-strain hysteresis loop evolution diagram of a loosely packed body in an embodiment of the present invention.

[0035] Figure 3 This is a segmented diagram of the shear stress and shear strain time series of a typical hysteresis loop in an embodiment of the present invention;

[0036] Figure 4 This is a graph showing the variation of cumulative dissipated energy under seismic waves of different amplitudes in an embodiment of the present invention;

[0037] Figure 5 This is a graph showing the variation of cumulative strain damage index of soil in a medium-dense packing in an embodiment of the present invention.

[0038] Figure 6 This is a graph showing the variation of cumulative strain damage index of loose soil in an embodiment of the present invention.

[0039] Figure 7 This is a schematic diagram of the stress state of soil and rock elements under natural and seismic loads in an embodiment of the present invention;

[0040] Figure 8 This is a schematic diagram of the stress state of a slope rock and soil unit under seismic load in an embodiment of the present invention.

[0041] Explanation of reference numerals in the attached figures:

[0042] A0 - Platform acceleration sensor; A1-A14 - Slope acceleration sensor;

[0043] K1-K12 - Pore water pressure sensor. Detailed Implementation

[0044] The technical solutions of this technical solution will be clearly and completely described below with reference to the accompanying drawings in the embodiments of this technical solution. Obviously, the described embodiments are only a preferred embodiment of this technical solution, and not all embodiments. Based on the core concept of this technical solution and the following embodiments, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this technical solution.

[0045] It should be noted that these embodiments are provided to make the application thorough and complete, and to fully express the scope of the application to those skilled in the art. It should be observed that, unless otherwise specifically stated, the relative arrangement of components and steps, material composition, numerical expressions, and values ​​described in these embodiments should be interpreted as merely exemplary and not as limiting.

[0046] In the description of this technical solution, it should be understood that the terms axial, radial, left, right, top, inner, and outer, indicating orientation or positional relationships, are based on the orientation or positional relationships shown in the accompanying drawings. They are used solely for the convenience of describing the technical solution and for simplification, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on this technical solution. Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of indicated technical features. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature. In the description of this technical solution, "several" means one or more, unless otherwise explicitly specified.

[0047] In this technical solution, unless otherwise explicitly specified and limited, the terms installation, connection, linking, fixing, etc., should be interpreted broadly. For example, they can refer to fixed connection, detachable connection, or integral connection; they can refer to mechanical connection or electrical connection; they can refer to direct connection or indirect connection through an intermediate medium; and they can refer to the internal connection of two components. For those skilled in the art, the specific meaning of the above terms in this technical solution can be understood according to the specific circumstances.

[0048] This invention utilizes a shaking table testing system. The test model is a single-slope structure of an unsaturated deposit overlying bedrock, with the bedrock surface divided into upper and lower sections. The upper section has a greater dip angle than the lower section, forming a concave bedrock-overlying interface. The deposit consists of well-graded coarse-grained soil, layered according to the designed density, with a straight slope. Before the test, constant-intensity rainfall is applied, and after static loading to allow seepage to stabilize, multiple levels of seismic loads are applied, simultaneously collecting acceleration and dynamic pore water pressure data. The core of this invention lies in constructing a damage analysis system from the dual dimensions of cumulative strain and energy dissipation, establishing a quantitative correlation between the two. This is described in detail below through several embodiments.

[0049] Basic Implementation

[0050] This embodiment uses measuring point A6-7 near the bedrock breakpoint of a loose deposit slope as the analysis object, and fully implements the complete analysis method of this invention. The specific steps are as follows:

[0051] S1. Construction of the shaking table test model: A rigid model box was used, with brick masonry bedrock inside. The bedrock surface was designed as a concave folded surface with an upper section inclination angle of 60° and a lower section inclination angle of 40°. The bedrock surface was roughened to simulate the roughness of a real interface. A loose stockpile was filled on top of the bedrock. The soil was prepared using a similar gradation scale-down method, compacted in layers to the designed dry density, and the slope was trimmed into a straight surface with an inclination angle of 50°. Slope acceleration sensors (A1-A14) and pore water pressure sensors (K1-K12) were deployed along the bedrock surface and slope surface, respectively. All sensors were positioned at the mid-surface of the model. The slope acceleration sensors were used to collect the horizontal acceleration time history, and the pore water pressure sensors were used to monitor the dynamic changes in dynamic pore water pressure. A table acceleration sensor A0 was set on the shaking table surface as an input reference. The sensor's planar layout is as follows... Figure 1 As shown, foam padding is used to line the front and rear walls of the model box to reduce boundary reflection effects.

[0052] S2-level seismic loading and data acquisition: First, a constant-intensity rainfall was applied for 1 hour, followed by a 2-hour settling period to allow the seepage field to stabilize. Then, multiple levels of seismic loads were applied in sequence, first natural waves and then artificial waves, with amplitudes increasing from low to high. Seismic wave types included Kobe waves, EL waves, and sine waves, with peak ground accelerations ranging from 0.06g to 0.9g. During loading, acceleration and dynamic pore water pressure time history data were simultaneously acquired at 0.01s sampling intervals at all measuring points. After each loading level, slope deformation and failure phenomena were recorded.

[0053] S3 cumulative strain damage parameter calculation: Select slope acceleration sensors at two adjacent elevations near the bedrock inflection point. Based on the acceleration time history data of the two points, obtain the displacement time history through quadratic integration. Combine the vertical distance between the two points to calculate the average shear strain time history.

[0054] The formula for calculating the mean shear strain is as follows:

[0055]

[0056] In the formula: The average shear strain between the two acceleration measurement points; The difference in horizontal displacement between the two measuring points is obtained by the second integral of the acceleration time history; h is the vertical distance between the two measuring points.

[0057] After obtaining the shear strain time history, the cumulative strain damage index is calculated by combining it with the soil shear wave velocity. The calculation formula is as follows:

[0058]

[0059] In the formula: DI is the cumulative strain damage index, and its dimension is time; For shear strain time history; ν is the soil shear wave velocity, determined by white noise scanning test; T is the seismic wave duration.

[0060] A sliding time window was used to update the damage indices point by point, with a window length of 0.1 s and a step size of 0.01 s, resulting in a continuous damage evolution time history curve. The cumulative strain damage time history curve of the loose aggregate at measuring point A6-7 is shown below. Figure 6 As shown.

[0061] S4 Energy Dissipation Time Series Calculation: Based on the shear stress and shear strain time history curves, the hysteretic energy dissipation per unit volume under a single-stage load is calculated using the following formula:

[0062]

[0063] In the formula: The hysteretic energy dissipated per unit volume under a single-stage load; Shear stress; For shear strain.

[0064] By accumulating the hysteretic energy dissipated by each stage in the loading sequence, the time-series variation curve of the accumulated dissipated energy is obtained. The calculation formula is as follows:

[0065]

[0066] In the formula: W is the cumulative energy dissipation; Let be the hysteretic dissipation energy under the i-th load level; n is the load level.

[0067] The cumulative dissipated energy variation curves under the action of seismic waves of different amplitudes are as follows: Figure 4 As shown.

[0068] S5 Energy-Damage Quantitative Mapping: This method performs point-by-point time matching between the development timeline of cumulative strain damage and the growth timeline of cumulative dissipated energy. Using the cumulative dissipated energy at the same time point as the x-axis and the cumulative strain damage index as the y-axis, an energy-damage mapping curve is plotted. The slope of each segment of the curve is calculated to obtain the damage increment corresponding to a unit energy input, i.e., the energy-damage conversion efficiency coefficient. Through staged fitting, the quantitative relationship between energy and damage at different loading stages is obtained, enabling the estimation of damage development level from the energy dissipation level.

[0069] S6 Damage Evolution Stage Identification: The first derivative of the time history curve of the cumulative strain damage index is taken to obtain the damage growth rate curve. Based on the rate change characteristics, the damage evolution stages are divided as follows: the initial damage stage is characterized by a rapid increase in damage rate followed by a decline during the initial loading phase; the middle stage is characterized by a relatively stable damage rate; and the later stage is characterized by a sharp increase in damage rate, representing a rapid deterioration stage. The results of the slope dynamic damage evolution stage division are as follows: Figure 8 As shown.

[0070] S7 Failure Trend Prediction: Based on the energy-damage mapping curve, the inflection point of the curve slope change is identified, and the cumulative dissipated energy corresponding to the inflection point is extracted as the critical energy threshold. The cumulative dissipated energy under the current loading level is compared with the critical threshold. If the current value is lower than the threshold, the damage is determined to be in a controllable development state; if it is close to or exceeds the threshold, the damage is determined to be about to enter a stage of rapid deterioration, and the risk of slope failure is significantly increased, thereby achieving the prediction of the slope dynamic failure development trend.

[0071] Preferred Example 1: Cumulative Strain Damage Calculation and Evolution Stage Division

[0072] This embodiment, based on the basic embodiment, further refines the plastic correction treatment and evolution stage division of cumulative strain damage, as detailed below:

[0073] The total strain of soil under cyclic loading consists of two parts: elastic strain and plastic strain. Elastic strain can recover after the load is removed and will not cause permanent damage to the soil. Only the continuous accumulation of plastic strain will induce progressive failure of the soil structure. Therefore, directly using the total strain to calculate the damage index will include interference from the reversible component and cannot accurately reflect the true degree of plastic damage.

[0074] This embodiment employs the hysteresis loop endpoint method to separate elastic and plastic strain: in the strain amplitude of a single hysteresis loop, the recoverable portion after unloading is elastic strain, while the remaining permanent deformation portion is plastic strain. After extracting the plastic strain component loop by loop, the damage index is corrected based on the cumulative plastic strain. The corrected calculation formula is as follows:

[0075]

[0076] In the formula: The modified plastic cumulative strain damage index; This is the time history of plastic shear strain.

[0077] Taking the calculation results of the loose aggregate A6-7 measuring point under 0.6gEL wave loading as an example, the total strain damage index before correction is about 7.56, and the plastic strain damage index after correction is about 5.23. About 31% of the reversible elastic strain component was removed, and the damage index is more in line with the true plastic damage state of the soil.

[0078] Based on the modified plastic damage time history curve, a three-stage division is performed using the first derivative change characteristics, with the following division criteria:

[0079] Initial damage stage: Within 1 second of loading, the damage rate rises rapidly to its peak and then falls back quickly. The initial structure of the soil is adjusted, the original pores are compacted, and the damage is mainly due to reversible structural adjustment, while plastic damage accumulates slowly.

[0080] Stable development stage: During the loading period of 1 to 6 seconds, the damage rate remains at a relatively stable low value, plastic strain accumulates slowly, the soil structure deteriorates progressively, and the damage development rate is basically matched with the energy input rate.

[0081] Rapid deterioration stage: After 6 seconds of loading, the damage rate increases sharply, the soil structure undergoes irreversible overall failure, plastic strain accumulates rapidly, and the damage index grows exponentially, corresponding to the appearance and expansion of macroscopic cracks in the slope.

[0082] The cumulative strain damage evolution curves of typical measuring points in medium-dense packings are as follows: Figure 5 As shown, its stage division pattern is consistent with that of loose aggregates, but the duration and damage growth rate of each stage are significantly different.

[0083] The plasticity correction and stage division in this embodiment can significantly improve the accuracy of damage quantification and the precision of stage identification, providing more reliable damage basis data for subsequent energy correlation analysis and damage prediction.

[0084] Preferred Implementation Example 2: Phased Statistics and Rate Matching of Energy Dissipation

[0085] This embodiment, based on the basic embodiment, further refines the phased statistics of energy dissipation and energy-damage rate matching, as detailed below:

[0086] The growth process of accumulated dissipated energy is not uniform, but exhibits distinct stage characteristics, which correspond intrinsically to the development stages of soil damage. This embodiment divides the accumulated dissipated energy into three stages based on the growth rate, and statistically analyzes the dissipation characteristics of each stage:

[0087] Rapid growth phase: In the initial loading stage, the soil has high stiffness and strong ability to absorb seismic energy. The energy is quickly converted into hysteretic dissipated energy, and the cumulative dissipated energy curve has a large slope and grows rapidly. This phase lasts for about 15% of the total duration and dissipates about 35% of the total dissipated energy.

[0088] Slow growth stage: In the middle of loading, the soil stiffness gradually decreases, the energy absorption rate decreases, the slope of the cumulative dissipation energy curve decreases, and the growth tends to be gentle. This stage lasts the longest, accounting for about 65% of the total duration, and the dissipated energy accounts for about 50% of the total dissipated energy.

[0089] Stable phase: In the later stages of loading, the soil is severely damaged, its stiffness is greatly reduced, its energy absorption capacity is significantly decreased, the cumulative dissipation energy curve tends to be horizontal, and the growth is extremely slow. The dissipation energy in this stage accounts for about 15% of the total dissipation energy.

[0090] The phased characteristics of accumulated dissipated energy under seismic waves of different amplitudes are as follows: Figure 4As shown, the higher the amplitude, the steeper the slope of the rapid growth phase, and the higher the total energy dissipation.

[0091] Based on this, the three stages of energy dissipation are time-matched with the three stages of damage development, and the energy dissipation rate and damage development rate of each stage are calculated to obtain the energy-damage conversion efficiency coefficients for each stage:

[0092] In the initial damage stage, the conversion efficiency coefficient is low, the plastic damage induced by unit energy input is small, and most of the energy is used for soil structure compaction and elastic deformation.

[0093] During the stable development stage, the conversion efficiency coefficient remains stable, and the unit energy input corresponds to a stable increase in plastic damage, with an approximately linear relationship between energy and damage.

[0094] During the rapid deterioration stage, the conversion efficiency coefficient increases sharply, and a large amount of plastic damage can be induced per unit energy input, and the energy-damage relationship enters a nonlinear steep increase stage.

[0095] Through the phased statistics and rate matching in this embodiment, a refined phased energy-damage correspondence rule is established. Compared with the overall average conversion coefficient, the prediction accuracy of phased matching can be improved by more than 20%, which significantly improves the reliability of energy-dimensional damage prediction.

[0096] Preferred Example 3: Energy Mechanism Analysis of Differential Response

[0097] This embodiment, based on the basic embodiment, further conducts a differentiated response analysis of soils at different locations and with different densities, revealing the underlying causes from the perspective of differences in energy absorption and dissipation capacity. The specific content is as follows:

[0098] The cumulative strain damage development process and energy dissipation characteristics were compared between two groups of test samples with different densities: A6-7 near the bedrock inflection point and A8-9 near the upper bedrock surface.

[0099] From the perspective of spatial location differences, the total cumulative energy dissipation at measuring points A6-7 near the bedrock inflection point is significantly greater than that at measuring points A8-9 on the upper bedrock surface, and the corresponding cumulative strain damage index is also higher. For example... Figure 5 , Figure 6 As shown, the damage index at measuring point A6-7 in the medium-dense bedrock group is approximately 109.73, and at measuring point A8-9 it is approximately 139.29; for the loose bedrock group, the index is approximately 7.56 at measuring point A6-7 and approximately 6.12 at measuring point A8-9. The fundamental reason for this difference lies in the abrupt change in topography and stiffness at the bedrock inflection point. When seismic waves propagate to this point, they are reflected and superimposed, resulting in the soil absorbing more seismic energy and dissipating a greater total amount of energy, thus inducing more severe cumulative damage.

[0100] From the perspective of density differences, the total cumulative energy dissipation and cumulative strain damage index of medium-dense packings are significantly higher than those of loose packings. Figures 4 to 7 Based on the principle diagram drawn according to the three-stage damage evolution pattern, it can be seen that under the same loading conditions, the damage index of the medium-dense soil group can be more than 10 times that of the loose soil group. From an energy perspective, the cause is as follows: the medium-dense soil particles are more tightly packed, the shear wave velocity is higher, and the ability to propagate seismic waves is stronger. It can absorb more seismic energy and convert it into hysteretic dissipated energy, so the total energy dissipation and total damage are greater. On the other hand, the loose soil particles have a looser distribution, which has a stronger attenuation effect on seismic waves and absorbs less total energy, so the total damage is relatively lower.

[0101] However, it is important to note that a large total damage does not necessarily mean that the slope is more prone to instability. Although medium-dense deposits have a large total damage, their initial strength is high, and the remaining strength after damage is still sufficient to maintain slope stability. On the other hand, although loose deposits have a small total damage, their initial strength is low, and their energy-damage conversion efficiency increases sharply in the later stages. A small amount of additional energy input can induce overall failure, so the risk of instability is actually higher.

[0102] Through the analysis in this embodiment, the intrinsic mechanism of the difference in dynamic response of the accumulation body is systematically explained from the essential level of energy absorption and dissipation capacity. This makes up for the shortcomings of the existing technology, which only describes the phenomenon and does not reveal the root cause, and deepens the theoretical understanding of the dynamic failure law of the accumulation body slope.

[0103] Preferred Implementation Example 4: Prediction of Damage Trends Based on Energy-Damage Correlation

[0104] This embodiment, based on the basic embodiment, further refines the slope failure trend prediction method based on energy-damage correlation, and verifies the accuracy of the method by combining experimental phenomena. The specific content is as follows:

[0105] The development of slope dynamic failure is a gradual process of continuous energy input and damage accumulation. When the energy input reaches a critical threshold, the damage transitions from stable development to rapid deterioration, corresponding to the slope moving from the deformation stage to the instability stage. This embodiment establishes a failure trend prediction method based on the inflection point characteristics of the energy-damage mapping curve. The specific steps are as follows:

[0106] The first step is to plot the energy-damage mapping curve of the target measurement point using the data from the previous multi-level loading test. The two-segment function relationship between the stable development stage and the rapid deterioration stage is obtained by fitting the curve. The intersection of the two curves is extracted as the inflection point of damage mutation. The cumulative dissipation energy corresponding to the inflection point is the critical damage energy threshold.

[0107] The second step is to calculate the current cumulative energy dissipation level in real time during actual monitoring or experimental loading, and compare it with the critical energy threshold.

[0108] The third step is to make a graded prediction based on the comparison results: when the cumulative dissipated energy is less than 70% of the threshold, it is judged as low risk and the damage is in a stable development stage; when it is between 70% and 90% of the threshold, it is judged as medium risk and the damage is close to the inflection point of sudden change, and monitoring needs to be strengthened; when it exceeds 90% of the threshold, it is judged as high risk and the damage is about to enter a stage of rapid deterioration, the risk of slope instability is significantly increased, and prevention and control measures need to be initiated.

[0109] Taking the experimental verification of a loosely deposited slope as an example, under a 0.6gEL wave load, the critical energy threshold at measuring point A6-7 was approximately 120 J / m³. At the end of the loading, the actual cumulative dissipated energy was approximately 108 J / m³, which is 90% of the threshold, indicating a high-risk state. This corresponds to the appearance of obvious macroscopic cracks and localized landslides on the slope during the experiment, perfectly matching the predicted results. For medium-dense deposits, under the same conditions, the cumulative dissipated energy was approximately 65% ​​of the threshold, indicating a low-risk state. This corresponds to the appearance of only minor cracks and no significant damage on the slope during the experiment, again demonstrating the accuracy of the predicted results.

[0110] The prediction method proposed in this embodiment does not require continuous monitoring of strain data. It can quickly assess the damage state and failure risk of slopes using only energy indicators. It is especially suitable for engineering sites with limited monitoring conditions and has strong engineering practicality and promotion value.

[0111] Preferred Implementation

[0112] This embodiment simultaneously covers two sets of sedimentary tests, one medium-dense and one loose, and synchronously analyzes two typical locations: the bedrock inflection point and the upper bedrock surface. It fully implements the whole-process analysis method of this invention and incorporates all theoretical derivations of the cumulative damage evolution mechanism and the energy-strain correlation mechanism, forming a complete analysis and verification system.

[0113] I. Basic Parameters of the Experimental System

[0114] The two sets of experiments used the exact same model dimensions, sensor placement, and loading scheme, differing only in the initial density and moisture content of the packing: the medium-density packing had a dry density of approximately 1.53 g / cm³. 3 The initial moisture content was approximately 9.06%, and the shear wave velocity was approximately 128 m / s; the dry density of the loose group was approximately 1.38 g / cm³. 3 The initial moisture content was approximately 6.02%, and the shear wave velocity was approximately 96 m / s. Each test group was equipped with 14 slope accelerometers (A1-A14) and 12 pore water pressure sensors (K1-K12), arranged in layers along the bedrock surface and slope. A platform accelerometer A0 was installed on the platform for input calibration. The arrangement was as follows: Figure 1 As shown. The seismic loading used a magnitude 35 load condition, which included white noise scanning, natural wave and sine wave loading, with the peak acceleration gradually increasing from 0.03g to 0.9g.

[0115] II. Full-process analysis

[0116] Cumulative strain damage calculation and plastic correction

[0117] Shear strain and cumulative strain damage were calculated at measuring points A6-7 and A8-9 in both sets of experiments. Before calculation, the acceleration signals were bandpass filtered from 0.3 to 50 Hz and baseline corrected to eliminate the effects of noise and baseline drift. The calculation results show that under the same loading conditions, the shear strain amplitude and cumulative damage index of the dense group are significantly greater than those of the loose group: under 0.8 gEL wave loading, the cumulative strain damage index of measuring point A8-9 in the dense group is approximately 139.29, and that of measuring point A6-7 is approximately 109.73; for the loose group, the index of measuring point A6-7 is approximately 7.56, and that of measuring point A8-9 is approximately 6.12.

[0118] After correction for plastic strain separation, the damage indices at both sets of measuring points decreased to varying degrees. The medium-dense group decreased by approximately 25% after correction, while the loose group decreased by approximately 31%. The loose group showed a greater decrease because loose soil has a higher proportion of elastic deformation and a greater reversible component. The corrected plastic damage indices more accurately reflect the degree of irreversible damage to the soil. The damage time history curves for the two groups are shown below. Figure 5 , Figure 6 As shown.

[0119] Energy dissipation calculation and phased statistics

[0120] Calculate the hysteresis dissipation energy and cumulative dissipation energy at the two sets of measuring points. A typical hysteresis loop shape is as follows: Figure 2 As shown, the cumulative energy dissipation curves at different amplitudes are as follows: Figure 4 As shown in the figure. The results show that the total cumulative energy dissipation of the medium-dense group under all working conditions is significantly higher than that of the loose group, about 8-12 times that of the loose group, which basically corresponds to the difference in damage index.

[0121] The phased statistical results show that the energy dissipation of both groups exhibits a three-stage characteristic, but the duration and dissipation ratio of each stage differ: the rapid growth stage of the medium-dense group lasts longer and the dissipation ratio is higher, indicating that its initial energy absorption capacity is stronger; the rapid growth stage of the loose group is short, and it quickly enters the slow growth stage, and the later stage tends to be more stable.

[0122] Energy-damage quantitative mapping and rate matching

[0123] refer to Figures 4 to 7 Energy-damage mapping curves for two sets of measuring points were plotted. Both curves exhibited a clear two-stage characteristic: approximately linear growth in the early stage, followed by a sharp increase in slope in the later stage. The energy-damage conversion efficiency coefficients for each stage were obtained through piecewise fitting; the conversion coefficient for the stable development stage of the medium-dense group was approximately 0.92 s·m.3 / J, the rapid degradation phase is approximately 3.76 s·m 3 / J; The stable development stage of the loose group is approximately 0.07 s·m 3 / J, the rapid degradation phase is approximately 0.58 s·m 3 / J.

[0124] It can be seen that although the absolute conversion coefficient of the loose group is smaller than that of the medium-dense group, the ratio of the coefficients of the rapidly deteriorating stage to the stable stage is higher. This indicates that once the loose soil enters the stage of drastic damage change, the increase in damage induced by unit energy is greater and the damage development is more rapid. This is also the inherent reason why the slope of loose deposits often fails more suddenly.

[0125] Damage Stage Classification and Failure Trend Verification

[0126] Based on the changes in damage rate, the two groups of measuring points were divided into three stages. The stable development stage of the medium-dense group lasted for a long time, the damage growth was slow, and the rapid deterioration stage appeared late. The stable development stage of the loose group was short, the rapid deterioration stage appeared early, and the growth was steeper.

[0127] The critical energy thresholds for each measuring point were extracted. For the medium-dense group (A6-7), the threshold was approximately 180 J / m³, and for the loose group, it was approximately 110 J / m³. Predictive verification was performed using two loading stages: 0.6g and 0.8g. Under 0.6g EL wave loading, the cumulative energy dissipation of the medium-dense group was approximately 62% of the threshold, indicating a low-risk prediction, and no significant damage was observed in the corresponding experiment. For the loose group, the cumulative energy dissipation was approximately 88% of the threshold, indicating a medium-to-high risk prediction, and significant cracks appeared in the corresponding experiment. The predicted results were completely consistent with the experimental phenomena. Under 0.8g EL wave loading, both groups exceeded the critical threshold, indicating a high-risk prediction, and varying degrees of collapse failure occurred in the corresponding experiments, verifying the accuracy of the prediction method.

[0128] III. Mechanism of Cumulative Damage Evolution and Energy Correlation

[0129] From a microscopic perspective, the cumulative strain damage of soil is essentially a process of gradual breakdown of interparticle bonds and gradual deterioration of pore structure, with energy dissipation being the energy manifestation of this process. After seismic energy is input into the soil, part of it is converted into elastic deformation energy and reversibly released, while the other part is used to overcome interparticle friction, break particle bonds, and generate plastic deformation, which is irreversibly dissipated in the form of hysteretic dissipation energy, accompanied by the accumulation of soil damage.

[0130] In the initial damage stage, energy is mainly used for the compaction of the original pores and the small slippage between particles, with little plastic damage and most of the dissipated energy being frictional energy. In the stable development stage, energy is continuously used for the gradual failure of particle bonds and the accumulation of plastic deformation, and damage and energy grow approximately linearly and synchronously. In the rapid deterioration stage, a through-type damage surface is formed inside the soil, and energy is concentrated on the expansion of the damage surface and relative slippage, the damage rate accelerates sharply, and the energy-damage relationship enters a nonlinear stage.

[0131] The impact of rainfall infiltration on this process is reflected in two aspects: on the one hand, rainfall increases soil saturation, reduces matrix suction, weakens the bonding strength between particles, and can induce more plastic damage under the same energy input, thereby improving the energy-damage conversion efficiency; on the other hand, rainfall changes the damping characteristics of the soil, affects the rate of energy absorption and dissipation, and thus changes the process of damage development.

[0132] The aforementioned microscopic mechanisms and macroscopic experimental analysis results corroborate each other, together forming a complete theoretical system relating cumulative strain damage and energy dissipation in accumulated bodies.

[0133] All aspects not detailed in this invention are conventional technical means known to those skilled in the art.

[0134] The above content shows and describes the basic principles, main features, and beneficial effects of this technical solution. The above description is merely a preferred embodiment of this technical solution and is not intended to limit the scope of this technical solution. Any modifications, equivalent substitutions, or improvements made within the spirit and principles of this technical solution should be included within the protection scope of this technical solution.

Claims

1. A method for analyzing the correlation between cumulative strain damage and energy in a mass under rainfall-earthquake coupling, characterized in that, Includes the following steps: S1 constructs a shaking table test model of an accumulation slope under rainfall-earthquake coupling, and sets up acceleration monitoring components and pore water pressure monitoring components inside the model; The S2 design employs a graded and progressive seismic loading scheme, applying multiple levels of seismic loads after rainfall infiltration and settling, while simultaneously collecting acceleration time history data and dynamic pore water pressure time history data at each monitoring point. S3 calculates the shear strain time history based on the time history data of adjacent elevation acceleration measurement points, and calculates the cumulative strain damage parameter by combining the soil shear wave velocity, thus characterizing the degree of plastic cumulative damage of the soil. S4 calculates the hysteretic dissipation energy under a single-level load, and accumulates it step by step to obtain the cumulative dissipation energy of the entire loading process, thereby obtaining the time sequence characteristics of energy absorption and dissipation of the soil. S5 performs point-by-point matching between the development timeline of cumulative strain damage and the growth timeline of cumulative energy dissipation to establish a quantitative mapping relationship between cumulative strain damage and energy dissipation. S6 classifies the evolution stages of cumulative strain damage based on the growth rate characteristics of damage indices; and identifies the energy-driven laws of damage development by combining the energy dissipation rate characteristics. Based on the quantitative mapping relationship between energy and damage and the stage evolution characteristics, S7 predicts the dynamic failure development trend of the accumulated slope.

2. The method for analyzing the correlation between cumulative strain damage and energy in a mass under rainfall-earthquake coupling as described in claim 1, characterized in that, In step S3, the calculation rule for the cumulative strain damage parameter is as follows: the absolute value of the shear strain time history is integrated in the time domain, normalized in combination with the soil shear wave velocity, and the damage index is updated point by point using a sliding time window to obtain a continuous damage evolution time history curve.

3. The method for analyzing the correlation between cumulative strain damage and energy in a mass under rainfall-earthquake coupling as described in claim 1, characterized in that, In step S4, the energy dissipation is calculated as follows: the hysteretic dissipation energy per unit volume is calculated by taking the area enclosed by the shear stress-shear strain hysteresis loop under a single load, and all single-stage dissipation energies are accumulated step by step according to the loading sequence to obtain the time-series variation curve of the accumulated dissipation energy.

4. The method for analyzing the correlation between cumulative strain damage and energy in a mass under rainfall-earthquake coupling as described in claim 2, characterized in that, Step S3 further includes plastic strain accumulation correction: separating the elastic strain component and the plastic strain component from the total shear strain, correcting the damage index based on the plastic accumulated strain, and eliminating the interference of the reversible component of elastic strain.

5. The method for analyzing the correlation between cumulative strain damage and energy in a mass under rainfall-earthquake coupling as described in claim 3, characterized in that, Step S4 also includes energy dissipation phase statistics: the cumulative energy dissipation is divided into three phases according to the growth rate: rapid growth, slow growth, and stabilization, and the energy dissipation rate and dissipation ratio of each phase are calculated respectively.

6. The method for analyzing the correlation between cumulative strain damage and energy in a mass under rainfall-earthquake coupling as described in claim 4, characterized in that, In step S6, the criteria for dividing the damage evolution stages are as follows: based on the change characteristics of the first derivative of the damage index, the entire loading process is divided into three characteristic stages: the initial damage stage, the stable development stage, and the rapid deterioration stage.

7. The method for analyzing the correlation between cumulative strain damage and energy in a mass under rainfall-earthquake coupling as described in claim 5, characterized in that, In step S5, the method for establishing the quantitative mapping relationship is as follows: calculate the damage increment corresponding to a unit energy input, obtain the energy-damage conversion efficiency coefficient, match the dissipation rate and damage development rate of each stage, and form a stage-specific energy-damage correspondence rule.

8. The method for analyzing the correlation between cumulative strain damage and energy in a mass under rainfall-earthquake coupling as described in claim 1, characterized in that, Step S6 also includes differential response analysis: comparing the damage development process and energy dissipation characteristics at different elevation locations and different initial compaction measurement points, and explaining the spatial differential causes of the dynamic response of the accumulation body from the perspective of the difference in soil energy absorption and dissipation capacity.

9. The method for analyzing the correlation between cumulative strain damage and energy in a mass under rainfall-earthquake coupling as described in claim 1, characterized in that, In step S7, the prediction rule for slope failure trend is as follows: based on the inflection point characteristics of the energy-damage mapping curve, identify the critical energy threshold for the transition from stable development to rapid deterioration of damage, and combine the current cumulative dissipated energy level to predict the dynamic failure development trend of the slope.

10. The method for analyzing the correlation between cumulative strain damage and energy in a mass under rainfall-earthquake coupling according to any one of claims 1-9, characterized in that, This method is applied to the seismic dynamic damage assessment and stability prediction of unsaturated deposit slopes with zigzag bedrock surfaces.

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