Stress analysis method of highway open cut tunnel in high intensity area under coupling load of earthquake and rockfall

Abstract

The present application relates to the high intensity area highway open cut tunnel stress analysis method under the coupling load of earthquake and rockfall, belongs to data processing analysis technical field, including the following steps: introducing disaster phase coupling factor to quantify the superposition relationship of seismic energy and rockfall load pulse; the time-space evolution process of the whole displacement field of open cut tunnel surface and the internal steel strain of open cut tunnel is calculated by using the earthquake rockfall time sequence coupling method, the multi-scale perception of open cut tunnel structure response is obtained; the dynamic coupling analysis algorithm is introduced to solve the structure inertia response caused by earthquake and the local dynamic response caused by rockfall load pulse, the multi-scale dynamic characteristics of high-frequency impact and low-frequency vibration are handled by hybrid integration strategy; the phase difference of earthquake and rockfall is calculated, the time-gravity distribution law of internal structure of open cut tunnel is obtained, and then the weak area of open cut tunnel under the coupling effect of multiple disasters is determined; the beneficial effects of the present application are: the low-frequency structure inertia response caused by earthquake and the high-frequency dynamic response caused by rockfall impact are obtained.

Description

Technical Field

[0001] This invention belongs to the field of data processing and analysis technology, and specifically relates to a method for stress analysis of highway tunnels in high-intensity seismic zones under coupled earthquake and rockfall loads, used for data analysis of stress conditions. Background Technology

[0002] As a crucial protective structure for mountainous highways and railways traversing steep slopes or dangerous rock formations, tunnels are widely used in high-intensity earthquake zones. Their primary function is to shield against gravity-related geological hazards such as falling rocks and landslides, while simultaneously possessing sufficient seismic resistance to ensure the safe operation of vital transportation routes during strong earthquakes. Traditional tunnel designs are mostly based on the load effects of a single hazard, assuming: rockfall resistance design typically employs static equivalent methods or simplified impact models, simplifying rockfall loads into concentrated forces or equivalent static loads; seismic design, according to codes, uses response spectrum methods or unidirectional seismic time history analysis, neglecting interactions with other hazards.

[0003] However, in high-intensity earthquake zones, ground motion and rockfall hazards often exhibit spatiotemporal coupling characteristics. Strong earthquakes can induce landslides and rock instability, leading to secondary rockfall impacts. The localized damage caused by rockfalls can then weaken the structure's load-bearing capacity under subsequent earthquakes. Current technologies do not consider the temporal phase relationship between earthquakes and rockfalls, the interaction of energy transfer paths, and the superposition effect of nonlinear structural responses. This results in a poor assessment of the actual stress state of the tunnel, posing safety hazards. Summary of the Invention

[0004] This invention provides a method for stress analysis of highway tunnels in high-intensity seismic zones under coupled earthquake and rockfall loads, addressing the technical problem of poor assessment of the actual stress state of tunnels. By introducing a dynamic coupling analysis algorithm, the low-frequency structural inertial response caused by earthquakes and the high-frequency local dynamic response caused by rockfall impacts are effectively separated and solved. Combined with a hybrid integration strategy, efficient and accurate processing of dynamic characteristics at different frequency scales is achieved, thus solving the technical problem of poor assessment of the actual stress state of tunnels.

[0005] To achieve the above objectives, the present invention is implemented through the following technical solution:

[0006] The method for stress analysis of open-cut tunnels on highways in high-intensity seismic zones under coupled earthquake and rockfall loads includes the following steps:

[0007] Based on the load time-series sensitive dynamic finite element model, a disaster phase coupling factor is introduced to quantify the superposition relationship between seismic energy and rockfall load pulse;

[0008] In the dynamic finite element model, the temporal coupling method of earthquake rockfall is used to calculate the spatiotemporal evolution of the full displacement field on the surface of the tunnel and the strain of the steel bars inside the tunnel, so as to obtain the multi-scale perception of the tunnel's structural response.

[0009] A dynamic coupling analysis algorithm is introduced to solve the structural inertial response caused by earthquakes and the local dynamic response caused by rockfall load pulses. A hybrid integration strategy is used to handle the multi-scale dynamic characteristics of high-frequency impacts and low-frequency vibrations.

[0010] Based on the superposition relationship between seismic energy and rockfall load pulses, the phase difference between earthquake and rockfall is calculated to obtain the time-gravity distribution law of the internal structure of the tunnel, thereby identifying the weak areas of the tunnel under the coupling effect of multiple disasters.

[0011] Optionally, the disaster phase coupling factor is defined as a measure of the degree of coupling between the rockfall impact and the ground motion energy at a certain moment; by integrating the total energy over the entire simulation time, the total amount of energy released by the ground motion during the time period of the rockfall impact is calculated, and the impact on the structure during the rockfall impact is measured.

[0012] Optionally, the superposition of seismic energy and rockfall load pulse is used to calculate the combined impact load effect on a unit area of ​​the structure or rock mass unit, and to describe the equivalent total energy input under the superposition of seismic energy and rockfall impact pulse in time.

[0013] Optionally, the full displacement field of the surface of the tunnel is calculated by introducing element-level damage variables to continuously model the gradual degradation of the stiffness of the structure under dynamic loads, so that the finite element analysis can truly reflect the entire process of the actual engineering structure from intact to damaged to failure.

[0014] Optionally, the spatiotemporal evolution of the strain of the steel reinforcement inside the tunnel is as follows: the shrinkage of concrete is constrained by the steel reinforcement or structure, which in turn causes tensile strain in the steel reinforcement. The constrained strain of the steel reinforcement structure by the shrinkage of concrete is calculated. By combining the stiffness ratio of concrete to steel reinforcement, the free shrinkage strain and bond performance are used to obtain the actual constrained shrinkage strain of concrete.

[0015] Optional, the dynamic coupling analysis algorithm calculates the seismic response using a combination of time-domain and frequency-domain correlation of the impact response, superimposing the frequency-domain seismic response and the time-domain impact response, resulting in a weighted mixture of the two responses as the total dynamic response.

[0016] By combining the overall structural vibration caused by the earthquake and the local impact response caused by the rockfall in proportion, the total response of the structure under the simultaneous influence of the earthquake response in the frequency domain and the impact response in the time domain is obtained.

[0017] Optionally, for the hybrid integral strategy, since the fixed step size cannot take into account both the instantaneity of high-frequency impact and the stability of low-frequency vibration, the gradient parameter descent optimization update method of the adaptive step size control mechanism is introduced to make the step size dynamically adjusted with the impact amplitude.

[0018] Specifically, the response calculated by hybrid integral is compared with the measured response, and the structural parameters are updated by gradient descent to describe the multi-scale dynamic characteristics of high-frequency impact and low-frequency vibration.

[0019] Optionally, the phase difference between an earthquake and a falling rock is defined as the angle by which the response lags behind the excitation. It is used to describe the response of a single-degree-of-freedom linear damped system under harmonic excitation and describes the phase lag angle between the output signal and the input excitation signal.

[0020] Optionally, the time-gravity distribution law is calculated by coupling the total gravity load borne by the tunnel structure with time. The total vertical load borne by the tunnel structure is calculated as the dynamic vertical stress applied by the external rock and soil mass multiplied by the area of ​​action, plus the weight of the structure itself.

[0021] The beneficial effects of this invention are:

[0022] 1. This invention utilizes a seismic rockfall temporal coupling method to simultaneously acquire the spatiotemporal evolution of the full displacement field on the surface of a tunnel and the strain of the internal steel reinforcement. This enables multi-scale, full-dimensional response perception from macroscopic displacement outside the structure to microscopic strain inside. Compared with traditional analysis methods that only focus on a single response index, this invention can more comprehensively reveal the dynamic stress process and evolution law of the tunnel under coupled loads, providing richer and more accurate data support for structural damage mechanism analysis.

[0023] 2. This invention utilizes multi-scale dynamic characteristics to solve bottlenecks and improves the accuracy of response calculations. By introducing a dynamic coupling analysis algorithm, it can effectively separate and solve the low-frequency structural inertial response caused by earthquakes and the high-frequency local dynamic response caused by rockfall impacts. Combined with a hybrid integration strategy, it achieves efficient and accurate processing of dynamic characteristics at different frequency scales. This overcomes the shortcomings of traditional single integration methods in solving multi-scale dynamic problems, such as insufficient accuracy or low efficiency, and significantly improves the accuracy and efficiency of dynamic response calculations for open-cut tunnel structures under coupled loads. Attached Figure Description

[0024] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0025] Figure 1 This is a schematic diagram of the workflow of the present invention. Detailed Implementation

[0026] The embodiments of this application will now be described in detail with reference to the accompanying drawings.

[0027] Example 1;

[0028] like Figure 1 As shown, this embodiment provides a method for stress analysis of open-cut tunnels in high-intensity seismic zones under coupled earthquake and rockfall loads, including the following steps:

[0029] Step 1: Based on the load-time sensitivity dynamic finite element model, a disaster phase coupling factor is introduced to quantify the superposition relationship between seismic energy and rockfall load pulses; (The dynamic finite element model is a numerical simulation technique based on the finite element method, used to analyze the dynamic load of a structure. It discretizes a continuous elastic body into a finite number of elements, and transforms the continuous differential equations into discrete differential equations by establishing the dynamic equilibrium equations between nodal displacements and nodal forces, thereby solving the response of the structure under dynamic loads (such as displacement, velocity, acceleration, and stress).

[0030] Step 2: In the dynamic finite element model, the temporal and spatial evolution process of the full displacement field on the surface of the tunnel and the strain of the steel reinforcement inside the tunnel is calculated using the earthquake rockfall temporal coupling method to obtain the multi-scale perception of the tunnel's structural response.

[0031] Step 3: Introduce a dynamic coupling analysis algorithm to solve the structural inertial response caused by earthquake and the local dynamic response caused by rockfall load pulse. Use a hybrid integration strategy to process the multi-scale dynamic characteristics of high-frequency impact (rockfall load pulse) and low-frequency vibration (structural inertia caused by earthquake).

[0032] Step 4: Based on the superposition relationship between seismic energy and rockfall load pulse, calculate the phase difference between the earthquake and the rockfall to obtain the time-gravity distribution law of the internal structure of the tunnel, and then identify the weak areas of the tunnel under the coupling effect of multiple disasters.

[0033] In this embodiment, steps 1-4 are all performed in a load-time-sensitive dynamic finite element model. The load-time sensitivity of the load-time-sensitive dynamic finite element model is the degree to which the structural response (e.g., displacement, stress, and strain) depends on the time history characteristics of the load application (e.g., loading sequence, rate, intermittent and cyclic modes). It is typically manifested as the response difference under loading sequences of large-to-small or small-to-large, the instantaneous peak effect of impact loads, and the cumulative damage effect of fatigue loads.

[0034] The dynamic finite element model is based on finite element discretization, coupled with mass, stiffness and damping matrices. By solving the known time-varying motion equations, it simulates the instantaneous and cumulative response of a structure under dynamic loads. The core is the introduction of inertial force and damping force, which distinguishes it from static analysis.

[0035] A load-time-sensitive dynamic finite element model, by coupling structural dynamics with finite element discretization, achieves a refined simulation of the structural response under time-varying loads. The core objective is to reveal time-dependent effects invisible in static analysis, providing a more realistic safety assessment basis for engineering design. In practical applications, key aspects such as material rate correlation, damping calibration, and time step selection must be carefully considered to ensure the model's accuracy and reliability.

[0036] This implementation achieves precise quantification of coupled loads, improving the reliability of model input. By introducing a disaster phase coupling factor, it accurately characterizes the superposition effect of seismic energy and rockfall load pulses, solving the technical challenges of independent modeling of multiple disaster loads and fuzzy superposition relationships in traditional analysis. The load-time-sensitive dynamic finite element model constructed based on the disaster phase coupling factor can fully capture the temporal characteristics and sensitivity differences of coupled loads, making the model input more closely match actual disaster conditions and providing a high-precision load basis for subsequent structural response analysis.

[0037] This approach enables multi-scale, multi-dimensional perception of structural response, enriching the dimensions of response analysis. Utilizing a seismic rockfall temporal coupling method, it can simultaneously acquire the spatiotemporal evolution of the full displacement field on the surface of the tunnel and the strain of the internal reinforcing steel, achieving multi-scale, multi-dimensional response perception from macroscopic displacement outside the structure to microscopic strain inside. Compared to traditional analysis methods that only focus on a single response index, this approach can more comprehensively reveal the dynamic stress process and evolution of the tunnel under coupled loads, providing richer and more accurate data support for structural damage mechanism analysis.

[0038] This method overcomes the bottleneck in solving multi-scale dynamic characteristics and improves the accuracy of response calculations. By introducing a dynamic coupling analysis algorithm, it can effectively separate and solve the low-frequency structural inertial response caused by earthquakes and the high-frequency local dynamic response caused by rockfall impacts. Combined with a hybrid integration strategy, it achieves efficient and accurate processing of dynamic characteristics at different frequency scales. This overcomes the shortcomings of traditional single integration methods in solving multi-scale dynamic problems, such as insufficient accuracy or low efficiency, and significantly improves the accuracy and efficiency of calculating the dynamic response of open-cut tunnel structures under coupled loads.

[0039] Precisely locating structurally weak areas enhances the targeted nature of disaster prevention and control. By calculating the phase difference based on the superposition relationship between seismic energy and rockfall load pulses, the time-gravity distribution pattern of the tunnel's internal structure is clarified, enabling precise identification of weak areas and critical stress components under the coupled effects of multiple disasters. This solves the problems of vague identification of weak areas and insufficient targeting in traditional analysis, providing precise technical basis for the optimized design, reinforcement, and disaster prevention and control strategies of highway tunnels in high-intensity seismic zones, significantly improving the disaster resistance and service safety of tunnel structures.

[0040] Example 2;

[0041] Based on Example 1, in step 1, the specific definition of the disaster phase coupling factor (DPCF) is as follows:

[0042] ;

[0043] in, The disaster phase coupling factor is used to measure the impact of falling rocks at time [time]. The degree of coupling between the event and the seismic energy; The point in time when the rockfall impact begins (i.e., the trigger moment); The duration of the rockfall impact (e.g., pulse width); Let be the normalized seismic energy density function, which is dimensionless. , A value closer to 1 indicates a stronger earthquake energy at the current moment. The value is close to 0, indicating weak surface ground motion or a period of inactivity.

[0044] Integration interval This indicates the time window of impact from falling rocks; within this time period, we should focus on the energy state of the earthquake. It is the total energy integral over the entire simulation time, used for normalization; It represents the total amount of energy released by the earthquake during the period of rockfall impact, and measures whether the structure was impacted during the rockfall.

[0045] Reflecting at any moment , A value close to 1 indicates that rockfalls occur during the peak energy period of an earthquake, posing a high risk of destructive damage. , The value is close to 0, the rockfall occurs during the seismic quiescent period, the risk of damage is low, and the structure is safer. At time... , The value is close to 0.5, indicating that the rockfall occurred during a moderate phase of the earthquake, and the risk of damage from the disaster is moderate.

[0046] The superposition of seismic energy and rockfall load pulses represents the combined impact load effect on a structural or rock mass unit per unit area. It describes the equivalent total energy input under the temporal superposition of seismic energy and rockfall impact pulses, specifically:

[0047] ;

[0048] in, The equivalent total impact energy when rockfall and ground motion act together on a structure or rock mass; The mass of the falling rocks; This represents the impact velocity of the falling rock. The kinetic energy of the falling rock is its mechanical energy. This represents the unit impulse function (Dirac delta function) or narrow window function, indicating that energy exists only in time. Released in a concentrated manner to simulate an instantaneous impact. Unit pulse value, It can be 0 or 1;

[0049] The impact kinetic energy of falling rocks represents the transient impact energy input when a rock hits a structure or rock mass, characterized by extremely high peak stress and short duration. The initial kinetic energy released instantaneously upon impact with a rock is a typical pulse-type impact load. Because the speed of falling rocks is usually very high (e.g., rolling down from a height), their kinetic energy is concentrated and released in a very short time, causing a violent impact on the structure.

[0050] The effective participation quality of a structure or rock mass reflects its response to seismic vibrations; The ground motion velocity time history (m / s) represents the velocity component of the seismic wave. The input seismic energy per unit time; integration interval The time window centered on the moment of rockfall impact is set at 0.1–0.5 s;

[0051] The seismic motion energy integral represents the continuous vibrational energy input caused by the earthquake during the brief period before and after the rockfall. It is the integral of the kinetic energy carried by the structural vibration caused by the seismic motion during the period before and after the rockfall, reflecting the dynamic response energy excited by the seismic waves in the structure.

[0052] This is a coupling enhancement term for the nonlinear synergistic effect. The kinetic energy of the falling rock load pulse. This represents the kinetic energy integral of the earthquake within the time window. The coupling coefficient is dimensionless and ranges from 0 to 0.3. This reflects the mutually reinforcing effect of rockfall load and seismic energy in terms of time and mechanical mechanisms. For example, earthquakes induce micro-cracks or shear deformation in rock masses, reducing rockfall resistance and increasing impact efficiency. It also indicates a mutually reinforcing effect between earthquakes and rockfall impacts. Even though the energy of each is limited when acting alone, their combined effect can lead to a greater structural response. This synergistic effect cannot be obtained through simple addition; a coupling coefficient must be introduced to achieve the coupling enhancement of the nonlinear synergistic effect.

[0053] Because earthquakes are continuous dynamic excitations, while rockfall impacts are instantaneous pulse loads, the moment a rockfall impacts a structure... If the earthquake occurs during a strong vibration phase (e.g., near peak ground acceleration), the structure is already under significant vibration. At this time, the impact of falling rocks will be superimposed on the existing vibration, leading to a significant increase in the risk of resonance or overload. The coupling of nonlinear synergistic effects is used to capture the amplification effect of the synergistic effect between earthquake energy and falling rock load pulses.

[0054] Example 3;

[0055] Based on Example 1, the earthquake rockfall timing coupling method used in step 2 has the following steps in engineering practice:

[0056] The first stage: from the occurrence of an earthquake to the dynamic response of the structure (e.g., structural displacement and strain).

[0057] The second stage involves analyzing the structural state after the earthquake (which may already be damaged) to the impact of falling rocks, then updating the structural response, and solving the problem by stepping through time.

[0058] The total displacement field on the surface of the Myeongdong is calculated as follows:

[0059] ;

[0060] in, for The overall structural stiffness at any given moment; This represents the total number of finite element elements in the structure. For the first The integration domain of each unit is the geometric volume; This is the strain-displacement matrix (the derivative of the shape function with respect to the coordinates). for The transpose of is used to correlate stress with displacement; For the first The damage variable for each unit is dimensionless. This indicates the degree of material stiffness degradation; This is the initial elasticity matrix (the constitutive tensor when there is no damage), such as the elastic tensor of concrete; The equivalent elastic matrix of the damaged material is represented by the stiffness reduction factor multiplied by the original stiffness. The stiffness reduction factor multiplied by the original stiffness is used to describe the decrease in the load-bearing capacity of the material due to microcracks, pores or plastic deformation. The stiffness reduction factor is a scalar or tensor function between 0 and 1, representing the proportion of material stiffness retained. The original stiffness refers to the elastic stiffness of the material in its intact state.

[0061] The damage stiffness of the element is obtained by integrating the space within the element. This represents the stiffness matrix of the entire structure, which is formed by assembling the stiffness of all the elements.

[0062] In traditional linear elastic finite element methods, the stiffness matrix assumes that all elements are intact, i.e. This is manifested as an undamaged state. ;

[0063] The stiffness matrix in the linear elastic finite element method of this invention is such that when some elements crack, such as when an earthquake causes tensile cracking in concrete, the stiffness of the structure will decrease, manifesting as a damaged state. ;

[0064] The entire formula of this invention embodies the application of the Myeongdong structure under the coupled effects of earthquakes and rockfalls:

[0065] Previous stage: Seismic action;

[0066] The tunnel is subjected to ground acceleration; tensile stress is generated in the concrete roof slab, microcracks appear, and local stiffness decreases; at this time... The stiffness matrix needs to be updated.

[0067] Later stage: Rockfall impact;

[0068] After an earthquake, the structure is already damaged and its stiffness is reduced; when rocks hit, the structure is more likely to deform or even be destroyed. Dynamic response analysis was conducted to predict displacement and steel strain under rockfall impact.

[0069] By introducing unit-level damage variables This enables continuous modeling of the gradual stiffness degradation of structures under dynamic loads, allowing finite element analysis to realistically reflect the entire process of actual engineering structures from integrity to damage and then to failure. Damage variables Derived from strain, energy, or stress criteria (e.g., principal tensile strain exceeds a threshold); if If the stiffness of a certain element drops to zero, it is equivalent to complete fracture.

[0070] For the calculation of the spatiotemporal evolution of steel reinforcement strain inside the tunnel, the concrete shrinkage is constrained by the steel reinforcement or structure, which in turn causes tensile strain in the steel reinforcement. The calculation is performed using the constraint strain of concrete shrinkage on the steel reinforcement structure.

[0071] ;

[0072] in, for The constrained shrinkage strain of concrete at any given moment is the actual shrinkage strain that occurs in the concrete, which is less than the free shrinkage strain due to the constraint of the steel reinforcement. for The elastic modulus of concrete at any given time (the modulus corresponding to the increase in concrete strength over time). This refers to the elastic modulus of the reinforcing steel. for The free shrinkage strain of concrete at any given time (the strain generated by the shrinkage of concrete itself when there is no steel reinforcement). The bond coefficient (reflecting the bond performance between steel reinforcement and concrete; when the bond is strong) When the bond is weak, the value is 1. Less than 1.

[0073] When concrete shrinks freely, it cannot deform freely due to the tension (constraint) of the reinforcing steel bars. The tendency of concrete to shrink (i.e.,...) This will generate bond stress between the steel bars and the concrete, which in turn causes tensile strain in the steel bars and compressive strain in the concrete (to offset some of the shrinkage).

[0074] The formula uses the stiffness ratio of concrete to steel reinforcement (…). By combining free shrinkage strain and bond properties, the actual constrained shrinkage strain of concrete is obtained. This quantifies how much concrete can actually shrink under the constraint of steel reinforcement. The smaller the stiffness ratio (the stiffer the reinforcement and the more flexible the concrete) and the stronger the bond, the smaller the constrained shrinkage strain of the concrete.

[0075] Example 4;

[0076] Based on Example 1, in step 3, the dynamic coupling analysis algorithm uses a combination of time-domain and frequency-domain correlation of seismic response to perform calculations:

[0077] ;

[0078] in, The hybrid response of the structure (e.g., physical quantities such as displacement and stress) is expressed as follows: At that moment, the Signal and the Signal hybrid correlation; These are weighting coefficients (used to allocate the proportion of the two responses). ); The overall inertial response of a structure caused by an earthquake (e.g., the overall vibration response of a structure under seismic loading) is expressed as follows: At that moment, the Signal and the The signals are correlated overall in the time domain; This is the local dynamic transfer function of rockfall impact, used to describe the rockfall load at frequency... The local response characteristics under the condition represent the first... Signal and the Signal, at time Time and Frequency Frequency domain correlation at that location; This is the frequency weighting function (reflecting the contribution of different frequency components to the response); The integration range is over all frequencies from 0 to the maximum frequency. Integrate to find the maximum frequency. It covers the main frequency range of rockfall impacts.

[0079] Represents the overall inertial response of an earthquake (e.g., the overall structural vibration caused by seismic waves). The local dynamic response to rockfall impact is represented by integrating the transfer function at different frequencies, which reflects the dynamic effect of rockfall pulse load in the local area.

[0080] It is a superposition of the frequency domain response of the earthquake and the time domain response of the impact, and it is the weighted average of the two responses. The combined dynamic response. The overall structural vibration caused by the earthquake and the local impact response caused by falling rocks are combined proportionally to obtain the total response of the structure when it is subjected to both of these forces simultaneously.

[0081] For the hybrid integral strategy, since a fixed step size cannot simultaneously account for the instantaneous nature of high-frequency impacts and the stability of low-frequency vibrations, an adaptive step size control mechanism with gradient parameter descent optimization update is introduced to dynamically adjust the step size according to the impact amplitude.

[0082] ;

[0083] in, For the updated parameters, such as the stiffness and damping of the structure, i.e., the multi-scale dynamic characteristic parameters that need to be calibrated; These are the initial parameters before the update; The learning rate is used to control the step size of parameter updates, avoiding updates that are too large or too small. For parameter operators The gradient (parameter operators represent the degree of influence of parameter changes on the objective function), parameter operators gradient It is a direction pointer used to update the parameters in the direction that the objective function decreases, which can gradually reduce the error between the calculated response and the measured response;

[0084] Let the objective function be the sum of squared residuals, and the summation is a subset of the objective function. The cumulative response error at each time point aims to minimize the error, specifically the squared error at a single time point. Squaring is used to make both positive and negative errors positive and to amplify larger errors, especially when the parameter operator... When inappropriate (e.g., stiffness set too low), the model uses the dynamic response calculated by multi-scale time integration. and measured dynamic response The difference is large, and the summation result will be very large. This can be addressed using parameter operators. (For example, by increasing stiffness), the dynamic response calculated by the model will gradually approach the actual dynamic response, and the summation result will become smaller. The ultimate goal is to minimize the summation result. At this point, the parameter operators... This allows us to describe the multi-scale dynamic characteristics of a structure under high-frequency rockfall and low-frequency earthquake conditions. for The dynamic response measured or tested at all times (e.g., structural displacement or acceleration under rockfall impact or earthquake vibration). For the first One target moment; For parameter operators Calculated by hybrid integration or multi-scale time integration For the dynamic response at any given moment, multi-scale time integration is a divide-and-conquer computational strategy, which means performing detailed calculations on the rapidly changing high-frequency components and coarse calculations on the slowly changing low-frequency components. This approach balances the accuracy of high-frequency impacts with the avoidance of redundant calculations for low-frequency vibrations.

[0085] The hybrid integration strategy uses small-step fine integration for high-frequency impacts and large-step efficient integration for low-frequency vibrations, while ensuring seamless transitions between different scales of response.

[0086] Since rockfall impacts are high-frequency pulses (short duration, large load changes) and earthquakes are low-frequency vibrations (long duration, gradual load changes), the time scales of the two are very different. Directly using a single integration step size for calculation would be inefficient and inaccurate. The purpose of the entire formula is to compare the response calculated by the mixed integration with the measured response, and update the structural parameters through gradient descent, such as the local stiffness corresponding to high-frequency impacts and the overall damping corresponding to low-frequency vibrations. Ultimately, this allows the model to accurately describe the multi-scale dynamic characteristics of high-frequency impacts and low-frequency vibrations.

[0087] Example 5;

[0088] Based on Example 1, in step 4, the superposition relationship between the quantified seismic energy and the rockfall load pulse is used as a basis. This superposition relationship has clarified the interaction mode of the two types of loads in the energy transfer process, which is the core basis for further analysis of phase characteristics and avoids isolated analysis that is detached from the actual load coupling state.

[0089] Calculating the phase difference between earthquakes and rockfalls essentially reflects the synchronicity or lag between the seismic load (low-frequency vibration) and the rockfall pulse (high-frequency load) in their timing. When the two types of loads are in phase, the energy superposition effect is most significant, and the peak instantaneous load on the structure is the largest. When there is a phase deviation, the energy superposition effect weakens or exhibits alternating action characteristics depending on the degree of deviation. By quantifying this phase difference, the timing of the synergistic effect of the two types of disaster loads on the tunnel structure can be accurately captured.

[0090] Furthermore, the phase difference between the earthquake and the falling rock is the angle by which the response lags behind the excitation, used to describe the response of a single-degree-of-freedom linear damped system under harmonic excitation. It is the phase lag angle between the output signal (e.g., displacement, velocity, or acceleration) and the input excitation signal, specifically calculated as follows:

[0091] ;

[0092] in, The phase difference represents the time delay (expressed in angular form) in which the response lags behind the external stimulus. The damping ratio; For excitation frequency; It is the natural frequency; For frequency ratio, A value less than 1 indicates that the response keeps up with the stimulus. A value of 1 indicates that the response lags completely behind the excitation, and the amplitude is at its maximum. If the value is greater than 1, the response cannot keep up with the stimulus. It is the arctangent function, used to convert frequency ratios into angles.

[0093] When the ground is at a certain frequency Vibration (e.g., earthquake): When a mass (e.g., a rock or structure) is attached to the ground and undergoes relative motion, the angle by which its motion lags behind the ground motion is called the relative angle. ,angle Known as phase lag, it reflects the dynamic response characteristics of the excitation, exhibiting different response speeds and phase delays to excitations of different frequencies.

[0094] By utilizing the phase lag angle of the damping system's response relative to the excitation under harmonic excitation, the dynamic response characteristics of the system to excitations of different frequencies are demonstrated, especially showing a significant phase delay near resonance, which can be used in scenarios where earthquakes trigger rockfalls and structural vibrations.

[0095] Based on the phase difference analysis results, the time-gravity distribution pattern of the internal structure of the tunnel was further clarified. The time-gravity distribution is not simply a distribution of gravity loads, but rather reflects the comprehensive stress state of various parts of the structure at different times due to the combined effects of seismic inertial response, rockfall impact response, and its own gravity. This pattern clearly presents the dynamic evolution of structural stress over time: for example, at critical moments of phase consistency, specific areas of the structure may experience peak stress; while in other time phases, the stress state exhibits different distribution characteristics.

[0096] Furthermore, the total gravity load borne by the tunnel structure consists of the self-weight stress of the backfill soil and the structure's own weight. The time-gravity distribution law is calculated by coupling the total gravity load borne by the tunnel structure with time, using the following formula:

[0097] ;

[0098] in, For the structure of Myeongdong The total gravitational load borne by the tunnel structure at any given moment indicates the tunnel structure's... The total vertical load at any given time is a time-varying function, indicating that the load changes over time, possibly due to external environmental factors (such as earthquakes, rainfall, and freeze-thaw cycles) or internal stress release.

[0099] The total stress; For structural area or influence coefficient, it is a geometric or mechanical parameter that represents the projected area of ​​the tunnel structure (e.g., horizontal projected area) or load distribution coefficient, used to convert stress into total force; Vertical stress per unit area originates from stress redistribution caused by earthquakes or construction disturbances. It is the effective vertical stress acting on the top of the tunnel or the surrounding rock and soil, and it varies with time.

[0100] The mass of the Myeongdong structure represents the mass of the Myeongdong structure itself, including the total mass of the lining, support, and waterproofing components. This is the acceleration due to gravity, used to calculate the gravitational load generated by the structure's own weight.

[0101] It is a variable load that changes with geological conditions, environmental factors, or time evolution; It is a constant load that does not change over time.

[0102] The total vertical load borne by the tunnel structure is equal to the dynamic vertical stress exerted by the external rock and soil mass multiplied by the area of ​​action (i.e., earth pressure), plus the weight of the structure itself.

[0103] By analyzing the time-gravity distribution patterns, the weak points of the tunnel under the coupled loads of earthquakes and rockfalls were identified. These weak points typically correspond to two scenarios: first, areas where the peak stress exceeds the structural bearing capacity when load phases are superimposed; and second, areas prone to fatigue damage due to long-term alternating loads during dynamic stress evolution. The analysis results provide precise and targeted guidance for optimizing structural disaster-resistant design (e.g., strengthening weak points and improving material performance), ensuring that disaster-resistant measures effectively address core stress risks.

[0104] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope described in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A method for analyzing the stress of highway tunnels in high-intensity seismic zones under coupled earthquake and rockfall loads, characterized in that... Includes the following steps: Based on the load time-series sensitive dynamic finite element model, a disaster phase coupling factor is introduced to quantify the superposition relationship between seismic energy and rockfall load pulse; The specific definition of the disaster phase coupling factor is as follows: ； in, The disaster phase coupling factor is used to measure the impact of falling rocks at time [time]. The degree of coupling between the event and the seismic energy; This refers to the point in time when the rockfall impact began; The duration of the rockfall impact; The normalized seismic energy density function; Integration interval This indicates the time window of impact from falling rocks; within this time period, we should focus on the energy state of the earthquake. It is the total energy integral over the entire simulation time, used for normalization; The superposition of seismic energy and rockfall load pulses represents the combined impact load effect on a structural or rock mass unit per unit area. It describes the equivalent total energy input under the temporal superposition of seismic energy and rockfall impact pulses, specifically: ； in, The equivalent total impact energy when rockfall and ground motion act together on a structure or rock mass; For the quality of falling rocks; This represents the impact velocity of the falling rock. The kinetic energy of the falling rocks; This represents a unit impulse function or a narrow window function; The impact kinetic energy of falling rocks; The effective participation quality of a structure or rock mass reflects its response to seismic vibrations; For ground motion velocity time history; The input seismic energy per unit time; integration interval The time window centered on the moment of rockfall impact; The seismic energy integral represents the continuous vibrational energy input caused by the earthquake during the brief period before and after the rockfall. This is a coupling enhancement term for a nonlinear synergistic effect. The kinetic energy of the falling rock load pulse. This represents the kinetic energy integral of the earthquake within the time window. The coupling coefficient; In the dynamic finite element model, the temporal coupling method of earthquake rockfall is used to calculate the spatiotemporal evolution of the full displacement field on the surface of the tunnel and the strain of the steel bars inside the tunnel, so as to obtain the multi-scale perception of the tunnel's structural response. The earthquake rockfall timing coupling method employed in engineering practice involves the following steps: Phase 1: From earthquake occurrence to structural dynamic response; The second stage: from the post-earthquake structural state to the impact of falling rocks, and then updating the structural response, coupled solutions are obtained by stepping through time. The total displacement field on the surface of the Myeongdong is calculated as follows: ； in, for The overall structural stiffness at any given moment; This represents the total number of finite element elements in the structure. For the first The integration field of each unit; This is the strain-displacement matrix; for The transpose of is used to correlate stress with displacement; For the first The damage variable of each element represents the degree of material stiffness degradation; The initial elasticity matrix; This is the equivalent elastic matrix of the damaged material, representing the stiffness reduction factor multiplied by the original stiffness; The damage stiffness of the element is obtained by integrating the space within the element. This represents the stiffness matrix of the entire structure assembled from the stiffness of all elements, reflecting a damage-free state; The spatiotemporal evolution calculation method for the strain of steel reinforcement inside the tunnel is as follows: the shrinkage of concrete is constrained by the steel reinforcement or structure, which in turn causes tensile strain in the steel reinforcement. The calculation is performed using the constraint strain of concrete shrinkage on the steel reinforcement structure. ； in, for The constrained shrinkage strain of concrete at any given time is the actual shrinkage strain that occurs in the concrete. for The elastic modulus of concrete at any given time; This refers to the elastic modulus of the reinforcing steel. for The free shrinkage strain of concrete at any given moment; The coefficient of adhesion; A dynamic coupling analysis algorithm is introduced to solve the structural inertial response caused by earthquakes and the local dynamic response caused by rockfall load pulses. A hybrid integration strategy is used to handle the multi-scale dynamic characteristics of high-frequency impacts and low-frequency vibrations. The dynamic coupling analysis algorithm uses a combination of time-domain and frequency-domain correlation of seismic response to calculate the impact response. ； in, For the hybrid power response of the structure; These are the weighting coefficients; The overall inertial response of the structure caused by the earthquake; Let be the local dynamic transfer function of the rockfall impact; For frequency weighting functions; The range of integration; Represents the overall inertial response of an earthquake; Represents the local dynamic response to the impact of falling rocks; Based on the superposition relationship between seismic energy and rockfall load pulses, the phase difference between earthquake and rockfall is calculated to obtain the time-gravity distribution law of the internal structure of the tunnel, thereby identifying the weak areas of the tunnel under the coupling effect of multiple disasters.

2. The method for stress analysis of open-cut highway tunnels in high-intensity seismic zones under coupled earthquake and rockfall loads as described in claim 1, characterized in that, The disaster phase coupling factor is defined as a measure of the degree of coupling between the rockfall impact and the ground motion energy at a certain moment. By integrating the total energy over the entire simulation time, the total amount of energy released by the ground motion during the rockfall impact period is calculated, and the impact on the structure during the rockfall impact is measured.

3. The method for stress analysis of open-cut highway tunnels in high-intensity seismic zones under coupled earthquake and rockfall loads as described in claim 1, characterized in that, The superposition of the seismic energy and the rockfall load pulse is used to calculate the combined impact load effect on a unit area of ​​the structure or rock mass unit, and to describe the equivalent total energy input under the superposition of the seismic energy and the rockfall impact pulse in time.

4. The method for stress analysis of open-cut highway tunnels in high-intensity seismic zones under coupled earthquake and rockfall loads as described in claim 1, characterized in that, The calculation of the total displacement field on the surface of the tunnel is achieved by introducing element-level damage variables to continuously model the gradual degradation of the structure's stiffness under dynamic loads.

5. The method for stress analysis of open-cut highway tunnels in high-intensity seismic zones under coupled earthquake and rockfall loads as described in claim 1, characterized in that, The spatiotemporal evolution of the strain of the steel reinforcement inside the tunnel is as follows: the shrinkage of concrete is constrained by the steel reinforcement or structure, which in turn causes tensile strain in the steel reinforcement. The constraint strain of the steel reinforcement structure on the shrinkage of concrete is calculated. By combining the stiffness ratio of concrete to steel reinforcement, and considering the free shrinkage strain and bond performance, the actual constrained shrinkage strain of concrete is obtained.

6. The method for stress analysis of open-cut highway tunnels in high-intensity seismic zones under coupled earthquake and rockfall loads as described in claim 1, characterized in that, The dynamic coupling analysis algorithm uses a method that combines the time domain correlation of seismic response with the frequency domain correlation of impact response to calculate the total dynamic response after weighted mixing of the two responses. By combining the overall structural vibration caused by the earthquake and the local impact response caused by the rockfall in proportion, the total response of the structure under the simultaneous influence of the earthquake response in the frequency domain and the impact response in the time domain is obtained.

7. The method for stress analysis of open-cut highway tunnels in high-intensity seismic zones under coupled earthquake and rockfall loads as described in claim 1, characterized in that, For the hybrid integration strategy, the response calculated by hybrid integration is compared with the measured response, and the structural parameters are updated by gradient descent to describe the multi-scale dynamic characteristics of high-frequency impact and low-frequency vibration.

8. The method for stress analysis of open-cut highway tunnels in high-intensity seismic zones under coupled earthquake and rockfall loads as described in claim 1, characterized in that, The phase difference between the earthquake and the falling rock is defined as the angle by which the response lags behind the excitation. It is used to describe the response of a single-degree-of-freedom linear damped system under harmonic excitation and describes the phase lag angle between the output signal and the input excitation signal.

9. The method for stress analysis of open-cut highway tunnels in high-intensity seismic zones under coupled earthquake and rockfall loads as described in claim 1, characterized in that, The time-gravity distribution law is calculated by coupling the total gravity load borne by the tunnel structure with time. The total vertical load borne by the tunnel structure is calculated as the dynamic vertical stress applied by the external rock and soil mass multiplied by the area of ​​action, plus the weight of the structure itself.

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