Damage probability prediction method for shed-tunnel structures under random rock impact events

Abstract

The present invention relates to the technical field of structural engineering data prediction, and discloses a method for predicting the damage probability of a shed-hole structure under a random rock rolling impact event, comprising the steps of: using Monte Carlo theory to establish a demand data set that can characterize a random rock rolling impact condition under statistical distribution; extracting parameters that affect the damage of the shed-hole structure from the demand data set based on ABAQUS nonlinear finite element analysis; constructing a damage characteristic index of the shed-hole according to the parameters that affect the damage of the shed-hole structure; defining a damage index based on the damage characteristic index to quantify the degree of damage to the shed-hole structure, wherein the damage index includes a bending damage index and a shear damage index. The present invention adopts advanced numerical modeling technology, which can transmit uncertainty and simulate structural failure modes in detail, thereby providing a more accurate explanation based on physical laws for the impact resistance of the shed-hole.

Description

Technical Field

[0001] The invention relates to the technical field of structural engineering data prediction, and in particular to a method for predicting the damage probability of a shed-tunnel structure under a random rock impact event. Background Art

[0002] A shed tunnel is a protective roof structure designed to protect roads, railways, and facilities in mountainous areas from damage or blockage caused by rockfall and other mountain hazards. However, shed tunnels that lack proper energy absorption mechanisms or have defects are still vulnerable to high-intensity rockfall disasters, resulting in serious damage to the structure. Therefore, it is crucial to evaluate and strengthen the impact resistance of these critical infrastructures to minimize the risks and impacts of rockfall disasters. Current techniques for shed tunnel impact analysis mainly rely on simplified analytical calculations or basic finite element modeling, which have many assumptions and limitations and are difficult to restore complex cracking patterns, crack development, structural fragmentation, and the phenomenon of rockfall oblique impact. At the same time, these methods also find it difficult to characterize the randomness and uncertainty of rockfall disasters in the real world. Summary of the invention

[0003] The purpose of the present invention is to adopt advanced numerical modeling technology, which can transmit uncertainty and simulate structural failure modes in detail, so as to provide a more accurate physical law-based explanation of the impact resistance of shed tunnels and a method for predicting the damage probability of shed tunnel structures under random rock impact events.

[0004] In order to achieve the above-mentioned object of the invention, the present invention provides the following technical solutions:

[0005] The damage probability prediction method of the shed-tunnel structure under the random rock impact event includes the following steps:

[0006] Step 1, using Monte Carlo theory to establish a demand data set that can characterize random rolling stone impact conditions under statistical distribution;

[0007] Step 2, based on ABAQUS nonlinear finite element analysis, extract the parameters that affect the damage of the shed tunnel structure in the demand data set;

[0008] Step 3, constructing a damage characteristic index of the shed-hole according to the parameters that affect the damage of the shed-hole structure;

[0009] Step 4: Based on the damage characteristic index, a damage index is defined to quantify the damage degree of the shed-tunnel structure. The damage index includes a bending damage index and a shear damage index.

[0010] Also includes:

[0011] Step 5, statistical analysis and toughness assessment of the shed-tunnel structure;

[0012] Step 6, establishing a quantitative relationship between the damage characteristic index and the damage index and the hazard intensity index of the rockfall impact on the shed-tunnel structure;

[0013] Step 7: Generate vulnerability assessment and vulnerability curve.

[0014] Compared with the prior art, the present invention has the following beneficial effects:

[0015] (1) The present invention adds a cushion layer to the shed-hole structure to absorb and dissipate most of the impact energy from the rolling stones, thereby significantly improving the impact resistance and toughness of the shed-hole structure;

[0016] (2) The present invention can reduce the possibility of damage to the shed-tunnel structure, such as limiting the crack width, reducing the punching shear vulnerability of the structure, and reducing the maximum displacement of the structure;

[0017] (3) The present invention provides a quantitative analysis framework for evaluating the effectiveness of the cushion layer by stochastically simulating the exceedance probability and hazard intensity vulnerability curves of different damage states and damage modes to adapt to specific site conditions and the instability changes of rockfall disasters;

[0018] (4) The present invention can improve the safety and reliability of transportation infrastructure and public facilities in areas prone to rockfall disasters, reduce the risk of failure of the tunnel structure, and thus reduce potential economic losses, environmental impacts and life threats.

[0019] (5) The present invention provides a robust probabilistic framework that can be used to evaluate the impact resistance and structural reliability of shed-tunnel structures. This framework can be used to guide the optimal cushion configuration, shear reinforcement details and displacement-based design criteria, thereby maximizing the safety of shed-tunnel structures while considering the inherent differences in the structures. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings required for use in the embodiments are briefly introduced below. It should be understood that the following drawings only show certain embodiments of the present invention and therefore should not be regarded as limiting the scope. For ordinary technicians in this field, other related drawings can be obtained based on these drawings without creative work.

[0021] Figure 1 It is a schematic diagram of a model of a rolling stone impacting a concrete slab according to the present invention;

[0022] Figure 2 (a) shows the tensile damage parameter d of the present invention t and the peak concrete stress f ct Schematic diagram of the relationship between

[0023] FIG2( b ) is a schematic diagram showing the relationship between the global tension damage index and the maximum displacement of the present invention;

[0024] Figure 3 is a flow chart of the method of the present invention;

[0025] FIG4( a ) is a schematic diagram of the three-parameter Weibull distribution of the present invention under the condition of a shed tunnel without cushion layer;

[0026] FIG4( b ) is a schematic diagram of the three-parameter log-normal distribution under the working condition of the shed tunnel with cushion layer of the present invention;

[0027] FIG4( c ) is a QQ diagram of a shed cave without cushion layer according to the present invention, using Weibull distribution;

[0028] Fig. 4(d) is a QQ diagram of the shed cave with cushion layer according to the present invention, using exponential distribution;

[0029] Figure 5(a) is a schematic diagram showing the relationship between the global tensile damage index and the maximum displacement in stage 1;

[0030] Figure 5(b) is a schematic diagram showing the relationship between the global tensile damage index and the maximum displacement in stage 2;

[0031] Figure 5(c) is a schematic diagram showing the relationship between the global tensile damage index and the maximum displacement in stage 3;

[0032] Figure 6 It is a schematic diagram of the relationship between the bending moment applied by the present invention and the crack width;

[0033] FIG. 7( a ) is a schematic diagram showing the relationship between the maximum impact force and the maximum displacement under the working condition of a shed tunnel without a cushion layer according to the present invention;

[0034] FIG7( b ) is a schematic diagram showing the relationship between the maximum impact force and the maximum displacement under the working condition of the shed tunnel with cushion layer of the present invention;

[0035] FIG8(a) shows the load force on the concrete slab under the condition of the shed tunnel with cushion layer in the present invention at stage D. f-S1 ~Phase D f-S3C Vulnerability curve diagram;

[0036] FIG8( b ) shows the load force on the concrete slab under the condition of the shed tunnel with cushion layer in the present invention at stage D s-S Phase D s-PS Vulnerability curve diagram;

[0037] FIG8(c) shows the concrete slab in the present invention with cushion layer under the condition of shed tunnel after being subjected to impact energy in stage D f-S1 ~Phase D f-S3C Vulnerability curve diagram;

[0038] FIG8(d) shows the concrete slab in the present invention with cushion layer under the condition of shed tunnel after being subjected to impact energy in stage D s-S Phase D s-PS Vulnerability curve diagram;

[0039] Figure 8 (e) shows the load force on the concrete slab under the condition of the shed tunnel without cushion layer in stage D f-S1 ~Phase D f-S3C Vulnerability curve diagram;

[0040] Figure 8 (f) shows the load force on the concrete slab under the condition of the shed tunnel without cushion layer in stage D s-S Phase D s-PS Vulnerability curve diagram;

[0041] Figure 8(g) shows the concrete slab in the present invention without cushion layer under the condition of shed tunnel after being subjected to impact energy in stage D f-S1 ~Phase D f-S3C Schematic diagram of the vulnerability curve;

[0042] Figure 8 (h) shows the concrete slab in the present invention without cushion layer under the condition of shed tunnel after being subjected to impact energy in stage D s-S Phase D s-PS Schematic diagram of the vulnerability curve. DETAILED DESCRIPTION

[0043] The technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. The components of the embodiments of the present invention generally described and shown in the drawings here can be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of the present invention provided in the drawings is not intended to limit the scope of the claimed invention, but merely represents the selected embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without making creative work belong to the scope of protection of the present invention.

[0044] It should be noted that similar numbers and letters represent similar items in the following figures, so once an item is defined in one figure, it does not need to be further defined and explained in subsequent figures. At the same time, in the description of the present invention, the terms "first", "second", etc. are only used to distinguish the description, and cannot be understood as indicating or implying relative importance, or implying any such actual relationship or order between these entities or operations. In addition, the terms "connected", "connected", etc. can be directly connected between elements, or indirectly connected via other elements.

[0045] The present invention is achieved through the following technical solutions: Figure 3 As shown, a method for predicting the damage probability of a shed-tunnel structure under a random rock impact event comprises the following steps:

[0046] Step 1: Use Monte Carlo theory to establish a required data set that can characterize random rolling stone impact conditions under statistical distribution.

[0047] This example studies two cases: a shed cave without cushion (RS) and a shed cave with cushion (RSC), where the cushion is preferably composed of sand or similar energy-absorbing materials. The random nature of the impact of rolling stones on the shed cave structure is represented by the load function Q(t0), which is used to describe the process of forming a random rolling stone impact at any given time t0, and is described probabilistically by the cumulative distribution function (CDF):

[0048]

[0049] Among them, F Q (x) represents the cumulative distribution function; P{.} represents the probability; x represents the threshold of the applied load function; t0 represents the current time; T represents the time length.

[0050] When describing the random rolling stone impact process, the required data sets involved include the following three aspects:

[0051] (1) Load conditions: stone mass, impact velocity, impact angle, impact position, etc.;

[0052] (2) Material properties: concrete properties, steel bar properties, etc.

[0053] (3) Geometric dimensions of structural components: cross-sectional dimensions of concrete slab, effective thickness of concrete slab, reinforcement layout, etc.

[0054] Among them, the load conditions are statistically distributed through the field data, and the random demand data set of the rolling stone event is generated by Monte Carlo theory simulation hundreds of times, which can greatly reflect various possible load conditions. The material properties of the shed tunnel structure are modeled using the log-normal distribution, and its statistical parameters are derived from relevant public literature. The geometric dimensions of the structural components are based on the measurement data of the shed tunnel structure, assuming that they follow the normal distribution, and their coefficient of variation (CoV) is relatively small, at 0.2%. The relevant references are:

[0055] 【1】Mirza SA, MacGregor JG. Variability of Mechanical Properties ofReinforcing Bars. J Struct Div 1979;105:921–37.

[0056] 【2】Mirza SA, MacGregor JG, Hatzinikolas M. Statistical Descriptions of Strength of Concrete. J Struct Div 1979;105:1021–37.

[0057] 【3】Barbato M, Gu Q, Conte JP. Probabilistic Push-Over Analysis of Structural and Soil-Structure Systems. J Struct Eng 2010;136:1330–41.

[0058] 【4】Melchers, RE, Beck AT. Structural reliability analysis and prediction. John Wiley & Sons; 2018.

[0059] The method of establishing the required data set can obtain the random variations existing in the material properties and geometric dimensions of the structural components, thereby more realistically characterizing the structural capacity of the shed cavity and its associated uncertainties.

[0060] Step 2: Based on ABAQUS nonlinear finite element analysis, extract the parameters that affect the damage of the shed-tunnel structure in the demand data set.

[0061] In order to facilitate the analysis of a large number of random scenarios, this program has developed a Python-based automation framework that is seamlessly integrated with ABAQUS and can effectively sample the defined multivariate distribution from the input demand data set (load conditions, material properties, and geometric dimensions of structural components). The Python code systematically generates the input file (i.e., the demand data set) for ABAQUS, starts the nonlinear finite element analysis, and post-processes the results, simplifying the entire computational workflow.

[0062] As an implementable method, the following is a pseudo-code algorithm flow extracted and converted from the source code:

[0063]

[0064]

[0065]

[0066]

[0067]

[0068]

[0069]

[0070]

[0071] Step 3: construct a damage characteristic index of the shed tunnel according to the parameters that affect the damage of the shed tunnel structure.

[0072] In this step, a series of damage characteristic indices that can quantify the performance of the shed-tunnel structure after the impact of the rolling stone are defined to comprehensively evaluate the staged loss failure mode of the shed-tunnel structure. These loss characteristic indices include:

[0073] (1) Crack width (w k ):

[0074] Aiming at the crack width loss characteristic index, the present invention proposes an innovative three-stage evaluation method for evaluating the evolution of crack width in a shed-tunnel structure impacted by rockfall.

[0075] Phase 1: Initial crack-free analysis phase.

[0076] Phase 1 has the following characteristics:

[0077] a. Applicable to the applied bending moment (M app ) is lower than the cracking moment bearing capacity of the concrete slab (i.e. the top slab of the shed-hole structure) (M cr );

[0078] b. The concrete and steel bars are fully bonded and can transfer effective stress, and the structure behaves in the linear elastic stage;

[0079] c. Cracking moment bearing capacity (M cr ) is calculated as follows:

[0080]

[0081] Among them, f ctm Indicates the average tensile strength of concrete, unit: MPa; I u It represents the total moment of inertia of the crack-free section, ignoring the steel bars in the calculation, in mm 4 ;x u It represents the distance from the neutral axis of the section to the edge of the compression zone, in mm; h represents the total thickness of the concrete slab, in mm.

[0082]

[0083]

[0084] Wherein, b represents the width of the concrete slab, in mm; represents the elastic modulus ratio, ; E s Indicates the elastic modulus of steel bars, unit: MPa; E cm Indicates the elastic modulus of concrete, unit: MPa; A s1 Indicates the area of ​​the tensile reinforcement, in mm 2 ; A s2 Indicates the area of ​​the compressed steel bar, in mm 2 ; d represents the thickness from the lowest reinforcement bar in the concrete slab to the top surface of the concrete slab, in mm; d c2 Indicates the thickness of the effective compression cover layer, in mm.

[0085] Phase 2: Crack section analysis phase.

[0086] Phase 2 has the following characteristics:

[0087] a. Applicable to the applied bending moment (M app ) is greater than the cracking moment bearing capacity of the concrete slab (M cr ), the concrete slab began to crack;

[0088] b. The bond between concrete and steel bars gradually fails, resulting in bond slippage, and the stress in the tensioning area of ​​the concrete structure decreases;

[0089] c. Crack width (w k ) is calculated as follows:

[0090]

[0091] Among them, S r,max Indicates the maximum crack spacing, in mm; represents the average strain between steel and concrete; represents the average strain of the reinforcement under the relevant loading conditions; represents the average strain of the concrete slab under the relevant loading conditions.

[0092]

[0093]

[0094] Among them, k1 represents the steel bar bonding performance coefficient, k1=0.8 for high-bond steel bars and k1=1.6 for prestressed steel bars; k2 represents the strain distribution coefficient, k2=0.5 for bending stress and k2=1.0 for pure tension stress; k3 and k4 are both fixed coefficients, with recommended values ​​of k3=3.4 and k4=0.425; c1 represents the protective layer thickness of the tensile steel bar, in mm; Indicates the diameter of the tensile steel bar, in mm; It indicates the effective reinforcement ratio under effective tension; Indicates the stress of the tensile reinforcement in the crack section, unit: MPa; k t It represents the time factor of continuous load application, and short-term load is k t = 0.6, long-term load is k t =0.4; f ct_eff The average value of the effective tensile strength of concrete when cracks are expected to appear for the first time, f ct_eff =f ctm , unit: MPa.

[0095]

[0096]

[0097]

[0098]

[0099]

[0100]

[0101] Where x represents the distance from the fiber to the neutral axis of the crack section under ultimate compression, representing the depth of the cross-section compression zone in the second and third stages, in mm; A c_eff Indicates the concrete cross-sectional area in the effective tension zone, in mm 2 ;h c_eff Indicates the height of the effective tension zone, in mm; I cr Indicates the equivalent section inertia moment (including concrete section and steel section) at the crack stage, unit: mm 4 .

[0102] Phase 3: Structural failure analysis phase.

[0103] Phase 3 has the following characteristics:

[0104] a. Applicable to the applied bending moment (M app ) is greater than the cracking moment bearing capacity of the concrete slab (M cr ), the concrete slab began to crack;

[0105] b. Evaluate three potential failure modes: ductile tensile failure (x <x b ), equilibrium failure, and brittle compression failure.

[0106]

[0107] Among them, Fcc Indicates the compressive strength of concrete, unit: MPa; f cd Indicates the design compressive strength, unit: MPa; f ck It indicates the strength of concrete cylinder, in MPa; represents the effective strength coefficient, when f ck ≤50MPa ; represents the effective height coefficient of the compression zone, when f ck ≤50MPa ; represents the safety factor of concrete, ; Indicates the factors that take into account the way the load is applied. ;x b It represents the distance from the edge of the compression zone to the neutral axis of the crack section under equilibrium conditions, in mm.

[0108] Rated bending moment (M n )for:

[0109]

[0110] Among them, F sc Indicates the tensile strength of the tensile steel bar, unit: MPa.

[0111] (2) Punching shear failure:

[0112] Punching shear failure (punching shear failure) is a key failure mode of the shed-hole structure under local impact loads. The vulnerability of the shed-hole structure under local impact loads is evaluated. Figure 1 As shown, the shear resistance of the shed-tunnel structure is evaluated from the following two key boundaries u0 and u1.

[0113] 1) The impact surface area (with u0 representing the perimeter of the impact surface area) represents the area where the impact load directly acts, including local crushing, cracks, and penetration of concrete. In this area, the load acts directly on the concrete slab, which may cause local damage, such as the formation and expansion of cracks, and may eventually lead to structural penetration damage of the concrete slab.

[0114] 2) The basic control surface area (the perimeter of the basic control surface area is represented by u1) represents the area at a certain distance outside the direct action area of ​​the impact load, which is used to evaluate the overall bidirectional shear bearing capacity. In this area, the overall response of the concrete slab when subjected to the impact load is considered, especially the distribution and transmission of the shear force.

[0115] Figure 1The upper middle part is the front view, the lower part is the top view, the purple area is the concrete slab, the yellow circle represents the rolling stone, the arrow pointing downward represents the rolling stone hitting the concrete slab, the dark purple line in the concrete slab represents the steel bar, and the perimeter of the impact surface area is u0. Due to the shear distribution and transmission, after impacting the concrete slab, the force area will diverge a certain distance outward from u0 to form a basic control surface area with a perimeter of u1. Assuming that the diameter of the rolling stone is D, and the thickness from the lowest steel bar in the concrete slab to the top surface of the concrete slab is d, then the diameter of the defined area u0 is D, and the diameter of the area u1 is D+4d.

[0116]

[0117] Among them, V ED,0 It represents the design value of shear force applied in the impact surface area, in MPa; represents the enhancement factor; F1 represents the impact force of rolling stones on the concrete slab, in N; d eff Indicates the effective thickness of the concrete slab in mm.

[0118]

[0119] Among them, V Rd,max It indicates the design value of the maximum shear strength, in MPa; Indicates the factors that take into account the way the load is applied. ;f ck It indicates the strength of concrete cylinder, in MPa; represents the safety factor of concrete, .

[0120]

[0121] Among them, V ED,1 It represents the design value of shear force applied in the basic control surface area, in MPa; d represents the thickness from the lowest steel bar in the concrete slab to the top surface of the concrete slab, in mm.

[0122]

[0123]

[0124]

[0125]

[0126]

[0127] Among them, V Rd,c It indicates the design value of shear strength of reinforced concrete slab in basic control surface area, in MPa; C Rd,c , k, 、V min is the intermediate parameter; They represent the effective bending reinforcement ratios in the x-direction and z-direction of the basic control surface area, respectively, which are related to the bonded tensile reinforcement in their respective directions. The values ​​are calculated as average values.

[0128] (3) Global tension damage index and maximum displacement:

[0129] Introducing the global tensile damage index ( ) to quantify the accumulation of tensile damage and its correlation with the maximum displacement (deflection). As shown in Figure 2(a) and Figure 2(b), this relationship is characterized in three different stages:

[0130] Stage 1: The structure is not damaged and exhibits completely elastic behavior, as shown in Figure 5(a);

[0131] Stage 2: Structural damage and maximum displacement increase proportionally, i.e., the global tensile damage index ( ) shows a linear relationship with the maximum displacement, as shown in Figure 5(b);

[0132] Stage 3: Structural damage increases dramatically, accompanied by a disproportionate increase in maximum displacement, i.e., the global tensile damage index ( ) shows a nonlinear relationship with the maximum displacement, as shown in Figure 5(c). This stage usually indicates that damage is about to occur.

[0133]

[0134]

[0135] The concrete slab is divided into n units, i=1,2,...,n; represents the maximum tensile damage parameter of the ith concrete slab element; d t represents the tensile damage parameter; It represents the axial stress of concrete on the descending branch, in MPa; f ct Indicates the peak stress of concrete, unit: MPa.

[0136] Figures 5(a), 5(b), and 5(c) show the relationship between the global tensile damage index and the maximum displacement under the two working conditions of the cushioned shed cave (RSC) and the uncushioned shed cave (RS). The fitting curves clearly show the three stages in Figures 5(a), 5(b), and 5(c), which correspond to the three stages in Figure 2(a) and the three stages in Figure 2(b), respectively. Under the two working conditions of RSC and RS, the stage when the structure is not damaged (i.e., stage 1, Figure 5(a)) and the stage when the structural damage ratio increases (i.e., stage 2, Figure 5(b)) until the maximum displacement is about 2.2 mm are the same, but after the structural damage increases sharply (i.e., stage 3, Figure 5(c)), there are obvious differences. As shown in Figures 5(b) and 5(c), when the global tensile damage index is the same, the maximum displacement of the cushioned shed cave (RSC) is significantly smaller than the maximum displacement of the uncushioned shed cave (RS). At the same time, it can be observed that only a few models have a maximum displacement that exceeds the service limit (based on the maximum displacement limit allowed for structures under a certain span in the EN-1992 standard), and only a few models in the RSC condition have a maximum displacement that exceeds the service limit. This shows that in most cases, the structure of the cushioned shed cavity (RSC) can withstand the expected external forces, and only in very few cases will there be a displacement that exceeds the design limit. In contrast, many models in the uncushioned shed cavity (RS) exceed the service limit (red line), with a maximum displacement of 88.5mm, indicating the presence of extensive cracks and tensile damage.

[0137] Step 4: Based on the damage characteristic index, a damage index is defined to quantify the damage degree of the shed-tunnel structure. The damage index includes a bending damage index and a shear damage index.

[0138] Introducing the bending damage index D f and shear damage index D s To measure the damage degree of the shed-tunnel structure, the bending damage index D f It is defined as the ratio of the bending moment applied to the shed-hole structure to the critical bending moment bearing capacity. The shear damage index D s It is defined as the ratio of the shear force applied to the shed-hole structure to the shear bearing capacity. These two damage indices can be used to systematically track the failure and damage progress of the shed-hole structure at various stages, including the linear elastic response stage (D f-S1 , D f-S2 )、Bending failure stage(D f-S3T , D f-S3B , D f-S3C )、Shear failure stage(D s-S , D s-PS , D s-FBC , D s-FRF ), which is used to quantitatively characterize the structural damage process. The specific classification basis and description are shown in Table 1.

[0139] Table 1 Damage characteristic index and structural damage degree

[0140]

[0141] Please refer to Table 1, with the bending damage index D f For example, D f-S1 represents the crack-free linear elastic stage, in which the bending moment (M app ) is less than the cracking moment bearing capacity (M cr As the load increases, the applied bending (M app ) exceeds the cracking moment bearing capacity (M cr ), cracks appear, and enter stage D f-S2 , resulting in bond slip between concrete and steel bars, and at the same time, the stress in the tension zone of the concrete structure is reduced. As the load increases further, the damage enters a higher level stage. Depending on the different stress conditions, it may be in the tensile failure stage of the tensile steel bar rupture. f-S3T , or in the equilibrium failure stage of concrete crushing and steel yielding D f-S3B , or in the brittle compression failure stage of concrete crushing D f-S3C , depends on the applied bending moment (M app ) and the distance between the center axis of the crack section (x) and the edge of the compression zone in the equilibrium state (x b ).

[0142] Similarly, the shear damage index D s Measured from stage D where shear reinforcement is not required s-S Stage D where shear reinforcement is required s-PS process, and the stage D of failure of the basic control surface area boundary s-FBC To the final stage of structural failure D s-FRF .

[0143] Figure 6 The relationship between crack width and applied bending moment for two cases, RSC and RS, is shown. Both cases follow a similar trend. As the bending moment increases, the crack width increases until stage D f-S2 Before the end, it represents the stage of stable crack width development. f-S3T After that, the crack width increases sharply, indicating that structural failure has begun. f-S1 The crack width within the acceptable range; when the bending moment continues to be applied to reach M cr , i.e. stage D f-S1 Towards Phase D f-S2 After the transition, the crack width is in an unacceptable range; when the bending moment is continuously applied to reach M n, i.e. stage D f-S2 Towards Phase D f-S3T After the transition, the crack width has caused damage to the shed-tunnel structure.

[0144] Step 5: Statistical analysis and toughness assessment of the shed-tunnel structure.

[0145] In order to characterize the variability of key response parameters in Monte Carlo simulation, the simulation data was fitted by probability distribution using Minitab statistical software. The software can identify the probability distribution model of suitable data based on the goodness of fit index, thereby explaining the unpredictability caused by changes in load conditions, material characteristics, and geometric dimensions of structural components in actual working conditions. By combining the probability distribution of multiple key response parameters (including impact force, transmission force, support reaction force, displacement, crack width, bending moment, global tension damage index, etc.), a comprehensive statistical analysis and toughness evaluation of the shed-tunnel structure can be performed.

[0146] The 3-parameter Gamma distribution provides the best fit description for the load forces on the concrete slab, both with and without cushion sheds. The reaction force can be best described by the 3-parameter Weibull distribution. In the case of cushion sheds, the 3-parameter Lognormal distribution can capture the maximum displacement well, as shown in Figure 4(b), while in the case of no cushion sheds, the 3-parameter Weibull distribution can capture the maximum displacement most accurately, as shown in Figure 4(a).

[0147] Figure 4(c) is the QQ diagram of the shed hole without cushion layer, and the Weibull distribution is adopted; Figure 4(d) is the QQ diagram of the shed hole with cushion layer, and the exponential distribution is adopted. Figures 4(c) and 4(d) are used to find a suitable probability model for the working conditions under the rolling stone probability impact test. They are used to describe the probability distribution of the force on the concrete slab, which usually needs to meet a certain probability score, that is, the result should fall within the upper and lower score lines as much as possible.

[0148] Step 6: Establish a quantitative relationship between the damage characteristic index and the damage index and the hazard intensity index of the rockfall impact on the shed tunnel structure.

[0149] This step establishes the quantitative relationship between the damage characteristic index and damage index and the hazard intensity index of the impact of rolling stones on the shed tunnel structure. The damage characteristic index and damage index are mainly the global tension damage index ( )、crack width(w k )、Bending damage index(D f ), shear damage index (D s). The introduced hazard intensity index describes the severity of the rockfall event, including applied bending moment, impact force, impact energy, maximum displacement, etc. Three basic relationships are established through this step method to link the damage characteristic index and damage index with the hazard intensity index: (1) maximum displacement and global tensile damage index; (2) applied bending moment and crack width; (3) maximum impact force and maximum displacement, maximum impact force and bending damage index D f , maximum impact force and shear damage index D s .

[0150] Figure 7(a) and Figure 7(b) show the relationship between the maximum impact force and the maximum displacement under the two working conditions of uncushioned shed tunnel (RS) and cushioned shed tunnel (RSC), respectively, with the focus on the punching shear effect. s The values ​​of the division stages are D s =1.00, D s =0.93, D s =0.46, the fitting curve shows a nonlinear change trend. With the increase of the maximum impact force, the maximum displacement also shows an accelerated growth, which indicates that under higher impact force, the deformation resistance of the concrete slab is decreasing, which may be caused by punching shear failure.

[0151] The points of the model (RSC) in Figure 7(b) mainly fall on D s = 0.46 or less, indicating that shear reinforcement is not required in most impact cases of cushioned sheds, which demonstrates the effectiveness of cushioned sheds in distributing impact forces and reducing local stress concentrations that may lead to punching shear failure. This is in sharp contrast to Figure 7(a), where many models (RS) exceed the failure threshold D s =1.00, which indicates that the shed-hole structure is more susceptible to punching shear damage in the absence of a cushion layer.

[0152] Step 7: Generate vulnerability assessment and vulnerability curve.

[0153] By combining distribution identification, random simulation and statistical damage quantification, a comprehensive method for assessing the vulnerability of shed tunnels under random rockfall events is established. Using the damage characteristic index and the relationship between damage index and hazard intensity index, a vulnerability curve can be generated. The vulnerability curve quantifies the probability of exceeding different damage states or failure modes, which is related to the impact force or impact energy generated by the rockfall. This overall framework supports the design and decision-making process, enabling relevant personnel to make accurate choices and optimize the disaster impact resistance performance of shed tunnel structures.

[0154] The generated vulnerability curve is as follows Figure 8(a) to Figure 8(h) As shown, Figure 8(a) to Figure 8(d)The load force on the concrete slab and the probability of structural failure at each stage after the impact energy are shown under the condition of a RSC. Figure 8(e) to Figure 8(h) The load forces on the concrete slab and the probability of structural failure at each stage after being subjected to impact energy under the uncushioned shed-hole (RS) condition are shown.

[0155] In summary, the fragility curve highlights the key role of the cushion layer in improving the toughness of the shed tunnel structure. The cushion layer can significantly reduce the probability of exceeding the limit of the structural damage state under various impact conditions and reduce the susceptibility of punching and shear failure. This is crucial for guiding the optimal design of the shed tunnel structure, and also provides a reliable basis for the formulation and decision-making of risk management, which helps to protect important infrastructure in mountainous areas prone to rockfall disasters.

[0156] The above is only a specific embodiment of the present invention, but the protection scope of the present invention is not limited thereto. Any person skilled in the art can easily think of changes or substitutions within the technical scope disclosed by the present invention, which should be included in the protection scope of the present invention. Therefore, the protection scope of the present invention should be based on the protection scope of the claims.

Claims

1. A damage probability prediction method for a shed-tunnel structure under a random rock impact event, characterized by: The following steps are involved: Step 1, using Monte Carlo theory to establish a demand data set that can characterize random rolling stone impact conditions under statistical distribution; Step 2, based on ABAQUS nonlinear finite element analysis, extract the parameters that affect the damage of the shed tunnel structure in the demand data set; Step 3, constructing a damage characteristic index of the shed-hole according to the parameters that affect the damage of the shed-hole structure; In step 3, the damage characteristic index constructed includes crack width; The evolution of crack width in a shed-tunnel structure subjected to rockfall was evaluated using a three-stage approach: Phase 1: Initial crack-free analysis phase; Phase 1 has the following characteristics: a. Applicable to the applied bending moment M app Lower than the cracking moment bearing capacity M of the concrete slab cr ; b. The concrete and steel bars are fully bonded and can transfer effective stress, and the structure behaves in the linear elastic stage; c. Cracking moment bearing capacity M cr The calculation formula is as follows: Among them, f ctm Represents the average tensile strength of concrete; I u represents the total moment of inertia of the crack-free section; x u represents the distance from the neutral axis of the section to the edge of the compression zone; h represents the total thickness of the concrete slab; Where, b represents the width of the concrete slab; represents the elastic modulus ratio, ; E s Represents the elastic modulus of steel bars; E cm Represents the elastic modulus of concrete; A s1 Represents the area of ​​the tensile reinforcement; A s2 represents the area of ​​the compressed steel bar; d represents the thickness from the lowest steel bar in the concrete slab to the top surface of the concrete slab; d c2 Indicates the thickness of the effective compression cover; Stage 2: Crack section analysis stage; Phase 2 has the following characteristics: a. Applicable to the applied bending moment M app Greater than the cracking moment bearing capacity M of the concrete slab cr , cracks began to appear on the concrete slab; b. The bond between concrete and steel bars gradually fails, resulting in bond slippage, and the stress in the tensioning area of ​​the concrete structure decreases; c. Crack width w k The calculation formula is as follows: Among them, S r,max represents the maximum crack spacing; represents the average strain between steel and concrete; represents the average strain of the reinforcement under the relevant loading conditions; represents the average strain of the concrete slab under the relevant loading conditions; Among them, k1 represents the steel bar bonding performance coefficient; k2 represents the strain distribution coefficient; k3 and k4 are both fixed coefficients; c1 represents the thickness of the protective layer of the tensile steel bar; Indicates the diameter of the tensile reinforcement; It indicates the effective reinforcement ratio under effective tension; represents the stress of the tensile reinforcement in the crack section; k t The time factor indicating the continuous application of load; f ct_eff The average value of the effective tensile strength of concrete when cracks are expected to appear for the first time, f ct_eff =f ctm ; Where x represents the distance from the fiber to the neutral axis of the crack section under ultimate compression; A c_eff Represents the concrete cross-sectional area in the effective tension zone; h c_eff Indicates the height of the effective tension zone; I cr represents the equivalent section moment of inertia at the crack stage; Phase 3: Structural failure analysis phase; Phase 3 has the following characteristics: a. Applicable to the applied bending moment M app Greater than the cracking moment bearing capacity M of the concrete slab cr , cracks began to appear on the concrete slab; b. Evaluate three potential failure modes: ductile tensile failure, equilibrium failure, and brittle compressive failure; Among them, F cc Indicates the compressive strength of concrete; f cd Indicates the design compressive strength; f ck Indicates the strength of concrete cylinder; represents the effective strength coefficient; It represents the effective height coefficient of the compression zone; represents the safety factor of concrete; Indicates the factors that take into account the way the load is applied; x b It represents the distance from the edge of the compression zone to the neutral axis of the crack section under equilibrium conditions; Rated bending moment M n for: Among them, F sc Indicates the tensile strength of the tensile steel bar; In step 3, the damage characteristic index constructed also includes punching shear failure; The following two key boundaries u0 and u1 are used to evaluate the shear resistance of the shed-tunnel structure: 1) The impact surface area represents the area where the impact load directly acts, and u0 represents the circumference of the impact surface area; 2) The basic control surface area represents the area at a certain distance outside the direct action area of ​​the impact load, which is used to evaluate the overall bidirectional shear bearing capacity. The perimeter of the basic control surface area is represented by u1; Assuming that the diameter of the rolling stone is D, and the thickness from the lowest steel bar in the concrete slab to the top surface of the concrete slab is d, then the diameter of area u0 is defined as D, and the diameter of area u1 is defined as D+4d; Among them, V ED,0 It represents the design value of shear force applied in the impact surface area; represents the enhancement factor; F1 represents the impact force of rolling stones on the concrete slab; d eff Indicates the effective thickness of the concrete slab; Among them, V Rd,max Indicates the design value of the maximum shear strength; Indicates the factors that take into account the way the load is applied; f ck Indicates the strength of concrete cylinder; represents the safety factor of concrete; Among them, V ED,1 It represents the design value of shear force applied in the basic control surface area; d represents the thickness from the lowest reinforcement in the concrete slab to the top surface of the concrete slab; Among them, V Rd,c Represents the design value of the shear strength of the reinforced concrete slab in the basic control surface area; C Rd,c , k, 、V min is the intermediate parameter; They represent the effective bending reinforcement ratios of the basic control surface area in the x-direction and the z-direction respectively; In step 3, the damage characteristic index constructed includes a global tensile damage index and a maximum displacement; in, represents the global tension damage index; the concrete slab is divided into n units, i=1,2,...,n; represents the maximum tensile damage parameter of the i-th concrete slab element; d t represents the tensile damage parameter; represents the axial stress of concrete on the descending branch; f ct Indicates the peak stress of concrete; Step 4: Based on the damage characteristic index, define the damage index to quantify the damage degree of the shed-tunnel structure. The damage index includes the bending damage index D f , shear damage index D s , bending damage index D f It is defined as the ratio of the bending moment applied to the shed-hole structure to the critical bending moment bearing capacity. The shear damage index D s It is defined as the ratio of the shear force applied to the shed-hole structure to the shear bearing capacity.

2. The damage probability prediction method for the shed-tunnel structure under the random rock impact event according to claim 1 is characterized by: The required data set includes: (1) Load conditions: stone mass, impact velocity, impact angle, and impact position; (2) Material properties: concrete properties, steel bar properties; (3) Geometric dimensions of structural components: cross-sectional dimensions of concrete slab, effective thickness of concrete slab, and reinforcement layout.

3. The damage probability prediction method for a shed-tunnel structure under a random rock impact event according to claim 1 is characterized in that: The step 4 specifically comprises the following steps: The damage degree of the shed-tunnel structure is quantified by dividing it into stages: (1) Phase D f-S1 :D f The value range is [0.00-0.60); stress condition M app <M cr ; The degree of damage is that there are no cracks in the concrete, and effective stress can be transmitted between the concrete and the steel bars; (2) Phase D f-S2 :D f The value range is [0.60-1.00); stress condition M app >M cr ; The degree of damage is that the concrete has cracks, there is bond slip between the concrete and the steel bars, and the concrete is compressed; (3) Stage D f-S3T :D f The value is 1.00; the stress condition M app ≥M cr And x <x b ; The damage degree is ductile tensile failure of the steel bars on the tension side, and stress yielding occurs; (4) Stage D f-S3B :D f The value is 1.00; the stress condition M app ≥M cr And x=x b ; The degree of damage is equilibrium destruction, concrete crushing and steel yielding; (5) Stage D f-S3C :D f The value is 1.00; the stress condition M app ≥M cr And x>x b ; The degree of damage is brittle crushing of concrete; (6) Stage D s-S :D s The value range is [0.00-0.46); stress condition V Rd,c <V ED,1 ; The damage level is such that shearing of the reinforcement is not required; (7) Stage D s-PS :D s The value range is [0.46-0.93); stress condition V Rd,c ≥V ED,1 ; The damage level is such that shear reinforcement is required; (8) Stage D s-FBC :D s The value range is [0.93-1.00); stress condition V ED,1 ≥2 Rd,c ; The damage level is such that shear reinforcement is required, and the boundary damage of the basic control surface area is basically controlled; (9) Stage D s-FRF :D s The value is 1.00; the stress condition V ED,0 ≥2 Rd,max ; The degree of damage is that shear reinforcement is required, boundary damage in the basic control surface area, and structural surface damage.

4. The damage probability prediction method for a shed-hole structure under a random rock impact event according to any one of claims 1 to 3, characterized in that: Also includes: Step 5, statistical analysis and toughness assessment of the shed-tunnel structure; Step 6, establishing a quantitative relationship between the damage characteristic index and the damage index and the hazard intensity index of the rockfall impact on the shed-tunnel structure; Step 7: Generate vulnerability assessment and vulnerability curve.

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