Reinforced concrete slab damage evaluation method based on M-V curve
By using a damage assessment method based on MV curves, the problem of damage assessment of reinforced concrete slabs under rockfall impact was solved, achieving rapid and accurate damage assessment and impact resistance performance prediction, thus supporting the prevention and control of rockfall disasters for reinforced concrete slabs.
Patent Information
- Application Number
- CN202511314454.0
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-09-15
- Publication Date
- 2025-12-30
AI Technical Summary
Existing technologies lack simple and accurate methods for assessing the damage to reinforced concrete slabs under the impact of falling rocks, making it difficult to quantitatively understand the damage status of tunnel structures and affecting emergency rescue and maintenance work.
A damage assessment method based on MV curves is adopted to achieve rapid and accurate assessment of damage to reinforced concrete slabs by clarifying design parameters, classifying damage levels, calculating critical values, plotting damage prediction curves, and simulating rockfall trajectories.
It enables rapid and accurate assessment of damage to reinforced concrete slabs, provides quantitative prediction of impact resistance, and offers a reference for the prevention and control of rockfall disasters.
Smart Images
Figure CN121234733A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of geological disaster prevention engineering technology, specifically to a method for evaluating damage to reinforced concrete slabs based on MV curves. Background Technology
[0002] Rockfall hazards are difficult to predict due to their randomness and suddenness, posing a serious threat to infrastructure such as roads and bridges. Reinforced concrete tunnel structures are one of the most commonly used engineering structures for rockfall hazard prevention, widely applied in rockfall protection projects at tunnel entrances, along cliff edges, and on mountain roads. The tunnel rockfall impact resistance system mainly consists of two parts: the tunnel structure and a buffer layer. The buffer layer on the tunnel structure effectively reduces the impact force of falling rocks, minimizing damage to the natural environment. After a tunnel is impacted by a rockfall, the difficulty in quantitatively assessing the damage state leads to significant challenges in post-disaster work such as emergency rescue, temporary support, and maintenance. Therefore, the operational safety of tunnels is a major challenge currently facing mountainous transportation construction and geological disaster risk management. The key to damage assessment is selecting evaluation criteria, which are related to the structural dynamic response mechanism and damage failure mode.
[0003] Although some scholars have used damage curves to assess the damage of structural components under impact loads, current damage assessment methods are too complicated and lack a simple and accurate method for assessing the damage of reinforced concrete slabs under rockfall impact. Summary of the Invention
[0004] To address the problems existing in the prior art, this invention provides a damage evaluation method for reinforced concrete slabs based on MV curves. Through full-scale rockfall impact tests and nonlinear explicit dynamic analysis, a damage evaluation formula based on MV curves is established, enabling rapid and accurate assessment of damage to reinforced concrete slabs. This provides a reference for the prevention and control of rockfall disasters and solves the problems mentioned in the background art.
[0005] To achieve the above objectives, the present invention provides the following technical solution: a method for evaluating damage to reinforced concrete slabs based on MV curves, comprising the following steps:
[0006] S1. Clarify the relevant design parameters of the reinforced concrete slab, specifically including: slab thickness t, concrete strength f. c , reinforcement ratio ρ and cushion layer type c;
[0007] S2. Based on the damage parameter k, the damage level is divided into mild damage, moderate damage, severe damage and complete failure, and the critical values β1, β2 and β3 for each damage level are calculated.
[0008] S3. Calculate the critical values M0 and V0 in the prediction formula of the MV damage assessment curve when the damage parameters k are β1, β2, and β3 respectively.
[0009] S4. Substitute the calculated critical values of M0 and V0 into the curve formula (M-M0)(V-V0)=1.25(M0 / 2+V0 / 2). 0.96 Plot three MV damage prediction curves for k=β1, k=β2, and k=β3;
[0010] S5. Scan the slope topography, simulate and predict the trajectory of falling rocks on steep slopes, and analyze and derive multiple combinations of mass and velocity of falling rocks (m1, v1), (m2, v2)...(m n ,v n );
[0011] S6. Input the actual mass and impact velocity (m) of each falling rock. i v i ), determine the location of the falling rock on the MV damage prediction curve and determine the damage level;
[0012] S7. Count the number of falling rocks in the lightly damaged area (n1), the moderately damaged area (n2), the severely damaged area (n3), and the failure area (n4); determine the probability of light, moderate, severe damage, and failure of the reinforced concrete slab after being impacted by falling rocks based on the numbers.
[0013] Preferably, in step S1, the thickness t of the concrete slab is 0.2 to 0.7 m.
[0014] Preferably, in step S1, the concrete strength f c The value ranges from 30 to 80 MPa.
[0015] Preferably, in step S1, the reinforcement ratio ρ is taken as 0.002 to 0.0350.
[0016] Preferably, in step S1, the type c of the cushion layer is the ratio of the elastic modulus of sand and other buffer materials, calculated using the following formula:
[0017] c=(E_sand×h_sand) / (E_other×h_other)
[0018] Where E_sand is the elastic modulus of sand, and h_sand is the thickness of the sand layer; E_other is the elastic modulus of other buffer materials, and h_other is the thickness of other buffer material layers.
[0019] Preferably, in step S2, β1 takes the value of 0.15 to 0.3, β2 takes the value of 0.6 to 0.80, and β3 takes the value of 0.9 to 1.0.
[0020] Preferably, in step S3, when the damage parameter k is β1, β2, and β3 respectively, the calculation formulas for the critical values M0 and V0 in the prediction formula of the MV damage assessment curve are as follows:
[0021] M0(β1)=exp(16.015β1t+0.145β1f c -24.96β1ρ-5.045β1c-2.834)
[0022] V0(β1)=exp(7.9505β1t+0.075β1f c -10.205β1ρ-2.865β1c+0.688)
[0023] M0(β2)=exp(1.618β2t+0.015β2f c -0.9438β2ρ-0.348β2c-0.394)
[0024] V0(β2)=exp(1.1488β2t+0.0125β2f c -0.403β2ρ-0.355β2c+1.591)
[0025] M0(β3)=exp(1.075β3t+0.0010β3f c -0.298β3ρ-0.289β3c-0.175)
[0026] V0(β3)=exp(0.7897β3t+0.008β3f c -0.367β3ρ-0.380β3c+1.792).
[0027] Preferably, in step S5, a digital spatial information model of the slope is reconstructed using digital scanning technology, and a digital slope disaster model is established in conjunction with geological surveys to determine the spatial location, mass, trajectory, impact velocity, and disaster-causing range of falling rocks.
[0028] Preferably, in step S6, the actual mass and impact velocity (m) of each falling rock are input. i v i Then calculate the value;
[0029] When the value is located in the lower left of the k=β1 damage curve, the damage level is judged as mild damage;
[0030] When the value is between k = β1 and k = β2, the damage level is judged as moderate damage.
[0031] When the value is between k = β2 and k = β3, the damage level is judged as severe damage.
[0032] When the value is located above and to the right of the damage curve of k=β3, the damage level is judged as destructive failure.
[0033] Preferably, in step S7, the formula for calculating the damage probability is as follows:
[0034] The probability of mild injury is P1 = n1 / N × 100%.
[0035] The probability of moderate injury, P2 = n2 / N × 100%
[0036] The probability of severe injury, P3, is calculated as n3 / N × 100%.
[0037] Probability of failure P4 = n4 / N × 100%
[0038] Where N = n1 + n2 + n3 + n4.
[0039] The beneficial effects of this invention are as follows: This invention proposes for the first time a damage evaluation method for reinforced concrete slabs based on MV curves, clarifies the calculation process for evaluating the impact damage of reinforced concrete slabs against falling rocks, and enables accurate and convenient assessment of the impact resistance of reinforced concrete slabs. This invention can rapidly quantify and predict the impact damage degree of composite cushion concrete slabs, and can be used to evaluate the impact resistance of reinforced concrete slabs of any cross-section covered by composite cushions of any thickness and any other, providing a reference for the prevention and control of rockfall disasters affecting reinforced concrete slabs. Attached Figure Description
[0040] Figure 1 This is a schematic diagram of the damage evaluation method for reinforced concrete slabs based on MV curves according to the present invention.
[0041] Figure 2 This is a conceptual diagram of the MV damage curve of the present invention;
[0042] Figure 3 This is a model diagram of a reinforced concrete slab in an embodiment of the present invention;
[0043] Figure 4 This is a flowchart of the damage assessment process in an embodiment of the present invention;
[0044] Figure 5 This is a MV damage curve diagram of the sand-EPS cushion concrete slab in an embodiment of the present invention;
[0045] Figure 6 This is a diagram illustrating the simulated trajectory of falling rocks on a slope, as shown in an embodiment of the present invention. Detailed Implementation
[0046] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.
[0047] Example 1
[0048] This invention provides a technical solution: a method for evaluating damage to reinforced concrete slabs based on MV curves, such as... Figure 1 As shown, it includes the following steps:
[0049] S1. Clarify the relevant design parameters of the reinforced concrete slab, specifically including: slab thickness t, concrete strength f. c The reinforcement ratio ρ and the type of subbase c are also considered. The concrete slab thickness t ranges from 0.2 to 0.7 m; the concrete strength f... c The value of is 30-80 MPa; the value of reinforcement ratio ρ is 0.002-0.0350.
[0050] Subbase type c is the ratio of the elastic modulus of sand and other buffer materials, calculated using the following formula:
[0051] c=(E_sand×h_sand) / (E_other×h_other)
[0052] Where E_sand is the elastic modulus of sand, and h_sand is the thickness of the sand layer; E_other is the elastic modulus of other buffer materials, and h_other is the thickness of other buffer material layers.
[0053] S2. Based on the damage parameter k, the damage levels are divided into minor damage, moderate damage, severe damage, and complete failure. The critical values β1, β2, and β3 for each damage level are calculated. Among them, β1 ranges from 0.15 to 0.3, β2 ranges from 0.6 to 0.80, and β3 ranges from 0.9 to 1.0.
[0054] S3. Calculate the critical values M0 and V0 in the prediction formula of the MV damage assessment curve when the damage parameters k are β1, β2, and β3 respectively.
[0055] When the damage parameter k is β1, β2, and β3 respectively, the calculation formulas for the critical values M0 and V0 in the prediction formula of the MV damage assessment curve are as follows:
[0056] M0(β1)=exp(16.015β1t+0.145β1fc -24.96β1ρ-5.045β1c-2.834)
[0057] V0(β1)=exp(7.9505β1t+0.075β1f c -10.205β1ρ-2.865β1c+0.688)
[0058] M0(β2)=exp(1.618β2t+0.015β2f c -0.9438β2ρ-0.348β2c-0.394)
[0059] V0(β2)=exp(1.1488β2t+0.0125β2f c -0.403β2ρ-0.355β2c+1.591)
[0060] M0(β3)=exp(1.075β3t+0.0010β3f c -0.298β3ρ-0.289β3c-0.175)
[0061] V0(β3)=exp(0.7897β3t+0.008β3f c -0.367β3ρ-0.380β3c+1.792).
[0062] S4. Substitute the calculated critical values of M0 and V0 into the curve formula (M-M0)(V-V0)=1.25(M0 / 2+V0 / 2). 0.96 Plot three MV damage prediction curves for k=β1, k=β2, and k=β3, as follows: Figure 2 As shown;
[0063] S5. Scan the slope topography to simulate and predict the trajectory of falling rocks on steep slopes (using digital scanning technology, reconstruct a digital spatial information model of the slope, combine with geological surveys to establish a digital slope disaster model, determine the spatial location, mass, trajectory, impact velocity, and disaster-causing range of falling rocks), and analyze multiple combinations of mass and velocity of falling rocks on the slope (m1, v1), (m2, v2)... (m n ,v n ).
[0064] S6. Input the actual mass and impact velocity (m) of each falling rock. i v i To determine the location of the falling rock on the MV damage prediction curve and assess the damage level, such as... Figure 4 As shown.
[0065] Input the actual mass and impact velocity (m) of each falling rock. i v i Then calculate the value;
[0066] When the value is located in the lower left of the k=β1 damage curve, the damage level is judged as mild damage;
[0067] When the value is between k = β1 and k = β2, the damage level is judged as moderate damage.
[0068] When the value is between k = β2 and k = β3, the damage level is judged as severe damage.
[0069] When the value is located above and to the right of the damage curve of k=β3, the damage level is judged as destructive failure.
[0070] S7. Count the number of falling rocks in the lightly damaged area (n1), the moderately damaged area (n2), the severely damaged area (n3), and the failure area (n4); determine the probability of light, moderate, severe damage, and failure of the reinforced concrete slab after being impacted by falling rocks based on the numbers.
[0071] The formula for calculating the probability of damage is as follows:
[0072] The probability of mild injury is P1 = n1 / N × 100%.
[0073] The probability of moderate injury, P2 = n2 / N × 100%
[0074] The probability of severe injury, P3, is calculated as n3 / N × 100%.
[0075] Probability of failure P4 = n4 / N × 100%
[0076] Where N = n1 + n2 + n3 + n4.
[0077] Example 2
[0078] Taking an impact test of a reinforced concrete slab as an example, the specific calculation process of this invention is explained in detail below:
[0079] I. Relevant design parameters for reinforced concrete slabs: thickness t = 0.3m, concrete strength f c The reinforced concrete slab model has a strength of 40 MPa, a reinforcement ratio ρ of 0.0327, and a cushion layer type c of 30cm EPS + 30cm sand. Figure 3 As shown.
[0080] 2. Take β1 = 0.2, β2 = 0.8, and β3 = 1.0.
[0081] 3. Define the critical damage parameters as β1, β2, and β3. Input the above plate design parameter values and substitute them into the prediction formula of the MV evaluation curve for damage parameters k, which are β1, β2, and β3 respectively, to calculate the critical values M0 and V0.
[0082] M0(β1)=exp(16.015β1t+0.145β1f c -24.96β1ρ-5.045β1c-2.834)
[0083] V0(β1)=exp(7.9505β1t+0.075β1f c -10.205β1ρ-2.865β1c+0.688)
[0084] M0(β2)=exp(1.618β2t+0.015β2f c -0.9438β2ρ-0.348β2c-0.394)
[0085] V0(β2)=exp(1.1488β2t+0.0125β2f c -0.403β2ρ-0.355β2c+1.591)
[0086] M0(β3)=exp(1.075β3t+0.0010β3f c -0.298β3ρ-0.289β3c-0.175)
[0087] V0(β3)=exp(0.7897β3t+0.008β3f c -0.367β3ρ-0.380β3c+1.792)
[0088] IV. Substitute the calculated three sets of M0 and V0 values into the curve formula (M-M0)(V-V0)=1.25(M0 / 2+V0 / 2) 0.96 In the figure, three MV damage prediction curves are plotted for k=0.2, k=0.8, and k=1.0 respectively, as shown below. Figure 5 As shown.
[0089] V. The topographic map of the slope was obtained by scanning. Using Rockfall software, 16 sets of mass and velocity (m, v) of falling rocks were obtained, namely (0.56t, 5.58m / s), (0.723t, 11.44m / s), (0.80t, 5.77m / s), (0.90t, 17.73m / s), (1.00t, 12.54m / s), (1.14t, 5.74m / s), (1.25t, 1... 4.71m / s), (1.30t, 18.29m / s), (1.41t, 18.81m / s), (1.50t, 10.73m / s), (1.65t, 5.95m / s) (1.7 3t, 14.41m / s), (1.80t, 12.36m / s), (2.10t, 19.41m / s) (2.30t, 5.74m / s), (2.40t, 13.11m / s).
[0090] VI. Input the (m,v) values for these 16 sets of falling rocks, such as... Figure 6 As shown, the location of the falling rock in the MV curve predicted by the formula was determined. Statistically, 6 points were located within the minor damage area, 9 points within the moderate damage area, and 1 point within the severe damage area.
[0091] Therefore, the probability of the reinforced concrete slab suffering minor damage from the impact of falling rocks is α = n1 / (n1+n2+n3)×100% = 6÷16×100% = 37.5%.
[0092] The probability of moderate injury is β = n² / (n₁ + n₂ + n₃) × 100% = 9 ÷ 16 × 100% = 56.25%.
[0093] The probability of severe injury is γ = n3 / (n1+n2+n3)×100% = 1÷16×100% = 6.25%.
[0094] The damage assessment method proposed in this invention can quickly quantify and predict the impact damage degree of composite cushion concrete slabs. It can be used to evaluate the impact resistance of reinforced concrete slabs of any cross-section covered by composite cushion layers of any thickness and any cross-section, providing a reference for the prevention and control of rockfall disasters in reinforced concrete slabs.
[0095] It should be noted that, in this document, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Unless otherwise specified, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.
[0096] The terminology used in the embodiments of this invention is for the purpose of describing particular embodiments only and is not intended to limit the invention. The singular forms “a,” “the,” and “the” as used in the embodiments of this invention and the appended claims are also intended to include the plural forms unless the context clearly indicates otherwise.
[0097] It should be understood that the term "and / or" used in this article is merely a description of the relationship between related objects, indicating that three relationships can exist. For example, A and / or B can represent: A existing alone, A and B existing simultaneously, and B existing alone. Additionally, the character " / " in this article generally indicates that the preceding and following related objects have an "or" relationship.
[0098] Depending on the context, the word "if" as used here can be interpreted as "when," "when," "in response to determination," or "in response to detection." Similarly, depending on the context, the phrase "if determination" or "if detection (of the stated condition or event)" can be interpreted as "when determination," "in response to determination," "when detection (of the stated condition or event)," or "in response to detection (of the stated condition or event)."
[0099] The terms "first" and "second" used in the embodiments are merely to distinguish similar objects and do not represent a specific ordering of objects. It is understood that "first" and "second" can be interchanged in a specific order or sequence where permitted. It should be understood that the objects distinguished by "first" and "second" can be interchanged where appropriate so that the embodiments described herein can be implemented in an order other than those illustrated or described herein.
[0100] Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.
Claims
1. A method for evaluating damage of a reinforced concrete slab based on M-V curve, characterized by, The method comprises the following steps: S1, determining the relevant design parameters of the reinforced concrete slab, specifically including: the thickness t of the concrete slab, the concrete strength f c , the reinforcement ratio p and the cushion type c; S2, according to the damage parameter k, the damage level is divided into slight damage, moderate damage, severe damage and failure, and the critical values β1, β2 and β3 of each damage level are calculated; S3, the critical values M0 and V0 in the prediction formula of the M-V damage evaluation curve when the damage parameter k is β1, β2 and β3 respectively are calculated; S4, substituting the calculated three sets of M0 and V0 critical values into the curve formula (M-M0)(V-V0)=1.25(M0 / 2+V0 / 2) 0.96 , drawing three M-V damage prediction curves of k=β1, k=β2, and k=β3. S5, scan the slope terrain, simulate and predict the motion trajectory of the rockfall of steep slope, analyze and obtain multiple sets of mass and speed combinations (m1, v1), (m2, v2)... (m n ,v n ); S6, input the actual mass and impact velocity (m i , v i ) of each rockfall, determine the position of the rockfall in the M-V damage prediction curve graph and determine the damage grade; S7, the number of falling rocks in the slight damage area n1, the number of falling rocks in the moderate damage area n2, the number of falling rocks in the severe damage area n3 and the number of falling rocks in the failure area n4 are counted, and the probabilities of slight damage, moderate damage, severe damage and failure of the reinforced concrete slab after being impacted by the falling rocks are determined according to the numbers.
2. The M-V curve-based reinforced concrete slab damage evaluation method according to claim 1, characterized by: In step S1, the thickness t of the concrete slab is 0.2-0.7 m.
3. The M-V curve-based reinforced concrete slab damage evaluation method according to claim 1, characterized by: In step S1, the concrete strength f c is valued between 30 and 80 MPa.
4. The M-V curve-based reinforced concrete slab damage evaluation method according to claim 1, characterized by: In step S1, the reinforcement ratio ρ is 0.002-0.0350.
5. The M-V curve-based reinforced concrete slab damage evaluation method according to claim 1, characterized by: In step S1, the cushion type c is the elastic modulus ratio of sand and other cushion materials, and is calculated by the following formula: c = (E _sand ×h _sand ) / (E _other ×h _other ) Wherein, E_sand is the elastic modulus of sand, h_sand is the thickness of the sand layer; E_other is the elastic modulus of other cushion materials, h_other is the thickness of the other cushion material layer.
6. The M-V curve-based reinforced concrete slab damage evaluation method according to claim 1, characterized by: In step S2, β1 is 0.15-0.3, β2 is 0.6-0.80, and β3 is 0.9-1.
0.
7. The M-V curve-based reinforced concrete slab damage evaluation method according to claim 1, characterized by: In step S3, when the damage parameter k is β1, β2 and β3 respectively, the calculation formulas of the critical values M0 and V0 in the prediction formula of the M-V damage evaluation curve are as follows: M0(β1) = exp(16.015β1t+ 0.145β1f c -24.96β1ρ-5.045β1c-2.834) V0(β1) = exp(7.9505β1t + 0.075β1f c -10.205β1ρ - 2.865β1c + 0.688) M0(β2) = exp(1.618β2t+ 0.015β2f c -0.9438β2ρ-0.348β2c-0.394) V0(β2) = exp(1.1488β2t + 0.0125β2f c -0.403β2ρ - 0.355β2c + 1.591) M0(β3) = exp(1.075β3t+0.0010β3f c -0.298β3ρ-0.289β3c-0.175) V0(β3) = exp(0.7897β3t + 0.008β3f c -0.367β3ρ - 0.380β3c + 1.792).
8. The M-V curve-based reinforced concrete slab damage evaluation method according to claim 1, characterized by: In step S5, the digital scanning technology is used to reconstruct the digital slope space information model, and the digital slope disaster model is established by combining the geological survey to determine the spatial position of the falling rock, the mass of the falling rock, the motion trajectory of the falling rock, the impact speed of the falling rock and the disaster range.
9. The M-V curve-based reinforced concrete slab damage evaluation method according to claim 1, characterized by: In step S6, the actual mass and impact velocity (mi, vi) of each rockfall are inputted, and the numerical value is calculated. i ) after calculation; When the value is located in the lower left of the k=β1 damage curve, the damage level is judged to be slight damage; When the value is located between k=β1 and k=β2, the damage level is judged to be moderate damage; When the value is located between k=β2 and k=β3, the damage level is judged to be severe damage; When the value is located in the upper right of the k=β3 damage curve, the damage level is judged to be failure.
10. The M-V curve-based reinforced concrete slab damage evaluation method according to claim 1, characterized by: In step S7, the damage probability calculation formula is as follows: Slight damage probability P1=n1 / N×100% Moderate damage probability P2=n2 / N×100% Severe damage probability P3=n3 / N×100% Failure probability P4=n4 / N×100% Wherein, N=n1+n2+n3+n4.