Evaluation method of ultimate bearing capacity of stone arch bridge based on load failure coefficient

Abstract

The application discloses a kind of stone arch bridge ultimate bearing capacity evaluation methods based on load damage coefficient, which can be according to the condition of heavy vehicle and the basic parameter of stone arch bridge, solve the ultimate bearing capacity of stone arch bridge;Compared with equivalent beam-column method, the aforementioned scheme considers the sliding damage and hinge damage between the masonry of stone arch ring, the accuracy is greatly improved, compared with finite element method, the scheme avoids obtaining some basic parameters representing joint interface;The beneficial technical effects of the application are: a kind of stone arch bridge ultimate bearing capacity evaluation methods based on load damage coefficient is proposed, and the evaluation accuracy can be greatly improved under the condition of limited known parameters.

Description

Technical Field

[0001] This invention relates to a health assessment technology for stone arch bridges, and more particularly to a method for evaluating the ultimate bearing capacity of stone arch bridges based on load failure coefficients. Background Technology

[0002] Although the construction of new stone arch bridges has ceased in recent years, they remain widely distributed throughout my country's highway network. Due to factors such as surrounding development, stone arch bridges located on county and township roads inevitably require the passage of heavy vehicles, making accurate assessment of their ultimate bearing capacity of significant engineering application value.

[0003] There are two main methods for assessing the ultimate bearing capacity of stone arch bridges in the existing technology. One is the equivalent beam-column method, which treats the arch as an equivalent beam-column and uses the beam-column bearing capacity calculation formula to calculate the arch's bearing capacity. This method is simple to operate and is adopted by JTG / T J21-2011 "Specification for Testing and Evaluation of Bearing Capacity of Highway Bridges". However, this method does not take into account the influence of dead load. At the same time, it mainly considers the action of a single concentrated load and is rarely applied to the situation of multiple loads acting together. This results in the assessment result being significantly lower than the actual bearing capacity, causing the stone arch bridge to be demolished unnecessarily and resulting in a waste of resources.

[0004] Another method is the finite element method. When the parameter values ​​are consistent with reality, the evaluation results can be very close to the actual bearing capacity. However, unlike the main arch ring of a reinforced concrete arch bridge, which can be regarded as a homogeneous material, the main arch ring of a stone arch bridge is composed of masonry blocks and masonry joints, which are non-homogeneous materials. The tensile, compressive-shear, and tensile-shear constitutive models of the masonry joints are difficult to describe accurately, so it is difficult to accurately evaluate its ultimate bearing capacity.

[0005] In conclusion, how to accurately and quickly assess the ultimate bearing capacity of stone arch bridges has become a problem that urgently needs to be solved by those skilled in the art. Summary of the Invention

[0006] To address the problems in the background art, this invention proposes a method for evaluating the ultimate bearing capacity of stone arch bridges based on load failure coefficients. Its innovation lies in the following: the method for evaluating the ultimate bearing capacity of stone arch bridges includes:

[0007] Obtain the basic parameters of the stone arch bridge; determine the dead load parameters of the upper structure of the arch rib based on the basic parameters; divide the arch rib into n blocks along the arch axis according to the location of the masonry joints, distribute the dead load to each block, and obtain the load borne by each block; statistically analyze the situation of common heavy vehicles in the location of the stone arch bridge, including wheelbase parameters, load parameters, and front and rear axle load distribution;

[0008] For each type of heavy vehicle, the corresponding ultimate bearing capacity of the stone arch bridge is determined according to the following steps:

[0009] 1) Based on the wheelbase parameters, load parameters, and front and rear axle load distribution of heavy vehicles, simulate the load arrangement along the bridge span direction: make the maximum axle load located at 8 positions on the bridge span: 0L, L / 8, 2L / 8, 3L / 8, 4L / 8, 5L / 8, 6L / 8, 7L / 8, and L. When the maximum axle load is located at a certain position, calculate the live load parameters of each block; when calculating the live load parameters, the live load is diffused and transferred in the bridge deck pavement and arch fill at 45°.

[0010] 2) Based on the positional relationships of the blocks and their equilibrium relationships under external loads, construct the block equilibrium equations for each block; the external loads include corresponding load and live load parameters; obtain the equilibrium matrix Eq-λf containing all blocks based on the block equilibrium equations. L =f D Where E is a 3n×3(n+1) matrix, q is the stress component, λ is the load failure factor, and f L For the live load component, f D This is the constant load component;

[0011] 3) The front faces of blocks 1 to n and the rear face of block n form a total of n+1 cross sections; construct the following constraint equations:

[0012] |S i |≤μN i ,|M i |≤0.5sN i

[0013] S i Let N be the shear force at the i-th section. i M is the axial force at the i-th cross section. i Let be the bending moment at the i-th section, μ be the friction coefficient (μ is taken as 0.6), and s be the arch thickness.

[0014] 4) Based on the equilibrium matrix and constraint equations, the solution matrix at the corresponding cross-sectional location is obtained:

[0015] maxλ

[0016]

[0017] The solution matrix yields the load failure coefficient at a given location and the corresponding stress components at each cross-sectional location.

[0018] Based on the solution matrix, eight load failure factors are obtained when the maximum axle load is located at the eight positions of the bridge span: 0L, L / 8, 2L / 8, 3L / 8, 4L / 8, 5L / 8, 6L / 8, 7L / 8, and L. The minimum value among the eight load failure factors is denoted as the ultimate failure factor. The product of the ultimate failure factor and the weight of the heavy vehicle is the ultimate bearing capacity of the stone arch bridge under the corresponding heavy vehicle condition.

[0019] Compared to the equivalent beam-column method, the aforementioned scheme considers the possible sliding failure and hinge failure between masonry sections of the stone arch ring, which greatly improves the accuracy. Compared to the finite element method, this scheme avoids obtaining some basic parameters characterizing the masonry joint interface, such as internal friction angle, cohesion, and shear dilatation angle, and can more accurately predict the ultimate bearing capacity.

[0020] The beneficial technical effect of this invention is that it proposes a method for evaluating the ultimate bearing capacity of stone arch bridges based on the load failure coefficient. This method can significantly improve the accuracy of the evaluation under the condition of limited known parameters. Attached Figure Description

[0021] Figure 1 Schematic diagram of a stone arch bridge;

[0022] Figure 2 Calculation diagram after discretization of the arch rib;

[0023] Figure 3 A schematic diagram of the axle load and wheelbase of the heavy-duty vehicle in the embodiment;

[0024] Figure 4 Schematic diagram of the forces acting on the block;

[0025] The names corresponding to the various markings in the diagram are as follows: 1. Arch base, 2. Masonry joint, 3. Stone block, 4. Arch filler, 5. Bridge deck paving. Detailed Implementation

[0026] A method for evaluating the ultimate bearing capacity of a stone arch bridge based on the load failure coefficient, characterized in that: the method for evaluating the ultimate bearing capacity of a stone arch bridge includes:

[0027] Obtain the basic parameters of the stone arch bridge; determine the dead load parameters of the upper structure of the arch rib based on the basic parameters; divide the arch rib into n blocks along the arch axis according to the location of the masonry joints, distribute the dead load to each block, and obtain the load borne by each block; statistically analyze the situation of common heavy vehicles in the location of the stone arch bridge, including wheelbase parameters, load parameters, and front and rear axle load distribution;

[0028] For each type of heavy vehicle, the corresponding ultimate bearing capacity of the stone arch bridge is determined according to the following steps:

[0029] 1) Based on the wheelbase parameters, load parameters, and front and rear axle load distribution of heavy vehicles, simulate the load arrangement along the bridge span direction: make the maximum axle load located at 8 positions on the bridge span: 0L, L / 8, 2L / 8, 3L / 8, 4L / 8, 5L / 8, 6L / 8, 7L / 8, and L. When the maximum axle load is located at a certain position, calculate the live load parameters of each block; when calculating the live load parameters, the live load is diffused and transferred in the bridge deck pavement and arch fill at 45°.

[0030] 2) Based on the positional relationships of the blocks and their equilibrium relationships under external loads, construct the block equilibrium equations for each block; the external loads include corresponding load and live load parameters; obtain the equilibrium matrix Eq-λf containing all blocks based on the block equilibrium equations. L =f D Where E is a 3n×3(n+1) matrix, q is the stress component, λ is the load failure factor, and f L For the live load component, f D This is the constant load component;

[0031] 3) The front faces of blocks 1 to n and the rear face of block n form a total of n+1 cross sections; construct the following constraint equations:

[0032] |S i |≤μN i ,|M i |≤0.5sN i

[0033] S i Let N be the shear force at the i-th section. i M is the axial force at the i-th cross section. i Let be the bending moment at the i-th section, μ be the friction coefficient (μ is taken as 0.6), and s be the arch thickness.

[0034] 4) Based on the equilibrium matrix and constraint equations, the solution matrix at the corresponding cross-sectional location is obtained:

[0035] maxλ

[0036]

[0037] The solution matrix yields the load failure coefficient at a given location and the corresponding stress components at each cross-sectional location.

[0038] Based on the solution matrix, eight load failure factors are obtained when the maximum axle load is located at the eight positions of the bridge span: 0L, L / 8, 2L / 8, 3L / 8, 4L / 8, 5L / 8, 6L / 8, 7L / 8, and L. The minimum value among the eight load failure factors is denoted as the ultimate failure factor. The product of the ultimate failure factor and the weight of the heavy vehicle is the ultimate bearing capacity of the stone arch bridge under the corresponding heavy vehicle condition.

[0039] Example:

[0040] like Figure 1 As shown, a solid-web stone arch bridge with a span of 20m is located on a rural road. Normally, small vehicles pass through it. Recently, due to the construction of surrounding projects, it is necessary to allow the passage of overweight vehicles for a long time. When the vehicles are fully loaded, they can weigh up to 80 tons. However, the actual load-bearing capacity of the bridge is still unclear and needs to be evaluated. The present invention is used to evaluate the load-bearing capacity of the bridge.

[0041] The stone arch bridge to be evaluated is a hingeless arch bridge with a span of 20m, a rise-to-span ratio of 1 / 5, and a circular arch. The discretized calculation diagram is as follows: Figure 2 As shown, at this time n=60. According to the principle that each block shares the dead load of the superstructure, the weight of the bridge deck pavement, the arch fill material, and the dead load acting on each block can be calculated based on the unit weight of each material.

[0042] The axle load and wheelbase of the heavy vehicles waiting to pass are as follows: Figure 3 As shown, the concentrated force is obviously greatest at the center points of the two rear axles. Therefore, the load failure coefficients are calculated by applying the center points to eight locations on the bridge span: 0L, L / 8, 2L / 8, 3L / 8, 4L / 8, 5L / 8, 6L / 8, 7L / 8, and L. The minimum value of these values ​​can be used to evaluate whether the bridge can accommodate heavy vehicles.

[0043] Taking the rear axle center point acting at L / 4 of the bridge span as an example, based on the live load being diffused and transmitted at 45° in the bridge deck pavement and arch fill, the influence area of ​​the rear axle is the 8th to 20th blocks, and the magnitude of the load is 59kN.

[0044] The force situation of any block is as follows Figure 4 As shown, by combining the positional relationships of the blocks, equilibrium equations can be constructed. The equilibrium equation for any block is as follows:

[0045]

[0046] In the formula,

[0047]

[0048]

[0049]

[0050] (x0, y0) is the center point of the block, (x i ,y i (x) represents the centroid of the front section of the block. i+1 ,y i+1 ) represents the centroid of the rear section of the block.

[0051] This yields the balance matrix Eq-λf containing all blocks. L =f D ;

[0052] Where E is a 60×63 matrix, related to the position of the block, and composed of the sine and cosine values ​​of its location. The stress component q can be expressed as q T ={N1,S1,M1,N2,S2,M2,……N 20 ,S 20 M 20 N 21 ,S 21 M 21}

[0053] Construct the following constraint equations:

[0054] |S i |≤μN i ,|M i |≤0.5sN i

[0055] μ is set to 0.6, and s can be obtained from the basic parameters;

[0056] The following solution matrix can be obtained from this:

[0057] Maxλ

[0058]

[0059] At this point, the problem is transformed into solving a linear programming problem. When the center point of the rear axle acts at position L / 4, the load failure factor of the rear axle at all other positions is 0.70. Similarly, the load failure factors at other positions can be obtained, as shown in the table below:

[0060] damage coefficient 3 0.93 0.70 0.80 1.11 0.72 0.61 0.96 3.5

[0061] As can be seen from the table, the minimum load failure factor is 0.70, which means that the maximum vehicle load that the bridge can withstand is 80 × 0.7 = 56 tons. Therefore, it is necessary to reduce the load for passage or to reinforce the bridge.

Claims

1. A method for evaluating the ultimate bearing capacity of a stone arch bridge based on the load failure coefficient, characterized in that: The method for evaluating the ultimate bearing capacity of stone arch bridges includes: Obtain the basic parameters of the stone arch bridge; determine the dead load parameters of the upper structure of the arch rib based on the basic parameters; divide the arch rib into n blocks along the arch axis according to the location of the masonry joints, distribute the dead load to each block, and obtain the load borne by each block; statistically analyze the situation of common heavy vehicles in the location of the stone arch bridge, including wheelbase parameters, load parameters, and front and rear axle load distribution; For each type of heavy vehicle, the corresponding ultimate bearing capacity of the stone arch bridge is determined according to the following steps: 1) Based on the wheelbase parameters, load parameters, and front and rear axle load distribution of heavy vehicles, simulate the load arrangement along the bridge span direction: make the maximum axle load located at 8 positions on the bridge span: 0L, L / 8, 2L / 8, 3L / 8, 4L / 8, 5L / 8, 6L / 8, 7L / 8, and L. When the maximum axle load is located at a certain position, calculate the live load parameters of each block; when calculating the live load parameters, the live load is diffused and transferred in the bridge deck pavement and arch fill at 45°. 2) Based on the positional relationships of the blocks and their equilibrium relationships under external loads, construct the block equilibrium equations for each block; the external loads include corresponding load and live load parameters; obtain the equilibrium matrix Eq-λf containing all blocks based on the block equilibrium equations. L =f D Where E is a 3n×3(n+1) matrix, q is the stress component, λ is the load failure factor, and f L For the live load component, f D This is the constant load component; 3) The front faces of blocks 1 to n and the rear face of block n form a total of n+1 cross sections; construct the following constraint equations: |S i |≤μN i ,|M i |≤0.5sN i S i Let N be the shear force at the i-th section. i M is the axial force at the i-th cross-section. i Let be the bending moment at the i-th section, μ be the friction coefficient (μ is taken as 0.6), and s be the arch thickness. 4) Based on the equilibrium matrix and constraint equations, the solution matrix at the corresponding cross-sectional location is obtained: maxλ The solution matrix yields the load failure coefficient at a given location and the corresponding stress components at each cross-sectional location. Based on the solution matrix, eight load failure factors are obtained when the maximum axle load is located at the eight positions of the bridge span: 0L, L / 8, 2L / 8, 3L / 8, 4L / 8, 5L / 8, 6L / 8, 7L / 8, and L. The minimum value among the eight load failure factors is denoted as the ultimate failure factor. The product of the ultimate failure factor and the weight of the heavy vehicle is the ultimate bearing capacity of the stone arch bridge under the corresponding heavy vehicle condition.

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