Method for calculating maximum transverse river direction stress of pier center section bottom

Abstract

The application discloses a method for calculating the maximum transverse river direction stress of the bottom of the center section of a gate pier, which comprises the following steps: step one, collecting data for calculation; step two, embedding a temperature sensor in the gate pier or obtaining the foundation temperature difference of the bottom of the gate pier by using a three-dimensional finite element method; step three, calculating the maximum transverse river direction temperature tensile stress σ max of the bottom of the center of the gate pier; and step four, calculating the maximum transverse river direction temperature tensile stress σ max of the bottom of the center section of the gate pier by using the following formula: σ max = σ max + σ max . The application has the advantages of simple calculation, high precision, reasonable reflection on the influence of the elastic modulus ratio of the gate pier to the bottom plate and the width of the bottom plate on the temperature stress of the cracking-prone position of the bottom of the gate pier, fast calculation of the maximum transverse river direction temperature stress of the bottom of the center section of the gate pier, small error and timely application in the temperature control and crack prevention work.

Description

Technical Field

[0001] This invention relates to the field of gate pier crack prevention technology, specifically to a method for calculating the maximum transverse stress at the bottom of the central section of a gate pier. Background Technology

[0002] The commissioning of large-scale water conservancy projects has helped achieve the "dual carbon" goals, injecting strong momentum into the sustainable development of the entire economy and society, promoting energy transformation, optimizing the energy structure, and moving towards clean, low-carbon, and high-efficiency goals. However, some problems remain despite this progress. Many completed or under-construction water conservancy projects contain thin concrete piers, which are highly susceptible to temperature stress, resulting in widespread cracking. Vertical, date-shaped cracks are prone to appear at the center bottom along the structural length, affecting project quality. Therefore, a formula for calculating the center bottom of gate piers that meets engineering design requirements is urgently needed. Academician Zhu Bofang previously proposed a method to estimate the maximum temperature stress at the bottom of the concrete pier based on the elastic modulus ratio of the foundation and the cast-in-place block. Therefore, it is necessary to build upon this method, incorporating the influence of the base plate width on the maximum transverse temperature stress at the bottom of the pier wall, and propose a new formula based on the structural characteristics of the gate pier. Summary of the Invention

[0003] The purpose of this invention is to overcome the above-mentioned shortcomings and provide a method for calculating the maximum transverse stress at the bottom of the central section of a gate pier. This method allows for a quick and easy calculation of the maximum transverse temperature tensile stress during the construction of the gate pier structure concrete under the constraint of the base plate. It can help improve related temperature control measures to achieve the purpose of crack prevention.

[0004] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is: a method for calculating the maximum transverse stress at the bottom of the central section of a gate pier, which includes the following steps:

[0005] Step 1: Collect the data used for calculation;

[0006] Step 2: Embed temperature sensors in the gate pier or calculate the foundation temperature difference at the bottom of the gate pier using the three-dimensional finite element method;

[0007] Step 3: Calculate the maximum transverse tensile temperature stress σ at the bottom center of the gate pier. max .

[0008] Furthermore, the data collected in step one includes the width of the base plate, the elastic modulus of the gate pier concrete, the elastic modulus of the base plate concrete, and the linear expansion coefficient of the gate pier concrete.

[0009] Furthermore, in step two, the highest and lowest temperatures are obtained by using temperature sensors embedded in the gate pier concrete, and the difference between them is used to obtain the foundation temperature difference; or the temperature field of the gate pier is calculated using the three-dimensional finite element method to obtain the foundation temperature difference.

[0010] Furthermore, in step three, σ max The calculation formula is as follows:

[0011]

[0012] In the formula: T is the base temperature difference, which is the difference between the highest and lowest temperatures during temperature changes; L is the width of the base plate; E c E represents the elastic modulus of the gate pier concrete. r denoted as the elastic modulus of the base slab concrete, and 'a' as the linear expansion coefficient of the gate pier concrete.

[0013] Furthermore, it also includes the following steps:

[0014] Step 4: Analyze the maximum transverse temperature stress at the bottom of the central section of the gate pier to study whether it affects the temperature control and crack prevention target, whether it is detrimental to the project quality, and take relevant measures.

[0015] Furthermore, the specific process of step four is as follows: collect concrete strength indicators and tensile strength, as well as the required temperature control and crack prevention indicators and temperature control scheme; then compare the calculated maximum transverse temperature stress with the tensile strength, and in combination with the design requirements, see if it exceeds the tensile strength, how large the safety margin is, and whether there is a risk of cracking; if it exceeds the tensile strength or the safety margin is small, it is necessary to strengthen temperature control measures and ensure the quality of the project from multiple aspects and angles.

[0016] Beneficial effects of this invention:

[0017] 1. This invention is simple to calculate and has high accuracy. It can reasonably reflect the influence of the elastic modulus ratio between the gate pier and the base plate and the width of the base plate on the temperature stress at the bottom of the gate pier where cracks are prone to occur. It can quickly calculate the maximum transverse temperature stress at the bottom of the central section of the gate pier with small error and can be applied to temperature control and crack prevention work in a timely manner.

[0018] 2. This invention can quickly and easily calculate the maximum transverse thermal tensile stress of the concrete structure of the gate pier under the constraint of the base plate during the construction period, which can help improve relevant temperature control measures to achieve the purpose of crack prevention; it can also be used for the calculation of thermal stress of thin-walled concrete structures, helping water conservancy and hydropower projects to predict thermal stress during the design and construction process. Attached Figure Description

[0019] Figure 1 This is a three-dimensional schematic diagram of the gate pier;

[0020] Figure 2 This is a finite element calculation model;

[0021] Figure 3A flowchart illustrating a method for calculating the maximum transverse stress at the bottom of the central section of a gate pier;

[0022] Figure 4 Temperature process curve at the bottom of the gate pier;

[0023] Figure 5 The transverse river stress process line at the bottom of the gate pier;

[0024] Figure 6 The stress process lines at the bottom of the gate pier under different elastic modulus ratios are shown. Detailed Implementation

[0025] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments.

[0026] Example 1: As Figure 3 As shown, a method for calculating the maximum transverse stress at the bottom of the central section of a gate pier includes the following steps:

[0027] Step 1: Collect the data used for calculation; the collected data includes the width of the base plate, the elastic modulus of the gate pier concrete, the elastic modulus of the base plate concrete, and the linear expansion coefficient of the gate pier concrete.

[0028] Step 2: Embed temperature sensors in the gate pier or calculate the foundation temperature difference at the bottom of the gate pier using the three-dimensional finite element method; that is, use temperature sensors embedded in the gate pier concrete to obtain the highest and lowest temperatures, and subtract them to obtain the foundation temperature difference; or use the three-dimensional finite element method to calculate the temperature field of the gate pier to obtain the foundation temperature difference.

[0029] Step 3: Calculate the maximum transverse tensile temperature stress σ at the bottom center of the gate pier. max .

[0030] σ max The calculation formula is as follows:

[0031]

[0032] In the formula: T is the base temperature difference, which is the difference between the highest and lowest temperatures during temperature changes; L is the width of the base plate; E c E represents the elastic modulus of the gate pier concrete. r denoted as the elastic modulus of the base slab concrete, and 'a' as the linear expansion coefficient of the gate pier concrete.

[0033] Step Four: Analyze the maximum transverse temperature stress at the bottom of the central section of the gate pier to study its impact on temperature control and crack prevention targets, whether it is detrimental to project quality, and take relevant measures. The specific process involves: collecting concrete strength indicators and tensile strength, as well as the required temperature control and crack prevention indicators and temperature control scheme; then comparing the calculated maximum transverse temperature stress with the tensile strength, and considering design requirements, determining whether it exceeds the tensile strength, the safety margin, and the risk of cracking; if it exceeds the tensile strength or the safety margin is too small, temperature control measures need to be strengthened, ensuring project quality from multiple aspects and angles.

[0034] Example 2:

[0035] Three-dimensional finite element method calculations were performed on gate pier models with different base slab widths and different elastic modulus ratios (elastic modulus of gate pier concrete / elastic modulus of base slab concrete). The results were compared with the calculated values ​​using formulas, and the implementation schemes were explained in detail. The gate pier forms are shown in [reference needed]. Figure 1 .

[0036] Assuming concrete is an isotropic material, its temperature field is calculated using the following equation:

[0037]

[0038] In the equation: τ: age, unit: d; a: thermal diffusivity, unit: m 2 / h; T: temperature, unit: ℃; θ: adiabatic temperature rise of concrete, unit: ℃; t: time, unit: d.

[0039] Boundary conditions: At the initial instant, the temperature field is a known function T0(x,y,z) of coordinates (x,y,z), that is, when τ=0,

[0040] T(x,y,z,0)=T0(x,y,z)

[0041] When in contact with air, the heat flow through the outside of the concrete material is given by the following formula, where λ is the thermal conductivity coefficient, and the unit is kJ / (m·h·℃).

[0042]

[0043] β is the surface heat transfer coefficient, with units of kJ / (m²). 2 ·h·℃); TT a (Concrete surface temperature - air temperature) is proportional to q (heat flow through the concrete surface), which is the third type of boundary condition, where n is the direction of the outward normal.

[0044]

[0045] The first type of boundary condition is that the concrete surface and water are in contact, and the temperature of the concrete surface is equal to the temperature of the water:

[0046] T(τ)=f(τ)

[0047] After the temperature field T of the concrete is solved, the temperature stress of each part needs to be further calculated.

[0048] Temperature deformation produces only linear strain, not shear strain; this linear strain can be considered as the initial strain of the object. When calculating temperature stress, first calculate the temperature-induced deformation ε0, and then obtain the equivalent nodal temperature load P caused by the corresponding initial strain. ε0 Then, the nodal displacements caused by temperature changes are obtained using the usual stress-solving methods, and then the temperature stress σ is obtained. The equivalent nodal temperature load of element e is... for:

[0049]

[0050] [B] is the transformation matrix between strain and displacement; [D] is the elasticity matrix.

[0051] The equivalent nodal load caused by temperature deformation can be used to... Combined with other load terms, the total stress, including temperature stress, is obtained.

[0052] The stress-strain relationship used to calculate stress includes an initial strain term:

[0053] σ=D(ε-ε0)

[0054] Overview of different models:

[0055] Working Condition 1: The model pier wall is 3m wide, 8m high, and 20m long; the base slab is 4m wide, 2m thick, and 20m long; the foundation is 20m wide, 40m high, and 20m long. The elastic modulus of the pier concrete is 33.5GPa, and the elastic modulus of the base slab concrete is 33.5GPa.

[0056] Condition 2: The model pier wall is 3m wide, 8m high, and 20m long; the base slab is 6m wide, 2m thick, and 20m long; the foundation is 20m wide, 40m high, and 20m long. The elastic modulus of the pier concrete is 33.5GPa, and the elastic modulus of the base slab concrete is 33.5GPa.

[0057] Working Condition 3: The model pier wall is 3m wide, 8m high, and 20m long; the base slab is 7m wide, 2m thick, and 20m long; the foundation is 20m wide, 40m high, and 20m long. The elastic modulus of the pier concrete is 33.5GPa, and the elastic modulus of the base slab concrete is 33.5GPa.

[0058] Condition 4: The model pier wall is 3m wide, 8m high, and 20m long; the base slab is 10m wide, 2m thick, and 20m long; the foundation is 20m wide, 40m high, and 20m long. The elastic modulus of the pier concrete is 33.5GPa, and the elastic modulus of the base slab concrete is 33.5GPa.

[0059] Condition 5: The model pier wall is 3m wide, 8m high, and 20m long; the base slab is 12m wide, 2m thick, and 20m long; the foundation is 20m wide, 40m high, and 20m long. The elastic modulus of the pier concrete is 33.5GPa, and the elastic modulus of the base slab concrete is 33.5GPa.

[0060] Condition 6: The model pier wall is 3m wide, 8m high, and 20m long; the base slab is 15m wide, 2m thick, and 20m long; the foundation is 20m wide, 40m high, and 20m long. The elastic modulus of the pier concrete is 33.5GPa, and the elastic modulus of the base slab concrete is 33.5GPa.

[0061] Condition 7: The model pier wall is 3m wide, 8m high, and 20m long; the base slab is 20m wide, 2m thick, and 20m long; the foundation is 20m wide, 40m high, and 20m long. The elastic modulus of the pier concrete is 33.5GPa, and the elastic modulus of the base slab concrete is 33.5GPa.

[0062] Working Condition 8: The model pier wall is 3m wide, 8m high, and 20m long; the base slab is 12m wide, 2m thick, and 20m long; the foundation is 20m wide, 40m high, and 20m long. The elastic modulus of the pier concrete is 33.5GPa, and the elastic modulus of the base slab concrete is 134GPa.

[0063] Working Condition 9: The model pier wall is 3m wide, 8m high, and 20m long; the base slab is 12m wide, 2m thick, and 20m long; the foundation is 20m wide, 40m high, and 20m long. The elastic modulus of the pier concrete is 33.5GPa, and the elastic modulus of the base slab concrete is 67GPa.

[0064] Working Condition 10: The model pier wall is 3m wide, 8m high, and 20m long; the base slab is 12m wide, 2m thick, and 20m long; the foundation is 20m wide, 40m high, and 20m long. The elastic modulus of the pier concrete is 33.5GPa, and the elastic modulus of the base slab concrete is 16.75GPa.

[0065] Working Condition 11: The model pier wall is 3m wide, 8m high, and 20m long; the base slab is 12m wide, 2m thick, and 20m long; the foundation is 20m wide, 40m high, and 20m long. The elastic modulus of the pier concrete is 33.5GPa, and the elastic modulus of the base slab concrete is 8.375GPa.

[0066] Temperature parameters are shown in Table 1, concrete parameters are shown in Table 2, and the calculation model is shown in Table 2. Figure 3Working conditions 8, 9, 10, and 11 use the same calculation model as working condition 5. Heat dissipation boundary conditions: the bottom of the foundation and its surrounding surfaces are adiabatic boundaries, and the upper surface is a third-type boundary; the concrete before pouring and covering is subject to third-type heat dissipation, including the influence of ambient temperature and sunlight on the structural surface; stress boundary conditions: normal constraints around the bedrock, and three-dimensional constraints at the bottom. A typical point is taken at the center section of the gate pier, 0.3m from the bottom slab.

[0067] Table 1 Temperature Parameters

[0068]

[0069] Table 2 Thermodynamic parameters of concrete

[0070]

[0071] Table 3 Comparison of Operating Conditions

[0072]

[0073] According to the formula:

[0074] In the formula: T is the base temperature difference, which is the difference between the highest and lowest temperatures during temperature changes; L is the width of the base plate; E c E represents the elastic modulus of the gate pier concrete. r This refers to the elastic modulus of the base slab concrete.

[0075] The maximum transverse temperature tensile stress obtained from the formula is as follows, and it is compared with the results obtained using three-dimensional finite element software.

[0076] Table 4 Comparison of Calculation Results

[0077] 1 -0.39 -0.35 -5.41％ 2 0.09 0.06 -33.33％ 3 0.22 0.20 -9.09％ 4 0.47 0.48 2.13％ 5 0.56 0.58 3.57％ 6 0.64 0.67 4.69％ 7 0.81 0.74 -8.64％ 8 0.65 0.66 1.54％ 9 0.62 0.63 1.61％ 10 0.47 0.50 6.38％ 11 0.36 0.35 -2.78％

[0078] As can be seen from the table above, the error between the maximum temperature stress value calculated by the formula and the finite element calculation result is small. Except for working condition 2, the calculation errors of the others are all between -10% and 7% (the error of working condition 2 is only 0.03MPa, because its stress is small, so the ratio is large).

[0079] Based on the comparative analysis, the calculated values ​​from the formula are not significantly different from those from the finite element method, therefore the formula is reasonable and reliable.

[0080] After obtaining the maximum transverse tensile stress at the bottom of the gate pier during the project, the rationality of the current temperature control scheme can be evaluated based on the magnitude of the tensile stress, and the results can be analyzed. In this example, operating conditions 4, 5, 6, and 7 are selected for analysis to study their temperature history lines and stress process lines.

[0081] By comparing the temperature process curves of typical points at the same location of the gate pier under operating conditions 4, 5, 6, and 7, the influence of the base slab width on the temperature at the bottom of the pier wall is derived. Figure 4 As we can see, the temperature curves for the four working conditions are basically the same, with very little difference. The highest temperature is reached on the fourth day after pouring, and then the lowest temperature is reached when winter arrives. As the seasons change and spring arrives the following year, the temperature inside the concrete also begins to rise as the air temperature rises.

[0082] By comparing the transverse stress process curves of the gate pier at the same typical location under working conditions 4, 5, 6, and 7, from... Figure 5 It can be seen that the temperature and stress process lines are inversely correlated; that is, high temperatures generally exhibit compressive stress, while low temperatures generally exhibit tensile stress. As the temperature decreases, compressive stress gradually transforms into tensile stress, with the maximum tensile stress occurring at the lowest temperature. Increasing the width of the base plate will increase the tensile stress at typical points, indicating that if the base plate is too wide, it will generate significant tensile stress, which is detrimental to crack prevention. For example, in working condition 7, the stress at the bottom of the gate pier is significantly greater than in other working conditions. Therefore, in actual engineering, care should be taken to ensure that the base plate is not too wide, as this will increase the transverse tensile stress at the bottom of the pier wall, making it prone to cracking.

[0083] By comparing the transverse stress process curves of typical points at the same location on the gate pier under working conditions 5, 8, 9, 10, and 11, the influence of different elastic modulus ratios (gate pier elastic modulus / bottom plate elastic modulus) on the transverse temperature stress at the center bottom of the gate pier was compared under the same base plate width. Figure 6 It can be seen that the larger the elastic modulus ratio, the smaller the tensile stress generated. Not only does the maximum tensile stress decrease, but the tensile stress throughout the entire cooling process also decreases accordingly.

[0084] The above embodiments are merely preferred technical solutions of the present invention and should not be considered as limitations on the present invention. The scope of protection of the present invention should be limited to the technical solutions described in the claims, including equivalent substitutions of the technical features described in the claims. That is, equivalent substitutions and improvements within this scope are also within the scope of protection of the present invention.

Claims

1. A method for calculating the maximum transverse stress at the bottom of the central section of a gate pier, characterized in that: It includes the following steps: Step 1: Collect the data used for calculation; Step 2: Embed temperature sensors in the gate pier or calculate the foundation temperature difference at the bottom of the gate pier using the three-dimensional finite element method; Step 3: Calculate the maximum transverse tensile temperature stress σ at the bottom center of the gate pier. max ; The data collected in step one includes the width of the base plate, the elastic modulus of the gate pier concrete, the elastic modulus of the base plate concrete, and the linear expansion coefficient of the gate pier concrete. In step three, σ max The calculation formula is as follows: σ max = [-0.4016EXP(-0.2154* L )+0.1336EXP(-0.1168* )]; In the formula: The base temperature difference is the difference between the highest and lowest temperatures during a temperature change; L is the width of the base plate. The elastic modulus of the gate pier concrete; This refers to the elastic modulus of the base slab concrete. The coefficient of linear expansion of the gate pier concrete is given.

2. The method for calculating the maximum transverse stress at the bottom of the central section of a gate pier according to claim 1, characterized in that: In step two, the highest and lowest temperatures are obtained by using temperature sensors embedded in the gate pier concrete, and the difference between them is used to obtain the foundation temperature difference; or the temperature field of the gate pier is calculated using the three-dimensional finite element method to obtain the foundation temperature difference.

3. The method for calculating the maximum transverse stress at the bottom of the central section of a gate pier according to claim 1, characterized in that: It also includes the following steps: Step 4: Analyze the maximum transverse temperature stress at the bottom of the central section of the gate pier to study whether it affects the temperature control and crack prevention target, whether it is detrimental to the project quality, and take relevant measures.

4. The method for calculating the maximum transverse stress at the bottom of the central section of a gate pier according to claim 3, characterized in that: The specific process of step four is as follows: collect concrete strength indicators and tensile strength, as well as the required temperature control and crack prevention indicators and temperature control scheme; then compare the calculated maximum transverse temperature stress with the tensile strength, and in combination with the design requirements, see if it exceeds the tensile strength, how large the safety margin is, and whether there is a risk of cracking; if it exceeds the tensile strength or the safety margin is small, it is necessary to strengthen temperature control measures and ensure the quality of the project from multiple aspects and angles.

Images