Method and system for calculating covering soil thickness of shallow covering soil UHPC culvert

Abstract

The invention relates to a shallow soil covering UHPC culvert soil covering thickness calculation method and system, and the method comprises the steps: obtaining a uniformly distributed load of a vehicle load diffused to a culvert top plate based on a vehicle vertical load, a wheel landing area size and a vehicle load diffusion angle; based on the uniformly distributed load and the width and the thickness of the culvert top plate, the normal stress at the maximum mid-span bending moment of the culvert top plate, the shear stress at the maximum shear force and the coupling stress at the bending-shear coupling position are obtained; comparing the normal stress, the shear stress and the coupling stress, and taking the maximum value; and determining the minimum soil covering thickness of the culvert based on the comparison of the maximum value and the concrete material performance parameters. According to the method, the uniformly distributed load is obtained based on vehicle load diffusion, the normal stress at the maximum mid-span bending moment of the culvert top plate, the shear stress at the maximum shear force and the coupling stress at the bending-shear coupling position are calculated, the maximum value of the three is compared with the tensile strength of the concrete material, and therefore the minimum soil covering thickness of the culvert is determined.

Description

Technical Field

[0001] This application relates to the field of construction engineering, specifically to a method and system for calculating the overburden thickness of shallow overburden UHPC culverts. Background Technology

[0002] Against the backdrop of insufficient performance of traditional culverts, urgent need for infrastructure upgrades, and promotion of green building policies, UHPC precast culverts, with their superior material properties, efficient construction processes, and significant life-cycle advantages, are becoming a key technological innovation direction for solving technical challenges in culvert engineering and promoting high-quality infrastructure development.

[0003] Currently, UHPC has accumulated rich experience in applications such as bridge component connections and bridge deck paving, laying a technical foundation for its large-scale application in culvert engineering. However, in existing highway culvert design specifications, the design calculation of the culvert top slab only considers bending moment and does not calculate the effect of shear force. But in the case of shallow overburden, the top slab will be subjected to bending moment and shear force. Traditional methods, by ignoring the shear force effect, cannot accurately determine the safe overburden thickness under shallow overburden conditions. This may lead to structural safety risks due to excessively thin overburden, or it may increase project costs due to overly conservative approaches. Summary of the Invention

[0004] This application provides a method and system for calculating the overburden thickness of shallow-covered UHPC culverts, which can solve the problem in the prior art that the shear effect is ignored in the strength design of the culvert top slab, resulting in the inability to determine the overburden thickness to ensure the safety of the top slab under shallow overburden conditions.

[0005] In a first aspect, embodiments of this application provide a method for calculating the overburden thickness of shallow-covered UHPC culverts, which includes: Based on the vehicle's vertical load, the size of the wheel contact area, and the vehicle load diffusion angle, the uniformly distributed load that the vehicle load diffuses to the top of the culvert is obtained. Based on the uniformly distributed load and the width and thickness of the culvert top slab, the normal stress at the mid-span bending moment of the culvert top slab with the maximum bending moment, the shear stress at the maximum shear force, and the coupling stress at the bending-shear coupling point are obtained. Compare the normal stress, shear stress, and coupled stress, and take the maximum value; Based on the comparison between the maximum value and the performance parameters of the concrete material, the minimum soil cover thickness of the culvert is determined.

[0006] In conjunction with the first aspect, in one embodiment, the dimensions of the wheel contact area include: the length of the wheel contact area and the width of the wheel contact area; Based on the vehicle's vertical load, the wheel contact area size, and the culvert roof width, the uniformly distributed load that spreads from the vehicle load to the culvert roof is obtained, specifically including: Based on the vehicle load diffusion angle, the length of the wheel contact area and the width of the wheel contact area, the length and width of the load diffusion area are obtained. Based on the vehicle's vertical load, the length of the wheel contact area, and the width of the wheel contact area, the uniformly distributed load that spreads from the vehicle load to the culvert roof is obtained.

[0007] In conjunction with the first aspect, in one implementation, based on the uniformly distributed load and the width and thickness of the culvert top slab, the normal stress at the mid-span point of maximum bending moment, the shear stress at the point of maximum shear force, and the coupled stress at the bending-shear coupling point of the culvert top slab are obtained, specifically including: Based on the uniformly distributed load and the width and thickness of the culvert top slab, the normal stress at the point of maximum mid-span bending moment of the culvert top slab is obtained. Based on the uniformly distributed load and the thickness of the culvert top slab, the shear stress at the point of maximum shear force on the culvert top slab is obtained. Based on the uniformly distributed load, the width and thickness of the culvert top slab, and the principal stress and minimum normal stress generated by the coupling effect of bending moment and shear force, the coupling stress at the bending-shear coupling point of the culvert top slab is obtained.

[0008] In conjunction with the first aspect, in one implementation, based on the uniformly distributed load and the width and thickness of the culvert top slab, the normal stress at the point of maximum mid-span bending moment of the culvert top slab is obtained, specifically including: Based on the uniformly distributed load and the width of the culvert top slab, the mid-span bending moment of the culvert top slab is obtained; Based on the mid-span bending moment and the thickness of the culvert top slab, the maximum normal stress at the point where the bending moment of the culvert top slab is maximum is obtained.

[0009] In conjunction with the first aspect, in one implementation, the shear stress at the point of maximum shear force on the culvert roof slab is obtained based on the uniformly distributed load and the thickness of the culvert roof slab, specifically including: Based on the uniformly distributed load, the shear force of the culvert top slab is obtained; Based on the shear force and the thickness of the culvert top slab, the shear stress at the point where the shear force of the culvert top slab is maximum is obtained.

[0010] In conjunction with the first aspect, in one embodiment, the coupling stress at the bending-shear coupling point of the culvert top slab is obtained based on the uniformly distributed load, the width and thickness of the culvert top slab, and the principal stress and minimum normal stress generated by the coupling effect of bending moment and shear force. Specifically, this includes: Based on the uniformly distributed load, the width and thickness of the culvert top slab, and the straight-line distance between the centroidal axis of the section at the set position and the bending-shear coupling position, the moment of inertia at the set position of the centroid of the section at the distance from the bending-shear coupling position in the culvert top slab is obtained. Based on the uniformly distributed load and the width of the culvert top slab, the bending moment at the bending-shear coupling point of the culvert top slab is obtained; Based on the uniformly distributed load, the shear force of the culvert top slab is obtained; Based on the width and thickness of the culvert top slab and the straight-line distance between the centroid axis of the cross section at the set position and the bending-shear coupling position, the first moment at the set position of the centroid of the cross section is obtained; Based on bending moment, shear force, culvert top slab thickness, moment of inertia, and first moment, the principal stress and minimum normal stress are obtained; Based on the principal stress, minimum normal stress, and concrete material properties, and using Mohr's strength theory, the coupled stress at the bending-shear coupling point of the culvert top slab is obtained.

[0011] In conjunction with the first aspect, in one implementation, the principal stresses and minimum normal stresses are obtained based on bending moment, shear force, culvert top slab thickness, moment of inertia, and first-order moment, specifically including: Based on bending moment, shear force, culvert top slab thickness, moment of inertia, and first moment, the normal stress and shear stress at a set position away from the centroid of the section are obtained; Based on normal stress and shear stress, the principal stress and minimum normal stress are obtained.

[0012] In conjunction with the first aspect, in one implementation, the normal stress and shear stress at a predetermined location at a distance from the centroid of the cross-section are obtained based on the bending moment, shear force, culvert top slab thickness, moment of inertia, and first moment. Specifically, this includes: Based on the bending moment, the thickness of the culvert top slab, and the moment of inertia, the normal stress at a set position away from the centroid of the cross section is obtained; Based on shear force, first moment, culvert top plate thickness, and moment of inertia, the shear stress at a set position away from the centroid of the cross section is obtained.

[0013] In conjunction with the first aspect, in one embodiment, the concrete material performance parameters include concrete tensile strength and concrete shear strength; Based on the comparison between the maximum value and the concrete material performance parameters, the minimum soil cover thickness of the culvert is determined, specifically including: When the maximum value is normal stress or coupled stress, the maximum value is compared with the tensile strength of concrete to ensure that the maximum value does not exceed the tensile strength of concrete, and the minimum soil cover thickness of the culvert is determined. When the maximum value is shear stress, the maximum value is compared with the concrete shear strength to ensure that the maximum value does not exceed the concrete shear strength, thereby determining the minimum soil cover thickness for the culvert.

[0014] Secondly, this application provides a shallow-cover UHPC culvert cover thickness calculation system, which includes: a first module, a second module, a third module, and a fourth module; the first module is used to obtain the uniformly distributed load of the vehicle load diffused to the top slab of the culvert based on the vehicle vertical load, the wheel contact area size, and the vehicle load diffusion angle; the second module is used to obtain the normal stress at the mid-span bending moment of the culvert top slab, the shear stress at the shear force at the mid-span bending moment, and the coupling stress at the bending-shear coupling point based on the uniformly distributed load, the width and thickness of the culvert top slab; the third module is used to compare the normal stress, shear stress, and coupling stress and take the maximum value; the fourth module is used to determine the minimum cover thickness of the culvert based on the comparison of the maximum value with the concrete material performance parameters.

[0015] The beneficial effects of the technical solutions provided in this application include: This application provides a method and system for calculating the soil cover thickness of shallow-covered UHPC culverts. By obtaining the uniformly distributed load based on vehicle load diffusion, the normal stress at the mid-span of the culvert top slab where the bending moment is maximum, the shear stress at the point where the shear force is maximum, and the coupled stress at the bending-shear coupling point are calculated. The maximum value of the three values ​​is compared with the performance parameters of the concrete material to determine the minimum soil cover thickness of the culvert. This solves the defect of traditional culvert design that only considers the bending moment and ignores the shear force effect.

[0016] Compared to existing standards, the shallow overburden condition additionally considers the shear effect of vehicle loads on the culvert roof slab and the bending-shear coupling effect, avoiding safety risks that may arise from neglecting shear effects in traditional designs. By introducing the calculation of coupled stress at the bending-shear coupling point (based on a comprehensive analysis of normal stress and shear stress), it ensures that the maximum stress value truly reflects the actual stress state of the roof slab, avoiding safety risks (such as roof slab cracking and failure due to excessively thin overburden) or engineering waste (such as increased material and construction costs due to excessively thick overburden) that may arise from neglecting shear effects in traditional designs. Ultimately, this calculation method optimizes the overburden thickness while ensuring structural safety, enabling UHPC culverts to meet strength requirements under shallow overburden conditions while avoiding overly conservative designs, thus improving engineering economy and safety. Attached Figure Description

[0017] Figure 1 This is a flowchart illustrating the method for calculating the overburden thickness of shallow-covered UHPC culverts in this application. Figure 2 This is a schematic diagram illustrating the calculation of vehicle load diffusion to the culvert in this application; Figure 3 A simplified calculation diagram of the vehicle load propagation onto the culvert roof slab in this application; Figure 4 This is a bending moment diagram of the culvert roof slab under vehicle load in this application; Figure 5This is a shear force diagram of the culvert roof slab under vehicle load in this application; Figure 6 This is a normal stress diagram of the culvert top slab section in this application; Figure 7 This is a diagram showing the shear stress of the culvert top slab section in this application; Figure 8 This is a schematic diagram showing the location of the normal stress and shear stress corresponding to the third case in the cross-section of the culvert top plate of this application.

[0018] In the picture: 1. Vehicle wheels; 2. Culvert; 3. Culvert roof. Detailed Implementation

[0019] To enable those skilled in the art to better understand the present application, the technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present application, and not all embodiments. Based on the embodiments in the present application, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present application.

[0020] This application provides a method and system for calculating the overburden thickness of shallow-covered UHPC culverts, which can solve the problem in the prior art that the shear effect is ignored in the strength design of the culvert top slab, resulting in the inability to determine the overburden thickness to ensure the safety of the top slab under shallow overburden conditions.

[0021] To make the objectives, technical solutions, and advantages of this application clearer, the embodiments of this application will be described in further detail below with reference to the accompanying drawings.

[0022] In a first aspect, embodiments of this application provide a method for calculating the overburden thickness of shallow-covered UHPC culverts, which includes: 101: Based on vehicle vertical load Wheel contact area size, vehicle load spread angle Obtain the uniformly distributed load of the vehicle load spreading to the top slab 3 of the culvert. ; 102: Based on uniformly distributed load and the culvert top slab 3 width and thickness Obtain the normal stress at the point of maximum bending moment at mid-span of the culvert top slab. Shear stress at the point of maximum shear force Coupled stress at the bending-shear coupling point ; 103: Comparison of normal stress Shear stress and coupling stress Take the maximum value; 104: Based on the comparison of the maximum value and the performance parameters of concrete materials, the minimum soil cover thickness of culvert 2 is determined.

[0023] In this application, the uniformly distributed load is obtained based on the diffusion of vehicle load, and the normal stress at the mid-span of the culvert top slab with the maximum bending moment, the shear stress at the maximum shear force, and the coupled stress at the bending-shear coupling point are calculated. The maximum value of the three values ​​is compared with the tensile strength of the concrete material to determine the minimum soil cover thickness of the culvert 2. This solves the defect of traditional culvert design that only considers the bending moment and ignores the shear force effect.

[0024] Compared to existing standards, the shallow overburden condition additionally considers the shear effect of vehicle loads on the culvert roof slab and the bending-shear coupling effect, avoiding safety risks that may arise from neglecting shear effects in traditional designs. By introducing the calculation of coupled stress at the bending-shear coupling point (based on a comprehensive analysis of normal stress and shear stress), the maximum stress value is ensured to accurately reflect the actual stress state of the roof slab, avoiding safety risks (such as roof slab cracking and failure due to excessively thin overburden) or engineering waste (such as increased material and construction costs due to excessively thick overburden) that may arise from neglecting shear effects in traditional designs. Ultimately, this calculation method optimizes the overburden thickness while ensuring structural safety, enabling UHPC culvert 2 to meet strength requirements under shallow overburden conditions while avoiding overly conservative design, thus improving engineering economy and safety.

[0025] It should be noted that the dimensions of the wheel contact area include: the length of the wheel contact area. Width of the wheel contact area In this application, the aforementioned vehicle specifically refers to a standardized experimental vehicle used in experimental testing, whose vertical load... and the dimensions of the wheel contact area (length of the wheel contact area) Hekuan All settings are based on industry-standard testing specifications to ensure the accuracy of the calculations.

[0026] Before performing the calculations, first obtain the parameters needed for the calculations: vehicle vertical load. The length of the vehicle's wheel contact area Hekuan culvert top slab width 3 Allowable tensile stress of UHPC (ultra-high performance concrete) and allowable compressive stress The tensile strength of UHPC and the shear strength of UHPC Among them, the allowable tensile stress of UHPC (ultra-high performance concrete) is... and allowable compressive stress The tensile strength of UHPC and the shear strength of UHPC All of these are performance parameters of concrete materials.

[0027] In this embodiment, since the vehicle load needs to consider the pressure diffusion range, when calculating the vertical earth pressure caused by the vehicle load on the culvert top, the vehicle wheels 1 are distributed downwards at a 30-degree angle along the edge of their contact area to account for the pressure diffusion range, thereby converting the vehicle load into a uniformly distributed load. Therefore, in this application, a diffusion angle is set. The angle is 30°. Furthermore, in the design of other culverts, the landing dimensions and diffusion angles of different vehicle models are dynamically matched using a preset library of vehicle load diffusion parameters. This ensures the consistency of parameters and the reliability of calculations in the load diffusion model across multiple projects, avoiding stress calculation deviations caused by differences in vehicle types.

[0028] Based on the above embodiments, in this embodiment, based on the vehicle's vertical load... Wheel contact area dimensions (length of wheel contact area) Hekuan ), culvert top slab width 3 Obtain the uniformly distributed load of the vehicle load spreading to the top slab 3 of the culvert. Specifically, this includes steps 1011 to 1012: Step 1011: Based on vehicle load diffusion angle Length of the wheel contact area Width of the wheel contact area Obtain the length of the load diffusion region. and width ; Specifically, according to the formula for the side length of the load diffusion region: ; ; Obtain the length of the load diffusion region and width Where H is the soil cover thickness, The angle is 30°, and W and L are the length and width of the area where the load spreads to a height of 3 on the top slab of the culvert.

[0029] Step 1012: Based on the vehicle's vertical load, the length of the wheel contact area, and the width of the wheel contact area, obtain the uniformly distributed load of the vehicle load spreading to the culvert top slab 3.

[0030] Specifically, based on the vehicle's vertical load Length of vehicle load diffusion zone and width Calculate the uniformly distributed load of the vehicle load spreading to the top slab 3 of the culvert. .

[0031] .

[0032] Based on the bending moment and shear force diagrams, three worst-case scenarios need to be considered. The first is the location of the maximum bending moment at mid-span, controlled by the bending moment (due to the dominant bending moment and significant stress concentration in the mid-span region). The second is the location of the maximum shear force, controlled by the shear force. The third is the bending-shear coupling effect, which requires the location of the bending-shear coupling point to be dynamically determined in advance based on a parametric model of the culvert top slab width 3a and the soil cover thickness H. In this application, this location is near the bottom of the top slab. This location has both large normal stress and large shear stress, and their coupling needs to be considered simultaneously.

[0033] Finally, these three scenarios are compared, and the most unfavorable scenario, i.e. the one with the greatest stress, is used for calculation to determine the relationship between the minimum soil cover thickness and the top slab thickness.

[0034] Therefore, based on the above embodiments, in this embodiment, based on the uniformly distributed load and the width and thickness of the culvert top slab 3, the normal stress at the mid-span with the maximum bending moment, the shear stress at the mid-span with the maximum shear force, and the coupled stress at the bending-shear coupling point of the culvert top slab 3 are obtained, specifically including: Based on the uniformly distributed load and the width and thickness of the culvert top plate 3, the normal stress at the point of maximum bending moment at the mid-span of the culvert top plate 3 is obtained. Based on the uniformly distributed load and the thickness of the culvert top slab 3, the shear stress at the point of maximum shear force in the culvert top slab 3 is obtained. Based on the uniformly distributed load, the width and thickness of the culvert top plate 3, and the principal stress and minimum normal stress generated by the coupling effect of bending moment and shear force, the coupling stress at the bending-shear coupling point of the culvert top plate 3 is obtained.

[0035] The three steps above correspond to three different scenarios.

[0036] Among them, based on the uniformly distributed load and the width and thickness of the culvert top slab 3, the normal stress at the mid-span bending moment of the culvert top slab 3 is obtained, specifically including: Based on uniformly distributed load and the culvert top slab 3 width Obtain the mid-span bending moment of the culvert top slab 3. ; Based on mid-span bending moment Thickness of 3mm for culvert top slab Obtain the maximum normal stress at the point of maximum bending moment on the culvert top slab. .

[0037] Specifically, this situation refers to the mid-span section of the top slab, because the bending moment is the largest at this location, which can cause bending failure of the slab. Therefore, the magnitude of the bending moment at this location must be considered. The formula for calculating the maximum normal stress at this location is as follows: ; ; in For the mid-span bending moment, This refers to the uniformly distributed load of the vehicle load spreading to the top slab 3 of the culvert. For the moment of inertia, The width of the culvert top slab is 3. For the thickness of the top plate, This represents the length of the load diffusion region.

[0038] When the vehicle load is diffused through the soil, it forms a uniformly distributed load on the top slab 3 of the culvert. Subsequently, according to the force model of a simply supported slab, the bending moment reaches its peak at the mid-span section (i.e., the geometric center of the slab), and its calculation formula is as follows: In this cross-section, the normal stress distribution exhibits a linear characteristic: the top of the section is under compression, the bottom under tension, and the maximum normal stress occurs at the edge of the section, while the normal stress at the neutral axis is zero. This directly leads to the concentration of bending failure risk in the mid-span region. Although the flexural strength of UHPC material is significantly higher than that of ordinary concrete, if the bending moment exceeds the design limit, it will still induce vertical bending cracks along the principal tensile stress direction, causing brittle bending failure of the top slab in the mid-span region, thereby affecting the overall load-bearing capacity and durability of the structure.

[0039] Through calculation The bending moment value was determined, and the bending performance parameters of UHPC were incorporated into the design verification to ensure that the bending moment bearing capacity meets the safety margin requirements under the minimum soil cover conditions. This effectively avoids the systematic risk of focusing only on shear force and ignoring the bending moment effect in traditional design, and provides a scientific basis and quantitative guarantee for the bending safety of the top slab 3 of the shallow soil cover culvert.

[0040] Specifically, based on the uniformly distributed load and the thickness of the culvert top slab 3, the shear stress at the point of maximum shear force in the culvert top slab 3 is obtained, including: Based on uniformly distributed load Obtain the shear force of the culvert top slab 3. ; Based on shear force Thickness of 3mm for culvert top slab Obtain the shear stress at the point of maximum shear force on the culvert roof slab. .

[0041] Specifically, this situation refers to the support sections on both sides of the culvert roof slab 3, which are the locations with the greatest shear force on both sides of the culvert roof slab 3. Because the shear force is large at these locations, it can cause shear failure of the culvert roof slab 3. Therefore, the magnitude of the shear force at these locations must be considered. In the section with the greatest shear force, the neutral axis shear stress is the greatest, and the normal stress is zero. The formula for calculating the maximum shear stress is as follows: ; ; in For shear force, For a first-order moment, This represents the maximum shear stress.

[0042] When the vehicle load is diffused through the soil, it forms a uniformly distributed load on the top slab 3 of the culvert. Subsequently, according to the force model of a simply supported slab, the shear force reaches its peak at the supports (i.e., the two edges of the top slab), and its value is... In this cross-section, the neutral axis, as a special location where the normal stress is zero, exhibits the theoretical maximum shear stress. This is due to the distribution pattern of shear force in the cross-section—the shear stress caused by shear force forms a parabolic distribution at the neutral axis, where the shear stress gradient is maximum. For UHPC materials, their shear strength is significantly lower than their compressive strength. Therefore, shear cracks are easily induced in shear concentration areas, leading to brittle failure of the top plate along the direction perpendicular to the principal tensile stress.

[0043] Through calculation The shear stress value incorporates the shear resistance of UHPC into the design considerations, avoiding the shortcomings of traditional designs that only focus on bending moment while neglecting shear force effects. This formula fully considers the vehicle load diffusion angle. (30°), soil cover thickness H and top slab thickness The coupling effect ensures that the shear strength safety requirements are still met under the condition of minimum soil cover.

[0044] Among them, based on the principal stress and minimum normal stress generated by the uniformly distributed load, the width and thickness of the culvert top slab 3, and the coupling effect of bending moment and shear force, the coupled stress at the bending-shear coupling point of the culvert top slab 3 is obtained, specifically including: Based on uniformly distributed load 3 widths of culvert top slab and thickness The straight-line distance between the centroidal axis of the section at the set position and the bending-shear coupling position. Obtain the moment of inertia at the centroid of the section at a set position relative to the bending-shear coupling position in the culvert top slab 3. : ; Based on uniformly distributed load 3 widths of culvert top slab In addition to the length of the load diffusion zone, the bending moment at the bending-shear coupling point of the culvert top slab is obtained. : ; Based on uniformly distributed load And the length of the load diffusion zone, to obtain the shear force of the culvert top slab 3. : ; Based on the width of the culvert top slab 3 and thickness The straight-line distance between the centroidal axis of the section at the set position and the bending-shear coupling position. Obtain the first moment at a set position relative to the centroid of the cross section. : ; Based on bending moment Shear force Thickness of culvert top slab 3 Moment of inertia and first moment Obtain principal stress and minimum normal stress ; Based on principal stress Minimum normal stress Based on the concrete material performance parameters, and using Mohr's strength theory, the coupled stress at the bending-shear coupling point of the culvert top slab was obtained. : The performance parameters of concrete materials include: the allowable tensile stress of UHPC. and allowable compressive stress .

[0045] Specifically, this process addresses the third scenario. In the design of the top slab of a shallow-covered UHPC culvert, scenario 3 refers to the area near the mid-span where shear forces are significant. This area is a high-risk zone for combined bending-shear failure because both shear force and bending moment values ​​are at high levels.

[0046] In this section, the coupling effect of bending normal stress and shear stress is prominent in the region near the bottom of the top plate, which leads to a sharp increase in principal tensile stress. This easily induces oblique bending cracks along the direction of principal tensile stress, and then causes brittle failure of the top plate under bending and shear interaction.

[0047] Although UHPC materials have better tensile strength than ordinary concrete, the combined bending and shear stress state is very likely to exceed the strength limit. Especially under the combined action of shear force and bending moment, the risk of failure is significantly higher than that of pure bending or pure shear conditions.

[0048] This step ensures that the combined bending and shear stress meets the safety margin requirements under minimum soil cover conditions, effectively avoiding the shortcomings of considering bending moment or shear force in isolation in traditional design.

[0049] Furthermore, based on bending moment, shear force, culvert top slab thickness, moment of inertia, and first moment, the principal stresses and minimum normal stresses are obtained, specifically including: Based on bending moment Shear force Thickness of culvert top slab 3 Moment of inertia and first moment Obtain the normal stress at a set position away from the centroid of the cross section. and shear stress : ; That is, based on the bending moment, the thickness of the culvert top slab, and the moment of inertia, the normal stress at a set position away from the centroid of the cross-section is obtained. Based on shear force, first moment, culvert top slab thickness, and moment of inertia, the shear stress at a predetermined location from the centroid of the cross-section is obtained. .

[0050] Based on normal stress and shear stress Obtain principal stress and minimum normal stress : .

[0051] The calculation formula is as follows: ; ; ; ; ; ; in Let the moment of inertia at a position defined at a distance from the centroid of the cross section be... The bending moment at the point of maximum shear force. Let the first moment be a position defined at a distance from the centroid of the cross section. Let the normal tangential stress be defined at a position relative to the centroid of the cross section. The shear stress is defined at a position relative to the centroid of the cross section.

[0052] Then, the principal stresses are calculated using the following formula. minimum normal stress ; ; Finally, according to Mohr's strength theory: ;in This represents the stress after bending-shear coupling.

[0053] Based on the above embodiments, in this embodiment, the minimum soil cover thickness of culvert 2 is determined by comparing the maximum value with the performance parameters of concrete materials, specifically including: When the maximum value is normal stress or coupled stress When the maximum value is compared with the tensile strength of concrete, By comparing the values, ensuring that the maximum value does not exceed the tensile strength of the concrete, the minimum soil cover thickness for culvert 2 is determined. When the maximum value is shear stress When the maximum value is compared with the concrete shear strength, The comparison ensures that the maximum value does not exceed the shear strength of the concrete. Determine the minimum soil cover thickness for culvert 2.

[0054] Comparing the three scenarios above, the scenario with the highest stress is considered the unfavorable one: that is... ;or This equation can be used to determine the relationship between the thickness of the overburden and the thickness of the top slab under the most unfavorable conditions.

[0055] For example: designing the thickness of the top plate Given a soil thickness of 15cm and an unknown overburden thickness of H, the stresses for ①, ②, and ③ are calculated based on the above. Specifically: ① is the stress calculated from the maximum bending moment, i.e. =6 / H (unit: MPa) ② is the stress calculated from the maximum shear force, i.e. =3 / H (unit: MPa) ③ is the stress calculated from the bending-shear coupling, i.e. =2 / H (unit: MPa) Comparing these three stresses (①, ②, and ③), we can see that stress in case ① is the highest. > > .

[0056] Therefore, the maximum stress (maximum value) is ① The tensile strength must be less than or equal to that of UHPC material. Settings here The pressure is 10 MPa. Therefore, 6 / H ≤ 10; that is, H ≥ 0.6 m. At this point, the minimum soil cover thickness for culvert 2 is 0.6 m.

[0057] Secondly, this application provides a shallow-cover UHPC culvert cover thickness calculation system, which includes: a first module, a second module, a third module, and a fourth module; the first module is used to obtain the uniformly distributed load of the vehicle load diffused to the culvert top slab 3 based on the vehicle vertical load, the wheel contact area size, and the vehicle load diffusion angle; the second module is used to obtain the normal stress at the mid-span bending moment of the culvert top slab 3, the shear stress at the shear force at the mid-span bending moment, and the coupling stress at the bending-shear coupling point based on the uniformly distributed load and the width and thickness of the culvert top slab 3; the third module is used to compare the normal stress, shear stress, and coupling stress and take the maximum value; the fourth module is used to determine the minimum cover thickness of the culvert 2 based on the comparison of the maximum value with the concrete material performance parameters.

[0058] In this application, the uniformly distributed load is obtained based on the diffusion of vehicle load, and the normal stress at the mid-span of the culvert top slab with the maximum bending moment, the shear stress at the maximum shear force, and the coupled stress at the bending-shear coupling point are calculated. The maximum value of the three values ​​is compared with the tensile strength of the concrete material to determine the minimum soil cover thickness of the culvert 2. This solves the defect of traditional culvert design that only considers the bending moment and ignores the shear force effect.

[0059] Compared to existing standards, the shallow overburden condition additionally considers the shear effect of vehicle loads on the culvert roof slab and the bending-shear coupling effect, avoiding safety risks that may arise from neglecting shear effects in traditional designs. By introducing the calculation of coupled stress at the bending-shear coupling point (based on a comprehensive analysis of normal stress and shear stress), the maximum stress value is ensured to accurately reflect the actual stress state of the roof slab, avoiding safety risks (such as roof slab cracking and failure due to excessively thin overburden) or engineering waste (such as increased material and construction costs due to excessively thick overburden) that may arise from neglecting shear effects in traditional designs. Ultimately, this calculation method optimizes the overburden thickness while ensuring structural safety, enabling UHPC culvert 2 to meet strength requirements under shallow overburden conditions while avoiding overly conservative design, thus improving engineering economy and safety.

[0060] The functions of each module in the shallow overburden UHPC culvert overburden thickness calculation system correspond to the steps in the above-mentioned shallow overburden UHPC culvert overburden thickness calculation method embodiment, and their functions and implementation processes will not be described in detail here.

[0061] Thirdly, this application provides a shallow overburden UHPC culvert overburden thickness calculation device, which can be a personal computer (PC), laptop computer, server or other device with data processing function.

[0062] In this embodiment of the application, the shallow overburden UHPC culvert overburden thickness calculation device may include a processor, a memory, a communication interface, and a communication bus.

[0063] The communication bus can be of any type and is used to interconnect the processor, memory, and communication interface.

[0064] The communication interface includes input / output (I / O) interfaces, physical interfaces, and logical interfaces used for interconnecting internal components of the shallow-cover UHPC culvert cover thickness calculation device, as well as interfaces used for interconnecting the shallow-cover UHPC culvert cover thickness calculation device with other devices (such as other computing devices or user equipment). Physical interfaces can be Ethernet interfaces, fiber optic interfaces, ATM interfaces, etc.; user equipment can be displays, keyboards, etc.

[0065] Memory can be various types of storage media, such as random access memory (RAM), read-only memory (ROM), non-volatile RAM (NVRAM), flash memory, optical storage, hard disk, programmable ROM (PROM), erasable PROM (EPROM), electrically erasable PROM (EEPROM), etc.

[0066] The processor can be a general-purpose processor, which can call the shallow-cover UHPC culvert cover thickness calculation program stored in the memory and execute the shallow-cover UHPC culvert cover thickness calculation method provided in the embodiments of this application. For example, the general-purpose processor can be a central processing unit (CPU). The method executed when the shallow-cover UHPC culvert cover thickness calculation program is called can refer to the various embodiments of the shallow-cover UHPC culvert cover thickness calculation method of this application, and will not be repeated here.

[0067] Fourthly, embodiments of this application also provide a computer-readable storage medium.

[0068] The present application stores a program for calculating the overburden thickness of a shallow overburden UHPC culvert on a computer-readable storage medium, wherein when the program is executed by a processor, it implements the steps of the above-described method for calculating the overburden thickness of a shallow overburden UHPC culvert.

[0069] The method implemented when the shallow overburden UHPC culvert overburden thickness calculation program is executed can be referred to in various embodiments of the shallow overburden UHPC culvert overburden thickness calculation method of this application, and will not be repeated here.

[0070] It should be noted that the sequence numbers of the embodiments in this application are for descriptive purposes only and do not represent the superiority or inferiority of the embodiments.

[0071] The terms "comprising" and "having," and any variations thereof, in the specification, claims, and accompanying drawings of this application are intended to cover non-exclusive inclusion. For example, a process, method, system, product, or apparatus that includes a series of steps or units is not limited to the listed steps or units, but may optionally include steps or units not listed, or may optionally include other steps or units inherent to such process, method, product, or apparatus. The terms "first," "second," and "third," etc., are used to distinguish different objects, etc., and do not indicate a sequence, nor do they limit "first," "second," and "third" to different types.

[0072] In the description of the embodiments of this application, terms such as "exemplary," "for example," or "for instance" are used to indicate examples, illustrations, or explanations. Any embodiment or design described as "exemplary," "for example," or "for instance" in the embodiments of this application should not be construed as being more preferred or advantageous than other embodiments or designs. Specifically, the use of terms such as "exemplary," "for example," or "for instance" is intended to present the relevant concepts in a concrete manner.

[0073] In the description of the embodiments of this application, unless otherwise stated, " / " means "or". For example, A / B can mean A or B. The "and / or" in the text is merely a description of the relationship between related objects, indicating that there can be three relationships. For example, A and / or B can mean: A exists alone, A and B exist simultaneously, and B exists alone. In addition, in the description of the embodiments of this application, "multiple" means two or more.

[0074] In some processes described in the embodiments of this application, multiple operations or steps are included in a specific order. However, it should be understood that these operations or steps may not be executed in the order they appear in the embodiments of this application, or they may be executed in parallel. The sequence number of the operation is only used to distinguish different operations, and the sequence number itself does not represent any execution order. In addition, these processes may include more or fewer operations, and these operations or steps may be executed sequentially or in parallel, and these operations or steps may be combined.

[0075] Through the above description of the embodiments, those skilled in the art can clearly understand that the methods of the above embodiments can be implemented by means of software plus necessary general-purpose hardware platforms. Of course, they can also be implemented by hardware, but in many cases the former is a better implementation method. Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product is stored in a storage medium (such as ROM / RAM, magnetic disk, optical disk) as described above, and includes several instructions to cause a terminal device to execute the methods described in the various embodiments of this application.

[0076] The above are merely preferred embodiments of this application and do not limit the patent scope of this application. Any equivalent structural or procedural transformations made using the content of this application's specification and drawings, or direct or indirect applications in other related technical fields, are similarly included within the patent protection scope of this application.

Claims

1. A method for calculating the overburden thickness of shallow-covered UHPC culverts, characterized in that, It includes: Based on the vehicle vertical load, the wheel contact area size, and the vehicle load diffusion angle, the uniformly distributed load of the vehicle load diffused to the culvert top plate (3) is obtained. Based on the uniformly distributed load and the width and thickness of the culvert top plate (3), the normal stress at the mid-span bending moment of the culvert top plate (3), the shear stress at the mid-span bending moment, and the coupling stress at the bending-shear coupling point are obtained. Compare the normal stress, shear stress, and coupled stress, and take the maximum value; Based on the comparison between the maximum value and the performance parameters of concrete materials, the minimum soil cover thickness of the culvert (2) is determined.

2. The method for calculating the overburden thickness of shallow-covered UHPC culverts as described in claim 1, characterized in that: The dimensions of the wheel contact area include: the length of the wheel contact area and the width of the wheel contact area; Based on the vehicle's vertical load, the wheel contact area size, and the vehicle load diffusion angle, the uniformly distributed load diffused from the vehicle load to the culvert roof (3) is obtained, specifically including: Based on the vehicle load diffusion angle, the length of the wheel contact area and the width of the wheel contact area, the length and width of the load diffusion area are obtained. Based on the vehicle's vertical load, the length of the wheel contact area, and the width of the wheel contact area, the uniformly distributed load of the vehicle load spreading to the top plate of the culvert (3) is obtained.

3. The method for calculating the overburden thickness of shallow-covered UHPC culverts as described in claim 1, characterized in that, Based on the uniformly distributed load and the width and thickness of the culvert top slab (3), the normal stress at the mid-span maximum bending moment, the shear stress at the maximum shear force, and the coupled stress at the bending-shear coupling point of the culvert top slab (3) are obtained, specifically including: Based on the uniformly distributed load and the width and thickness of the culvert top plate (3), the normal stress at the mid-span bending moment of the culvert top plate (3) with the maximum value is obtained; Based on the uniformly distributed load and the thickness of the culvert top plate (3), the shear stress at the point where the shear force of the culvert top plate (3) is maximum is obtained; Based on the uniformly distributed load, the width and thickness of the culvert top plate (3), the principal stress and minimum normal stress generated by the coupling effect of bending moment and shear force, the coupling stress at the bending-shear coupling point of the culvert top plate (3) is obtained.

4. The method for calculating the overburden thickness of shallow-covered UHPC culverts as described in claim 3, characterized in that, Based on the uniformly distributed load and the width and thickness of the culvert top slab (3), the normal stress at the mid-span bending moment of the culvert top slab (3) is obtained, specifically including: Based on the uniformly distributed load and the width of the culvert top plate (3), the mid-span bending moment of the culvert top plate (3) is obtained; Based on the mid-span bending moment and the thickness of the culvert top plate (3), the normal stress at the point where the bending moment of the culvert top plate (3) is maximum is obtained.

5. The method for calculating the overburden thickness of shallow-covered UHPC culverts as described in claim 3, characterized in that, Based on the uniformly distributed load and the thickness of the culvert top slab (3), the shear stress at the point of maximum shear force in the culvert top slab (3) is obtained, specifically including: Based on the uniformly distributed load, the shear force of the culvert top slab (3) is obtained; Based on the shear force and the thickness of the culvert top plate (3), the shear stress at the point where the shear force of the culvert top plate (3) is maximum is obtained.

6. The method for calculating the overburden thickness of shallow-covered UHPC culverts as described in claim 3, characterized in that, Based on the uniformly distributed load, the width and thickness of the culvert top slab (3), and the principal stress and minimum normal stress generated by the coupling effect of bending moment and shear force, the coupling stress at the bending-shear coupling point of the culvert top slab (3) is obtained, specifically including: Based on the uniformly distributed load, the width and thickness of the culvert top plate (3), and the straight-line distance between the centroid axis of the section at the set position and the bending-shear coupling position, the moment of inertia at the set position of the centroid of the section at the bending-shear coupling position in the culvert top plate (3) is obtained; Based on the uniformly distributed load and the width of the culvert top plate (3), the bending moment at the bending-shear coupling point of the culvert top plate (3) is obtained; Based on the uniformly distributed load, the shear force of the culvert top slab (3) is obtained; Based on the width and thickness of the culvert top plate (3) and the straight-line distance between the centroid axis of the section at the set position and the bending-shear coupling position, the first moment at the set position of the centroid of the section is obtained; Based on bending moment, shear force, culvert top slab (3) thickness, moment of inertia and first moment, the principal stress and minimum normal stress are obtained; Based on the principal stress, minimum normal stress and concrete material performance parameters, and through Mohr strength theory, the coupling stress at the bending-shear coupling point of the culvert top slab (3) is obtained.

7. The method for calculating the overburden thickness of shallow-covered UHPC culverts as described in claim 6, characterized in that, Based on bending moment, shear force, culvert top slab (3) thickness, moment of inertia, and first moment, the principal stress and minimum normal stress are obtained, specifically including: Based on bending moment, shear force, culvert top plate (3) thickness, moment of inertia and first moment, the normal stress and shear stress at a set position away from the centroid of the section are obtained; Based on normal stress and shear stress, the principal stress and minimum normal stress are obtained.

8. The method for calculating the overburden thickness of shallow-covered UHPC culverts as described in claim 7, characterized in that, Based on bending moment, shear force, culvert top slab (3) thickness, moment of inertia, and first moment, the normal stress and shear stress at a set position away from the centroid of the section are obtained, specifically including: Based on the bending moment, the thickness of the culvert top plate (3), and the moment of inertia, the normal stress at a set position away from the centroid of the section is obtained; Based on shear force, first moment, culvert top plate (3) thickness and moment of inertia, the shear stress at a set position away from the centroid of the cross section is obtained.

9. The method for calculating the overburden thickness of shallow-covered UHPC culverts as described in claim 1, characterized in that: The concrete material performance parameters include concrete tensile strength and concrete shear strength; Based on the comparison between the maximum value and the concrete material performance parameters, the minimum soil cover thickness of the culvert (2) is determined, specifically including: When the maximum value is normal stress or coupled stress, the maximum value is compared with the tensile strength of concrete to ensure that the maximum value does not exceed the tensile strength of concrete, and the minimum soil cover thickness of culvert (2) is determined. When the maximum value is shear stress, the maximum value is compared with the concrete shear strength so that the maximum value does not exceed the concrete shear strength, and the minimum soil cover thickness of the culvert (2) is determined.

10. A system for calculating the overburden thickness of shallow-covered UHPC culverts, characterized in that, It includes: The first module is used to obtain the uniformly distributed load of the vehicle load spreading to the top plate of the culvert (3) based on the vehicle vertical load, the wheel contact area size, and the vehicle load diffusion angle. The second module is used to obtain the normal stress at the mid-span bending moment of the culvert top plate (3), the shear stress at the maximum shear force, and the coupling stress at the bending-shear coupling point based on the uniformly distributed load and the width and thickness of the culvert top plate (3). The third module is used to compare the normal stress, shear stress, and coupling stress, and take the maximum value. The fourth module is used to determine the minimum soil cover thickness of the culvert (2) based on a comparison of the maximum value with the performance parameters of the concrete material.

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