A Design Method for Hollow Curb Stones Based on High-Performance Concrete

Abstract

The present invention relates to a design method for hollow curb stones based on high-performance concrete, belonging to the field of curb stone design. It includes initially determining the dimensions of the hollow curb stones, calculating the flexural tensile stress generated by the hollow curb stones under lateral forces and horizontal thrusts, and obtaining the flexural strength design value by taking the larger value; taking an appropriate value as the compressive strength design value of the hollow curb stones; conducting concrete mix design; using full-scale tests or numerical simulations to check the flexural strength and compressive strength of the hollow curb stones; if the strength check passes, the design is completed; if not, the structural dimensions are determined again or the mix design is redone until the strength check passes. Based on the existing specifications for ordinary concrete curb stones, the present invention provides a design method for hollow curb stones based on high-performance concrete to fill the gap in the design method for high-performance concrete hollow curb stones, providing design reference and theoretical supplement for the successful application of high-performance concrete in hollow curb stones.

Description

Technical Field

[0001] The present invention relates to a design method for hollow curb stones based on high-performance concrete, including the design of the size of the hollow curb stones, the mix ratio design, and the strength inspection, belonging to the technical field of curb stone design. Background Art

[0002] Curb stones are the marker stones set between the road surface and other structures, and there is a huge demand during the construction and operation and maintenance of traffic infrastructure such as urban roads and highways. Their main functions are as follows: First, they separate different functional plates of the municipal road (such as the carriageway and the median strip, the carriageway and the sidewalk); second, they play a good role in protecting the edge of the road surface; third, they are used to intercept and converge the rainwater on the road surface.

[0003] At present, most curb stones are solid structures, which require a large amount of raw materials, have a large self-weight, and are not convenient for transportation and construction, etc. In view of the problems existing in the solid curb stones, many scholars have adopted the structural form of hollow curb stones to reduce the amount of raw materials used for preparation and reduce the self-weight of the curb stones, thereby reducing the transportation and construction difficulties. However, at present, there is still a lack of a complete design theory and design method for the design of hollow curb stones, resulting in uneven quality of hollow curb stones, time-consuming and laborious, and unable to meet the actual engineering needs.

[0004] Based on this, the present invention proposes a design method for hollow curb stones based on high-performance concrete. On the one hand, the excellent mechanical properties and durability of high-performance concrete are used to improve the bearing capacity and service life of the hollow curb stones; on the other hand, a design method for hollow curb stones based on this high-performance concrete is provided, including the internal structure, size design, material mix ratio design and strength inspection of the hollow curb stones, providing theoretical and method guidance for the design of hollow curb stones and their subsequent wide application in actual projects, and having important theoretical significance and application value. Summary of the Invention

[0005] Aiming at the deficiencies of the existing technology, the present invention provides a design method for hollow curb stones based on high-performance concrete. On the basis of the existing specifications for ordinary concrete curb stones, aiming at the gap in the design method of high-performance concrete hollow curb stones, a design method for high-performance concrete hollow curb stones is provided, providing a design reference and theoretical supplement for the successful application of high-performance concrete in hollow curb stones.

[0006] The present invention adopts the following technical solutions:

[0007] A design method for hollow curb stones based on high-performance concrete, including:

[0008] Step 1: Initially determine the height, width, length and wall thickness of the hollow curb stone;

[0009] Step 2: Calculate the bending tensile stress generated by the hollow curbstone when subjected to lateral force;

[0010] Step 3: Calculate the bending tensile stress generated by the hollow curb under horizontal thrust;

[0011] Step 4: Combine the bending tensile stresses calculated in step 2 and step 3, take the larger value as the reference value of the bending tensile strength of the raw material for preparing the hollow curbstone, consider the safety factor, and obtain the design value of the bending tensile strength;

[0012] Step 5: According to the compressive strength limit of high performance concrete, take an appropriate value as the compressive strength design value of the hollow curbstone;

[0013] Step 6: Design the concrete mix ratio according to the design values ​​of the flexural tensile strength and compressive strength of the hollow curbstone;

[0014] Step 7: Use full-scale tests or numerical simulations to verify the flexural tensile strength and compressive strength of the hollow curbstone;

[0015] Step 8: If the flexural strength and compressive strength obtained in step 7 are respectively greater than or equal to the design value of the flexural strength of the hollow curbstone and the design value of the compressive strength of the hollow curbstone, the strength verification passes and the design step is completed; if the strength verification fails, the structural dimensioning of step 1 or the mix design of step 6 is repeated until the strength verification passes.

[0016] Preferably, step 2 is specifically:

[0017] In actual working conditions, curbstones are subject to lateral forces. For example, prefabricated hollow curbstones may be subjected to overlapping forces during transportation. Therefore, in the design of hollow curbstones, the curbstones must withstand lateral forces without being damaged. The lateral forces of the curbstones are simplified to a plate consolidated at both ends to bear bending loads. The simplified process and calculation diagram are shown in Figure 2 , the length of the plate is equivalent to the height of the curb, the width of the plate is equivalent to the length of the curb, and the thickness of the plate is equivalent to the wall thickness of the curb. Hollow curbs are generally cast in one piece, so the two ends of the plate are regarded as consolidation constraints;

[0018] The calculation process of the bending tensile stress generated by the hollow curb under the side force is as follows:

[0019] 2.1. Calculate the bending section modulus according to the wall thickness t, height h and calculation diagram of the curb:

[0020]

[0021] 2.2. According to the stress conditions and the length l of the curb, calculate the bending moment value of the most dangerous section. In order to make the calculation result more reliable, the curb superposition force F1 acts on the mid-span section in the form of concentrated load. The force and bending moment values ​​are calculated as follows:

[0022] F1=n×m 石 g

[0023]

[0024] Where: n is the number of curbstones above the bottom curbstone when the curbstones are stacked; m 石 is the mass of a single curbstone; g is the acceleration due to gravity;

[0025] 2.3. According to the above bending section modulus and the bending moment value of the mid-span section, calculate the bending tensile stress:

[0026]

[0027] Preferably, step 3 is specifically:

[0028] In actual working conditions, curbstones may be subjected to horizontal thrust, such as the horizontal force generated when a vehicle drives onto the curbstone. Therefore, in the design of hollow curbstones, the curbstone must withstand horizontal thrust without being damaged. The situation where the curbstone is subjected to horizontal thrust is simplified to a rigid frame with both ends fixed to withstand horizontal thrust. The process and calculation diagram are shown in Figure 3 The width of the steel frame is equivalent to the width of the curb, the height of the steel frame is half the height of the curb (in actual working conditions, the curb is buried on both sides of the road, and the effective load-bearing height is only above the upper half of the road surface), and the thickness of the steel frame is equivalent to the wall thickness of the curb;

[0029] The calculation process of the bending tensile stress generated by the hollow curb under the condition of horizontal thrust is as follows:

[0030] 3.1. Calculate the bending section modulus based on the wall thickness t, length l and calculation diagram of the curbstone:

[0031]

[0032] 3.2. According to the stress conditions and the width b and height h of the curb, calculate the bending moment value of the most dangerous section. The horizontal component force is calculated based on the condition that the vehicle presses the curb at a 45° angle. The pressure of the vehicle tire on the curb is taken as 1 / 4 of the total weight of the vehicle. For safety reasons, the horizontal component force is applied horizontally to the top of the rigid frame in the form of a concentrated load. The horizontal component force and bending moment values ​​are calculated as follows:

[0033]

[0034]

[0035]

[0036] Where: m 车 is the vehicle mass; g is the acceleration due to gravity; E is the modulus of elasticity; I is the moment of inertia of the cross-section; x is the redundant unknown force in the force method calculation formula in structural mechanics;

[0037] 3.3. Calculate the flexural tensile stress according to the above flexural section modulus and the bending moment value of the most dangerous section:

[0038]

[0039] Preferably, in step 5, when the wall thickness of the hollow kerbstone is 10 - 25 mm and the length is 500 - 750 mm, the design value of the flexural tensile strength of the high-performance concrete should be 7 - 30 MPa, and the design value of the compressive strength should be not less than 80 MPa. Take 80 MPa as the design value of the compressive strength of the hollow kerbstone. The high-performance concrete requires a minimum compressive strength of 80 MPa, and the appropriate value should be greater than or equal to this limit. At the same time, concrete is compressive but not tensile, and this limit can basically avoid the compressive failure of the hollow kerbstone during construction and service.

[0040] Preferably, in step 4, the safety factor is 1.3, that is, the design value of the flexural tensile strength is 1.3 times the reference value of the flexural tensile strength.

[0041] For those aspects not elaborated in the present invention, existing technologies can be adopted.

[0042] The beneficial effects of the present invention are as follows:

[0043] (1) Aiming at the problem that there is a lack of design theory and design methods for current hollow kerbstones, the present invention can provide a design method for hollow kerbstones based on high-performance concrete, including the design of the hollow kerbstone size, material mix design, and strength inspection.

[0044] (2) The present invention proposes a mechanical calculation model for the stress of the hollow kerbstone, and uses the mechanical calculation models of the fixed plate and the fixed rigid frame to simulate the stress conditions of the kerbstone during transportation and service, and uses this as the strength basis for the design of the kerbstone.

[0045] (3) The present invention proposes a strength design method for the kerbstone with flexural tensile stress and construction requirements as the strength design indicators, providing a basis for the design of the high-performance concrete mix ratio.

[0046] (4) The present invention proposes hollow curb stones with different thicknesses and lengths, and the recommended ranges of the design values of the flexural tensile strength and compressive strength of high-performance concrete. When the wall thickness of the hollow curb stone is 10 - 25 mm and the length is 500 - 750 mm, the design value of the flexural tensile strength of high-performance concrete should be 7 - 30 MPa, and the design value of the compressive strength should be not less than 80 MPa. Take 80 MPa as the design value of the compressive strength of the hollow curb stone. Description of the Drawings

[0047] Figure 1 It is the flow chart of the design method of the hollow curb stone based on high-performance concrete of the present invention;

[0048] Figure 2 It is the schematic diagram of the simplified process of the lateral force condition of the curb stone;

[0049] Figure 3 It is the schematic diagram of the simplified process of the horizontal thrust borne by the curb stone;

[0050] Figure 4 It is the schematic diagram of the structural dimensions of the hollow curb stone in Embodiment 1;

[0051] Figure 5 It is the schematic diagram of the structural dimensions of the hollow curb stone in Embodiment 2. Detailed Embodiments

[0052] To make the technical problems, technical solutions and advantages to be solved by the present invention clearer, the following will be described in detail with reference to the drawings and specific embodiments, but not limited to this. For those not elaborated in the present invention, they are all conventional technologies in the art.

[0053] Embodiment 1:

[0054] A design method of a hollow curb stone based on high-performance concrete, including:

[0055] Step 1: Initially determine the height, width, length and wall thickness of the hollow curb stone;

[0056] According to "Concrete Curb Stone" (JC / T 899 - 2016), on the basis of the traditional H3 type solid curb stone (height 300 mm, width 200 mm), all the interior of the curb stone is hollowed out, and the inner walls are all processed with rounded corners. The structural dimensions are as Figure 4 shown. It is determined that the length of the curb stone is 500 mm and the wall thickness is 10 mm. Then the volume of one curb stone is about 0.005 m 3 . The density of high-performance concrete is approximately taken as 2500 kg / m 3 .

[0057] Step 2: Calculate the flexural tensile stress generated by the hollow curb stone under the condition of lateral force;

[0058] According to the calculation diagram as Figure 2 shown, calculate the flexural section modulus of the hollow curb:

[0059]

[0060] Calculate the acting force. The acting force is taken as the total weight of four curbs to simulate the actual superimposed pressure:

[0061] F1 = n × m 石 g = n × ρ 石 V 石 g = 4 × 2500 × 0.005 × 9.8 = 490N

[0062] Among them, V 石 is the volume of a single curb, that is, 0.005m 3 , 2500 is the density of high-performance concrete. The above formula represents the total weight of 4 curbs;

[0063] Calculate the bending moment value of the most dangerous section:

[0064]

[0065] Calculate the flexural and tensile stress generated by the hollow curb under the lateral force:

[0066]

[0067] Step 3: Calculate the flexural and tensile stress generated by the hollow curb under the horizontal thrust;

[0068] According to the calculation diagram as Figure 3 shown, calculate the flexural section modulus of the hollow curb:

[0069]

[0070] Calculate the acting force. The vehicle mass is assumed to be 2400 kg, and the acting force is calculated as follows:

[0071]

[0072] Calculate the bending moment value of the most dangerous section:

[0073]

[0074]

[0075] Calculate the flexural and tensile stress:

[0076]

[0077] Step 4: Combine the flexural tensile stresses obtained in Step 2 and Step 3, and take the larger value, i.e., 22.11 MPa, as the reference value of the flexural tensile strength of the raw materials for preparing the hollow curbstone. Considering the safety factor, it is preferably 1.3 times the reference value of the flexural tensile strength, i.e., 28.74 MPa, and 30 MPa is taken as the designed value of the flexural tensile strength;

[0078] Step 5: According to the compressive strength limit of the high-performance concrete, 80 MPa is selected as the designed value of the compressive strength of the high-performance concrete.

[0079] Step 6: According to the designed values of the flexural tensile strength and compressive strength of the hollow curbstone, conduct the concrete mix design;

[0080] According to the above-mentioned designed values of the flexural tensile strength and compressive strength, conduct the mix design of the high-performance concrete. The commonly used raw materials for preparing the high-performance concrete are cement, silica fume, mineral powder, river sand, admixture, and water. In order to improve the toughness of the matrix, a certain volume of fibers is usually added. The initial dosages of cement, silica fume, and mineral powder are respectively 90%, 5%, and 5% of the binder, the mortar-binder ratio is 1:1, the water-binder ratio is 0.18, PVA fibers are selected as the fibers, the volume dosage is 0.6%, and the admixtures are polycarboxylate-based high-performance powder water reducer and defoamer, and the dosages are respectively 1% and 0.4% of the binder. The specific mix is shown in Table 1 below:

[0081] Table 1: Mix Design of Example 1

[0082] Raw materials Cement Mineral powder Silica fume River sand Water reducing agent Defoaming agent Fiber Water <![CDATA[kg / m 3 > 1121 62 62 1246 13 5 8 224

[0083] Step 7: Use the full-scale test to check the flexural tensile strength and compressive strength of the hollow curbstone;

[0084] According to the above-mentioned curbstone dimensions and mix, prepare the full-scale curbstone model. Refer to "Concrete Curbstone" (JC / T 899-2016) for the flexural test and compressive test to check the flexural and compressive strengths of the curbstone. The test results and design values are shown in Table 2 below:

[0085] Table 2: Test Results of Full-scale Test of Example 1

[0086]

[0087]

[0088] Step 8: From the above inspection results, it can be seen that the flexural and compressive strengths of the designed curbstone meet the design requirements, and the design process ends.

[0089] Example 2:

[0090] A design method for a hollow curbstone based on high-performance concrete, including:

[0091] Step 1: Preliminary determination of the height, width, length, and wall thickness of the hollow curbstone;

[0092] Based on the "Concrete Curbstone" (JC / T 899-2016), on the basis of the traditional solid H3-type curbstone (height 300 mm, width 200 mm), the inside of the curbstone is completely hollowed out, and the inner walls are all treated with rounded corners. The structural dimensions are as Figure 5 shown. The length of the curbstone is determined to be 750 mm, and the wall thickness is 25 mm. Then the volume of one curbstone is approximately 0.017 m 3 . The density of the high-performance concrete is approximately taken as 2500 kg / m 3 .

[0093] Step 2: Calculate the flexural tensile stress generated by the hollow curbstone under lateral force;

[0094] According to the calculation diagram as Figure 2 shown, calculate the flexural section modulus of the hollow curbstone:

[0095]

[0096] Calculate the acting force. The acting force is taken as the total weight of four curbstones to simulate the actual stacking effect:

[0097] F1 = n × m 石 g = n × ρ 石 V 石 g = 4 × 2500 × 0.017 × 9.8 = 1666 N

[0098] Calculate the bending moment value of the most dangerous section:

[0099]

[0100] Calculate the flexural tensile stress generated by the hollow curbstone under lateral force:

[0101]

[0102] Step 3: Calculate the flexural tensile stress generated by the hollow curbstone under horizontal thrust;

[0103] According to the calculation diagram as Figure 3 shown, calculate the flexural section modulus of the hollow curbstone:

[0104]

[0105] Calculate the acting force. The vehicle mass is determined to be 2400 kg, and the acting force is calculated as follows:

[0106]

[0107] Calculate the bending moment value of the most dangerous section:

[0108]

[0109]

[0110] Calculate the flexural tensile stress:

[0111]

[0112] Step 4: Combine the flexural tensile stress calculated in Step 2 and Step 3, and take the larger value, which is 5.00 MPa, as the reference value of the flexural tensile strength of the raw materials for preparing the hollow curb. Considering the safety factor, it is preferably 1.3 times the reference value of the flexural tensile strength, that is, 6.50 MPa, and take 7.00 MPa as the design value of the flexural tensile strength;

[0113] Step 5: Select 80 MPa as the design value of the compressive strength of the high-performance concrete according to the compressive strength limit of the high-performance concrete.

[0114] Step 6: Carry out the concrete mix design according to the design values of the flexural tensile strength and compressive strength of the hollow curb;

[0115] According to the above design values of the flexural tensile strength and compressive strength, carry out the mix design of the high-performance concrete. The commonly used raw materials for preparing the high-performance concrete are cement, silica fume, mineral powder, river sand, admixture, and water. In order to improve the toughness of the matrix, a certain volume of fiber is usually added. The initial dosages of cement, silica fume, and mineral powder are respectively 90%, 5%, and 5% of the cementitious material, the mortar ratio is 1:1, the water-cementitious material ratio is 0.19, the fiber is selected as PVA fiber, the volume dosage is 1.8%, and the admixtures are selected as polycarboxylate-based high-performance powder water reducer and defoamer, and the dosages are respectively 1% and 0.4% of the cementitious material. The specific mix is shown in Table 3 below:

[0116] Table 3: Mix Design of Example 2

[0117] Raw materials Cement Mineral powder Silica fume River sand Water reducing agent Defoaming agent Fiber Water <![CDATA[kg / m 3 > 1116 62 62 1240 12 5 23 236

[0118] Step 7: Check the flexural tensile strength and compressive strength of the hollow curb by full-scale test;

[0119] Carry out the strength inspection of the curb by full-scale test. According to the above curb size and mix ratio, prepare a full-scale curb model. Refer to "Concrete Curb" (JC / T 899-2016) for the flexural test and compressive test to check the flexural and compressive strength of the curb. The test results and design values are shown in Table 4 below:

[0120] Table 4: Test Results of Full-scale Test of Example 2

[0121] Test items Measured value (MPa) Design value (MPa) Flexural test 11.59 7.00 Compressive test 106.3 80

[0122] Step 8: From the above test results, it can be seen that the flexural and compressive strengths of the designed curbstone both meet the design requirements, and the design process ends.

[0123] The above is the preferred embodiment of the present invention. It should be noted that for those of ordinary skill in the art, without departing from the principle described in the present invention, several improvements and refinements can be made, and these improvements and refinements should also be regarded as the protection scope of the present invention.

Claims

1. A design method for hollow curb stones based on high-performance concrete, characterized in that, include: Step 1: Preliminary design of the height, width, length and wall thickness of the hollow curbstone; Step 2: Calculate the bending tensile stress generated by the hollow curbstone when subjected to lateral force; Step 3: Calculate the bending tensile stress generated by the hollow curb under horizontal thrust; Step 4: Combine the bending tensile stresses calculated in step 2 and step 3, take the larger value as the reference value of the bending tensile strength of the raw material for preparing the hollow curbstone, consider the safety factor, and obtain the design value of the bending tensile strength; Step 5: According to the compressive strength limit of high performance concrete, take an appropriate value as the compressive strength design value of the hollow curbstone; Step 6: Design the concrete mix ratio according to the design values ​​of the flexural tensile strength and compressive strength of the hollow curbstone; Step 7: Use full-scale tests or numerical simulations to verify the flexural tensile strength and compressive strength of the hollow curbstone; Step 8: If the flexural tensile strength and compressive strength obtained in step 7 are respectively greater than or equal to the design value of the flexural tensile strength of the hollow curbstone and the design value of the compressive strength of the hollow curbstone, the strength verification is passed and the design step is completed; If the strength verification fails, redo the structural dimensioning in step 1 or the mix design in step 6 until the strength verification passes.

2. The method for designing hollow curbstones based on high performance concrete according to claim 1, characterized in that step 2 specifically comprises: In actual working conditions, the curbstone is subjected to lateral forces. The lateral forces of the curbstone are simplified to a plate fixed at both ends to bear bending loads. The length of the plate is equivalent to the height of the curbstone, the width of the plate is equivalent to the length of the curbstone, and the thickness of the plate is equivalent to the wall thickness of the curbstone. The calculation process of the bending tensile stress generated by the hollow curb under the side force is as follows: 2.

1. Calculate the bending section modulus based on the wall thickness t and height h of the curb: 2.

2. According to the stress conditions and the length l of the curb, calculate the bending moment value of the most dangerous section. Apply the curb pressure force F1 to the mid-span section in the form of a concentrated load. The force and bending moment values ​​are calculated as follows: F1 = n × m 石 g Where: n is the number of curb stones above the bottommost curb stone when the curb stones are stacked; m 石 is the mass of a single curb stone; g is the acceleration due to gravity; 2.

3. According to the above bending section modulus and the bending moment value of the mid-span section, calculate the bending tensile stress:

3. The hollow curbstone design method based on high performance concrete according to claim 2, characterized in that step 3 specifically comprises: In actual working conditions, the curbstone may be subjected to horizontal thrust. The situation in which the curbstone is subjected to horizontal thrust is simplified to a situation in which a rigid frame fixed at both ends is subjected to horizontal thrust. The width of the rigid frame is equal to the width of the curbstone, the height of the rigid frame is half of the height of the curbstone, and the thickness of the rigid frame is equal to the wall thickness of the curbstone. The calculation process of the bending tensile stress generated by the hollow curb under the condition of horizontal thrust is as follows: 3.

1. Calculate the bending section modulus based on the wall thickness t and length l of the curbstone: 3.

2. According to the stress conditions and the width b and height h of the curb, calculate the bending moment value of the most dangerous section. The horizontal component force is calculated based on the condition that the vehicle presses the curb at a 45° angle. The pressure of the vehicle tire on the curb is taken as 1 / 4 of the total weight of the vehicle. The horizontal component force is applied horizontally to the top of the rigid frame in the form of a concentrated load. The horizontal component force and bending moment values ​​are calculated as follows: Where: m 车 is the vehicle mass; g is the acceleration due to gravity; E is the modulus of elasticity; I is the moment of inertia of the cross-section; x is the redundant unknown force in the force method calculation formula in structural mechanics; 3.

3. Calculate the flexural tensile stress based on the above flexural section modulus and the bending moment value of the most dangerous section:

4. The design method of the hollow curbstone based on high-performance concrete according to claim 1, characterized in that In Step 5, when the wall thickness of the hollow curb is 10 - 25 mm and the length is 500 - 750 mm, the design value of the flexural tensile strength of the high-performance concrete is 7 - 30 MPa, and the design value of the compressive strength is not less than 80 MPa. Take 80 MPa as the design value of the compressive strength of the hollow curb.

5. The design method of the hollow curb based on high-performance concrete according to claim 4, characterized in that In Step 4, the safety factor is 1.3, that is, the design value of the flexural tensile strength is 1.3 times the reference value of the flexural tensile strength.

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