Method for determining shear bearing capacity of a multiple-doped solid waste concrete beam column

Abstract

The application provides a method for determining the shear bearing capacity of a complexly doped solid waste concrete beam, and relates to the technical field of bridge and culvert engineering in the transportation industry. The method can effectively measure the shear bearing capacity of the concrete under controlled experimental conditions by preparing a plurality of proportioned concrete beam samples and applying a systematic incremental shear load, can establish a dynamic model between the performance and construction behavior of the concrete by recording and analyzing the state of the cracks during the loading process, and can further optimize the proportion selection of the concrete by selecting the sample with the shear bearing capacity exceeding the expected value and optimizing the crack change trend.

Description

Technical Field

[0001] This invention relates to the field of bridge and culvert engineering technology in the transportation industry, specifically a method for determining the shear bearing capacity of concrete beams and columns with mixed solid waste. Background Technology

[0002] The technology of compounding solid waste concrete has attracted increasing attention. It improves the physical and mechanical properties of concrete by replacing a portion of cement with industrial byproducts and multi-solid waste materials (such as fly ash, steel slag, phosphogypsum, blast furnace slag, and construction waste). For example, the use of fly ash can not only improve the fluidity and compressive strength of concrete but also enhance its durability. However, despite the many performance advantages of concrete with compounded solid waste, research on its shear capacity remains insufficient, especially regarding how to systematically and accurately assess the shear capacity of concrete beams and columns prepared with different mix proportions. Current research focuses primarily on compressive properties, lacking specific methods for determining shear capacity.

[0003] The existing technology, with publication number CN117150729A, entitled "A Method for Determining the Shear Capacity of Multi-Solid Waste Synergistic Reinforced Concrete Beams," comprises the following steps: 1) Testing the basic parameters of the multi-solid waste synergistic reinforced concrete beam and determining the shear span ratio based on these parameters; 2) Testing the axial tensile strength ft of the multi-solid waste synergistic reinforced concrete and obtaining the shear force Vc borne by the multi-solid waste synergistic reinforced concrete based on ft; 3) Testing the stirrup parameters and obtaining the shear force borne by the stirrups based on these parameters; 4) Obtaining the calculation formula for the shear capacity of the multi-solid waste synergistic reinforced concrete beam based on the shear capacity of the concrete and the shear capacity of the stirrups. This specific calculation formula can accurately calculate the shear capacity of MSWC beams, solving the problem that existing standard shear capacity formulas are not applicable to MSWC beams, and providing a calculation basis for the shear design of MSWC beams.

[0004] Current methods for assessing shear capacity typically rely on traditional loading tests, applying a single load and monitoring crack development to determine the performance of concrete members. This approach limits a comprehensive understanding of complex crack behavior and fails to effectively reflect the shear capacity variations of multi-component concrete beams and columns in actual service. Furthermore, existing methods often lack dynamic monitoring and data analysis of crack states under different loading processes, making it difficult to fully consider the impact of concrete deformation and crack development on load-bearing performance during design.

[0005] The information disclosed in the background section above is only intended to enhance the understanding of the background of this disclosure, and therefore may include information that does not constitute prior art known to those skilled in the art. Summary of the Invention

[0006] The purpose of this invention is to provide a method for determining the shear bearing capacity of concrete beams and columns with mixed solid waste, so as to solve the problems mentioned in the background art.

[0007] To achieve the above objectives, the present invention provides the following technical solution:

[0008] A method for determining the shear bearing capacity of concrete beams and columns with mixed solid waste, comprising the following steps:

[0009] Step S1: Prepare multiple composite solid waste concrete beam samples with different proportions;

[0010] Step S2: Apply incremental shear loads of the same magnitude to each composite solid waste concrete beam specimen to determine the shear capacity of each composite solid waste concrete beam specimen.

[0011] The expected value of the shear bearing capacity required for the composite solid waste concrete beam specimens was set, and composite solid waste concrete beam specimens with shear bearing capacity above the expected value were selected to form a candidate specimen set.

[0012] Step S3: Based on the candidate sample set, the time spent on each incremental shear load is recorded as the loading period, and the crack state data of the surface cracks of the composite solid waste concrete beam sample under each loading period are recorded.

[0013] Step S4: Receive and analyze the crack state data of each composite solid waste concrete beam specimen in the candidate specimen set under different loading periods, so as to calculate the load variation factor of each composite solid waste concrete beam specimen separately; the load variation factor is used to characterize the crack variation trend of the corresponding composite solid waste concrete beam specimen.

[0014] Step S5: The final optimization objectives are to maximize the difference between the shear capacity and the expected value of the shear capacity, and to minimize the crack change trend corresponding to the load variation factor; and to set the constraint conditions for the composite solid waste concrete beam specimen.

[0015] Based on the final optimization objective and constraints, the optimal composite solid waste concrete beam sample was selected from the candidate sample set.

[0016] Step S6: Perform an environmental load variation calibration strategy on the selected optimal composite solid waste concrete beam specimens to determine the final shear capacity of the selected optimal composite solid waste concrete beam specimens.

[0017] Preferably, the formula for calculating the load variation factor is defined as follows:

[0018]

[0019] Among them, ZHYz i1 It is the load variation factor of the i1th composite solid waste concrete beam specimen; ZHYzi1 The smaller the value, the smaller the trend of crack opening displacement or equivalent temperature rise, which in turn represents the smaller trend of crack change in the composite solid waste concrete beam sample.

[0020] Kd1 i1,j+1 With Kd1 i1,j These are the crack opening displacements of the i1th composite solid waste concrete beam sample under the j+1th and jth loading periods, respectively.

[0021] ΔT i1,j+1 With ΔT i1,j These are the equivalent temperature rises of the i1th composite solid waste concrete beam sample during the j+1th and jth loading periods, respectively.

[0022] b1 and b2 are the weight coefficients of the corresponding parameters, and the values ​​of b1 and b2 are in the interval (0,1); b1+b2=1.

[0023] Preferably, according to KQJ i1 The difference between ≥KQJ′ is sorted from largest to smallest from the candidate sample set {1,2,…,i1,…,N1}; then the top three mixed solid waste concrete beam samples are selected as pre-selected samples.

[0024] The load variation factor of each composite solid waste concrete beam specimen in the pre-selected samples was obtained and denoted as ZHYz. i2 ZHYz i3 and ZHYz i4 And {i2, i3, i4} are contained in {1, 2, ..., N1}; the constraints include the following conditions one and two: Condition one:

[0025]

[0026] Condition two:

[0027]

[0028] in, This means rounding up to the nearest integer, and setting the integers from 1 to the nearest integer. The loading period is considered the pre-loading phase; The subsequent loading period is considered the late loading period; i′∈{i2, i3, i4}; CB i′ It is the cost value of using the mixed solid waste in the i′th mixed solid waste concrete beam sample;

[0029] and These are the cost values ​​of steel slag, slag powder, and phosphogypsum powder, respectively.

[0030] When condition one is met, it means that the crack change trend of the composite solid waste concrete beam sample in the early stage of loading is less than that in the later stage of loading.

[0031] Calculate the difference Q1 between the conditions corresponding to the early and late stages of loading:

[0032]

[0033] From the three pre-selected specimens, priority is given to selecting the composite solid waste concrete beam specimen that meets condition one of the constraint conditions;

[0034] If at least two pre-selected samples meet the constraints, the pre-selected sample with the smallest Q1 value shall be selected.

[0035] If there is no case that meets condition one of the constraints, then from ZHYz i2 ZHYz i3 and ZHYz i4 Select the smallest value or CB i′ The smallest composite solid waste-admixed concrete beam specimen;

[0036] Based on the final selected pre-selected samples, the corresponding multi-solid waste material ratio and shear bearing capacity are determined.

[0037] Compared with the prior art, the beneficial effects of the present invention are: by preparing concrete beam samples with various mix proportions and applying a systematic incremental shear load, not only can the shear bearing capacity of concrete be effectively measured under controlled experimental conditions, but also a dynamic model can be established between concrete performance and structural behavior by recording and analyzing the state of cracks during loading, thereby optimizing the selection of concrete mix proportions; and by selecting samples with shear bearing capacity exceeding the expected value and optimizing the crack change trend. Attached Figure Description

[0038] Figure 1 This is a schematic diagram of the overall method flow of the present invention. Detailed Implementation

[0039] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to specific embodiments.

[0040] It should be noted that, unless otherwise defined, the technical or scientific terms used in this invention should have the ordinary meaning understood by one of ordinary skill in the art to which this invention pertains. The terms "first," "second," and similar terms used in this invention do not indicate any order, quantity, or importance, but are merely used to distinguish different components. Terms such as "comprising" or "including" mean that the element or object preceding the word encompasses the elements or objects listed following the word and their equivalents, without excluding other elements or objects. Terms such as "connected" or "linked" are not limited to physical or mechanical connections, but can include electrical connections, whether direct or indirect. Terms such as "upper," "lower," "left," and "right" are used only to indicate relative positional relationships; when the absolute position of the described object changes, the relative positional relationship may also change accordingly.

[0041] Example 1:

[0042] Please see Figure 1 The present invention provides a technical solution:

[0043] A method for determining the shear bearing capacity of concrete beams and columns with mixed solid waste admixtures is applied to the preparation of samples with multiple known mix proportions of concrete with mixed solid waste admixtures. The specific steps include:

[0044] Step S1: Prepare multiple composite solid waste concrete beam samples with different proportions;

[0045] Step S2: Apply incremental shear loads of the same magnitude to each composite solid waste concrete beam specimen to determine the shear capacity of each composite solid waste concrete beam specimen.

[0046] The expected value of the shear bearing capacity required for the composite solid waste concrete beam specimens was set, and composite solid waste concrete beam specimens with shear bearing capacity above the expected value were selected to form a candidate specimen set.

[0047] Step S3: Based on the candidate sample set, the time spent on each incremental shear load is recorded as the loading period, and the crack state data of the surface cracks of the composite solid waste concrete beam sample under each loading period are recorded.

[0048] Step S4: Receive and analyze the crack state data of each composite solid waste concrete beam specimen in the candidate specimen set under different loading periods, so as to calculate the load variation factor of each composite solid waste concrete beam specimen separately; the load variation factor is used to characterize the crack variation trend of the corresponding composite solid waste concrete beam specimen.

[0049] Step S5: The final optimization objectives are to maximize the difference between the shear capacity and the expected value of the shear capacity, and to minimize the crack change trend corresponding to the load variation factor; and to set the constraint conditions for the composite solid waste concrete beam specimen.

[0050] Based on the final optimization objective and constraints, the optimal composite solid waste concrete beam sample was selected from the candidate sample set.

[0051] Step S6: Perform an environmental load variation calibration strategy on the selected optimal composite solid waste concrete beam specimens to determine the final shear capacity of the selected optimal composite solid waste concrete beam specimens.

[0052] A predefined mix design range for preparing composite solid waste-admixed concrete beam samples is established. Within this range, multiple mix design combinations are randomly generated. Based on these combinations, composite solid waste-admixed concrete beam samples with different mix designs are prepared. The index of the composite solid waste-admixed concrete beam sample is denoted by i, where i∈N. + N + Let A represent a positive integer. Then, the mix proportion corresponding to the i-th composite solid waste concrete beam sample is: A1 of steel slag as a percentage of the coarse aggregate volume. i %; Slag powder accounts for A2 of the mass of cementitious materials i %; A3 of the volume of phosphogypsum powder in cementitious materials i %;

[0053] Determining the shear capacity of each of the composite solid waste concrete beam specimens includes: continuously applying an increasing shear load of the same magnitude to the composite solid waste concrete beam specimen until the composite solid waste concrete beam specimen fails in shear, and taking the shear load at the time of shear failure as the shear capacity of the composite solid waste concrete beam specimen.

[0054] Steel slag accounts for A1 of the volume of coarse aggregate i %; Example A1 i The percentage range is 30%-50%, used as a partial replacement of coarse aggregate;

[0055] Slag powder accounts for A2 of the mass of cementitious materials i %; Example A2 i The percentage range is 20%-30%, used as an admixture to enhance potential pozzolanic reactions;

[0056] The volume of phosphogypsum powder in the cementitious material is A3 i %. This example A3 i The percentage range is 5%-10%, used as an interface filler and thermal buffer material;

[0057] Following the standard concrete preparation process, the above materials are mixed evenly with cement, water and other admixtures to produce multi-solid waste concrete.

[0058] After the concrete was poured into the mold, it was vibrated and shaped, and then cured for 28 days under standard laboratory conditions to obtain a composite solid waste concrete beam sample.

[0059] On the loading device consisting of a three-point bending tester, a shear load is gradually applied to the composite solid waste concrete beam specimen through the loading device; the loading rate of the shear load is (0.01N, mm / s), where 0.01N represents 0.01 Newtons, until the composite solid waste concrete beam specimen fails in shear.

[0060] Let KQJ be the shear bearing capacity of the i-th composite solid waste concrete beam sample. i The expected shear capacity of the composite solid waste concrete beam specimen is denoted as KQJ′; the specimen conforming to KQJ′ is... i Several composite solid waste concrete beam samples with ≥KQJ′ are used as candidate sample sets. The candidate sample set is denoted as set {1,2,…,i 1,…,N1}, where i 1 represents the index mark of the composite solid waste concrete beam sample in the candidate sample set, and N1 is the total number of composite solid waste concrete beam samples in the candidate sample set.

[0061] The shear failure is defined as follows: the surface crack depth of the composite solid waste concrete beam specimen extends to half the current longitudinal height of the composite solid waste concrete beam specimen;

[0062] The crack condition data includes the equivalent temperature rise and crack opening displacement of the surface cracks of the composite solid waste concrete beam specimen under different loading periods. The loading period sequence corresponding to the i-th composite solid waste concrete beam specimen is defined as {1,2,…,j,…,M}, where j represents the index of the loading period and M is the total number of loading periods.

[0063] Further explanation: The formula for calculating the load variation factor is defined as follows:

[0064]

[0065] Among them, ZHYz i1 It is the load variation factor of the i1th composite solid waste concrete beam specimen; ZHYz i1 The smaller the value, the smaller the trend of crack opening displacement or equivalent temperature rise, which in turn represents the smaller the crack change trend of the composite solid waste concrete beam sample and the stronger the shear resistance.

[0066] Kd1 i1,j+1 With Kd1 i1,j These are the crack opening displacements of the i1th composite solid waste concrete beam sample under the j+1th and jth loading periods, respectively.

[0067] This represents the average change in crack opening displacement under adjacent loading periods. The smaller the value, the slower the crack development trend of the composite solid waste concrete beam sample under the current increasing shear load, indicating stronger compressive strength. A smaller average change in crack opening displacement indicates that the material can better suppress further crack propagation.

[0068] Crack opening displacement is defined as the relative displacement between adjacent mass points on both sides of a crack on the surface of a composite solid waste concrete beam sample under stress, along a direction perpendicular to the crack surface. In this embodiment, the adjacent mass points are set on the inner side walls of the crack on the surface of the composite solid waste concrete beam sample; the selection rules for adjacent mass points are as follows:

[0069] Let wk be the crack width of the i1th composite solid waste concrete beam sample during the j+1th loading period. i1,j+1 (Unit: mm), wk i1,j+1 It is the actual width of the cracks that opened on the surface of the concrete beam sample with mixed solid waste;

[0070] The distance Jd between a particle and the edge of a surface crack is defined as follows:

[0071] Jd=k·wk i1,j+1

[0072] Where k is a scaling factor, and its value ranges from 0.1 to k to 0.2.

[0073] If the crack width is wk i1,j+1 =10 mm, then:

[0074] When k = 0.1, Jd = 0.1 × 10 = 1 mm.

[0075] When k = 0.2, Jd = 0.2 × 10 = 2 mm.

[0076] Therefore, it is recommended to select a particle distance between 1 mm and 2 mm.

[0077] The selected Jd is near the crack edge to ensure that crack activity or deformation can be effectively captured.

[0078] The required measurement value for crack opening displacement is obtained using the following components:

[0079] Crack Opening Displacement (COD) is expressed as follows: displacement sensors (such as linear variable differential transformers (LVDT) or image correlation methods (DIC) are installed across the crack tip to measure the opening displacement between the crack surfaces.

[0080] Inductive or capacitive displacement sensors: These sensors can be used for high-precision and non-contact measurement of crack opening displacement.

[0081] Displacement measurement patch: Adhesive to both sides of a crack to monitor deformation of the material surface and displacement of the crack opening.

[0082] Further: Kd1 i1,j+1 The example calculation formula is as follows:

[0083]

[0084] Among them, |WY1 i1,j+1 -WY2 i1,j+1 | represents the relative displacement between adjacent mass points on both sides of the i1th composite solid waste concrete beam sample during the j+1th loading period; WY1 i1,j+1 and WY2 i1,j+1 These are the displacements of the particles on both sides;

[0085] (WY1 x WY1 y WY1 z ) indicates WY1 i1,j+1 Displacement in the x, y, and z axes;

[0086] (WY2 x WY2 y WY2 z ) represents WY2 i1,j+1 Displacement in the x, y, and z axes;

[0087] ΔT i1,j+1 With ΔT i1,j These are the equivalent temperature rises of the i1th composite solid waste concrete beam sample during the j+1th and jth loading periods, respectively.

[0088] This represents the equivalent temperature rise during adjacent loading periods. The smaller the value, the smaller the thermal energy of the surface cracks of the composite solid waste concrete beam sample under the current increasing shear load. This, in turn, represents a smaller relative sliding friction amplitude between the two side walls inside the surface cracks of the composite solid waste concrete beam sample, and a smaller amount of heat generated by the solid waste material inside the composite solid waste concrete beam sample.

[0089] b1 and b2 are the weight coefficients of the corresponding parameters, and the values ​​of b1 and b2 are in the interval (0,1); b1+b2=1.

[0090] b1 and b2 are used to adjust the contribution of crack opening displacement and equivalent temperature rise to the load change factor, respectively.

[0091] When b1>b2, it means that the contribution of the crack opening displacement is greater than the equivalent temperature rise;

[0092] Further explanation: Using ΔTmulti-interface Characterizing ΔT i1,j+1 or ΔT i1,j ΔT multi-interface The calculation method is as follows:

[0093] ΔT multi-interface =a1·ΔT steel +a2·ΔT slag

[0094] Where, ΔT steel It is the average temperature rise of one sidewall inside the surface crack of the composite solid waste concrete beam sample during the loading period;

[0095] ΔT slag It is the average temperature rise of the other sidewall inside the surface crack of the composite solid waste concrete beam sample during the loading period;

[0096] a1 and a2 are the weight coefficients of the corresponding parameters, and a1+a2=1, with the values ​​of a1 and a2 both within the interval (0,1).

[0097] ΔT multi-interface The larger the value, the higher the thermal energy of the surface cracks of the composite solid waste concrete beam sample during the loading period, which is not conducive to the stability of the surface cracks of the composite solid waste concrete beam sample.

[0098] Due to ΔT steel or ΔT slag An increase in temperature indicates that more heat is generated in the corresponding area, leading to a higher temperature on one or the other sidewall of the surface cracks in the composite solid waste concrete beam sample. This increased temperature will have the following effects on the surface cracks of the composite solid waste concrete beam sample:

[0099] (1) Stress concentration caused by temperature rise:

[0100] Non-uniform expansion induces internal stress: Due to the uneven temperature rise within the material of the composite solid waste concrete beam specimen (e.g., the surface temperature rises faster than the interior), different locations within the structure experience varying degrees of thermal expansion, creating stress differences. This non-uniform thermal stress often concentrates at the crack edges, leading to crack propagation.

[0101] Stress amplification at the tip of the original crack: The tip of an existing crack is a stress concentration point. When temperature changes cause thermal expansion or cold contraction, the stress concentration effect at the crack tip will further exert its effect, promoting crack propagation.

[0102] (2) Degradation of internal structure:

[0103] Increased temperature can affect the internal microstructure of materials, causing shrinkage or expansion reactions in the cement-based materials of concrete beam samples containing mixed solid waste. Excessively high temperatures may even lead to the collapse of amorphous structures or the decomposition of hydration products (such as the dehydration of CSH gel), reducing the overall strength of the structure and creating conditions for crack propagation.

[0104] When ΔT steel or ΔT slag A higher temperature indicates that these regions receive more heat energy; since heat accumulation leads to temperature rise, they directly increase the overall equivalent temperature rise ΔT. multi-interface The value.

[0105] In summary, ΔT multi-interface The larger value directly indicates that the surface cracks of the composite solid waste concrete beam sample have higher overall thermal activity, representing a higher state of thermal energy accumulation.

[0106] ΔT steel or ΔT slag Measurement method: Infrared thermal imager was used to capture the thermal distribution data of the inner two side walls of the cracks on the surface of the composite solid waste concrete beam sample;

[0107] The mean temperature at multiple points on both sides of the inner sidewalls of the cracks on the surface of the composite solid waste concrete beam sample was calculated; the following formula was used to characterize the mean temperature at multiple points:

[0108]

[0109] T steel,u T1 is the temperature value at the end of the loading period at the u-th measurement point inside one side wall of the surface crack of the composite solid waste concrete beam sample; initial is the average reference temperature of the inner sidewall of the surface crack of the composite solid waste concrete beam sample at the beginning of the loading period; n is the total number of measurement points in the inner sidewall of the surface crack of the composite solid waste concrete beam sample; u is the index mark of the measurement point in the inner sidewall of the surface crack of the composite solid waste concrete beam sample.

[0110] ΔT slag Measurement method: Using an infrared thermal imager, the average temperature change at each measurement point in the other side wall inside the crack on the surface of the composite solid waste concrete beam sample was calculated to determine the average temperature rise.

[0111] Formula Analysis:

[0112]

[0113] T slag,jT2 is the temperature value at the end of the loading period at the h-th measurement point inside the crack on the surface of the composite solid waste concrete beam sample; m is the total number of measurement points inside the crack on the surface of the composite solid waste concrete beam sample; h is the index mark of the measurement point inside the crack on the surface of the composite solid waste concrete beam sample; T2 initial It is the average reference temperature of the other side wall inside the surface crack of the composite solid waste concrete beam sample at the beginning of the loading period.

[0114] To further explain, according to KQJ i1 The difference between ≥KQJ′ is sorted from largest to smallest from the candidate sample set {1,2,…,i1,…,N1}; then the top three mixed solid waste concrete beam samples are selected as pre-selected samples.

[0115] The load variation factor of each composite solid waste concrete beam specimen in the pre-selected samples was obtained and denoted as ZHYz. i2 ZHYz i3 and ZHYz i4 The calculation of this factor not only provides specific data support for evaluating the shear performance of concrete, but also provides an important basis for subsequent design and helps to optimize the efficiency of material use.

[0116] And {i2, i3, i4} are contained in {1, 2, ..., N1}; the constraints include the following conditions one and two:

[0117] Condition one:

[0118]

[0119] Condition two:

[0120]

[0121] in, This means rounding up to the nearest integer, and setting the integers from 1 to the nearest integer. The loading period is considered the pre-loading phase; The subsequent loading period is considered the late loading period; i′∈{i2, i3, i4}; CB i′ It is the cost value of using the mixed solid waste in the i′th mixed solid waste concrete beam sample;

[0122] and These are the cost values ​​of steel slag, slag powder, and phosphogypsum powder, respectively.

[0123] It should be noted that when condition one of the constraints is met, it means that the crack change trend of the composite solid waste concrete beam sample in the early stage of loading is less than that in the later stage of loading.

[0124] The gradual increase in crack size reflects the progressive damage characteristics of the composite solid waste concrete beam specimen. The initial smaller crack size indicates that the solid waste components in the material act as anchors to the cracks and prevents their rapid propagation, partly due to the toughening effect of components such as fly ash and slag.

[0125] The intensified crack changes in the later stages reflect the reduced energy required for crack initiation and propagation under accumulated stress. Surface microcracks subsequently lose their constraint, forming a network and rapidly expanding. This process also helps identify the specific impact of solid waste blending ratios on material structural stability, guiding material selection and optimization.

[0126] The relatively small crack changes in the early stages of loading help provide a more stable safety margin in engineering. This not only ensures the initial safety of the structure, but also allows for the prediction of the entire service life of the beam structure. By monitoring the rate of crack change, maintenance and replacement times can be rationally scheduled.

[0127] Calculate the difference Q1 between the conditions corresponding to the early and late stages of loading:

[0128]

[0129] From the three pre-selected specimens, priority is given to selecting the composite solid waste concrete beam specimen that meets condition one of the constraint conditions;

[0130] This reflects a high degree of attention to engineering safety and economic benefits. While ensuring structural performance, it further improves the adaptability and economy of materials, which helps to control the timeliness and cost of engineering projects.

[0131] If at least two pre-selected samples meet the constraints, the pre-selected sample with the smallest Q1 value shall be selected.

[0132] If there is no case that meets condition one of the constraints, then from ZHYz i2 ZHYz i3 and ZHYz i4 Select the smallest value or CB i′ The smallest composite solid waste-admixed concrete beam specimen;

[0133] Based on the final selected pre-selected samples, the corresponding multi-solid waste material ratio and shear bearing capacity are determined.

[0134] Further explanation: The pre-measured shear capacity of the optimal composite solid waste concrete beam sample is denoted as KQJ. i′ And i′∈{i1, i2, i3}; the final shear capacity of the optimal composite solid waste concrete beam specimen is denoted as KQJ″. i′ ;

[0135] Based on the service environment of the concrete beams and columns with mixed solid waste, the environmental conditions are determined, including data on changes in environmental loads and environmental factors.

[0136] A calibration operation based on environmental conditions was performed on the new optimal composite solid waste concrete beam specimen to determine the final shear capacity of the optimal composite solid waste concrete beam specimen.

[0137] Environmental condition-based calibration operations specifically include:

[0138] 6.1) The environmental factor change data includes preset range values ​​for ambient temperature and ambient humidity. The ambient temperature and ambient humidity are set as preset range values. In this embodiment, the ambient temperature is 25℃±1℃ and the ambient humidity is 60%±5%. The environmental load change data is implemented by installing an environmental load simulation device to ensure continuous and stable load increase during the subsequent loading process.

[0139] 6.2) Within the preset range of environmental factor variation data, initiate the environmental load calibration procedure to apply a continuous and stable shear load to the optimal composite solid waste concrete beam specimen. This loading operation is performed according to a predetermined quantification scheme, i.e., the loading level is set to 5%, and the duration of each loading stage is not less than 60 seconds, until the shear bearing capacity of the optimal composite solid waste concrete beam specimen reaches or exceeds the shear bearing capacity KQJ measured in step S2. i′ The load was set to 105% of the total load; and the total number of load cycles in this loading process was set to m1; during the loading process, crack opening displacement, equivalent temperature rise data and loading time data were collected in real time to ensure that the sample response data under continuous environmental load conditions were obtained.

[0140] 6.3) During the loading process, crack state data at each loading level are recorded using pre-calibrated sensors, and the average load variation factor under m1 loading cycles is calculated. The final shear bearing capacity of the composite solid waste concrete beam samples was collected under environmental factor variations, and all test data were automatically stored using a data acquisition system.

[0141] The final shear capacity was used as the output using a linear regression method, KQJ i′ and The data is used as input for fitting, and finally obtained...

[0142] Where j1′ is the index of the number of loading cycles during the load loading process; η6 and η7 are fitting factors, and c8 is a constant adjustment term. It should be noted that η6, η7, and c8 are used in MATLAB's polyfit and polyval functions for linear regression analysis to ensure the accuracy and reliability of the fit.

[0143] η6 represents the sensitivity of the contribution of the initial shear strength of the material to the final shear capacity;

[0144] η7 represents the weakening effect of "crack damage accumulation" on the final bearing capacity;

[0145] c8 is used to correct systematic biases during measurement or testing.

[0146] It should be noted that the pre-measured shear bearing capacity KQJ i′ The physical meaning of this is that in the shear test of a concrete beam with mixed solid waste, when the specimen is first loaded, the cracks have not yet fully developed, and its bearing capacity is mainly determined by the concrete mix proportion, cement interface strength, cross-sectional geometry, etc.

[0147] The KQJ measured from this i′ This value reflects the intrinsic strength characteristics of the specimen under "no significant damage" conditions and is a preliminary estimate of its load-bearing capacity before final failure. The higher the value, the better the overall performance, including material grade, aggregate gradation, and interfacial bonding.

[0148] The physical meaning is as follows: As loading cycles continue, cracks will initiate, propagate, or new microcracks will form inside the beam. Crack status data for each loading cycle is recorded using pre-calibrated sensors. i′,j1′ Then take the average to get

[0149] This average value comprehensively reflects the cumulative damage caused by crack propagation across all loading cycles. More cracks, or greater severity, indicate higher damage. The larger the value, the weaker the beam's strength and the lower its stiffness, which negatively impacts the final shear capacity.

[0150] Experimental observations show that the final shear capacity of the composite solid waste concrete beam depends on both the "material strength in the undamaged state" and the KQJ... i′ The characterization also depends on "the weakening of strength due to crack accumulation during loading" by... reflect.

[0151] Linear superposition form The two effects can be combined by weight:

[0152] When the crack is very slight, The smaller the number of cases, the more dominant factor shifted to KQJ. i′ ;

[0153] When the crack is predicted to be severe, If the value is larger, the "crack weakening" term will lower the predicted value more.

[0154] This form is consistent with the actual failure mechanism: the initial strength of the material and the loading damage each contribute to the final performance, and can be approximately superimposed in a linear manner.

[0155] If only KQJ is used i′ Predicting the final shear capacity by using this method ignores the weakening effect of crack evolution during loading; the result often overestimates or underestimates the true limit.

[0156] If only Predicting this would also lose the fundamental contribution of materials to load-bearing capacity under varying environmental factors.

[0157] Combining the two can reflect both the material's intrinsic strength and the cumulative effect of damage, thereby improving prediction accuracy.

[0158] The above formulas are all dimensionless calculations. The formulas are derived from software simulations based on a large amount of collected data to obtain the most recent real-world results. The preset parameters in the formulas are set by those skilled in the art according to the actual situation.

[0159] The above embodiments can be implemented, in whole or in part, by software, hardware, firmware, or any other combination thereof. When implemented in software, the above embodiments can be implemented, in whole or in part, as a computer program product. Those skilled in the art will recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented by electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution.

[0160] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment, depending on actual needs.

[0161] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application.

Claims

1. A method for determining the shear bearing capacity of concrete beams and columns with mixed solid waste admixtures, applied to the preparation of samples with multiple known mixed solid waste admixture concrete mix proportions, characterized in that, The specific steps include: Step S1: Prepare multiple composite solid waste concrete beam samples with different proportions; Step S2: Apply incremental shear loads of the same magnitude to each composite solid waste concrete beam specimen to determine the shear capacity of each composite solid waste concrete beam specimen. The expected value of the shear bearing capacity required for the composite solid waste concrete beam specimens was set, and composite solid waste concrete beam specimens with shear bearing capacity above the expected value were selected to form a candidate specimen set. The candidate sample set is denoted as set {1,2,…,i1,…,N1}, where i1 represents the index mark of the composite solid waste concrete beam sample in the candidate sample set, and N1 is the total number of composite solid waste concrete beam samples in the candidate sample set. Step S3: Based on the candidate sample set, the time spent on each incremental shear load is recorded as the loading period, and the crack state data of the surface cracks of the composite solid waste concrete beam sample under each loading period are recorded. The crack condition data includes: the equivalent temperature rise and crack opening displacement of the surface cracks of the composite solid waste concrete beam specimen under different loading periods, and the loading period sequence corresponding to the i1th composite solid waste concrete beam specimen is defined as {1,2,…,j,…,M}, where j represents the index of the loading period and M is the total number of loading periods; Step S4: Receive and analyze the crack state data of each composite solid waste concrete beam specimen in the candidate specimen set under different loading periods, so as to calculate the load variation factor of each composite solid waste concrete beam specimen separately; the load variation factor is used to characterize the crack variation trend of the corresponding composite solid waste concrete beam specimen. Step S5: The final optimization objectives are to maximize the difference between the shear capacity and the expected value of the shear capacity, and to minimize the crack change trend corresponding to the load variation factor; and to set the constraint conditions for the composite solid waste concrete beam specimen. Based on the final optimization objective and constraints, the optimal composite solid waste concrete beam sample was selected from the candidate sample set. Step S6: Apply an environmental load variation calibration strategy to the selected optimal composite solid waste concrete beam specimens to determine their final shear capacity; The formula for calculating the load variation factor is defined as follows: ； in, It is the load variation factor of the i1th composite solid waste concrete beam specimen; The smaller the value, the smaller the trend of crack opening displacement or equivalent temperature rise, which in turn represents the smaller trend of crack change in the composite solid waste concrete beam sample. and These are the crack opening displacements of the i1th composite solid waste concrete beam sample under the j+1th and jth loading periods, respectively. and These are the equivalent temperature rises of the i1th composite solid waste concrete beam sample during the j+1th and jth loading periods, respectively. and These are the weighting coefficients of the corresponding parameters, and and The value is within the interval (0,1); .

2. The method for determining the shear bearing capacity of concrete beams and columns with mixed solid waste as described in claim 1, characterized in that: The preparation of multiple composite solid waste concrete beam samples with different proportions includes: A predefined mix proportion constraint range was established for the preparation of composite solid waste-admixed concrete beam samples. Within this range, multiple mix proportion combinations were randomly generated. Based on these combinations, composite solid waste-admixed concrete beam samples with different mix proportions were prepared. The index mark indicates the type of concrete beam sample containing mixed solid waste, and ; If the integer represents a positive integer, then the first... The mix proportions corresponding to the individual solid waste-admixed concrete beam samples are as follows: steel slag accounts for the following percentage of coarse aggregate volume. Slag powder accounts for a certain percentage of the mass of cementitious materials. The volume of phosphogypsum powder in the cementitious material ; Determining the shear capacity of each of the composite solid waste concrete beam specimens includes: continuously applying an increasing shear load of the same magnitude to the composite solid waste concrete beam specimen until the composite solid waste concrete beam specimen fails in shear, and taking the shear load at the time of shear failure as the shear capacity of the composite solid waste concrete beam specimen. Let the shear bearing capacity of the i-th composite solid waste concrete beam sample be denoted as . The expected value of the shear bearing capacity required for the composite solid waste concrete beam specimen is denoted as . ; will conform Several composite solid waste-admixed concrete beam samples were selected as the candidate sample set. The shear failure is defined as follows: the surface crack depth of the composite solid waste concrete beam specimen extends to half the current longitudinal height of the composite solid waste concrete beam specimen.

3. The method for determining the shear bearing capacity of concrete beams and columns with mixed solid waste as described in claim 2, characterized in that: according to The difference values ​​are sorted from largest to smallest from the candidate sample set {1,2,...,i1,...,N1}; then the top three mixed solid waste concrete beam samples are selected as pre-selected samples. The load variation factor of each composite solid waste concrete beam specimen in the pre-selected samples was obtained and denoted as follows: , and And {i2, i3, i4} are contained in {1, 2, ..., N1}; the constraints include the following conditions one and two: Condition one: ； Condition two: ； in, This means rounding up to the nearest integer, and setting the integers from 1 to the nearest integer. The loading period is considered the pre-loading phase; The subsequent loading period is considered the later loading stage; ; It is the first The cost of using solid waste in a concrete beam sample with mixed solid waste; , and These are the cost values ​​of steel slag, slag powder, and phosphogypsum powder, respectively. When condition one is met, it means that the crack change trend of the composite solid waste concrete beam sample in the early stage of loading is less than that in the later stage of loading. Calculate the difference Q1 between the conditions corresponding to the early and late stages of loading: ； From the three pre-selected specimens, the pre-selected specimen that meets condition one of the constraints is selected as the optimal composite solid waste concrete beam specimen. If at least two pre-selected specimens meet the constraints, the pre-selected specimen with the smallest Q1 value shall be selected as the optimal composite solid waste concrete beam specimen. If there is no case that meets condition one of the constraints, then from , and Select the smallest value or The smallest pre-selected sample was used as the optimal composite solid waste concrete beam sample.

4. The method for determining the shear bearing capacity of concrete beams and columns with mixed solid waste as described in claim 3, characterized in that: The pre-measured shear bearing capacity of the optimal composite solid waste concrete beam sample is denoted as . ,and The final shear capacity of the optimal composite solid waste concrete beam specimen is denoted as . ; Based on the service environment of the concrete beams and columns with mixed solid waste, the environmental conditions are determined, including data on changes in environmental loads and environmental factors. An environmentally-based calibration procedure was performed on the new optimal composite solid waste concrete beam specimen to determine its final shear capacity. .

5. The method for determining the shear bearing capacity of concrete beams and columns with mixed solid waste as described in claim 4, characterized in that: Environmental condition-based calibration operations specifically include: The environmental factor change data includes preset range values ​​for ambient temperature and ambient humidity, and the ambient temperature and ambient humidity are set to preset range values; Within the preset range of environmental factor variation data, the environmental load calibration procedure is initiated, applying a continuous and stable shear load to the optimal composite solid waste concrete beam specimen; until the shear bearing capacity of the optimal composite solid waste concrete beam specimen reaches or exceeds the shear bearing capacity measured in step S2. 105%; and set the total number of loading cycles in this load loading process as m1; Calculate the average load variation factor under m1 loading cycles. The final shear capacity of composite solid waste concrete beam samples was collected under varying environmental factors, and a linear regression method was used to output the final shear capacity. and The data is used as input for fitting, and finally obtained... ; in, It is the index of the number of load cycles during the load loading process; and It is a fitting factor. It is a constant adjustment term.

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