Method, device and storage medium for determining multi-axial strength of freeze-thawed concrete

Abstract

This disclosure relates to a method, apparatus, and storage medium for determining the multiaxial strength of freeze-thawed concrete. The method includes: obtaining the uniaxial compressive strength of the concrete after freeze-thaw and the uniaxial compressive strength of the concrete before freeze-thaw, and determining the relative uniaxial compressive strength of the concrete. The relative uniaxial compressive strength is used to characterize the influence of different freeze-thaw factors on the multiaxial strength of the concrete; based on the relative uniaxial compressive strength of the concrete, the multiaxial strength of the concrete after freeze-thaw can be determined by the relationship between the uniaxial compressive strength and the multiaxial strength. The method, apparatus, and storage medium of this application have a unified parameter (relative uniaxial compressive strength), which is applicable to concrete with different freeze-thaw factors. It eliminates the need for extensive and complex multiaxial strength tests for parameter calibration for each freeze-thaw factor, significantly improving efficiency, reducing costs, broadening applicability, improving prediction accuracy, and facilitating practical applications.

Description

Technical Field

[0001] This disclosure relates to the field of concrete mechanics, and in particular to a method, apparatus and storage medium for determining the multiaxial strength of freeze-thaw concrete. Background Technology

[0002] Concrete often suffers freeze-thaw damage during service in cold regions such as polar regions and high plateaus, leading to cracking and a decline in mechanical properties. Simultaneously, load-bearing concrete is frequently subjected to complex multiaxial stress states. Therefore, accurate characterization of the multiaxial strength of concrete after freeze-thaw damage is of great significance for ensuring the safe service of concrete structures in cold regions.

[0003] Existing research has shown that traditional multiaxial strength criteria for undamaged concrete are inapplicable when determining the multiaxial strength of freeze-thawed concrete. Current methods for determining the multiaxial strength of freeze-thawed concrete require a large number of complex multiaxial strength tests to establish the relationship between multiaxial strength and the number of freeze-thaw cycles. Because the freeze-thaw cycle of concrete is influenced by numerous factors with varying effects on multiaxial strength, each factor requires a series of multiaxial strength tests to calibrate the parameters of the strength criteria. This results in a huge number of tests, high research costs, and numerous forms and parameters of the strength criteria, making it difficult to encompass all freeze-thaw influencing factors, leading to low applicability and difficulties in engineering applications. Therefore, a novel method for determining the multiaxial strength of freeze-thawed concrete is urgently needed, which should be widely applicable, cost-effective, and improve prediction accuracy for convenient practical application. Summary of the Invention

[0004] In view of this, this disclosure proposes a method, apparatus and storage medium for determining the multiaxial strength of freeze-thaw concrete.

[0005] According to one aspect of this disclosure, a method for determining the multiaxial strength of freeze-thaw concrete is provided. The method includes:

[0006] The uniaxial compressive strength of concrete after freeze-thaw and before freeze-thaw are obtained to determine the relative uniaxial compressive strength of concrete. The relative uniaxial compressive strength is used to characterize the influence of different freeze-thaw factors on the multiaxial strength of concrete. Based on the relative uniaxial compressive strength of concrete, the multiaxial strength of concrete after freeze-thaw is determined by the relationship between the uniaxial compressive strength and multiaxial strength of concrete after freeze-thaw.

[0007] In one possible implementation, the relative uniaxial compressive strength of concrete is the ratio of the uniaxial compressive strength of concrete after freeze-thaw to the uniaxial compressive strength of concrete before freeze-thaw.

[0008] In one possible implementation, the relationship between the uniaxial compressive strength and multiaxial strength of the freeze-thawed concrete is represented by the normalized failure surface of the freeze-thawed concrete under multiaxial stress. The method may further include: determining the normalized failure surface by normalizing the concrete by dividing it by the uniaxial compressive strength of the freeze-thawed concrete based on the relative uniaxial compressive strength of the concrete. The normalized failure surface is the normalized failure surface under the principal stress space and the Heraeus-Westergaard stress space.

[0009] In one possible implementation, the normalized failure surface is described by the tensile-compressive meridian and the off-plane envelope, which is described by the Lode angle, the mean principal stress, and the mean shear stress.

[0010] In one possible implementation, the relationship between the uniaxial compressive strength and multiaxial strength of freeze-thawed concrete is expressed piecewise in response to different degrees of constraint, where the degree of constraint is the ratio of the average principal stress after freeze-thaw to the uniaxial compressive strength of the freeze-thawed concrete.

[0011] In one possible implementation, the method may further include: in response to a constraint degree not being less than a critical value, determining the multiaxial strength of the frozen-thawed concrete based on the relative uniaxial compressive strength of the concrete by means of the relationship between the uniaxial compressive strength and multiaxial strength of the unfrozen concrete; wherein the ratio of uniaxial tensile-compressive strength of the unfrozen concrete to the ratio of uniaxial tensile-compressive strength of the frozen-thawed concrete to the ratio of uniaxial tensile-compressive strength of the frozen-thawed concrete in the relationship between the uniaxial compressive strength and multiaxial strength of the unfrozen concrete is replaced by the ratio of uniaxial tensile-compressive strength of the frozen-thawed concrete, and the uniaxial compressive strength of the unfrozen concrete is replaced by the uniaxial compressive strength of the frozen-thawed concrete.

[0012] In one possible implementation, the multiaxial strength of the concrete after freeze-thaw is determined based on the relative uniaxial compressive strength of the concrete and through the relationship between the uniaxial compressive strength and multiaxial strength of the concrete after freeze-thaw, including: in response to the constraint degree being less than a critical value, the multiaxial strength of the concrete after freeze-thaw is determined based on the relative uniaxial compressive strength of the concrete and through the relationship between the uniaxial compressive strength and multiaxial strength of the concrete after freeze-thaw.

[0013] The relationship between the uniaxial compressive strength and multiaxial strength of concrete after freeze-thaw cycles is represented by the normalized failure surface of the concrete under multiaxial stress. The normalized failure surface is described by the tensile-compressive meridian and the deviated plane envelope. The tensile-compressive meridian is calculated as follows:

[0014]

[0015] Where, σ m f represents the principal stress after freeze-thaw cycles. cD This represents the uniaxial compressive strength of confined concrete in an unconfined state after freeze-thaw cycles. ρ is the deviated plane stress in the Heraeus-Westergaard stress space;

[0016] The calculation method for m0 is as follows:

[0017]

[0018] The calculation method for m1 is as follows:

[0019]

[0020] The calculation method for m2 is as follows:

[0021]

[0022] Among them, R c This represents the relative uniaxial compressive strength of concrete. k0, k1, and k2 are preset parameters for the tension-compression meridians corresponding to unfrozen concrete. The preset thresholds are: n = 0.3 for the pull meridian and n = 0.11 for the press meridian.

[0023] In one possible implementation, the concrete includes confined concrete, and the method may further include: in response to a confinement degree not being less than a critical value, determining the multiaxial strength of the confined concrete under confinement after freeze-thaw cycles by means of a relationship between the uniaxial compressive strength of the unconstrained confined concrete under unconstrained states and its multiaxial strength under confinement states, based on the relative uniaxial compressive strength of the confined concrete under unconstrained states; wherein, in the relationship between the uniaxial compressive strength of the unconstrained confined concrete under unconstrained states and its multiaxial strength under confinement states, the ratio of the uniaxial tensile-compressive strength of the unconstrained confined concrete under unconstrained states is replaced by the uniaxial tensile-compressive strength of the confined concrete under unconstrained states after freeze-thaw cycles, and the uniaxial compressive strength of the unconstrained confined concrete under unconstrained states is replaced by the uniaxial compressive strength of the confined concrete under unconstrained states after freeze-thaw cycles.

[0024] In one possible implementation, the concrete includes confined concrete. The multiaxial strength of the concrete after freeze-thaw is determined based on its relative uniaxial compressive strength, through the relationship between the uniaxial compressive strength and multiaxial strength of the concrete after freeze-thaw. This includes: in response to a constraint degree being less than a critical value, determining the multiaxial strength of the confined concrete under constrained conditions based on its relative uniaxial compressive strength in the unconstrained state and the confining pressure acting on the confined concrete, through the relationship between the uniaxial compressive strength in the unconstrained state and the multiaxial strength under constrained conditions. The relationship between the uniaxial compressive strength in the unconstrained state and the multiaxial strength under constrained conditions is obtained based on the relationship between the uniaxial compressive strength and multiaxial strength of the concrete after freeze-thaw.

[0025] The calculation method for the multiaxial strength of confined concrete under confinement after freeze-thaw cycles is as follows:

[0026]

[0027] Among them, f ccD f represents the multiaxial strength of confined concrete under confinement after freeze-thaw cycles. r f represents the confining pressure exerted on the confined concrete. cD R represents the uniaxial compressive strength of confined concrete in the unconfined state after freeze-thaw cycles. c It represents the relative uniaxial compressive strength of confined concrete in an unconfined state.

[0028] In one possible implementation, the critical value of the constraint degree is -0.8.

[0029] In one possible implementation, the freeze-thaw influencing factors include one or more of the following: concrete grade, air content of concrete, pore structure of concrete, water saturation of concrete, type of freeze-thaw liquid, lower limit of freeze-thaw temperature, and stress state during freeze-thaw.

[0030] According to another aspect of this disclosure, an apparatus for determining the multiaxial strength of freeze-thaw concrete is provided. The apparatus includes:

[0031] The first determining module is used to obtain the uniaxial compressive strength of concrete after freeze-thaw and the uniaxial compressive strength of concrete before freeze-thaw, and to determine the relative uniaxial compressive strength of concrete. The relative uniaxial compressive strength is used to characterize the influence of different freeze-thaw factors on the multiaxial strength of concrete. The second determining module is used to determine the multiaxial strength of concrete after freeze-thaw based on the relative uniaxial compressive strength of concrete and the relationship between the uniaxial compressive strength and multiaxial strength of concrete after freeze-thaw.

[0032] In one possible implementation, the relative uniaxial compressive strength of concrete is the ratio of the uniaxial compressive strength of concrete after freeze-thaw to the uniaxial compressive strength of concrete before freeze-thaw.

[0033] In one possible implementation, the relationship between the uniaxial compressive strength and multiaxial strength of the freeze-thawed concrete is represented by the normalized failure surface of the freeze-thawed concrete under multiaxial stress. The device may further include a third determining module for determining the normalized failure surface based on the relative uniaxial compressive strength of the concrete by normalizing it by dividing it by the uniaxial compressive strength of the freeze-thawed concrete. The normalized failure surface is the normalized failure surface under the principal stress space and the Heer-Westergaard stress space.

[0034] In one possible implementation, the normalized failure surface is described by the tensile-compressive meridian and the off-plane envelope, which is described by the Lode angle, the mean principal stress, and the mean shear stress.

[0035] In one possible implementation, the relationship between the uniaxial compressive strength and multiaxial strength of freeze-thawed concrete is expressed piecewise in response to different degrees of constraint, where the degree of constraint is the ratio of the average principal stress after freeze-thaw to the uniaxial compressive strength of the freeze-thawed concrete.

[0036] In one possible implementation, the device may further include: a fourth determining module, configured to determine the multiaxial strength of the concrete after freeze-thaw based on the relationship between the uniaxial compressive strength and multiaxial strength of the unfrozen concrete, in response to a constraint degree not being less than a critical value; wherein the ratio of uniaxial tensile-compressive strength of the unfrozen concrete to the ratio of uniaxial tensile-compressive strength of the unfrozen concrete to the multiaxial strength of the concrete after freeze-thaw, and the uniaxial compressive strength of the unfrozen concrete to the uniaxial compressive strength of the concrete after freeze-thaw.

[0037] In one possible implementation, the second determining module is used to: in response to the constraint degree being less than a critical value, determine the multiaxial strength of the concrete after freeze-thaw by means of the relationship between the uniaxial compressive strength and multiaxial strength of the concrete after freeze-thaw based on the relative uniaxial compressive strength of the concrete.

[0038] The relationship between the uniaxial compressive strength and multiaxial strength of concrete after freeze-thaw cycles is represented by the normalized failure surface of the concrete under multiaxial stress. The normalized failure surface is described by the tensile-compressive meridian and the deviated plane envelope. The tensile-compressive meridian is calculated as follows:

[0039]

[0040] Where, σ m f represents the principal stress after freeze-thaw cycles. cD This represents the uniaxial compressive strength of confined concrete in an unconfined state after freeze-thaw cycles. ρ is the deviated plane stress in the Heraeus-Westergaard stress space;

[0041] The calculation method for m0 is as follows:

[0042]

[0043] The calculation method for m1 is as follows:

[0044]

[0045] The calculation method for m2 is as follows:

[0046]

[0047] Among them, R c This represents the relative uniaxial compressive strength of concrete. k0, k1, and k2 are preset parameters for the tension-compression meridians corresponding to unfrozen concrete. The preset thresholds are: n = 0.3 for the pull meridian and n = 0.11 for the press meridian.

[0048] In one possible implementation, the concrete includes confined concrete, and the device may further include: a fifth determining module, configured to, in response to a constraint degree not being less than a critical value, determine the multiaxial strength of the confined concrete under a freeze-thaw condition based on the relative uniaxial compressive strength of the confined concrete under an unconstrained state, through the relationship between the uniaxial compressive strength of the unfrozen confined concrete under an unconstrained state and its multiaxial strength under a constrained state; wherein, in the relationship between the uniaxial compressive strength of the unfrozen confined concrete under an unconstrained state and its multiaxial strength under a constrained state, the ratio of the uniaxial tensile-compressive strength of the unfrozen confined concrete under an unconstrained state is replaced by the uniaxial tensile-compressive strength of the confined concrete under a freeze-thaw condition under an unconstrained state, and the uniaxial compressive strength of the unfrozen confined concrete under an unconstrained state is replaced by the uniaxial compressive strength of the confined concrete under a freeze-thaw condition under an unconstrained state.

[0049] In one possible implementation, the concrete includes confined concrete. A second determining module is configured to: in response to a constraint degree less than a critical value, determine the multiaxial strength of the confined concrete under confinement based on the relative uniaxial compressive strength of the confined concrete in the unconstrained state and the confining pressure on the confined concrete, by means of the relationship between the uniaxial compressive strength of the confined concrete under the unconstrained state and the multiaxial strength under the confinement state, wherein the relationship between the uniaxial compressive strength of the confined concrete under the unconstrained state and the multiaxial strength under the confinement state is obtained based on the relationship between the uniaxial compressive strength and the multiaxial strength of the confined concrete under the freeze-thaw.

[0050] The calculation method for the multiaxial strength of confined concrete under confinement after freeze-thaw cycles is as follows:

[0051]

[0052] Among them, f ccD f represents the multiaxial strength of confined concrete under confinement after freeze-thaw cycles. r f represents the confining pressure exerted on the confined concrete. cD R represents the uniaxial compressive strength of confined concrete in the unconfined state after freeze-thaw cycles. c It represents the relative uniaxial compressive strength of confined concrete in an unconfined state.

[0053] In one possible implementation, the critical value of the constraint degree is -0.8.

[0054] In one possible implementation, the freeze-thaw influencing factors include one or more of the following: concrete grade, air content of concrete, pore structure of concrete, water saturation of concrete, type of freeze-thaw liquid, lower limit of freeze-thaw temperature, and stress state during freeze-thaw.

[0055] According to another aspect of this disclosure, a device for determining the multiaxial strength of freeze-thaw concrete is provided, comprising: a processor; a memory for storing processor-executable instructions; wherein the processor is configured to implement the above method when executing the instructions stored in the memory.

[0056] According to another aspect of this disclosure, a non-volatile computer-readable storage medium is provided that stores computer program instructions thereon, wherein the computer program instructions, when executed by a processor, implement the above-described method.

[0057] According to another aspect of this disclosure, a computer program product is provided, including computer-readable code, or a non-volatile computer-readable storage medium carrying computer-readable code, wherein when the computer-readable code is run in a processor of an electronic device, the processor in the electronic device performs the above-described method.

[0058] According to the embodiments of this application, by characterizing the influence of different freeze-thaw factors on the multiaxial strength of concrete using the relative uniaxial compressive strength of concrete, the established relationship between the uniaxial compressive strength and multiaxial strength of frozen-thawed concrete has a unified parameter (relative uniaxial compressive strength), which is applicable to concrete with different freeze-thaw factors. This eliminates the need for numerous complex multiaxial strength tests for parameter calibration for each freeze-thaw factor, improving efficiency and reducing costs. The relationship between the uniaxial compressive strength and multiaxial strength of frozen-thawed concrete established in this application for determining the multiaxial strength of frozen-thawed concrete has a wide range of applications and improves prediction accuracy.

[0059] Other features and aspects of this disclosure will become clear from the following detailed description of exemplary embodiments with reference to the accompanying drawings. Attached Figure Description

[0060] The accompanying drawings, which are included in and form part of this specification, illustrate exemplary embodiments, features, and aspects of this disclosure together with the specification and serve to explain the principles of this disclosure.

[0061] Figure 1 A schematic diagram illustrating an application scenario according to an embodiment of this application is shown.

[0062] Figure 2 A flowchart illustrating a method for determining the multiaxial strength of freeze-thawed concrete according to an embodiment of this application is shown.

[0063] Figure 3A schematic diagram of a meridian according to an embodiment of this application is shown.

[0064] Figure 4 This diagram illustrates the relationship between the uniaxial compressive strength and multiaxial strength of concrete after freeze-thaw cycles, according to an embodiment of this application.

[0065] Figure 5 A schematic diagram of a normalized destruction surface according to an embodiment of this application is shown.

[0066] Figure 6 This diagram illustrates fitting a calculation formula according to an embodiment of the present application.

[0067] Figure 7 A structural diagram of a device for determining the multiaxial strength of freeze-thawed concrete according to an embodiment of this application is shown.

[0068] Figure 8 This is a block diagram illustrating an apparatus 1900 for determining the multiaxial strength of freeze-thaw concrete according to an exemplary embodiment. Detailed Implementation

[0069] Various exemplary embodiments, features, and aspects of this disclosure will now be described in detail with reference to the accompanying drawings. The same reference numerals in the drawings denote elements that have the same or similar functions. Although various aspects of the embodiments are shown in the drawings, they are not necessarily drawn to scale unless specifically indicated otherwise.

[0070] The term “exemplary” as used herein means “serving as an example, embodiment, or illustration.” Any embodiment illustrated herein as “exemplary” is not necessarily to be construed as superior to or better than other embodiments.

[0071] Furthermore, to better illustrate this disclosure, numerous specific details are set forth in the following detailed description. Those skilled in the art will understand that this disclosure can be practiced without certain specific details. In some instances, methods, means, components, and circuits well known to those skilled in the art have not been described in detail in order to highlight the main points of this disclosure.

[0072] Concrete often suffers freeze-thaw damage during service in cold regions such as polar regions and high plateaus, leading to cracking and a decline in mechanical properties. Simultaneously, load-bearing concrete is frequently subjected to complex multiaxial stress states. Therefore, accurate characterization of the multiaxial strength of concrete after freeze-thaw damage is crucial for ensuring the safe service of concrete structures in cold regions. Existing research indicates that traditional multiaxial strength criteria for undamaged concrete are inapplicable when determining the multiaxial strength of freeze-thawed concrete. Current methods for determining the multiaxial strength of freeze-thawed concrete require a series of complex multiaxial strength tests to establish the relationship between multiaxial strength and the number of freeze-thaw cycles. Because freeze-thaw factors affecting concrete are numerous and their impact on multiaxial strength varies greatly, each factor requires a series of multiaxial strength tests to calibrate the parameters of the strength criteria. This results in a massive number of tests, high research costs, and numerous forms and parameters of the strength criteria, making it difficult to encompass all freeze-thaw factors, leading to low applicability and difficulties in engineering applications. Therefore, a novel method for determining the multiaxial strength of freeze-thawed concrete is urgently needed, which should be widely applicable, cost-effective, and improve prediction accuracy for practical application.

[0073] In view of this, this application proposes a method, apparatus, and storage medium for determining the multiaxial strength of freeze-thawed concrete. The method of this application characterizes the influence of different freeze-thaw factors on the multiaxial strength of concrete by using the relative uniaxial compressive strength of the concrete. The established relationship between the uniaxial compressive strength and multiaxial strength of freeze-thawed concrete has a unified parameter (relative uniaxial compressive strength), applicable to concretes with different freeze-thaw factors. It eliminates the need for numerous complex multiaxial strength tests and parameter calibration for each freeze-thaw factor, improving efficiency and reducing costs. Determining the multiaxial strength of freeze-thawed concrete through the relationship between the uniaxial compressive strength and multiaxial strength established in this application has a wide range of applications and improves prediction accuracy.

[0074] Figure 1 This diagram illustrates an application scenario according to an embodiment of the present application. The method of this embodiment can be applied to determining the multiaxial strength of freeze-thaw concrete under different freeze-thaw influencing factors. In traditional research, the main influencing factor of freeze-thaw damage is the number of freeze-thaw cycles. However, with the development of harsher service environments for concrete and new materials and structural forms, factors such as concrete pore structure, water saturation, type of freeze-thaw liquid, lower freeze-thaw limit temperature, and stress state during freeze-thaw cycles all significantly affect freeze-thaw damage in concrete. Figure 1 As shown, when concrete suffers freeze-thaw damage, the uniaxial compressive strength of the concrete after freeze-thaw (as shown in f in the figure) can be obtained according to the method of the embodiments of this application. cD ) and the uniaxial compressive strength of concrete before freeze-thaw (as shown in the figure f) c Determine the relative uniaxial compressive strength (R in the figure). c), with R c The effects of various freeze-thaw factors on freeze-thaw damage to concrete are characterized. The multiaxial strength of concrete is obtained by establishing a pre-defined relationship between the uniaxial compressive strength and the multiaxial strength of concrete after freeze-thaw.

[0075] The method described in this application can be used on a terminal device or a server. The terminal device can be any one or more of the following: mobile phone, foldable electronic device, tablet computer, desktop computer, laptop computer, handheld computer, laptop, ultra-mobile personal computer (UMPC), netbook, cellular phone, personal digital assistant (PDA), and in-vehicle device. This application does not impose any special limitation on the specific type of terminal device; it can have wired or wireless communication capabilities.

[0076] Servers can be located locally or in the cloud, and can be physical devices or virtual devices such as virtual machines and containers. They possess wireless communication capabilities, which can be configured within the server's chip (system) or other components. Wireless communication capabilities can be implemented through mobile communication technologies such as 2G / 3G / 4G / 5G, as well as Wi-Fi, Bluetooth, frequency modulation (FM), data radio, and satellite communication. Wired connections can also be used to communicate and interact with other devices.

[0077] The following is passed Figures 2-6 This paper introduces the method for determining the multiaxial strength of freeze-thawed concrete according to embodiments of this application.

[0078] Figure 2 A flowchart illustrating a method for determining the multiaxial strength of freeze-thaw concrete according to an embodiment of this application is shown. This method can be used in terminal devices or servers, such as… Figure 2 As shown, the method may include:

[0079] Step S201: Obtain the uniaxial compressive strength of the concrete after freeze-thaw and the uniaxial compressive strength of the concrete before freeze-thaw, and determine the relative uniaxial compressive strength of the concrete.

[0080] Uniaxial compressive strength generally refers to the load per unit area that a standard concrete specimen can withstand under uniaxial compression until failure. For example, it can be determined through freeze-thaw cycle tests, uniaxial strength tests, or other existing simulation methods to determine the uniaxial compressive strength (which can be referred to as f) of the concrete specimen before freeze-thaw cycles. c ) and the uniaxial compressive strength after freeze-thaw (which can be called f) cDThe relative uniaxial compressive strength of concrete is (which can be referred to as R). c The ratio of the uniaxial compressive strength of concrete after freeze-thaw to the uniaxial compressive strength of concrete before freeze-thaw is called R. c =f cD / f c .

[0081] Relative uniaxial compressive strength can be used to characterize the influence of different freeze-thaw factors on the multiaxial strength of concrete. Freeze-thaw factors include one or more of the following: concrete grade, air content, pore structure, water saturation, type of freeze-thaw liquid, lower freeze-thaw limit temperature, and stress state during freeze-thaw cycles. See also... Figure 3 This illustrates a schematic diagram of a meridian according to an embodiment of this application. Figure 3 As shown, under different freeze-thaw influencing factors, when the relative uniaxial compressive strength R c At the same time, the meridian ( Figure 3 The curve in σ m / f cD τ can represent the mean principal stress of the normalized multiaxial principal stresses. m / f cD The mean shear stress (which can represent the normalized multiaxial shear stress) lies on a single curve, and the meridian can be used to express a typical cross-section of the failure surface of concrete. In particular, with... Figure 3 Taking the right side as an example, Figure 3 The right-side view is R in the left-side view c =0.6~0.8 corresponding meridians. It can be seen that under different freeze-thaw influencing factors (such as different types of concrete, different types of freeze-thaw liquids, etc.), as long as the relative uniaxial compressive strength R c If they are identical or sufficiently close, the meridians lie essentially on a single curve. This indicates the relative uniaxial compressive strength R. c It can replace different freeze-thaw influencing factors to uniformly reflect their impact on the multiaxial strength of concrete.

[0082] Step S202: Based on the relative uniaxial compressive strength of concrete, the multiaxial strength of concrete after freeze-thaw is determined by the relationship between the uniaxial compressive strength and multiaxial strength of concrete after freeze-thaw.

[0083] The multiaxial strength of freeze-thawed concrete generally refers to the maximum value of the three principal stresses at failure under multiaxial stress, with positive values ​​under tension and negative values ​​under compression. The relationship between the uniaxial compressive strength and multiaxial strength of freeze-thawed concrete can be represented by the normalized failure surface of freeze-thawed concrete under multiaxial stress.

[0084] Normalized failure surface and R of concrete after freeze-thaw under multiaxial stress cThe relevant relationships can be established in advance, so that in S202, when R... c When determined, establish a specific R c The relationship between the uniaxial compressive strength and multiaxial strength of concrete after freeze-thaw cycles was investigated to further determine the multiaxial strength of concrete after freeze-thaw cycles. (See also...) Figure 4 This diagram illustrates the relationship between the uniaxial compressive strength and multiaxial strength of freeze-thawed concrete according to an embodiment of this application. The relationship can be established in advance based on existing multiaxial strength data of freeze-thawed concrete under various freeze-thaw influencing factors (including freeze-thaw cycle count, pore structure, and freeze-thaw fluid type, as shown in the diagram). The data points are normalized by dividing by the uniaxial compressive strength after freeze-thaw, thus establishing R0. c The normalized failure surface of concrete after freeze-thaw cycles under multiaxial stress (the description of this normalized failure surface is...) Figure 4 The correlation between the multiaxial strength criteria after freeze-thaw cycles (e.g.) Figure 4 As shown, it can be represented as R c The shapes of the normalized failure surfaces of concrete after freeze-thaw cycles differ under multiaxial stress. When determining the multiaxial strength of concrete after freeze-thaw cycles, data from freeze-thaw cycle tests, uniaxial strength tests, or simulations can be used to obtain the changes in uniaxial compressive strength before and after freeze-thaw cycles, and R can be selected. c Instead of using multiple freeze-thaw influencing factors as indicators, based on a pre-established R... c By establishing the correlation between the normalized failure surface of freeze-thawed concrete under multiaxial stress and the uniaxial compressive strength of the concrete, the relationship between uniaxial compressive strength and multiaxial strength can be established, thereby determining the multiaxial strength of the concrete. Compared with the prior art, the method of this application establishes a unified parameter for the relationship between uniaxial compressive strength and multiaxial strength of freeze-thawed concrete, applicable to concretes with different freeze-thaw influencing factors. It eliminates the need for extensive and complex multiaxial strength tests for parameter calibration for each freeze-thaw influencing factor, improving efficiency, reducing costs, broadening applicability, improving prediction accuracy, facilitating practical application, and effectively promoting research on the influence of a wider range of freeze-thaw factors on the multiaxial strength of concrete, thus contributing to the development of cold-region and polar engineering in my country.

[0085] According to the embodiments of this application, by characterizing the influence of different freeze-thaw factors on the multiaxial strength of concrete using the relative uniaxial compressive strength of concrete, the established relationship between the uniaxial compressive strength and multiaxial strength of frozen-thawed concrete has a unified parameter (relative uniaxial compressive strength), which is applicable to concrete with different freeze-thaw factors. This eliminates the need for numerous complex multiaxial strength tests for parameter calibration for each freeze-thaw factor, improving efficiency and reducing costs. The relationship between the uniaxial compressive strength and multiaxial strength of frozen-thawed concrete established in this application for determining the multiaxial strength of frozen-thawed concrete has a wide range of applications and improves prediction accuracy.

[0086] For the normalized failure surface of freeze-thawed concrete under multiaxial stress, the method may further include:

[0087] Based on the relative uniaxial compressive strength of concrete, the normalized failure surface is determined by normalizing it by dividing it by the uniaxial compressive strength of concrete after freeze-thaw cycles.

[0088] The normalized failure surface is defined in both the principal stress space (σ1,σ2,σ3) and the Heer-Westergaard stress space (ξ,ρ,θ). The principal stress space represents a spatial coordinate system with the three principal stress components σ1, σ2, and σ3 as coordinate axes. In the Heer-Westergaard stress space (ξ,ρ,θ), ξ represents hydrostatic pressure, ρ represents deviatoric plane stress, and θ represents the Lode angle. Unlike existing technologies, this application normalizes the failure surface by dividing by the uniaxial compressive strength of the freeze-thawed concrete. From the failure surface established after this normalization, we discovered that the relationship between the uniaxial compressive strength and multiaxial strength of the freeze-thawed concrete can be expressed piecewise in response to different constraint degrees, thus enabling a more accurate and efficient description of the actual failure of the freeze-thawed concrete and improving prediction accuracy.

[0089] The multiaxial strength of concrete after freeze-thaw cycles can be determined by the normalized failure surface of the concrete after freeze-thaw cycles. The failure surface is described by the tensile-compressive meridian and the deviated plane envelope. The tensile-compressive meridian is described by the Lode angle, the mean principal stress, and the mean shear stress.

[0090] Figure 5 A schematic diagram showing a normalized failure surface according to an embodiment of this application is provided. See also: Figure 5 To describe the normalized failure surface using the principal stress space and the Heyer-Westergard stress space, σ1 / f cD σ2 / f cD σ3 / f cD These are the normalized principal stresses of the triaxial stresses in principal stress space (using the uniaxial compressive strength f after freeze-thaw cycles). cD (Normalizing the principal stresses), ξ / f cD These are the parameters in the normalized Heyer-Westergaard stress space, expressed as a quadratic parabola. The failure surface changes as the relative uniaxial compressive strength changes. Based on the relative uniaxial compressive strength, the failure surface of concrete can be determined (i.e., the relationship between the uniaxial compressive strength and multiaxial strength of concrete after freeze-thaw cycles is determined), and thus the multiaxial strength of concrete can be determined. The method for determining the failure surface will be described in detail later.

[0091] The method in this application introduces the concept of constraint degree, which is the ratio of the average principal stress after freeze-thaw to the uniaxial compressive strength of the concrete after freeze-thaw. This constraint degree is used to express the relationship between the uniaxial compressive strength and multiaxial strength of the concrete after freeze-thaw in segments in response to different constraint degree magnitudes.

[0092] In one possible implementation, segmentation can be omitted (i.e., the relationship between the uniaxial compressive strength and multiaxial strength of the concrete after freeze-thaw is not considered to be unrelated to freeze-thaw damage). It can be assumed that the relationship between the uniaxial compressive strength and multiaxial strength of the concrete after freeze-thaw is related to freeze-thaw damage. In this case, the multiaxial strength of the concrete after freeze-thaw can be determined uniformly by the relationship between the uniaxial compressive strength and multiaxial strength of the concrete after freeze-thaw that is related to freeze-thaw damage.

[0093] To improve prediction accuracy and make the obtained multiaxial strength of frozen-thawed concrete more consistent with the actual damage of frozen-thawed concrete, it is also possible to segment the normalized failure surface of frozen-thawed concrete based on the pre-established normalized failure surface, distinguish whether the relationship between the uniaxial compressive strength and multiaxial strength of frozen-thawed concrete is related to freeze-thaw damage, and calculate the multiaxial strength of frozen-thawed concrete under different conditions.

[0094] This allows the relationship between the uniaxial compressive strength and multiaxial strength of freeze-thawed concrete to be expressed piecewise in response to different degrees of constraint, where the constraint is the ratio of the average principal stress after freeze-thaw to the uniaxial compressive strength of the concrete. The critical value of the constraint can be -0.8.

[0095] like Figure 5 As shown, in the experimental analysis, the constraint degree can be defined based on the normalized mean principal stress of the multiaxial principal stresses after freeze-thaw cycles, and the critical value of the constraint degree can be obtained by fitting the experimental data. Above the critical value, the relationship between the uniaxial compressive strength and multiaxial strength of the concrete after freeze-thaw cycles can be considered independent of freeze-thaw damage; below the critical value, the relationship between the uniaxial compressive strength and multiaxial strength of the concrete after freeze-thaw cycles can be considered related to freeze-thaw damage. Figure 5 As shown, with the increase of freeze-thaw damage, the shape of the failure surface gradually expands outward (see the different cases in the figure: undamaged concrete, freeze-thaw damaged concrete, and concrete with increased freeze-thaw damage). It can be seen that the shape of the normalized failure surface is different for different relative uniaxial compressive strengths. The following... Figure 5 Based on this, we will introduce the method of determining the multiaxial strength of concrete after freeze-thaw cycles in segments.

[0096] When the relationship between the uniaxial compressive strength and multiaxial strength of concrete after freeze-thaw cycles is independent of freeze-thaw damage, the method may further include:

[0097] In response to the constraint degree being not less than the critical value, the multiaxial strength of the concrete after freeze-thaw is determined based on the relative uniaxial compressive strength of the concrete after freeze-thaw and by the relationship between the uniaxial compressive strength and multiaxial strength of the unfrozen concrete.

[0098] In the relationship between the uniaxial compressive strength and multiaxial strength of unfrozen concrete, the ratio of uniaxial tensile-compressive strength of unfrozen concrete is replaced with the ratio of uniaxial tensile-compressive strength of frozen-thawed concrete, and the uniaxial compressive strength of unfrozen concrete is replaced with the uniaxial compressive strength of frozen-thawed concrete.

[0099] The uniaxial compressive strength after freeze-thaw can be obtained based on S201, and the relationship between the uniaxial compressive strength and multiaxial strength of unfrozen concrete can be obtained based on relevant technologies. This application does not impose any restrictions on this.

[0100] The ratio of uniaxial compressive strength to uniaxial tensile strength of concrete after freeze-thaw is the ratio of uniaxial compressive strength to uniaxial tensile strength of concrete after freeze-thaw. The uniaxial tensile strength after freeze-thaw can be obtained by measurement or other methods.

[0101] One method for determining the uniaxial tensile-compressive strength ratio after freeze-thaw cycles is shown in formula (1):

[0102] f tD / f cD = R c 0.34 f t / f c Formula (1)

[0103] Among them, f tD / f cD It can represent the ratio of uniaxial tensile and compressive strength after freeze-thaw cycles, f t / f c R can represent the ratio of uniaxial tensile to compressive strength of concrete after freeze-thaw cycles. c This can represent the relative uniaxial compressive strength of concrete. Formula (1) can be obtained based on regression methods; see [reference needed]. Figure 6 This illustrates a schematic diagram of fitting a calculation formula according to an embodiment of this application. Figure 6 As shown, the horizontal axis represents the ratio of uniaxial compressive strength before and after freeze-thaw, and the vertical axis represents the ratio of uniaxial tensile strength before and after freeze-thaw. The data used for fitting (as shown in the figure, the data volume is 32) can be obtained in advance through experiments, etc. In this embodiment, the coefficient of determination R for fitting is... 2 (As shown in the figure, this indicates how well the data fits the model; the closer to 1, the better the fit.) The value is 0.78.

[0104] Therefore, the multiaxial strength of concrete after freeze-thaw is determined when the relationship between the uniaxial compressive strength and multiaxial strength of the concrete after freeze-thaw is independent of freeze-thaw damage.

[0105] When the relationship between the uniaxial compressive strength and multiaxial strength of concrete after freeze-thaw cycles is related to freeze-thaw damage, the above S202 may include:

[0106] In response to the constraint degree being less than the critical value, the multiaxial strength of the concrete after freeze-thaw is determined based on the relative uniaxial compressive strength of the concrete after freeze-thaw by means of the relationship between the uniaxial compressive strength and the multiaxial strength of the concrete after freeze-thaw.

[0107] Since the relationship between the uniaxial compressive strength and multiaxial strength of concrete after freeze-thaw cycles can be represented by the normalized failure surface of concrete after freeze-thaw cycles under multiaxial stress, and the normalized failure surface can be described by the tensile-compressive meridian and the deviated plane envelope, the characterization method of the normalized failure surface established in this application will be introduced below.

[0108] One method for determining the tensile and compressive meridians of the normalized failure surface after freeze-thaw cycles can be found in formula (2):

[0109]

[0110] Where, σ m It can represent the mean principal stress after freeze-thaw cycles, i.e., σ. m = (σ1+σ2+σ3) / 3, where σ1, σ2, and σ3 are the three principal stresses in the principal stress space, and σ m / f cD It can represent the uniaxial compressive strength f of concrete after freeze-thaw cycles. cD The mean principal stress after normalization. ρ is the deviated plane stress in the Heraeus-Westergaard stress space.

[0111] One way to determine m0 is to refer to formula (3):

[0112]

[0113] Among them, R c It can represent the relative uniaxial compressive strength of concrete, k0 can represent the preset parameters of the tension-compression meridian corresponding to unfrozen concrete, σ cr / f cD The preset threshold is -0.8; n for the pull meridian is 0.3, and n for the press meridian is 0.11.

[0114] One way to determine m1 is to refer to formula (4):

[0115] m1 = R c n k1 formula (4)

[0116] Where k1 can represent the preset parameters of the tension-compression meridian corresponding to unfrozen concrete.

[0117] One way to determine m2 is to refer to formula (5):

[0118] m2=R c n k2 formula (5)

[0119] Where k2 can represent the preset parameters of the tension-compression meridian corresponding to unfrozen concrete.

[0120] One method for determining the partial plane envelope of the normalized damage surface after freeze-thaw is shown in formula (6):

[0121]

[0122] Here, ρ(θ) can represent the deviatoric plane stress. θ is the Lode angle in the Heyer-Westergaard stress space. c ρ is when θ is 60°. t It is ρ when θ is 0°.

[0123] In this application, by fitting the experimental data, the value of n in the above formulas (3)-(5) is 0.3 when θ is 0° (corresponding to the pull meridian) and 0.11 when θ is 60° (corresponding to the compressive meridian). Based on the value of n obtained by fitting in this application, the multiaxial strength after freeze-thaw can be determined more accurately.

[0124] The relationship between multiaxial principal stresses and deviatoric plane stresses can be found in formula (7):

[0125]

[0126] One method for calculating the Lode angle θ can be found in formula (8):

[0127]

[0128] Formulas (2) and (6) above can represent the normalized failure surface after freeze-thaw cycles (see [reference to previous section] for details). Figure 5 In determining multiaxial strength, at least two principal stresses (any two of σ1, σ2, and σ3) or the relationship between the three principal stresses are known, and the relative uniaxial compressive strength R of the concrete is also known. c We can substitute these values ​​into formulas (2)-(8) to solve for the principal stresses to be determined (i.e., the terms to be determined in σ1, σ2, and σ3).

[0129] In one possible implementation, the concrete may include confined concrete, which is concrete under confining pressure. When the relationship between the uniaxial compressive strength of the confined concrete in the unconfined state and its multiaxial strength in the confined state after freeze-thaw is related to freeze-thaw damage, the aforementioned S202 includes:

[0130] In response to the constraint degree being less than the critical value, based on the relative uniaxial compressive strength of the confined concrete in the unconstrained state and the confining pressure on the confined concrete, the multiaxial strength of the confined concrete in the constrained state after freeze-thaw is determined by the relationship between the uniaxial compressive strength of the confined concrete in the unconstrained state and the multiaxial strength in the constrained state.

[0131] The critical value is, for example, -0.8. According to the characteristics of confined concrete, the two principal stresses in its multiaxial principal stresses after freeze-thaw are the same (i.e., σ1 = σ2), which is the magnitude of the confining pressure on the confined concrete.

[0132] The relationship between the uniaxial compressive strength of unconfined concrete and its multiaxial strength under confinement after freeze-thaw cycles can be obtained based on the relationship between the uniaxial compressive strength and multiaxial strength of the concrete after freeze-thaw cycles. Specifically, by transforming and simplifying the above formulas (2)-(8), the following formula (9) can be obtained, which serves as the relationship between the uniaxial compressive strength of unconfined concrete and its multiaxial strength under confinement after freeze-thaw cycles, thus determining the multiaxial strength of the confined concrete under confinement after freeze-thaw cycles:

[0133]

[0134] Among them, f ccD It can represent the multiaxial strength of confined concrete under confinement after freeze-thaw cycles, f ccD / f cD This can represent the uniaxial compressive strength f of concrete under unconfined conditions after freeze-thaw cycles. cD Normalized multiaxial strength of confined concrete under confinement after freeze-thaw cycles. r It can represent the magnitude of the confining pressure on the confined concrete.

[0135] When the relationship between the uniaxial compressive strength of confined concrete under unconfined conditions and its multiaxial strength under confined conditions after freeze-thaw cycles is independent of freeze-thaw damage, the method may further include:

[0136] In response to the constraint degree not being less than the critical value, based on the relative uniaxial compressive strength of the confined concrete in the unconstrained state, the multiaxial strength of the confined concrete in the constrained state after freeze-thaw is determined by the relationship between the uniaxial compressive strength of the unfrozen confined concrete in the unconstrained state and the multiaxial strength of the confined concrete in the constrained state.

[0137] In the relationship between the uniaxial compressive strength of unconfined concrete in the unconfined state and its multiaxial strength in the confined state, the ratio of the uniaxial tensile and compressive strength of unconfined concrete in the unconfined state is replaced by the uniaxial tensile and compressive strength of confined concrete after freeze-thaw in the unconfined state, and the uniaxial compressive strength of unconfined concrete in the unconfined state is replaced by the uniaxial compressive strength of confined concrete after freeze-thaw in the unconfined state.

[0138] The relationship between the uniaxial compressive strength of unconfined concrete in an unconfined state and its multiaxial strength in a confined state can be obtained based on relevant technologies, and this application does not impose any limitations on this.

[0139] The ratio of uniaxial compressive strength to uniaxial tensile strength of unconfined concrete after freeze-thaw cycles is the ratio of its uniaxial compressive strength to its uniaxial tensile strength under the same conditions. This ratio can be determined using the formula (1) above. The uniaxial tensile strength of unconfined concrete after freeze-thaw cycles can be obtained through methods such as measurement.

[0140] See Table 1 for a comparison of the implementation effects of the method of this application embodiment with those of the prior art.

[0141] Table 1

[0142] Prior Art 1 0.748 1.548 Existing technology 2 1.921 0.954 No segmentation 0.940 0.184 Segmentation 1.006 0.119

[0143] The mean and covariance represent the average and covariance between the experimental and predicted values. As shown in Table 1, the method based on the embodiments of this application can more accurately determine the multiaxial strength of concrete after freeze-thaw cycles under various freeze-thaw influencing factors compared to existing technologies, and has a wide range of applications. Furthermore, as shown in Table 1, the embodiments of this application achieve higher prediction accuracy by segmenting based on critical values.

[0144] Figure 7 A structural diagram of a device for determining the multiaxial strength of freeze-thaw concrete according to an embodiment of this application is shown. Figure 7 As shown, the device includes:

[0145] The first determining module 701 obtains the uniaxial compressive strength of concrete after freeze-thaw and the uniaxial compressive strength of concrete before freeze-thaw, and determines the relative uniaxial compressive strength of concrete. The relative uniaxial compressive strength is used to characterize the influence of different freeze-thaw factors on the multiaxial strength of concrete.

[0146] The second determining module 702 is used to determine the multiaxial strength of concrete after freeze-thaw by means of the relationship between the uniaxial compressive strength and multiaxial strength of concrete after freeze-thaw, based on the relative uniaxial compressive strength of concrete.

[0147] In one possible implementation, the freeze-thaw influencing factors include one or more of the following: concrete grade, air content of concrete, pore structure of concrete, water saturation of concrete, type of freeze-thaw liquid, lower limit of freeze-thaw temperature, and stress state during freeze-thaw.

[0148] In one possible implementation, the relative uniaxial compressive strength of concrete is the ratio of the uniaxial compressive strength of concrete after freeze-thaw to the uniaxial compressive strength of concrete before freeze-thaw.

[0149] In one possible implementation, the relationship between the uniaxial compressive strength and multiaxial strength of freeze-thawed concrete is represented by a normalized failure surface of the freeze-thawed concrete under multiaxial stress. The device may further include:

[0150] The third determination module is used to determine the normalized failure surface based on the relative uniaxial compressive strength of concrete by normalizing it by dividing it by the uniaxial compressive strength of concrete after freeze-thaw. The normalized failure surface is the normalized failure surface under the principal stress space and the Heer-Westergaard stress space.

[0151] In one possible implementation, the normalized failure surface is described by the tensile-compressive meridian and the off-plane envelope, which is described by the Lode angle, the mean principal stress, and the mean shear stress.

[0152] In one possible implementation, the relationship between the uniaxial compressive strength and multiaxial strength of freeze-thawed concrete is expressed piecewise in response to different degrees of constraint, where the degree of constraint is the ratio of the average principal stress after freeze-thaw to the uniaxial compressive strength of the freeze-thawed concrete.

[0153] In one possible implementation, the device may further include:

[0154] The fourth determination module is used to determine the multiaxial strength of the concrete after freeze-thaw by means of the relationship between the uniaxial compressive strength and multiaxial strength of the unfrozen concrete, based on the relative uniaxial compressive strength of the concrete and the constraint degree not less than the critical value.

[0155] In the relationship between the uniaxial compressive strength and multiaxial strength of unfrozen concrete, the ratio of uniaxial tensile-compressive strength of unfrozen concrete is replaced with the ratio of uniaxial tensile-compressive strength of frozen-thawed concrete, and the uniaxial compressive strength of unfrozen concrete is replaced with the uniaxial compressive strength of frozen-thawed concrete.

[0156] In one possible implementation, the critical value of the constraint degree is -0.8.

[0157] In one possible implementation, the second determining module 702 is used for:

[0158] In response to the constraint degree being less than the critical value, based on the relative uniaxial compressive strength of concrete, the multiaxial strength of concrete after freeze-thaw is determined by the relationship between the uniaxial compressive strength and multiaxial strength of concrete after freeze-thaw.

[0159] The relationship between the uniaxial compressive strength and multiaxial strength of concrete after freeze-thaw cycles is represented by the normalized failure surface of the concrete under multiaxial stress. The normalized failure surface is described by the tensile-compressive meridian and the deviated plane envelope. The tensile-compressive meridian is calculated as follows:

[0160]

[0161] Where, σ m f represents the principal stress after freeze-thaw cycles. cD This represents the uniaxial compressive strength of confined concrete in an unconfined state after freeze-thaw cycles. ρ is the deviated plane stress in the Heraeus-Westergaard stress space;

[0162] The calculation method for m0 is as follows:

[0163]

[0164] The calculation method for m1 is as follows:

[0165]

[0166] The calculation method for m2 is as follows:

[0167]

[0168] Among them, R c This represents the relative uniaxial compressive strength of concrete. k0, k1, and k2 are preset parameters for the tension-compression meridians corresponding to unfrozen concrete. The preset thresholds are: n = 0.3 for the pull meridian and n = 0.11 for the press meridian.

[0169] In one possible implementation, the concrete includes confined concrete, and the device may further include:

[0170] The fifth determination module is used to determine the multiaxial strength of the confined concrete under confinement in response to the constraint degree not being less than the critical value. Based on the relative uniaxial compressive strength of the confined concrete in the unconstrained state, the multiaxial strength of the confined concrete under confinement in the unconstrained state is determined by the relationship between the uniaxial compressive strength of the un-freeze-thaw confined concrete and the multiaxial strength under confinement.

[0171] In the relationship between the uniaxial compressive strength of unconfined concrete in the unconfined state and its multiaxial strength in the confined state, the ratio of the uniaxial tensile and compressive strength of unconfined concrete in the unconfined state is replaced by the uniaxial tensile and compressive strength of confined concrete after freeze-thaw in the unconfined state, and the uniaxial compressive strength of unconfined concrete in the unconfined state is replaced by the uniaxial compressive strength of confined concrete after freeze-thaw in the unconfined state.

[0172] In one possible implementation, the concrete includes confined concrete, and the second determining module 702 is used for:

[0173] In response to the constraint degree being less than the critical value, based on the relative uniaxial compressive strength of the confined concrete in the unconstrained state and the confining pressure on the confined concrete, the multiaxial strength of the confined concrete in the confined state after freeze-thaw is determined by the relationship between the uniaxial compressive strength of the confined concrete in the unconstrained state and the multiaxial strength in the confined state. The relationship between the uniaxial compressive strength of the confined concrete in the unconstrained state and the multiaxial strength in the confined state after freeze-thaw is obtained based on the relationship between the uniaxial compressive strength and the multiaxial strength of the concrete after freeze-thaw.

[0174] The calculation method for the multiaxial strength of confined concrete under confinement after freeze-thaw cycles is as follows:

[0175]

[0176] Among them, f ccD f represents the multiaxial strength of confined concrete under confinement after freeze-thaw cycles. r f represents the confining pressure exerted on the confined concrete. cD R represents the uniaxial compressive strength of confined concrete in the unconfined state after freeze-thaw cycles. c It represents the relative uniaxial compressive strength of confined concrete in an unconfined state.

[0177] According to the embodiments of this application, by characterizing the influence of different freeze-thaw factors on the multiaxial strength of concrete using the relative uniaxial compressive strength of concrete, the established relationship between the uniaxial compressive strength and multiaxial strength of frozen-thawed concrete has a unified parameter (relative uniaxial compressive strength), which is applicable to concrete with different freeze-thaw factors. This eliminates the need for numerous complex multiaxial strength tests for parameter calibration for each freeze-thaw factor, improving efficiency and reducing costs. The relationship between the uniaxial compressive strength and multiaxial strength of frozen-thawed concrete established in this application for determining the multiaxial strength of frozen-thawed concrete has a wide range of applications and improves prediction accuracy.

[0178] In some embodiments, the functions or modules of the apparatus provided in this disclosure can be used to perform the methods described in the above method embodiments. The specific implementation can be referred to the description of the above method embodiments, and for the sake of brevity, it will not be repeated here.

[0179] This disclosure also proposes a computer-readable storage medium storing computer program instructions that, when executed by a processor, implement the above-described method. The computer-readable storage medium can be volatile or non-volatile.

[0180] This disclosure also proposes an electronic device, including: a processor; and a memory for storing processor-executable instructions; wherein the processor is configured to implement the above method when executing the instructions stored in the memory.

[0181] This disclosure also provides a computer program product, including computer-readable code, or a non-volatile computer-readable storage medium carrying computer-readable code, wherein when the computer-readable code is run in a processor of an electronic device, the processor in the electronic device performs the above-described method.

[0182] Figure 8 This is a block diagram illustrating an apparatus 1900 for determining the multiaxial strength of freeze-thaw concrete according to an exemplary embodiment. For example, apparatus 1900 may be provided as a server or terminal device. (Refer to...) Figure 8 The apparatus 1900 includes a processing component 1922, which further includes one or more processors, and memory resources represented by memory 1932 for storing instructions, such as application programs, that can be executed by the processing component 1922. The application programs stored in memory 1932 may include one or more modules, each corresponding to a set of instructions. Furthermore, the processing component 1922 is configured to execute instructions to perform the methods described above.

[0183] Device 1900 may also include a power supply component 1926 configured to perform power management of device 1900, a wired or wireless network interface 1950 configured to connect device 1900 to a network, and an input / output interface 1958 (I / O interface). Device 1900 can operate on an operating system, such as Windows Server, stored in memory 1932. TM macOS X TM Unix TM Linux TM FreeBSD TM Or similar.

[0184] In an exemplary embodiment, a non-volatile computer-readable storage medium is also provided, such as a memory 1932 including computer program instructions that can be executed by a processing component 1922 of the device 1900 to perform the above-described method.

[0185] This disclosure can be a system, method, and / or computer program product. A computer program product may include a computer-readable storage medium having computer-readable program instructions loaded thereon for causing a processor to implement various aspects of this disclosure.

[0186] Computer-readable storage media can be tangible devices capable of holding and storing instructions for use by an instruction execution device. Computer-readable storage media can be, for example—but not limited to—electrical storage devices, magnetic storage devices, optical storage devices, electromagnetic storage devices, semiconductor storage devices, or any suitable combination thereof. More specific examples (a non-exhaustive list) of computer-readable storage media include: portable computer disks, hard disks, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), static random access memory (SRAM), portable compact disc read-only memory (CD-ROM), digital multifunction disc (DVD), memory sticks, floppy disks, mechanical encoding devices, such as punch cards or recessed protrusions storing instructions thereon, and any suitable combination thereof. The computer-readable storage media used herein are not to be construed as transient signals themselves, such as radio waves or other freely propagating electromagnetic waves, electromagnetic waves propagating through waveguides or other transmission media (e.g., light pulses through fiber optic cables), or electrical signals transmitted through wires.

[0187] The computer-readable program instructions described herein can be downloaded from computer-readable storage media to various computing / processing devices, or downloaded via a network, such as the Internet, local area network, wide area network, and / or wireless network, to an external computer or external storage device. The network may include copper transmission cables, fiber optic transmission, wireless transmission, routers, firewalls, switches, gateway computers, and / or edge servers. A network adapter card or network interface in each computing / processing device receives the computer-readable program instructions from the network and forwards them to the computer-readable storage media in the respective computing / processing device.

[0188] Computer program instructions used to perform the operations of this disclosure may be assembly instructions, instruction set architecture (ISA) instructions, machine instructions, machine-dependent instructions, microcode, firmware instructions, status setting data, or source code or object code written in any combination of one or more programming languages, including object-oriented programming languages ​​such as Smalltalk, C++, etc., and conventional procedural programming languages ​​such as the "C" language or similar programming languages. The computer-readable program instructions may execute entirely on the user's computer, partially on the user's computer, as a standalone software package, partially on the user's computer and partially on a remote computer, or entirely on a remote computer or server. In cases involving a remote computer, the remote computer may be connected to the user's computer via any type of network—including a local area network (LAN) or a wide area network (WAN)—or may be connected to an external computer (e.g., via the Internet using an Internet service provider). In some embodiments, electronic circuitry, such as programmable logic circuitry, field-programmable gate arrays (FPGAs), or programmable logic arrays (PLAs), is personalized by utilizing the status information of the computer-readable program instructions to implement various aspects of this disclosure.

[0189] Various aspects of this disclosure are described herein with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this disclosure. It should be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer-readable program instructions.

[0190] These computer-readable program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, or other programmable data processing apparatus to produce a machine such that, when executed by the processor of the computer or other programmable data processing apparatus, they create means for implementing the functions / actions specified in one or more blocks of the flowchart and / or block diagram. These computer-readable program instructions can also be stored in a computer-readable storage medium that causes a computer, programmable data processing apparatus, and / or other device to operate in a particular manner; thus, the computer-readable medium storing the instructions comprises an article of manufacture that includes instructions for implementing aspects of the functions / actions specified in one or more blocks of the flowchart and / or block diagram.

[0191] Computer-readable program instructions may also be loaded onto a computer, other programmable data processing apparatus, or other device to cause a series of operational steps to be performed on the computer, other programmable data processing apparatus, or other device to produce a computer-implemented process, thereby causing the instructions executed on the computer, other programmable data processing apparatus, or other device to perform the functions / actions specified in one or more boxes of a flowchart and / or block diagram.

[0192] The flowcharts and block diagrams in the accompanying drawings illustrate the architecture, functionality, and operation of possible implementations of systems, methods, and computer program products according to various embodiments of the present disclosure. In this regard, each block in a flowchart or block diagram may represent a module, segment, or portion of an instruction containing one or more executable instructions for implementing a specified logical function. In some alternative implementations, the functions marked in the blocks may occur in a different order than those shown in the drawings. For example, two consecutive blocks may actually be executed substantially in parallel, and they may sometimes be executed in reverse order, depending on the functions involved. It should also be noted that each block in the block diagrams and / or flowcharts, and combinations of blocks in the block diagrams and / or flowcharts, may be implemented using a dedicated hardware-based system that performs the specified function or action, or using a combination of dedicated hardware and computer instructions.

[0193] The various embodiments of this disclosure have been described above. These descriptions are exemplary and not exhaustive, nor are they limited to the disclosed embodiments. Many modifications and variations will be apparent to those skilled in the art without departing from the scope and spirit of the described embodiments. The terminology used herein is chosen to best explain the principles, practical application, or technical improvements to the embodiments in the market, or to enable others skilled in the art to understand the embodiments disclosed herein.

Claims

1. A method for determining the multiaxial strength of freeze-thaw concrete, characterized in that, The method includes: The uniaxial compressive strength of concrete after freeze-thaw and the uniaxial compressive strength of concrete before freeze-thaw are obtained, and the relative uniaxial compressive strength of concrete is determined. The relative uniaxial compressive strength is used to characterize the influence of different freeze-thaw factors on the multiaxial strength of concrete. Based on the relative uniaxial compressive strength of the concrete, the multiaxial strength of the concrete after freeze-thaw is determined by the relationship between the uniaxial compressive strength and multiaxial strength of the concrete after freeze-thaw.

2. The method according to claim 1, characterized in that, The relative uniaxial compressive strength of the concrete is the ratio of the uniaxial compressive strength of the concrete after freeze-thaw to the uniaxial compressive strength of the concrete before freeze-thaw.

3. The method according to claim 1, characterized in that, The relationship between the uniaxial compressive strength and multiaxial strength of the freeze-thawed concrete is represented by the normalized failure surface of the freeze-thawed concrete under multiaxial stress. The method further includes: Based on the relative uniaxial compressive strength of concrete, the normalized failure surface is determined by normalizing it by dividing it by the uniaxial compressive strength of concrete after freeze-thaw cycles. The normalized failure surface is the normalized failure surface under the principal stress space and the Heraeus-Westergaard stress space.

4. The method according to claim 3, characterized in that, The normalized failure surface is described by the tensile-compressive meridian and the off-plane envelope, which is described by the Lode angle, the mean principal stress, and the mean shear stress.

5. The method according to claim 1, characterized in that, The relationship between the uniaxial compressive strength and multiaxial strength of the freeze-thawed concrete is expressed in segments according to different degrees of constraint, where the degree of constraint is the ratio of the average principal stress after freeze-thaw to the uniaxial compressive strength of the freeze-thawed concrete.

6. The method according to claim 1, characterized in that, The method further includes: In response to the constraint degree being not less than the critical value, based on the relative uniaxial compressive strength of the concrete, the multiaxial strength of the concrete after freeze-thaw is determined by the relationship between the uniaxial compressive strength and multiaxial strength of the unfrozen concrete. In the relationship between the uniaxial compressive strength and multiaxial strength of unfrozen concrete, the ratio of uniaxial tensile-compressive strength of unfrozen concrete is replaced with the ratio of uniaxial tensile-compressive strength of frozen-thawed concrete, and the uniaxial compressive strength of unfrozen concrete is replaced with the uniaxial compressive strength of frozen-thawed concrete.

7. The method according to claim 1, characterized in that, The determination of the multiaxial strength of the concrete after freeze-thaw cycles, based on the relative uniaxial compressive strength of the concrete and through the relationship between the uniaxial compressive strength and multiaxial strength, includes: In response to the constraint degree being less than the critical value, the multiaxial strength of the concrete after freeze-thaw is determined based on the relative uniaxial compressive strength of the concrete and the relationship between the uniaxial compressive strength and multiaxial strength of the concrete after freeze-thaw. The relationship between the uniaxial compressive strength and multiaxial strength of the freeze-thawed concrete is represented by the normalized failure surface of the freeze-thawed concrete under multiaxial stress. This normalized failure surface is described by the tensile-compressive meridian and the deviated plane envelope. The tensile-compressive meridian is calculated as follows: Where, σ m f represents the principal stress after freeze-thaw cycles. cD This represents the uniaxial compressive strength of confined concrete in an unconfined state after freeze-thaw cycles. ρ is the deviated plane stress in the Heraeus-Westergaard stress space; The calculation method for m0 is as follows: The calculation method for m1 is as follows: The calculation method for m2 is as follows: Among them, R c This represents the relative uniaxial compressive strength of concrete. k0, k1, and k2 are preset parameters for the tension-compression meridians corresponding to unfrozen concrete. The preset threshold is set; n for the pull meridian is 0.3, and n for the press meridian is 0.

11.

8. The method according to claim 1, characterized in that, The concrete includes confined concrete, and the method further includes: In response to the constraint degree not being less than the critical value, based on the relative uniaxial compressive strength of the confined concrete in the unconfined state, the multiaxial strength of the confined concrete in the confined state after freeze-thaw is determined by the relationship between the uniaxial compressive strength of the unfrozen confined concrete in the unconfined state and the multiaxial strength in the confined state. In the relationship between the uniaxial compressive strength of unconfined concrete in the unconfined state and its multiaxial strength in the confined state, the ratio of the uniaxial tensile and compressive strength of unconfined concrete in the unconfined state is replaced by the uniaxial tensile and compressive strength of confined concrete after freeze-thaw in the unconfined state, and the uniaxial compressive strength of unconfined concrete in the unconfined state is replaced by the uniaxial compressive strength of confined concrete after freeze-thaw in the unconfined state.

9. The method according to claim 1, characterized in that, The concrete includes confined concrete. The determination of the multiaxial strength of the concrete after freeze-thaw cycles, based on the relative uniaxial compressive strength of the concrete and through the relationship between the uniaxial compressive strength and multiaxial strength of the concrete after freeze-thaw cycles, includes: In response to the constraint degree being less than a critical value, based on the relative uniaxial compressive strength of the constrained concrete in the unconstrained state and the confining pressure on the constrained concrete, the multiaxial strength of the constrained concrete in the constrained state after freeze-thaw is determined by the relationship between the uniaxial compressive strength of the constrained concrete in the unconstrained state and the multiaxial strength in the constrained state. The relationship between the uniaxial compressive strength of the constrained concrete in the unconstrained state and the multiaxial strength in the constrained state after freeze-thaw is obtained based on the relationship between the uniaxial compressive strength and the multiaxial strength of the concrete after freeze-thaw. The calculation method for the multiaxial strength of confined concrete under confinement after freeze-thaw cycles is as follows: Among them, f ccD f represents the multiaxial strength of confined concrete under confinement after freeze-thaw cycles. r f represents the confining pressure exerted on the confined concrete. cD R represents the uniaxial compressive strength of confined concrete in the unconfined state after freeze-thaw cycles. c It represents the relative uniaxial compressive strength of confined concrete in an unconfined state.

10. The method according to claim 6 or 7, characterized in that, The critical value of the constraint degree is -0.

8.

11. The method according to claim 1, characterized in that, The factors affecting freeze-thaw cycles include one or more of the following: concrete grade, air content of concrete, pore structure of concrete, water saturation of concrete, type of freeze-thaw liquid, lower limit temperature of freeze-thaw, and stress state during freeze-thaw.

12. A device for determining the multiaxial strength of freeze-thaw concrete, characterized in that, The device includes: The first determining module is used to obtain the uniaxial compressive strength of concrete after freeze-thaw and the uniaxial compressive strength of concrete before freeze-thaw, and to determine the relative uniaxial compressive strength of concrete. The relative uniaxial compressive strength is used to characterize the influence of different freeze-thaw factors on the multiaxial strength of concrete. The second determining module is used to determine the multiaxial strength of the concrete after freeze-thaw by means of the relationship between the uniaxial compressive strength and the multiaxial strength of the concrete after freeze-thaw, based on the relative uniaxial compressive strength of the concrete.

13. A device for determining the multiaxial strength of freeze-thaw concrete, characterized in that, include: processor; Memory used to store processor-executable instructions; The processor is configured to implement the method of any one of claims 1 to 11 when executing instructions stored in the memory.

14. A non-volatile computer-readable storage medium storing computer program instructions thereon, characterized in that, When the computer program instructions are executed by the processor, they implement the method described in any one of claims 1 to 11.

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