A multi-target-based soil solidifying material mix proportion design method for permafrost regions

Abstract

The present application belongs to the technical field of soil solidification material mix design, and particularly relates to a permafrost region soil solidification material mix design method based on multiple targets. The method proposes a comprehensive evaluation method of solidification material performance based on multiple targets such as strength and hydration heat release, constructs a prediction model of hydration heat release and compressive strength of the solidification material at low temperature through test data, defines a low-temperature performance comprehensive index, correlates hydration heat release and strength and other factors, performs multiple target evaluation of the solidification material performance, optimizes the mix ratio based on the low-temperature performance comprehensive index, and realizes quantitative and synergistic optimization of low heat release, high strength and easy construction of the solidification material.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of soil solidification material mix design, and particularly relates to a soil solidification material mix design method based on multiple targets in a frozen soil area. BACKGROUND

[0002] Under the influence of multiple factors such as strong heat absorption effect of asphalt pavement and long-term effect of heavy traffic, serious subsidence diseases occur in the in-service highways in the frozen soil area such as the Qinghai-Tibet Highway, and the underlying frozen soil in some sections has irreversible degradation. The frozen soil degradation forms a deep and weak soil layer with high water content, weak mechanical properties and strong compressibility, and it is difficult to prevent the continuous deformation of the formed weak layer under the action of gravity and traffic load only by relying on the cooling means of the roadbed. Therefore, effective means are needed to improve the mechanical properties of the underlying weak layer of the roadbed in the frozen soil area and to enhance its anti-deformation ability. Cement-based materials are tried to be used for roadbed improvement and foundation treatment in the frozen soil area, but the frozen soil in the subsidence section is sensitive to changes in water and heat state, the hydration heat release of cement material is high, and improper application will exacerbate the melting of frozen soil; and the strength of cement and the amount of hydration heat release are closely related, and it is difficult to coordinate the contradiction between high strength and low heat release. Therefore, a material with low temperature strength and low heat release needs to be selected to solidify the underlying weak soil layer of the frozen soil roadbed.

[0003] Inorganic solidifying agents using fly ash, steel slag or various types of slag as raw materials, combined with activators and admixtures, and multi-component organic solidifying agents can meet the soil solidification requirements in special scenarios. However, the mix design method of soil solidifying agents in conventional areas has limitations. The new type of solidifying agent has complex components and many performance influencing factors, and a large number of test tests need to be carried out in the design process of full factors and orthogonal design, which is low in design process efficiency and difficult to ensure the accuracy of mix design and optimization; the traditional design focuses on single performance indicators such as strength and cannot comprehensively reflect the engineering performance of the solidifying agent in the low temperature environment, so it is difficult to evaluate the applicability of the solidifying agent in the frozen soil engineering.

[0004] In summary, the existing technology cannot meet the engineering construction needs of the solidification of the underlying weak soil layer in the frozen soil, and it is necessary to research a comprehensive performance evaluation method of solidifying materials based on multiple targets such as strength and hydration heat release, establish a multi-parameter performance prediction model, and carry out parameterized design and accurate optimization of the mix ratio of the solidifying agent in the specific engineering environment in the frozen soil area. SUMMARY

[0005] The purpose of the present application is to overcome the problems of single evaluation index, low design process efficiency and inability to meet the specific engineering construction needs in the frozen soil area in the prior art soil solidifying agent mix design method, and to provide a soil solidifying material mix design method based on multiple targets in a frozen soil area.

[0006] The present application provides a soil solidifying material mix design method based on multiple targets in a frozen soil area, comprising the following steps:

[0007] Step 1: determining the design temperature T of the solidified material based on the environmental parameters of the application site, and the heat release Q of the cement at the design temperature T c as a reference value of the heat release target value Q of the solidified material t as a reference value of the unconfined compressive strength UCS of the cement at the design temperature T c as a reference value of the unconfined compressive strength target value UCS of the solidified material t as a reference value of the unconfined compressive strength target value UCS of the solidified material

[0008] Step 2: determining the type and composition of the solidified material based on the strength index, and screening the mix proportion variables; the solidified material is an inorganic solidified agent, and the mix proportion variables include A-slag content, B-alkali activator content, and C-alkali activator modulus

[0009] Step 3: testing the compressive strength UCS and heat release Q of the solidified material at the design temperature T, collecting low-temperature performance data of the solidified material; using the Box-Behnken design method to form a test list of multiple different mix proportions, and performing hydration heat and unconfined compressive strength tests to obtain low-temperature performance data

[0010] Step 4: establishing a low-temperature performance prediction model of the solidified material according to the low-temperature performance data obtained in step 3, and performing multi-objective evaluation of the performance of the solidified material at low temperature based on the low-temperature performance comprehensive index LPCI; the expression of the low-temperature performance comprehensive index LPCI is:

[0011]

[0012] wherein UCS is a strength prediction model at low temperature, Q is a hydration heat release prediction model at low temperature; UCS t is the target value of the compressive strength of the solidified material, Q t is the target value of the hydration heat release; α and β are influence weights, respectively, and satisfy α+β=1;

[0013] Step 5: optimizing and determining the final mix proportion of the solidified material based on the evaluation results; according to the value range of the mix proportion variables, the maximum value of the low-temperature performance comprehensive index LPCI is obtained, and the final mix proportion is obtained by adjusting the mix proportion variables corresponding to the maximum LPCI.

[0014] The method of the present application proposes a multi-target comprehensive evaluation method of the performance of solidified materials based on strength, hydration heat and other targets. The method comprehensively considers the two key performance indicators of the unconfined compressive strength and hydration heat of the soil solidified material in the frozen soil area under low temperature environment, realizes the synergistic optimization of strength and heat release characteristics through multi-target design, and avoids the limitations of single index design. The design target is determined based on the environmental parameters (such as temperature) of the application site, so that the mix proportion design is more targeted and engineering applicable, especially suitable for special low temperature environment such as frozen soil area. The Box-Behnken experimental design method is adopted, and the response surface model is constructed through a limited number of experiments, which significantly reduces the number of experiments, improves the efficiency of mix proportion design, and ensures the reliability of the prediction model. The low temperature performance of the material is quantified by establishing a weighted comprehensive index, and the contributions (weights α, β can be adjusted) of strength and heat release are balanced according to the engineering requirements of different types of frozen soil areas, which provides a clear mathematical basis for multi-target optimization and facilitates decision-making. The optimization process is clear and controllable: the optimal mix proportion range is determined by solving the maximum value of LPCI, and the final mix proportion is adjusted according to the actual engineering requirements, so that the final mix proportion not only meets the theoretical optimization but also has engineering feasibility. The present scheme selects slag-fly ash based polymer as the solidified material, and optimizes the slag content, alkali activator content and modulus and other key variables to control the hydration heat while ensuring the low temperature strength, avoid the thermal disturbance of frozen soil, and enhance the long-term stability of the solidified soil body. The method has clear framework and adjustable parameters, and is suitable for different low temperature environment conditions and material types, which provides reliable material design support for cold region engineering construction.

[0015] A prediction model of the hydration heat and compressive strength of the solidified material under low temperature is constructed by experimental data, a low temperature performance comprehensive index is defined, factors such as hydration heat and strength are related, a multi-target evaluation of the performance of the solidified material is carried out, and the mix proportion is optimized based on the low temperature performance comprehensive index, so as to realize the quantitative synergistic optimization of low heat release, high strength and easy construction of the solidified material.

[0016] Preferably, in step 1, Q t / Q c = 0.5-0.9, UCS t / UCS c = 1.1-1.5.

[0017] The strength and hydration heat of the solidified material are two closely related indicators. Generally, high strength is accompanied by high hydration heat. The coordination between strength and hydration heat is the key to realizing the strength and low heat release of the soil solidified material in the frozen soil area. Too low hydration heat represents slow material reaction progress, and it is difficult to form material strength. Too high hydration heat represents violent reaction, which will cause abnormal development of the late strength of the material, reduce the long-term service performance, and intensify the melting of frozen soil. Therefore, the target value Q t is less than 1 times Qc Unconfined compressive strength target value UCS t Take more than 1 times UCS c Reasonable, the target material needs to continuously react to form strength at the design temperature T, and is accompanied by a lower heat release amount.

[0018] In the method of the present application, the unconfined compressive strength UCS of the cement at the design temperature T in step 1 c is the unconfined compressive strength of the cement paste prepared into a 50mm*50mm*50mm cube test block after curing at the design temperature T, and is obtained by 7-day unconfined compressive strength test, and three parallel samples are set for each test; the heat release amount Q c is the hydration heat release amount of the cement at the design temperature T for 7 days, which is measured by the semi-adiabatic method (direct method) in GB / T 12959-2024 Determination of Hydration Heat of Cement, and the curve of the temperature change of the cement sample in the calorimeter with time at the design temperature T is calculated.

[0019] Preferably, the solidified material is an inorganic solidified agent or an organic solidified agent, the basic composition of the inorganic solidified agent includes a main cementitious material, a mineral admixture, an activator and a functional additive, and the basic composition of the organic solidified agent includes a cementitious resin, a modifier, a diluent and an auxiliary crosslinking agent.

[0020] In this scheme, the solidified material is selected as a slag-fly ash-based polymer, and the solidified material includes slag powder, fly ash, an alkaline activator and water.

[0021] The alkaline activator is selected as water glass, and the modulus of the water glass is adjusted by sodium hydroxide.

[0022] Preferably, in step 2, the mixing proportion variable is screened including the following steps:

[0023] Step 2.1, selecting a mixing proportion variable that has an effect on the strength of the solidified material;

[0024] Step 2.2, setting 3-5 levels for each variable to cover the possible action range of the variable;

[0025] Step 2.3, fixing other variables, and performing single-factor test of the target variable;

[0026] Step 2.4, according to the test results, performing variance analysis to evaluate the influence degree of each variable on the target value, and screening out three high-impact variables, wherein the high-impact variables include A-slag content, B-alkali activator content and C-alkali activator modulus.

[0027] The single factor test in step 2.3 is to prepare the curing agent neat paste into a 50mm*50mm*50mm cubic test block, and after standard curing, a 7-day-old unconfined compressive strength test is performed, and 3 parallel samples are set for each test.

[0028] In step 2.4, the influence degree of each variable on the target value is judged according to the F value and P value in the variance analysis of the test results. P value < 0.05 is high influence, 0.05 ≤ P value < 1 is medium influence, and P value ≥ 0.1 is low influence. The higher the corresponding F value, the stronger the influence.

[0029] Preferably, in step 3, the factor level of the Box-Behnken design method has three: -1, 0, +1, representing low, medium and high levels, respectively, and the center point n c 5, the test number is 2k(k 1)+n c =17, and the test list is generated by Design-Expert software.

[0030] More specifically, in step 3, the central composite sequential design, central composite bounded design, and central composite bounded design can also be used. Among them, the factor level of the central composite sequential design has five (-α, -1, 0, +1, +α), the factor level of the central composite bounded design has five (-1, -1 / α, 0, +1 / α, +1), and the factor level of the central composite bounded design has three (-1, 0, +1).

[0031] Further, the calculation formula of the alpha is as follows:

[0032]

[0033] In the formula, k is the number of factors.

[0034] The test number N of the central composite sequential design, the central composite bounded design, and the central composite surface design is 2 k +2k+n c , and the test number N of the Box-Behnken design is 2k(k 1)+n c . Among them, k is the number of factors; n c is the number of center points, which is used to estimate experimental error and detect model curvature, and 3-6 is taken to ensure statistical reliability.

[0035] In step 3, the strength test experiment is to prepare the curing agent neat paste into a 50mm*50mm*50mm cubic test block, after curing at the design temperature T, the 7-day-old unconfined compressive strength test is carried out, and 3 parallel samples are set for each test; The hydration heat release amount test refers to the semi-adiabatic method (direct method) in GBT12959-2024 Cement Hydration Heat Determination Method, measures the temperature-time curve of the curing material sample in the calorimeter at the design temperature T, and calculates the hydration heat release amount of the material at 7 days.

[0036] Preferably, in step 4, the low-temperature performance prediction model includes a low-temperature strength prediction model and a low-temperature hydration heat release amount prediction model, and the model calculation formula is as follows:

[0037]

[0038] In the formula, Y is the target value; X i is the ratio variable determined in step 2; β0, β i , β ii , β ij are regression coefficients. By inputting the test data in step 3, the regression coefficients can be solved to obtain the prediction model of strength UCS and hydration heat release amount Q with respect to the ratio variable X i .

[0039] .

[0040] The low-temperature performance comprehensive index LPCI is a normalized index that couples factors such as strength and heat release in a geometric mean form. When the index value tends to or is greater than or equal to 1, the curing material at this time has excellent comprehensive performance. The low-temperature performance comprehensive index can be adapted to different engineering scenarios by adjusting the target value, and the balanced weights α, β can realize the flexible switching of strength preservation and heat control. The nonlinear form makes the low-temperature performance comprehensive index significantly decay when any target deviates from the target value, which can avoid the excessive offset of single performance to other defects. The low-temperature performance comprehensive index quantifies and jointly evaluates the strength and heat release of the curing material in the permafrost region, and can realize the quantitative and collaborative optimization of multi-objective curing materials.

[0041] Preferably, the influence weights α and β are adjusted by engineering requirements, when the underlying of the application site is high-temperature extremely unstable permafrost, α>β; when the underlying of the application site is high-temperature unstable permafrost or low-temperature basically stable permafrost, α<β.

[0042] When the application site is underlain by high-temperature and extremely unstable permafrost, the degradation process of the permafrost under long-term thermal influence is basically completed, the permafrost is distributed in island shape or is about to disappear, the soft layer above the permafrost is deep, and the soft layer continuously deforms under traffic and self-weight load, so the mix proportion design focuses more on strength (α>β) and emphasizes on improving the bearing capacity of the soft layer; when the application site is underlain by high-temperature unstable permafrost or low-temperature basically stable permafrost, the thermal stability of the permafrost at the site is generally good, the permafrost is sensitive to climate change and engineering activities and is easily affected to continuously degrade to form a soft layer, so the mix proportion design focuses more on low heat release (α<β) to reduce the influence of the solidified soft layer on the permafrost during the solidification of the soft layer, and the mix proportion design is preferably applied together with special roadbed measures such as heat insulation and cooling to achieve a synergistic effect.

[0043] Preferably, in step 5, the final mix proportion is determined according to the following steps:

[0044] The mix proportion variable obtained in step 5 is adjusted based on the working performance and economy, the low-temperature performance comprehensive index LPCI of the solidified material after the mix proportion is adjusted is solved, and the final mix proportion is determined according to the optimization result.

[0045] Preferably, the low-temperature performance comprehensive index LPCI is obtained by a numerical method of gradient ascent and grid search.

[0046] Preferably, in step 1, the environmental parameters include the maximum and minimum ground temperatures in the application site in the past 2 years, the average ground temperature of the permafrost under the application site, the type of the permafrost under the application site, the thickness of the soft layer under the application site, and the thickness of the permafrost layer under the application site.

[0047] Compared with the prior art, the method has the following beneficial effects:

[0048] The method of the application proposes a multi-target performance comprehensive evaluation method of solidified materials based on strength, hydration heat release and the like, which comprehensively considers two key performance indexes of the unconfined compressive strength and the hydration heat release of the soil solidified material in the permafrost region under a low-temperature environment, realizes the collaborative optimization of the strength and the heat release characteristics through multi-target design, and avoids the limitations of single-index design.

[0049] The design target is determined based on the environmental parameters (such as temperature) of the application site, so that the mix proportion design is more targeted and engineering applicable, and is especially suitable for special low-temperature environments such as permafrost regions. The Box-Behnken experimental design method is adopted, a response surface model is constructed through a limited number of experiments, the number of experiments is significantly reduced, the efficiency of the mix proportion design is improved, and the reliability of the prediction model is ensured.

[0050] The low-temperature performance of the material is quantified by establishing a weighted comprehensive index, and the contributions of strength and heat release are balanced (the weights a and b can be adjusted) according to the engineering requirements of different types of permafrost regions, so as to provide a clear mathematical basis for multi-objective optimization and facilitate decision-making. The optimization process is clear and controllable: the optimal mixing ratio range is determined by solving the maximum value of LPCI, and the actual engineering requirements are adjusted to make the final mixing ratio meet the theoretical optimization and engineering feasibility.

[0051] In the scheme of the application, slag-fly ash geopolymer is selected as the solidification material, and by optimizing the key variables such as slag content, alkali activator content and modulus, the hydration heat release is controlled while the low-temperature strength is ensured, the thermal disturbance of permafrost is avoided, and the long-term stability of the solidified soil body is enhanced. The method framework is clear and the parameters are adjustable, which is suitable for different low-temperature environmental conditions and material types, and provides reliable material design support for cold region engineering construction. BRIEF DESCRIPTION OF DRAWINGS

[0052] Figure 1 Fig. 1 is a schematic diagram of the influence of the interaction between slag content and alkali activator content on the hydration heat release of the solidified material;

[0053] Figure 2 Fig. 2 is a schematic diagram of the influence of the interaction between slag content and alkali activator modulus on the hydration heat release of the solidified material;

[0054] Figure 3 Fig. 3 is a schematic diagram of the influence of the interaction between alkali activator content and activator modulus on the hydration heat release of the solidified material;

[0055] Figure 4 Fig. 4 is a schematic diagram of the influence of the interaction between slag content and alkali activator content on the unconfined compressive strength of the solidified material;

[0056] Figure 5 Fig. 5 is a schematic diagram of the influence of the interaction between slag content and alkali activator modulus on the unconfined compressive strength of the solidified material;

[0057] Figure 6 Fig. 6 is a schematic diagram of the influence of the interaction between alkali activator content and activator modulus on the unconfined compressive strength of the solidified material. DETAILED DESCRIPTION

[0058] The application will be further described in detail below with reference to specific embodiments. However, it should not be understood that the scope of the above-mentioned subject matter of the application is limited to the following embodiments, and any technology realized based on the content of the application falls within the scope of the application.

[0059] A kind of based on multi-objective permafrost region soil solidification material mix proportion design method, this design method is practiced in certain frozen soil area, the characteristics of certain frozen soil area are summarized: the natural moisture content of soft layer in application site is higher than 30%, liquid limit is 29.6%, plastic limit is 18.1%, belongs to silty clay, the temperature variation range of soft layer in nearly one year is-1.43 ℃~6.59 ℃, the frozen soil temperature under soft layer is-1.09 ℃, belongs to high temperature unstable frozen soil, the thickness of soft layer is 3 m, and the frozen soil thickness is greater than 5 m.To ensure that the design material can continuously react to form strength in this environment, the design temperature T is determined as-1.5 ℃.

[0060] Example 1

[0061] This embodiment provides a kind of based on multi-objective permafrost region soil solidification material mix proportion design method, combined with Figure 1 Understand, including the following steps:

[0062] Step 1: based on the environmental parameters of application site, determine the design temperature of solidification material, the heat release Q of cement under design temperature T c As the reference value of solidification material heat release target value Q t The unconfined compressive strength UCS of cement under design temperature T c As the reference value of solidification material unconfined compressive strength target value UCS t ;

[0063] In the above steps, environmental parameters include: the maximum value of ground temperature in nearly one year, the minimum value of ground temperature, the average ground temperature of frozen soil under application site, the type of frozen soil under application site, the thickness of soft layer under application site, the thickness of frozen soil layer under application site.

[0064] Wherein, mixed 425 Portland cement, antifreeze and water are used to prepare cement paste, the antifreeze is CaCl2 (analytical pure), the dosage is 3%, and the water-cement ratio is 0.4, the water-cement ratio refers to the ratio of water quantity and cement mass in concrete or cement mortar, the cement paste is prepared into 50mm*50mm*50mm cubic test block, after curing at-1.5 ℃, the unconfined compressive strength test of 7 days age is carried out, 3 parallel samples are set in each test, and the unconfined compressive strength UCS c Of cement under design temperature-1.5 ℃ is 23.04 MPa.

[0065] Furthermore, referring to the semi-insulated method (direct method) in GB / T 12959-2024 "Methods for Determining the Heat of Hydration of Cement," the heat release during hydration of cement at a design temperature of -1.5℃ for 7 days was determined. The semi-insulated device consisted of a cork stopper, insulation cotton, a plastic liner, and an insulated cylinder. The cylinder had a diameter of 130mm, a height of 190mm, and a capacity of approximately 1.5L. The cylinder wall was a vacuum insulation layer. The insulation cotton ensured that the heat dissipation coefficient of the device met the requirements. After mixing, the sample was poured into the plastic liner and placed inside the insulated cylinder. During the test, the temperature change of the sample was collected by a monitoring system consisting of a data acquisition instrument, thermocouple sensors, and a computer. The test temperature was -1.5℃, and the entire test was conducted in a walk-in environmental model test chamber, which provided a constant temperature for the test. The heat release during hydration was calculated using the following formula:

[0066]

[0067] In the formula: q x The heat released during hydration; C p The total heat capacity of the sample and the semi-insulated device; t x t0 is the temperature of the mortar at the end of the test; t0 is the initial temperature of the mortar; K is the heat dissipation constant of the semi-insulation device, measured by standard methods; F 0~X G represents the area between the ambient temperature curve and the mortar temperature change curve from the start to the end of the experiment; G is the total mass of the powder used in the experiment.

[0068]

[0069] Where: m i The mass of each component of the semi-insulated device and the various components of the sample it contains, including the cork, insulation cylinder, plastic liner, copper sleeve, insulation cotton, and sample; c i The specific heat of each category.

[0070] Furthermore, the heat release Q of cement at the design temperature of -1.5℃ was measured. c It is 222.03 J / g.

[0071] More preferably, Q t Take 0.6 times Q c UCS t Take 1.2 times the UCS c In this embodiment, the target value Q of the heat release of the curing material at a design temperature of -1.5℃ is... t Take 0.6 times Q c The target value for unconfined compressive strength is 133.22 J / g. t Take 1.2 times the UCS c The value is 27.65 MPa.

[0072] Step 2: determining the kind and composition of the solidified material based on the strength index, and screening the mix proportion variables; the mix proportion variables include A-slag content, B-alkali activator content, and C-alkali activator modulus;

[0073] In this embodiment, slag-fly ash geopolymer is selected as the solidified material, and the basic composition thereof includes slag powder, fly ash, alkali activator, and water. The slag powder is S95 grade, the fly ash is secondary fly ash, the water glass is selected as the alkali activator, and the modulus of the water glass is adjusted by adding a proper amount of solid NaOH. The mass fraction of the water glass is 35%, the modulus thereof is 3.4, the solid NaOH is analytical pure, and the water-cement ratio of the solidified material neat paste is 0.4.

[0074] In Step 2, the screening of the mix proportion variables includes the following steps:

[0075] Step 2.1: selecting the mix proportion variables that have an influence on the strength of the solidified material.

[0076] In this embodiment, preferably, the slag content (ratio of the slag to the total mass of the powder), the alkali activator content (ratio of the mass of the solid alkali activator to the mass of the powder), and the modulus of the alkali activator are selected as the mix proportion variables A, B, and C, respectively.

[0077] Step 2.2: setting 3-5 levels for each variable to cover the possible action range of the variable.

[0078] The level factor table is shown in Table 1:

[0079] Table 1: Mix proportion variable level factor table

[0080]

[0081] Step 2.3: performing single-factor test of the target variable while fixing other variables. When performing single-factor test of one variable, the test levels of other factors are fixed to the third test level and remain unchanged.

[0082] Step 2.4: performing variance analysis according to the test results to evaluate the influence degree of each variable on the target value, and screening out three high-influence variables. The test results show that the P values of the single-factor test results of the slag content, the alkali activator content, and the modulus of the alkali activator are all <0.05, indicating that the mix proportion variables A, B, and C are all high-influence variables. The high-influence variables include A-slag content, B-alkali activator content, and C-alkali activator modulus.

[0083] Step 3: testing the compressive strength UCS and the heat release Q of the solidified material at the design temperature T, collecting the low-temperature performance data of the solidified material, and using the Box-Behnken design method to form a test list of multiple different mix proportions to perform hydration heat and unconfined compressive strength tests to obtain the low-temperature performance data.

[0084] Step 3.1 Select the experimental design method. The experimental design method includes any one of central composite design, central composite bounded design, central composite surface design and Box-Behnken design. In this embodiment, the Box-Behnken design method is selected.

[0085] Step 3.2 Determine the factor level and the number of tests, and generate the test list. In this embodiment, the factor level of the Box-Behnken design method has three levels (-1, 0, +1), which respectively represent low, medium and high levels, and the central point n c = 5, and the number of tests is 2k(k 1)+n c = 17, and the test list can be generated by Design-Expert software.

[0086] Step 3.3 According to the test list, carry out the strength test and the hydration heat test of the curing material at the design temperature T. The test method of the strength test and the hydration heat test is the same as step 1, and the results of the strength test and the hydration heat test of the curing material at -1.5℃ are shown in Table 2.

[0087] Table 2: Test results of hydration heat and unconfined compressive strength of curing material at 7 days based on Box-Benhnken design

[0088]

[0089] Step 4: According to the low temperature performance data obtained in step 3, obtain a low temperature performance prediction model, establish a low temperature performance prediction model of the curing material, and perform multi-objective evaluation of the performance of the curing material at low temperature based on the low temperature performance comprehensive index LPCI; wherein the low temperature performance prediction model includes a strength prediction model at low temperature and a hydration heat prediction model at low temperature, and the model calculation formula is as follows:

[0090]

[0091] In the above formula, Y is the target value; X i is the proportioning variable determined in step 2; β0, β i , β ii , β ij are regression coefficients.

[0092] By inputting the test data in step 3, the regression coefficients can be solved, and the prediction model of the strength UCS and the hydration heat Q about the proportioning variable

[0093] X i is obtained as follows:

[0094]

[0095] Further, according to the low-temperature performance data of the solidified material obtained in step 3, a low-temperature performance prediction model is solved. Regression fitting is performed on the test data in step 3, and a low-temperature performance prediction model is obtained, including a low-temperature strength prediction model and a low-temperature hydration heat release prediction model, and the model equations are as follows:

[0096]

[0097] The calculation formula of the low-temperature performance comprehensive index LPCI is as follows:

[0098]

[0099] In the formula, LPCI is the low-temperature performance comprehensive index; UCS and Q are the low-temperature strength prediction model and the low-temperature hydration heat release prediction model; UCS t and Q t are the target values of the compressive strength and the hydration heat release of the solidified material; and a and β are influence weights, satisfying a + β = 1.

[0100] The influence weights a and β can be flexibly adjusted according to engineering requirements. When the underlying permafrost at the application site is high-temperature extremely unstable permafrost, a > β; when the underlying permafrost at the application site is high-temperature unstable permafrost or low-temperature basically stable permafrost, a < β; for example, when the underlying permafrost of the roadbed is high-temperature extremely unstable permafrost, the permafrost is island-shaped distribution or is about to disappear, the strength is given priority to, and (a, β) can be taken as (0.6, 0.4); when the underlying permafrost of the roadbed is high-temperature unstable permafrost, the permafrost continuously degrades under the influence of heat to form a weak layer, and the heat release should be strictly constrained, and (a, β) can be taken as (0.4, 0.6).

[0101] The variance analysis and reliability analysis of the low-temperature strength prediction model and the low-temperature hydration heat release prediction model are shown in Tables 3 and 4.

[0102] Table 3 is a summary of the variance analysis data of the regression model of the low-temperature hydration heat release and the unconfined compressive strength of the solidified material

[0103]

[0104] In Table 3, according to the P value range, the significance is different, p < 0.05 indicates the most significant, indicated by “***”, 0.05 ≤ p < 0.1 indicates a significant comparison, indicated by “**”, and when p ≥ 0.1, the significance is weak, indicated by “*”.

[0105] Table 4 is the model reliability analysis data

[0106]

[0107] Further, the interaction of the ratio variables on the hydration heat release of the solidified material is shown in Figure 1 、 Figure 2 and Figure 3 . It can be seen from Figure 1 that when the modulus of the activator is 1.5, the hydration heat release of the solidified material increases first and then stabilizes with the increase of the slag content; it can be seen from Figure 2 that when the alkali activator content is 0.2, the hydration heat release of the solidified material increases with the increase of the slag content when the modulus of the alkali activator is less than 1.25, and the hydration heat release of the solidified material increases first and then decreases with the increase of the slag content when the modulus of the alkali activator is greater than 1.25, and the hydration heat release of the solidified material always increases with the decrease of the modulus of the alkali activator; it can be seen from Figure 3 that when the slag content is 0.8, the hydration heat release of the solidified material gradually decreases with the increase of the alkali activator content when the modulus of the alkali activator is less than 0.75, the hydration heat release of the solidified material increases first and then decreases with the increase of the alkali activator content when the modulus of the alkali activator is greater than 0.75 and less than 1.75, and the hydration heat release of the solidified material increases with the increase of the alkali activator content when the modulus of the alkali activator is greater than 1.75.

[0108] Further, the interaction of the ratio variables on the unconfined compressive strength of the solidified material is shown in Figure 4 、 Figure 5 and Figure 6 . It can be seen from Figure 4 that when the modulus of the activator is 1.5, the unconfined compressive strength of the solidified material increases first and then stabilizes with the increase of the slag content; when the alkali activator content is 0.2, the unconfined compressive strength of the solidified material increases first and then decreases with the decrease of the modulus of the alkali activator; when the slag content is 0.8, the unconfined compressive strength of the solidified material increases first and then decreases with the decrease of the modulus of the alkali activator.

[0109] It can be seen that the strength of the slag-fly ash geopolymer increases first and then decreases with the increase of the hydration heat release, the hydration heat release of the geopolymer increases with the decrease of the modulus of the activator and the increase of the alkali activator content, but the lower modulus of the activator and the higher alkali activator content will reduce the strength of the geopolymer, because increasing the activator content and reducing the modulus of the activator will promote the precipitation and hydration of silicon and aluminum ions in the solidified raw materials, and the formation of gels such as sodium aluminum silicate N-A-S-H and calcium aluminum silicate C-A-S-H, improve the reaction process, and increase the hydration heat release, but excessive activator will reduce the fluidity of the solidified material, shorten the setting time, cause insufficient contact between the solidified raw materials and the activator, residual raw materials, low uniformity of the sample, and excessive NaOH will inhibit the polymerization reaction of Ca ions, generate N-A-S-H with lower cohesion, and further reduce the strength of the material.

[0110] Further, the UCS at low temperature is used as the strength prediction model, and the Q is used as the hydration heat prediction model, and the UCS is used as the target value of the compressive strength of the solidified material t and the Q is used as the target value of the hydration heat t The impact weights a and b are brought into the low-temperature performance comprehensive index LPCI, wherein, in the embodiment, the underlying frozen soil of the roadbed is a transition type frozen soil, the frozen soil layer is thick and continuously degrades, and the heat release is strictly constrained, and (a, b) is taken as (0.4, 0.6).

[0111] In the embodiment, preferably, the LPCI calculation formula is as follows:

[0112]

[0113] Step 5: Based on the evaluation result, the final mixture ratio of the solidified material is optimized and determined; according to the value range of the mixture ratio variable, the maximum value of the low-temperature performance comprehensive index LPCI is obtained, and the mixture ratio variable corresponding to the maximum LPCI is adjusted to obtain the final mixture ratio.

[0114] Step 5.1 According to the value range of the mixture ratio variable, the maximum value of the low-temperature performance comprehensive index LPCI and the mixture ratio variable corresponding to the maximum LPCI are obtained by using the numerical methods of gradient descent and grid search.

[0115] Further, the target function LPCI is converted, and the function g(A, B, C) is defined:

[0116]

[0117] Further, the constant M is ignored, and the maximum value of g(A, B, C) = 0.4ln(UCS)-0.6ln(Q) in the constraint domain 0.6

[0118] Further, the numerical optimization method of gradient descent and grid search is used to solve by means of MATLAB or Python software. The grid step is set, for example, A is from 0.6 to 1.0 with a step of 0.05; B is from 0.1 to 0.3 with a step of 0.02; and C is from 0.5 to 2.5 with a step of 0.1, totally 9x11x21=2079 points. The g value of each point is calculated, and the maximum value region is located. The partial derivatives of the function g with respect to the variables A, B and C are calculated, and the maximum value in the located region is found by gradient analysis.

[0119] Further, in this embodiment, the maximum value of LPCI is 1.17, and the corresponding (A, B, C) is (0.88, 0.30, 1.94), at this time, the UCS is 23.37 MPa, and Q is 91.43 J / g. LPCI is greater than 1, indicating that the low-temperature performance of the solidified material is better than the reference value in the application environment of this embodiment.

[0120] Step 5.2 Adjust the ratio obtained in step 5.1 based on work performance and economy, and solve the low-temperature performance comprehensive index LPCI of the solidified material after adjusting the ratio, and determine the final ratio according to the optimization result. When the ratio variables (A, B, C) are (0.88, 0.30, 1.94), the initial setting time of the solidified material neat paste under this ratio is 58 min, and the fluidity is 132 mm, which meets the CJT 526-2018 soft soil solidifying agent standard. In order to improve the economy of the solidification measure, the amount of alkali activator can be appropriately reduced, and the ratio variables (A, B, C) are (0.88, 0.25, 1.94). At this time, the UCS of the solidified material is 21.89 MPa, Q is 92.34 J / g, the initial setting time is 69 min, the fluidity is 158 mm, and LPCI is 1.14. The low-temperature performance index of the material is basically unchanged, and the economy is obviously improved, so in this embodiment, the slag-fly ash-based polymer is selected to solidify the soft weak layer under the roadbed in permafrost region, and the optimal ratio is determined as slag content 0.88, alkali activator content 0.25, and alkali activator modulus 1.94, and the material water-cement ratio is 0.4.

[0121] Example 2

[0122] In this embodiment, the natural water content of the soft weak layer at the application site is higher than 30%, the liquid limit is 23.8%, and the plastic limit is 14.6%, which belongs to silty clay. The temperature change range of the soft weak layer in the past year is-1.49℃~7.06℃, the temperature of the frozen soil under the soft weak layer is-0.46℃, which belongs to high-temperature extremely unstable permafrost, the thickness of the soft weak layer is 6m, and the thickness of the frozen soil is less than 2m. In order to ensure that the designed material can continuously react to form strength in this environment, the design temperature T is determined as-1.5℃. The slag-fly ash-based polymer is selected as the solidified material, and the design method is step 1.

[0123] Further, the low-temperature strength prediction model UCS and the low-temperature hydration heat prediction model Q of the solidified material are brought into the low-temperature performance comprehensive index LPCI, and the target values UCS t and Q of the hydration heat of the solidified material t , the influence weights α and β are brought into the low-temperature performance comprehensive index LPCI, wherein considering that the permafrost under the roadbed in this embodiment has been degraded in a large area, the soft weak layer is deep and thick, and the frozen soil layer is relatively thin, the material strength is given priority to in the design, and (α, β) is taken as (0.6, 0.4). The LPCI calculation formula in this embodiment is as follows:

[0124]

[0125] Further, in the embodiment, the maximum value of LPCI is 1.024, and the corresponding (A, B, C) is (0.79, 0.26, 1.54), at this time, the UCS is 25.74 MPa, and Q is 111.56 J / g. LPCI is greater than 1, which indicates that the low-temperature performance of the solidified material is better than the reference value in the application environment of the embodiment.

[0126] When the mixing variable (A, B, C) is (0.79, 0.26, 1.54), the initial setting time of the solidified material net paste under the mixing ratio is 40 min, and the fluidity is 90 mm, which does not meet the CJ / T 526-2018 soft soil solidifying agent standard. In order to improve the working performance of the material, the amount of alkali activator is appropriately reduced, the mixing variable (A, B, C) is (0.79, 0.20, 1.54), at this time, the UCS of the solidified material is 24.41 MPa, Q is 111.11 J / g, the initial setting time is 55 min, the fluidity is 117 mm, and LPCI is 1.00. The low-temperature performance index of the material is 1, and the workability is obviously improved, so in the embodiment, the slag-fly ash-based polymer is selected to solidify the frozen soil area roadbed underlying soft layer, the optimal mixing ratio is determined as slag content 0.79, alkali activator content 0.20 and alkali activator modulus 1.54, and the water-cement ratio of the material is 0.4.

[0127] The above only describes the preferred embodiments of the present application and is not intended to limit the present application, and any modification, equivalent replacement and improvement made within the spirit and principle of the present application shall be included in the protection scope of the present application.

Claims

1. A multi-objective method for designing mix proportions of soil stabilization materials in permafrost regions, characterized in that, It includes the following steps: Step 1: Based on the environmental parameters of the application site, determine the design temperature of the curing material. Use the heat release of cement at the design temperature as a reference value for the target value of the heat release of the curing material, and use the unconfined compressive strength of cement at the design temperature as a reference value for the target value of the unconfined compressive strength of the curing material. Step 2: Determine the type and composition of the curing material based on the strength index, and screen the mix proportion variables; the curing material is an inorganic curing agent, and the mix proportion variables include slag content, alkali activator content, and alkali activator modulus; Step 3: Test the compressive strength and heat release of the cured material at the design temperature, and collect the low-temperature performance data of the cured material; use the Box-Behnken design method to form a test list with multiple different ratios, conduct hydration heat and unconfined compressive strength tests, and obtain low-temperature performance data; Step 4: Based on the low-temperature performance data obtained in Step 3, establish a low-temperature performance prediction model for the cured material, and conduct a multi-objective evaluation of the performance of the cured material at low temperatures based on the comprehensive low-temperature performance index. The expression for the Low Temperature Performance Index (LPCI) is as follows: Wherein, LPCI is the low-temperature performance comprehensive index, UCS is the compressive strength obtained from the low-temperature strength prediction model, and Q is the heat of hydration at low temperature; UCS t Q is the target value of the compressive strength of the cured material. t α represents the target value of the heat release from hydration of the solidified material; α and β are the influence weights, satisfying α+β=1; Step 5: Based on the evaluation results, optimize and determine the final mix proportion of the curing material; according to the range of values ​​of the mix proportion variables, find the maximum value of the low-temperature performance comprehensive index, and adjust the mix proportion variables corresponding to the maximum value of the low-temperature performance comprehensive index to obtain the final mix proportion.

2. The method for designing mix proportions of soil stabilization materials in permafrost regions based on multiple objectives as described in claim 1, characterized in that, In step 1, Q t / Q c =0.5-0.9, UCS t / UCS c =1.1-1.

5.

3. The method for designing mix proportions of soil stabilization materials in permafrost regions based on multiple objectives as described in claim 1, characterized in that, The curing material is selected from slag-fly ash based polymers. The curing material includes slag powder, fly ash, alkaline activator and water. The alkaline activator is selected from water glass, and the modulus of the water glass is adjusted by sodium hydroxide.

4. The method for designing mix proportions of soil stabilization materials in permafrost regions based on multiple objectives as described in claim 1, characterized in that, Step 2, screening the mix proportion variables includes the following steps: Step 2.1: Select the proportioning variables that affect the strength of the cured material; Step 2.2: Set 3 to 5 levels for each variable to cover its possible scope of influence; Step 2.3: Fix other variables and conduct a single-factor experiment on the target variable; Step 2.4: Based on the experimental results, perform an analysis of variance to assess the influence of each variable on the target value and screen out three high-impact variables, including slag content, alkali activator content, and alkali activator modulus.

5. The method for designing mix proportions of soil stabilization materials in permafrost regions based on multiple objectives as described in claim 1, characterized in that, In step 3, the Box-Behnken design method uses three factor levels: -1, 0, and +1, representing low, medium, and high levels respectively, with the center point n. c Take 5 samples, and conduct 2k (k) trials. 1)+n c =17, the experimental list was generated using Design-Expert software, where k represents the number of factors.

6. The method for designing mix proportions of soil stabilization materials in permafrost regions based on multiple objectives as described in claim 5, characterized in that, In step 4, the low-temperature performance prediction model includes a low-temperature strength prediction model and a low-temperature hydration heat release prediction model. The model calculation formulas are as follows: In the formula, Y is the target value; X i X j All are matching variables, determined in step 2; k represents the number of factors; β0, β i β ii β ij The regression coefficients are used as inputs; by substituting the experimental data from step 3, the regression coefficients can be solved to obtain the prediction model of intensity UCS and hydration heat release Q with respect to the ratio variable Xi: 。 7. The method for designing mix proportions of soil stabilization materials in permafrost regions based on multiple objectives as described in claim 6, characterized in that, The influence weights α and β are adjusted according to engineering requirements. When the application site is under unstable permafrost, α > β; when the application site is under metastable or transitional permafrost, α < β.

8. The method for designing mix proportions of soil stabilization materials in permafrost regions based on multiple objectives as described in claim 1, characterized in that, In step 5, the final mix proportions are determined according to the following steps: Based on the ratio variables obtained in step 5 for adjusting performance and economy, the low-temperature performance comprehensive index LPCI of the cured material after adjusting the ratio is calculated, and the final ratio is determined based on the optimization results.

9. The method for designing mix proportions of soil stabilization materials in permafrost regions based on multiple objectives as described in claim 8, characterized in that, The comprehensive low-temperature performance index was obtained through numerical methods of gradient ascent and grid search.

10. The method for designing mix proportions of soil stabilization materials in permafrost regions based on multiple objectives according to any one of claims 1-9, characterized in that, In step 1, the environmental parameters include the maximum and minimum ground temperature of the application site over 1-2 years, the annual average ground temperature of the permafrost at the application site, the type of permafrost at the application site, the thickness of the weak layer at the application site, and the thickness of the permafrost layer at the application site.

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