A method for resolving pore water pressure of cement-based materials under non-isothermal conditions

Abstract

The application discloses a filling body pore water pressure analytic method under non-isothermal conditions and belongs to the field of underground disposal methods of tailings, and proposes an analytic solution of a filling body non-isothermal pore water pressure control equation, which can accurately and unbiasedly solve the filling body water pressure evolution law under different environmental temperature conditions through strict mathematical operation. The application only needs to use open-source and free mathematical software to complete numerical calculation and then provide accurate and correct prediction data for filling and stoping work of deep mineral resources.

Description

Technical Field

[0001] This invention belongs to the field of underground mining, specifically relating to a method for analyzing pore water pressure in cement-based materials under non-isothermal conditions. Background Technology

[0002] While underground mining provides essential mineral resources for socio-economic development, it inevitably generates large amounts of tailings waste and underground goafs, seriously threatening mine safety and the natural environment. Driven by increasingly stringent safety standards and environmental protection pressures, underground tailings disposal has gradually become an important approach to achieving green and clean mining of mineral resources. By mixing tailings, cementing agents, and water in a specific ratio and backfilling them into underground goafs, this tailings backfilling technology not only avoids large-scale exposure and accumulation of tailings on the surface but also significantly improves the stability of the surrounding rock in underground mining areas. Furthermore, it allows for the absence of pillars, thereby increasing ore recovery rates.

[0003] While tailings backfilling technology has continuously brought significant environmental and economic benefits to underground resource extraction, recent field monitoring has repeatedly revealed abnormal behavior of backfill bodies in deep mines. This is mainly manifested in the rapid increase in pore water pressure and soil pressure even after backfilling has ceased. However, current research has not yet established a comprehensive understanding of the behavioral response laws of backfill bodies under complex temperature conditions. Since the temperature of the surrounding rock in the mining area will continuously rise with increasing resource extraction depth under the influence of the geothermal gradient, an analytical solution for the evolution of pore water pressure in non-isothermal backfill bodies under adiabatic undrained conditions is proposed. This is crucial for correcting multi-field coupled mathematical models of backfill bodies applicable to deep mining environments, thereby promoting sustainable mine production.

[0004] The existing technical solution is as follows: This technical solution uses third-party numerical simulation software to perform numerical solutions, thereby obtaining the evolution laws of filling body temperature, water pressure and earth pressure.

[0005] The disadvantages of existing technology one are: It is costly, as it relies on numerical solutions and typically requires expensive numerical simulation software to calculate a series of independent variables and solutions. This technology, however, provides the specific functional form of the solution, thus requiring only open-source and free mathematical software for calculation. Furthermore, this technology neglects the thermal expansion and deformation of pore water, therefore failing to adequately capture the hydrothermal pressurization effect of the filling material caused by the differential thermal expansion of the fluid-solid two-phase system.

[0006] The technical solution of the existing technology 2 is as follows: This technical solution obtains the evolution law of temperature, water pressure and earth pressure in the filling body by numerically solving the coupled model of temperature-seepage-mechanical-chemical field of the filling body under given accuracy conditions.

[0007] The disadvantages of prior art two are as follows: This technique cannot control computational errors. While it considers the thermal expansion and deformation of pore water, thus reasonably capturing the hydrothermal pressurization effect of the filling material caused by the differential thermal expansion of the fluid-solid two phases, the numerical solution can only be obtained through numerical calculation, and the independent variables cannot be arbitrarily given and the calculated values ​​obtained. Prior art two, on the other hand, can only obtain a specific solution under certain parameter selections through numerical methods. Therefore, this scheme has uncontrollable computational errors and lacks the generality of analytical solutions. Summary of the Invention

[0008] In order to solve the technical problems existing in the background art, the present invention aims to provide an analytical method for pore water pressure of cement-based materials under non-isothermal conditions. Based on the theoretical framework of pore thermoelasticity, an analytical solution for the non-isothermal evolution of pore water pressure of filling body is established. The influence law of different ambient temperatures on the water pressure of filling body is solved by rigorous formula, providing technical guidance for achieving safe and efficient mining.

[0009] To solve the technical problem, the technical solution of the present invention is as follows:

[0010] A method for analyzing pore water pressure in cement-based materials under non-isothermal conditions, the method comprising:

[0011] The total hydration water consumption and hydration heat release of the filling body are determined based on the chemical composition of cement, and the stiffness evolution process of the filling body under room temperature conditions is determined by wave velocity test or triaxial compression test.

[0012] The equivalent chemical reaction time is defined using the Arrhenius formula, and then the hydration degree index of the cement reaction process is established. It is then used to characterize the evolution of the hydration water consumption, hydration heat release, and stiffness of the filling body as determined by the above experiments.

[0013] Considering the temperature sensitivity of the thermal expansion coefficient of water, and incorporating the evolution of the above parameters into the pore water pressure control equation of the filling unit under non-isothermal conditions for analytical solution, the following steps are included:

[0014] The initial temperature of interest is determined, the equivalent chemical reaction time series to be studied is specified, and then the change process of pore water pressure of the filling unit under the initial temperature condition with the equivalent chemical reaction time is determined by analytical calculation using the pore water pressure control equation of the filling unit under non-isothermal conditions.

[0015] Based on the definition of hydration degree, calculate the hydration degree index sequence corresponding to the above equivalent chemical reaction time sequence, and then use the Arrhenius formula to analyze and determine the actual chemical reaction time required to reach the specified hydration degree index under the initial temperature condition.

[0016] By correlating the pore water pressure corresponding to the equivalent chemical reaction time series with the actual chemical reaction time, the evolution analysis results of the pore water pressure of the filling material under the corresponding initial temperature conditions can be obtained.

[0017] Furthermore, the method also includes:

[0018] Based on the theoretical framework of pore thermoelasticity, a non-isothermal pore water pressure control equation for the filling body is established by considering the water consumption of hydration reaction.

[0019] Taking the adiabatic non-drained filling unit as the research object, the thermoelastic mechanical constitutive relationship under constant confining pressure and the temperature change caused by hydration heat release are substituted into the above-mentioned governing equations to obtain the pore water pressure governing equations of the filling unit under non-isothermal conditions.

[0020] Furthermore, based on the pore thermoelasticity theoretical framework of Selvadurai and Suvorov, a non-isothermal pore water pressure control equation for the filling body is established by considering the water volume change caused by the water consumption of the hydration reaction, i.e., the chemical shrinkage effect:

[0021]

[0022] Where α represents the Biot coefficient, α = 1 – K d / K s In the formula, K d Let K be the bulk modulus of the infill skeleton, n be the porosity, and K be the density of the infill skeleton. s and K w p represents the bulk modulus of the solid phase and water, respectively. w The pore water pressure is represented by β, t is the reaction time, and β is the pore water pressure. s and β w These are the coefficients of thermal expansion of the solid phase and water, respectively, where T represents the current temperature and ε is the coefficient of thermal expansion. v Let ε be the volumetric strain, k be the permeability coefficient, η be the dynamic viscosity of water, and ε be the viscosity of water. shf Let ξ be the total water consumed in the chemical reaction process, and ξ be the degree of hydration.

[0023] Furthermore, neglecting the compressibility of solid particles compared to the filling skeleton, i.e., K d < <K s Therefore, we can assume that the Biot coefficient α is approximately 1. Meanwhile, we focus on the effect of temperature load on the pore water pressure of the filling body. Therefore, we take the filling body unit as the research object, and then eliminate the seepage term and simplify equation (1) to:

[0024]

[0025] Under given confining pressure conditions, the change in effective stress is equal to the change in pore water pressure, i.e. Assuming solid-phase compression is negative, the volumetric deformation of the filling element can be expressed as the following derivative:

[0026]

[0027] Finally, under the assumption of small strain, substituting equation (3) into equation (2) yields the pore water pressure control equation for the filling unit under non-isothermal conditions:

[0028]

[0029] As can be seen from the above expression, the change in pore water pressure of the filling unit is mainly the result of the competition between hydration water consumption and hydrothermal pressurization under temperature load.

[0030] Furthermore, the bulk modulus of the filling unit during the hydration reaction can be expressed as:

[0031]

[0032] Among them, K di κ represents the initial bulk modulus of the filling material before hydration begins, λ represents the ratio of the bulk modulus of the filling material in its final state to that in its initial state, and κ represents the initial bulk modulus of the filling material. K Used to describe the rate of evolution of bulk modulus over time, t e Reference temperature T r The reference reaction time is at 293.15 K.

[0033] The evolution of the stiffness of the filling material during the above hydration reaction process can be determined by wave velocity testing or triaxial compression testing.

[0034] According to the Arrhenius formula, the actual time t and the reference time t e The relationship can be represented as:

[0035]

[0036] Among them, E a R represents the activation energy required for a chemical reaction. a It is the universal gas constant, R a =8.314 J / mol / K; Furthermore, assuming the virtual triaxial hydration pressure chamber is completely adiabatic, meaning the filling unit cannot conduct or convectively transfer heat with the surrounding environment, the temperature change of the filling under adiabatic non-drainage conditions is solely due to the heat release from hydration. Therefore, the filling temperature can be defined as:

[0037]

[0038] Where T0 represents the initial temperature, Q f It is the heat released during a chemical reaction, which can be determined based on the chemical composition of cement (ρC). eff Indicates effective heat capacity (ρC) eff = (1–n)ρ s C s + nρ w C w C s and C w ρ represents the specific heat capacity of the solid and liquid phases, respectively. s and ρ w These are the densities of the solid phase and water, respectively.

[0039] Degree of hydration ξ and reference reaction time t e The relationship can be expressed as:

[0040]

[0041] Among them, κ ξ Used to describe the rate of evolution of hydration degree over a reference time;

[0042] Similarly, by multiplying the above formula by the total volume of free water consumed in the hydration reaction, we can obtain the real-time free water consumption during the hydration reaction process, as shown on the right side of the equation (2).

[0043] The total volume of free water consumed in the hydration reaction can be determined by the chemical composition of the cement.

[0044] The evolution of the thermal expansion coefficient of water with temperature can be described using the following formula:

[0045]

[0046] in, The fitting coefficients are denoted as .

[0047] Furthermore, using the defined filling temperature equation (7) to represent the filling temperature, the governing equation (4) can be rewritten as the following expression:

[0048]

[0049] Finally, multiply both sides of equation (10) by dt / dt. e Substituting these equations into equation (8), we can finally obtain the non-isothermal pore water pressure control equation for the filling body:

[0050]

[0051] Therefore, at any given preparation temperature T0 and associated equivalent time t e0 Under the condition, for both sides of equation (11) with t e Integrating the integral variable yields the pore water pressure change Δp. w Regarding the initial temperature T0 and the reference time t e0 Bivariate functional relations:

[0052]

[0053] The above integral can be analyzed and calculated using Gaussian hypergeometric functions, and can thus be expressed as:

[0054]

[0055] Parameters of equation (13):

[0056]

[0057] The solution to the above equation is the change of pore water pressure in the filling material with equivalent chemical reaction time under a specified initial temperature condition.

[0058] Among them, with the equivalent chemical reaction time or reference time t e As an abstract auxiliary variable in the derivation process, while the actual reaction time t is of concern in engineering applications and experimental research, the following expression can be obtained by using the incremental expression (6) and differentiating ξ on both sides of the equation:

[0059]

[0060] Among them, t e The derivative with respect to ξ can be expressed as the inverse function of equation (8):

[0061]

[0062] Substituting equations (7) and (16) into equation (15), we obtain the differential equation for the actual reaction time t with respect to the degree of hydration ξ and the initial temperature T0:

[0063]

[0064] Integrating equation (17) with respect to ξ, we can finally obtain the time t required to reach the specified degree of hydration ξ0 under a given preparation temperature T0:

[0065]

[0066] Equation (18) can be calculated using the following formula:

[0067]

[0068] Equation (19) parameters:

[0069]

[0070] Therefore, solving the inverse function of equation (19) yields the degree of hydration ξ after any reaction time t0 at a given preparation temperature T0:

[0071]

[0072] Then, substituting equation (21) into equation (8) yields the differential equation of the reference reaction time t with respect to the actual reaction time t0 and the initial temperature T0:

[0073]

[0074] Finally, by substituting equation (22) into equation (13), the pore water pressure change Δp after any reaction time t0 under a given preparation temperature T0 can be obtained. w :

[0075]

[0076] The hydration index sequence corresponding to the above equivalent chemical reaction time sequence is calculated according to the definition of hydration degree (8), and then the actual chemical reaction time required to reach the specified hydration degree index under the initial temperature condition is determined by analytical calculation using equation (19).

[0077] Furthermore, the hydration degree index and the equivalent chemical reaction time under the same initial temperature conditions correspond one-to-one. By correlating the pore water pressure of the filling body corresponding to the same equivalent chemical reaction time with the actual chemical reaction time data, the pore water pressure development process of the filling body unit under non-isothermal conditions can be obtained.

[0078] Compared with the prior art, the advantages of the present invention are as follows:

[0079] This invention proposes for the first time an analytical solution to the non-isothermal pore water pressure control equation for filling bodies. Through rigorous mathematical calculations, the evolution of water pressure in filling bodies under different ambient temperature conditions can be accurately and without deviation. This invention only requires open-source, free mathematical software to complete the numerical calculations, thus providing accurate predictive data for the filling and recovery of deep mineral resources. Attached Figure Description

[0080] Figure 1 Graph showing water pressure variation of the filling material under different initial temperatures and curing times;

[0081] Figure 2 1. Evolution of pore water pressure in filling materials under different initial temperature conditions;

[0082] Figure 3 A graph showing the pore water pressure variation obtained from indoor testing (discrete points) and model prediction (solid line);

[0083] Figure 4. Water pressure variation of infill bodies with cement content of 1% (a) and 9% (b) under different initial temperatures and curing times;

[0084] Figure 5. Evolution of pore water pressure in filling bodies with cement content of 1% (a) and 9% (b) under different initial temperature conditions.

[0085] Figure 6 The main flowchart of this invention. Detailed Implementation

[0086] The specific implementation of the present invention is described below with reference to embodiments:

[0087] It should be noted that the structures, proportions, sizes, etc. shown in this specification are only used to complement the content disclosed in the specification for those skilled in the art to understand and read, and are not intended to limit the conditions under which the present invention can be implemented. Any modifications to the structure, changes in the proportions, or adjustments to the size, without affecting the effects and objectives that the present invention can produce, should still fall within the scope of the technical content disclosed in the present invention.

[0088] Furthermore, the terms such as "upper," "lower," "left," "right," "middle," and "one" used in this specification are merely for clarity of description and are not intended to limit the scope of the invention. Any changes or adjustments to their relative relationships, without substantially altering the technical content, should also be considered within the scope of the invention.

[0089] Example 1:

[0090] like Figure 6 As shown, this invention proposes an analytical solution method for pore water pressure in a packed body under non-isothermal conditions, the method comprising the following steps:

[0091] Establish the governing equations:

[0092] This invention is based on the pore thermoelasticity theory framework of Selvadurai and Suvorov, and establishes a non-isothermal pore water pressure control equation for the filling body by considering the water volume change caused by water consumption in hydration reactions (i.e., chemical shrinkage):

[0093] (twenty three)

[0094] Where α represents the Biot coefficient (α = 1 – K) d / K s In the formula, K d (where n is the bulk modulus of the infill skeleton), and K is the porosity. s and K w p represents the bulk modulus of the solid phase and water, respectively. w The pore water pressure is represented by β, t is the reaction time, and β is the pore water pressure. s and β w These are the coefficients of thermal expansion of the solid phase and water, respectively, where T represents the current temperature and ε is the coefficient of thermal expansion. v Let ε be the volumetric strain, k be the permeability coefficient, η be the dynamic viscosity of water, and ε be the viscosity of water. shf Let ξ be the total water consumed in the chemical reaction process, and ξ be the degree of hydration.

[0095] Since the compressibility of solid particles is negligible compared to the filling skeleton (i.e., K... d << K s Therefore, we can assume that the Biot coefficient α is approximately 1. Meanwhile, since this invention mainly focuses on the effect of temperature load on the pore water pressure of the filling body, the filling body unit is taken as the research object, and the seepage term is eliminated, and equation (1) is simplified to:

[0096] (twenty four)

[0097] Under given confining pressure conditions, the change in effective stress is equal to the change in pore water pressure (i.e., (Assuming solid-phase compression is negative), the volumetric deformation of the filling element can be expressed as the following derivative form:

[0098] (25)

[0099] Finally, under the assumption of small strain, substituting equation (3) into equation (2) yields the pore water pressure control equation for the filling unit under non-isothermal conditions:

[0100] (26)

[0101] As can be seen from the above expression, the change in pore water pressure of the filling unit is mainly the result of the competition between hydration water consumption and hydrothermal pressurization under temperature load.

[0102] Model parameters:

[0103] According to the research of Doherty and Muir Wood, the bulk modulus of the filling unit during the hydration reaction can be expressed as:

[0104] (27)

[0105] Among them, K di κ represents the initial bulk modulus of the filling material before hydration begins, λ represents the ratio of the elastic modulus of the filling material in its final state to that in its initial state, and κ represents the elastic modulus of the filling material in its final state to that in its initial state. K Used to describe the rate of evolution of the elastic modulus over time, t e Reference temperature T r Reference reaction time under (293.15K) conditions.

[0106] According to the Arrhenius formula, the actual time t and the reference time t e The relationship can be represented as:

[0107] (28)

[0108] Among them, E a R represents the activation energy required for a chemical reaction. a It is the universal gas constant (R a =8.314 J / mol / K). Furthermore, this invention assumes that the virtual triaxial hydration pressure chamber is completely adiabatic, meaning that the filling unit cannot generate heat conduction or convective heat transfer with the surrounding environment. Therefore, the temperature change of the filling under adiabatic, non-drained conditions is solely due to the heat release from hydration. Thus, the filling temperature can be defined as:

[0109] (29)

[0110] Where T0 represents the initial temperature, Q f It is the heat released during a chemical reaction (ρC). eff This represents the effective heat capacity (ρC). eff = (1–n)ρ s C s + nρ w C w ), C s and C w ρ represents the specific heat capacity of the solid and liquid phases, respectively. s and ρ w These are the densities of the solid phase and water, respectively.

[0111] Degree of hydration ξ and reference reaction time t e The relationship can be expressed as:

[0112] (30)

[0113] Among them, κ ξ Used to describe the rate of evolution of hydration degree over a reference time.

[0114] Taking the tailings backfill used in the Kanowna Belle gold mine in Australia as an example, the physicochemical model parameters of the tailings in the above equations are shown in Table 1. Finally, since the thermal expansion coefficient of water is highly sensitive to temperature (Table 2), the following formula is used to describe the evolution of the thermal expansion coefficient of water with temperature:

[0115] (31)

[0116] Wherein, the fitting coefficient β w0 As shown in Table 1, the coefficient R is determined. 2 =0.98 as shown in Table 2.

[0117] Thus, the above parameter analysis has clarified all evolutionary characteristics with respect to T0 and t. e Therefore, by using equation (7) to represent the filling temperature, the governing equation (4) can be rewritten as the following expression:

[0118] (32)

[0119] Finally, multiply both sides of equation (10) by dt / dt. e Substituting these equations into equation (8), we can finally obtain the non-isothermal pore water pressure control equation for the filling body:

[0120] (33)

[0121] Therefore, at any given preparation temperature T0 and associated equivalent time t e0 Under the condition, for both sides of equation (13) with t e By integrating the integral variable, the change in pore water pressure Δp can be obtained. w Regarding the initial temperature T0 and the reference time t e0 Bivariate functional relations:

[0122] (34)

[0123] The above integral can be analyzed and calculated using Gaussian hypergeometric functions, and can thus be expressed as:

[0124] (35)

[0125] Parameters of equation (13):

[0126] (36)

[0127] Reference time t e This is merely an abstract auxiliary variable in the calculation derivation process, while engineering applications and experimental research are concerned with the actual reaction time t. Therefore, by using the incremental expression (6) and differentiating ξ on both sides of the equation, the following expression can be obtained:

[0128] (37)

[0129] Among them, t e The derivative with respect to ξ can be expressed as the inverse function of equation (8):

[0130] (38)

[0131] Substituting equations (7) and (16) into equation (15), we obtain the differential equation for the actual reaction time t with respect to the degree of hydration ξ and the initial temperature T0:

[0132] (39)

[0133] Integrating equation (17) with respect to ξ, we can finally obtain the time t required to reach the specified degree of hydration ξ0 under a given preparation temperature T0:

[0134] (40)

[0135] Equation (18) can be calculated using the following formula:

[0136] (41)

[0137] Equation (19) parameters:

[0138] (42)

[0139] Therefore, solving the inverse function of equation (19) yields the degree of hydration ξ after any reaction time t0 at a given preparation temperature T0:

[0140] (43)

[0141] Then, substituting equation (21) into equation (8) yields the differential equation of the reference reaction time t with respect to the actual reaction time t0 and the initial temperature T0:

[0142] (44)

[0143] Finally, by substituting equation (22) into equation (13), the pore water pressure change Δp after any reaction time t0 under a given preparation temperature T0 can be obtained.w :

[0144] (45)

[0145] However, since equation (19) is quite complex, it is difficult to solve its inverse function. Therefore, analytical calculation can be achieved through the following method.

[0146] The hydration index sequence corresponding to the above equivalent chemical reaction time sequence is calculated according to the hydration degree definition formula (8), and then the actual chemical reaction time required to reach the specified hydration degree under the initial temperature condition is determined by analytical calculation using formula (19).

[0147] Since the degree of hydration index and the equivalent chemical reaction time correspond one-to-one under the same initial temperature conditions, the development process of pore water pressure of the filling unit under non-isothermal conditions can be obtained by correlating the pore water pressure of the filling body corresponding to the same equivalent chemical reaction time with the actual chemical reaction time data.

[0148] Example 2:

[0149] The effect of initial temperature on pore water pressure:

[0150] The geographical location of the mine and seasonal climate change have a significant impact on the initial temperature of the backfill. Furthermore, the frictional heating during pipeline transportation also alters the initial temperature of the freshly mixed material. Therefore, this invention utilizes the aforementioned analytical methods to determine the pore water pressure changes of the backfill unit under different initial temperatures and curing times. Figure 1 Furthermore, the influence of temperature on the behavior characteristics of filling materials was investigated.

[0151] Figure 1 This indicates that when the initial temperature is low, the pore water pressure in the infill material dissipates rapidly with increasing curing time. Conversely, when the initial temperature is high, the pore water pressure rises rapidly due to a stronger hydrothermal pressurization effect and remains stable after the hydration reaction is complete. Notably, once the temperature reaches a certain critical value, the pore water pressure hardly changes with the passage of reaction time. This case study will delve into the influence of initial temperature on the behavior characteristics of the infill material through a detailed analysis of the T0 profile of the three-dimensional water pressure distribution.

[0152]

[0153] The evolution of pore water pressure in a filling unit in an adiabatic, non-drained environment under different initial temperature conditions is as follows: Figure 2 As shown. Figure 2This indicates that the water pressure in the filling material at any given time initially decreases and then increases with increasing initial temperature. This is because increasing the curing temperature of the low-temperature filling material accelerates the chemical reaction rate, thereby promoting the dissipation of pore pressure caused by hydration water consumption. Simultaneously, since the thermal expansion coefficient of water remains relatively small at lower temperatures (Table 2), the thermal expansion effect caused by hydration heat release is not significant. Therefore, the pore water pressure will ultimately decrease continuously with increasing temperature, dominated by hydration water consumption. However, as the initial temperature continues to rise, although the chemical reaction rate of the filling material will further accelerate, the thermal expansion coefficient of water will also continue to increase. Therefore, when the temperature exceeds the critical threshold, the hydrothermal pressurization effect caused by hydration heat release will exceed the hydration water consumption effect, thus causing the pore water pressure to increase with increasing initial temperature.

[0154]

[0155] from Figure 2 It can also be seen that when the hydration reaction is in its initial stage (t=24h), as the initial temperature gradually increases, the water pressure change of the filling body is not obvious in the initial low temperature gradient range (i.e. 0℃~45℃). However, when the temperature reaches the critical threshold, a higher pore water pressure is generated due to the stronger hydrothermal pressurization effect. In addition, the water pressure change in the range of 48~168h shows a more obvious non-monotonicity. Therefore, this phenomenon indicates that the competitive effect between hydration dissipation and hydrothermal pressurization is particularly obvious when the cement hydration reaction is active.

[0156] After a prolonged chemical reaction (t=336h), the pore water pressure, although slightly decreasing below 5℃, almost monotonically increases with increasing initial temperature. This is because the hydration reaction is essentially complete at this point; that is, the filling materials at different initial temperatures all experience the same temperature rise and chemical contraction under the action of the hydration reaction. However, due to the greater thermal expansion coefficient of water at higher temperatures, the filling materials will generate higher pore water pressure under a stronger hydrothermal pressurization effect. The above calculation results indicate that although increasing the initial temperature can enhance the early hydration water consumption and thus promote water pressure dissipation, low-temperature filling materials will inhibit the thermal expansion of pore fluids and ultimately produce a significant pressure reduction effect.

[0157] It is worth noting that the critical initial temperature at which pore water pressure transitions from a decrease to an increase is closely related to the chemical reaction time of the infill material; the longer the chemical reaction time, the lower the critical temperature for pore water pressure. This is because low temperatures reduce the rate of heat release during hydration, requiring a longer time to generate a sufficient temperature rise so that the thermal expansion effect completely offsets the pressure reduction caused by water consumption during hydration. Similarly, as the curing temperature continues to rise, the chemical reaction rate of the infill material further accelerates, and the coefficient of thermal expansion of water also continues to increase. Therefore, the hydrothermal pressurization effect caused by heat release during hydration will exceed the water consumption effect during hydration in the early stages of the reaction, resulting in a monotonically increasing pore water pressure with increasing initial temperature.

[0158] The effect of binder content on pore water pressure:

[0159] After being backfilled into underground goaf areas, the backfill material needs to possess sufficient strength to meet the requirements of mechanical stability, thereby ensuring the safe and efficient development of the mine. In actual backfilling operations, increasing the amount of cementitious agent can significantly improve the mechanical properties of the backfill material, but it also leads to high backfilling costs. Therefore, studying the effect of cementitious agent dosage is of great significance for determining a reasonable mix proportion and controlling construction costs.

[0160] The comparison of pore water pressure obtained by monitoring the hydration pressure chamber and model prediction based on the physicochemical properties of the filling material in Table 1 is as follows: Figure 3 As shown in Figure 4. It is worth noting that since the experiment was not conducted in an adiabatic environment, the temperature dependence of the physicochemical properties of the filling material is not considered in this application. Simultaneously, this scheme scales the stiffness and chemical shrinkage of the filling body proportionally according to the cement content. The consistency between the model predictions and experimental measurements further confirms the reliability of the analytical method proposed in this application, and also demonstrates the high reliability of the above scaling method in characterizing the behavior of filling bodies with different mix designs. This application continues to use the above analytical method to determine the pore water pressure distribution of the filling samples under cement content of 1% and 9%, as shown in Figure 4. Figure 4 shows that increasing the binder content leads to significant changes in pore water pressure under different initial temperatures and curing times. Furthermore, it also indicates that with increasing binder dosage, the large amount of heat released by cement hydration will significantly accelerate the chemical reaction rate of the low-temperature filling body, thereby leading to the premature termination of pore pressure dissipation.

[0161] Figure 5 shows the evolution of pore water pressure with initial temperature at different times. Figure 5 indicates that, under any cement content condition, pore water pressure exhibits a non-monotonic evolution with initial temperature. The comparison of data in Figures 5(a) and 5(b) also shows that increasing cement content leads to a significant decrease in pore water pressure in low-temperature infill bodies. This is because, at lower initial temperatures, the coefficient of thermal expansion of water is extremely small; therefore, the promoting effect of temperature rise on hydration water consumption will exceed the hydrothermal pressurization effect. Thus, infill bodies with higher cement content will exhibit a significant water pressure dissipation effect under the same initial temperature conditions.

[0162] Figure 5 also shows that fillers with higher binder content can still produce a significant hydrothermal pressurization effect under high temperature conditions. This is because the coefficient of thermal expansion of water is larger at higher initial temperatures, so the pressure reduction caused by hydration water consumption is difficult to offset the hydrothermal pressurization effect caused by temperature rise. At the same time, since the higher the cement content, the greater the stiffness of the filler, the pore water pressure will increase sharply with the increase of initial temperature.

[0163] Therefore, while increasing the amount of cement can cause significant water pressure dissipation when the initial temperature of the filling body is low, it can also produce a significant hydrothermal pressurization effect when the temperature is high due to the stronger hydration heat release. Thus, blindly increasing the amount of binder during filling work in hot seasons may cause instability and damage to the filling system.

[0164] The preferred embodiments of the present invention have been described in detail above. However, the present invention is not limited to the above embodiments. Within the scope of knowledge possessed by those skilled in the art, various changes can be made without departing from the spirit of the present invention.

[0165] Many other changes and modifications can be made without departing from the concept and scope of this invention. It should be understood that this invention is not limited to the specific embodiments, and the scope of this invention is defined by the appended claims.

Claims

1. A method for analyzing pore water pressure in cement-based materials under non-isothermal conditions, characterized in that, The method includes: The total hydration water consumption and hydration heat release of the filling body are determined based on the chemical composition of cement, and the stiffness evolution process of the filling body under room temperature conditions is determined by wave velocity test or triaxial compression test. The equivalent chemical reaction time is defined using the Arrhenius formula, and then the hydration degree index of the cement reaction process is established. It is then used to characterize the evolution of the hydration water consumption, hydration heat release, and stiffness of the filling body as determined by the above experiments. Considering the temperature sensitivity of the thermal expansion coefficient of water, and incorporating the evolution of the above parameters into the pore water pressure control equation of the filling unit under non-isothermal conditions for analytical solution, the following steps are included: The initial temperature of interest is determined, the equivalent chemical reaction time series to be studied is specified, and then the change process of pore water pressure of the filling unit under the initial temperature condition with the equivalent chemical reaction time is determined by analytical calculation using the pore water pressure control equation of the filling unit under non-isothermal conditions. Based on the definition of hydration degree, calculate the hydration degree index sequence corresponding to the above equivalent chemical reaction time sequence, and then use the Arrhenius formula to analyze and determine the actual chemical reaction time required to reach the specified hydration degree index under the initial temperature condition. By correlating the pore water pressure corresponding to the equivalent chemical reaction time series with the actual chemical reaction time, the evolution analysis results of the pore water pressure of the filling material under the corresponding initial temperature conditions can be obtained.

2. The method for analyzing pore water pressure in cement-based materials under non-isothermal conditions according to claim 1, characterized in that, The method further includes: Based on the theoretical framework of pore thermoelasticity, a non-isothermal pore water pressure control equation for the filling body is established by considering the water consumption of hydration reaction. Taking the adiabatic non-drained filling unit as the research object, the thermoelastic mechanical constitutive relationship under constant confining pressure and the temperature change caused by hydration heat release are substituted into the above-mentioned governing equations to obtain the pore water pressure governing equations of the filling unit under non-isothermal conditions.

3. The method for analyzing pore water pressure in cement-based materials under non-isothermal conditions according to claim 2, characterized in that, Based on the pore thermoelasticity theory framework of Selvadurai and Suvorov, a non-isothermal pore water pressure control equation is established for the filling body by considering the water volume change caused by the water consumption of hydration reaction, i.e., chemical shrinkage: ， Where α represents the Biot coefficient, α = 1 – K d / K s In the formula, K d Let K be the bulk modulus of the infill skeleton, n be the porosity, and K be the density of the infill skeleton. s and K w p represents the bulk modulus of the solid phase and water, respectively. w The pore water pressure is represented by β, t is the reaction time, and β is the pore water pressure. s and β w These are the coefficients of thermal expansion of the solid phase and water, respectively, where T represents the current temperature and ε is the coefficient of thermal expansion. v Let ε be the volumetric strain, k be the permeability coefficient, η be the dynamic viscosity of water, and ε be the viscosity of water. shf Let ξ be the total water consumed in the chemical reaction process, and ξ be the degree of hydration.

4. The method for analyzing pore water pressure in cement-based materials under non-isothermal conditions according to claim 3, characterized in that, Ignoring the compressibility of solid particles compared to the filling skeleton, i.e., K d < <K s Therefore, we can assume that the Biot coefficient α is approximately 1, α≈1. Meanwhile, we focus on the effect of temperature load on the pore water pressure of the filling body. Therefore, we take the filling body unit as the research object, and then eliminate the seepage term and simplify equation (1) to: ， Under given confining pressure conditions, the change in effective stress is equal to the change in pore water pressure, i.e. Assuming solid-phase compression is negative, the volumetric deformation of the filling element can be expressed as the following derivative: ， Finally, under the assumption of small strain, substituting equation (3) into equation (2) yields the pore water pressure control equation for the filling unit under non-isothermal conditions: ， As can be seen from the above expression, the change in pore water pressure of the filling unit is mainly the result of the competition between hydration water consumption and hydrothermal pressurization under temperature load.

5. The method for analyzing pore water pressure in cement-based materials under non-isothermal conditions according to claim 1, characterized in that, The bulk modulus of the filling unit during the hydration reaction can be expressed as: ， Among them, K di κ represents the initial bulk modulus of the filling material before hydration begins, λ represents the ratio of the bulk modulus of the filling material in its final state to that in its initial state, and κ represents the initial bulk modulus of the filling material. K Used to describe the rate of evolution of bulk modulus over time, t e Reference temperature T r The reference reaction time is at 293.15 K. The evolution of the stiffness of the filling material during the above hydration reaction process can be determined by wave velocity testing or triaxial compression testing. According to the Arrhenius formula, the actual time t and the reference time t e The relationship can be represented as: ， Among them, E a R represents the activation energy required for a chemical reaction. a It is the universal gas constant, R a =8.314 J / mol / K; Furthermore, assuming the virtual triaxial hydration pressure chamber is completely adiabatic, meaning the filling unit cannot conduct or convectively transfer heat with the surrounding environment, the temperature change of the filling under adiabatic non-drainage conditions is solely due to the heat release from hydration. Therefore, the filling temperature can be defined as: ， Where T0 represents the initial temperature, Q f It is the heat released during a chemical reaction, which can be determined based on the chemical composition of cement (ρC). eff Indicates effective heat capacity (ρC) eff = (1–n)ρ s C s + nρ w C w C s and C w ρ represents the specific heat capacity of the solid and liquid phases, respectively. s and ρ w These are the densities of the solid phase and water, respectively. Degree of hydration ξ and reference reaction time t e The relationship can be expressed as: ， Among them, κ ξ Used to describe the rate of evolution of hydration degree over a reference time; Similarly, by multiplying the above formula by the total volume of free water consumed in the hydration reaction, we can obtain the real-time free water consumption during the hydration reaction process, as shown on the right side of the equation (2). The total volume of free water consumed in the hydration reaction can be determined by the chemical composition of the cement. The evolution of the thermal expansion coefficient of water with temperature can be described using the following formula: ， in, The fitting coefficients are denoted as .

6. The method for analyzing pore water pressure in cement-based materials under non-isothermal conditions according to claim 5, characterized in that, Using the defined filling temperature equation (7) to represent the filling temperature, the control equation (4) can be rewritten as the following expression: ， Finally, multiply both sides of equation (10) by dt / dt. e Substituting these equations into equation (8), we can finally obtain the non-isothermal pore water pressure control equation for the filling body: ， Therefore, at any given preparation temperature T0 and associated equivalent time t e0 Under the condition, for both sides of equation (11) with t e Integrating the integral variable yields the pore water pressure change Δp. w Regarding the initial temperature T0 and the reference time t e0 Bivariate functional relations: ， The above integral can be analyzed and calculated using Gaussian hypergeometric functions, and can thus be expressed as: ， Parameters of equation (13): ， The solution to the above equation is the change of pore water pressure in the filling material with equivalent chemical reaction time under a specified initial temperature condition. Among them, with the equivalent chemical reaction time or reference time t e As an abstract auxiliary variable in the derivation process, while the actual reaction time t is of concern in engineering applications and experimental research, the following expression can be obtained by using the incremental expression (6) and differentiating ξ on both sides of the equation: ， Among them, t e The derivative with respect to ξ can be expressed as the inverse function of equation (8): ， Substituting equations (7) and (16) into equation (15), we obtain the differential equation for the actual reaction time t with respect to the degree of hydration ξ and the initial temperature T0: ， Integrating equation (17) with respect to ξ, we can finally obtain the time t required to reach the specified degree of hydration ξ0 under a given preparation temperature T0: ， Equation (18) can be calculated using the following formula: ， Equation (19) parameters: ， Therefore, solving the inverse function of equation (19) yields the degree of hydration ξ after any reaction time t0 at a given preparation temperature T0: ， Then, substituting equation (21) into equation (8) yields the differential equation of the reference reaction time t with respect to the actual reaction time t0 and the initial temperature T0: ， Finally, by substituting equation (22) into equation (13), the pore water pressure change Δp after any reaction time t0 under a given preparation temperature T0 can be obtained. w : ， The hydration index sequence corresponding to the above equivalent chemical reaction time sequence is calculated according to the definition of hydration degree (8), and then the actual chemical reaction time required to reach the specified hydration degree index under the initial temperature condition is determined by analytical calculation using equation (19).

7. The method for analyzing pore water pressure in cement-based materials under non-isothermal conditions according to claim 1, characterized in that, The degree of hydration under the same initial temperature conditions corresponds one-to-one with the equivalent chemical reaction time. By correlating the pore water pressure of the filling body corresponding to the same equivalent chemical reaction time with the actual chemical reaction time data, the development process of pore water pressure of the filling body unit under non-isothermal conditions can be obtained.

Images