CN114923945B - Simulation method and application of pore water pressure in tailings filling body in high temperature stope - Google Patents

Abstract

The invention discloses a method for simulating pore water pressure of a tailings filling body in a high-temperature stope and its application, including: establishing a non-isothermal pore water pressure evolution model of a filling body based on a theoretical framework of pore thermoelasticity, and analyzing filling bodies with different initial temperatures The evolution law of pore water pressure of the unit under the action of temperature load, and then clarify the response mechanism of filling body behavior under complex geothermal environment conditions, and provide theoretical support for proposing targeted filling optimization schemes and realizing safe and clean mining of deep resources.

Description

Simulation method and application of pore water pressure of tailings filling in high temperature mining area

Technical Field

The invention relates to the technical field of mineral resource development, and in particular to a method for simulating pore water pressure of a tailings filling body in a high-temperature stope and application thereof.

Background Art

Mineral resource development is an important way to provide material resources for society. However, conventional mining processes will produce a large number of underground goafs and surface accumulation of tailings, which will cause serious harm to mine safety production and natural ecological environment (Benzaazoua et al., 2004; Kesimal et al., 2005; Bussière, 2007; Xu Wenbin et al., 2015; Wu Aixiang et al., 2016). Driven by the continuous improvement of safety production standards and environmental protection pressure, underground disposal of tailings has gradually become an important way to achieve green and clean mining of mineral resources (N asir and Fall, 2009; Ghirian and Fall, 2013a; Wu Aixiang et al., 2018). By mixing tailings, binders and water in a certain proportion and backfilling them into underground goafs, this tailings filling technology not only avoids the large-scale exposure and accumulation of tailings on the surface, but also significantly improves the stability of the surrounding rock of underground mines. At the same time, it allows no pillars to be left, thereby increasing the ore recovery rate (Kesimal et al., 2005; Klein and Simon, 2006; Witteman and Simms, 2017; Lu et al., 2020a).

Although tailings filling technology continues to bring huge environmental and economic benefits to underground resource mining, field monitoring work in recent years has repeatedly discovered abnormal behavior of filling bodies in deep mines, mainly manifested in the fact that pore water pressure and earth pressure can still increase sharply when filling is stopped (Thompson et al., 2011, 2012, 2014; Hasan et al., 2014). Since the force exerted on the bottom retaining wall during the filling process determines the stability of the filling system, the pressure anomaly found in field monitoring may cause the filling retaining wall to be damaged, thus seriously threatening the safety of underground personnel and mine production efficiency. However, current research work has not yet established a complete understanding of the response law of filling body behavior under complex temperature environment conditions at depth. Since the temperature of the surrounding rock in the mining area will continue to rise with the increasing depth of resource mining under the influence of geothermal gradient (Fall et al., 2010; Belle et al., 2018; Wang et al., 2019; He Manchao et al., 2005; Xie Heping et al., 2015; Gu Desheng et al., 2003), it is of great theoretical and engineering significance to carry out research on the multi-field coupling response of filling bodies under complex temperature environment conditions and then reveal the behavior mechanism of filling bodies in high-temperature mining areas for the safe and clean development and utilization of deep resources.

Prior art 1 established a backfill temperature-seepage-mechanical-chemical field coupling model by considering the energy generation and migration process, which can be used to predict the evolution law of backfill temperature, water pressure, and earth pressure (Cui and Fall, 2015, 2016, 2017, 2018).

Prior art 1 does not take into account the thermal expansion effect of water: the exothermic process of cement hydration will consume free water, thereby causing water pressure dissipation. However, since the thermal expansion coefficient of water is generally larger than that of solid particles, the temperature rise caused by the heat release of cement hydration will cause the pore water pressure of the filling body to rise. At the same time, the hydrothermal pressurization phenomenon has been confirmed by the in-situ test of Thompson et al (2012). The study found that even if the filling process is terminated, the filling body may still produce abnormal water pressure rise due to the temperature rise caused by the heat release of cement hydration. However, the prior art solution 1 ignores the thermal expansion effect of water, and therefore cannot describe the abnormal water pressure phenomenon caused by thermal expansion deformation.

The second existing technology establishes a seepage-mechanical-chemical field coupling model of the filling body by considering the free water consumption caused by hydration reaction and the evolution of physical and mechanical properties, which can be used to predict the evolution law of water pressure and soil pressure of the filling body (Helinski et al., 2007, 2011; Muir Wood et al., 2016; Lu, 2017).

The second prior art does not take into account the influence of temperature: the exothermic process of cement hydration will not only accelerate the chemical reaction rate and the strength of the filling body, but also cause water evaporation, thereby reducing the pore water pressure. At the same time, temperature changes will also cause changes in the viscosity of the fluid, thereby affecting the evolution of the seepage field. In addition, as the depth of mining activities continues to increase, the ambient temperature of the mining area will continue to rise under the influence of the geothermal gradient, so the influence of temperature on the behavior characteristics of deep filling bodies will become more prominent. However, the second prior art solution ignores the effect of temperature on the filling body, and therefore cannot accurately describe the behavior characteristics of the filling body in a complex storage environment.

References

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Summary of the invention

In view of the defects of the prior art, the present invention provides a method for simulating pore water pressure of tailings filling bodies in high-temperature mining areas and its application.

In order to achieve the above invention object, the technical solution adopted by the present invention is as follows:

A method for simulating pore water pressure of tailings filling body in a high-temperature stope comprises the following steps:

Step 1: Based on the pore thermoelasticity theory framework of Selvadurai and Suvorov, the non-isothermal pore water pressure control equation of the filling body under creep loading conditions is established by considering the water volume change caused by the hydration reaction (i.e., chemical shrinkage):

Among them, α represents the Biot coefficient, α=1–K _d /K _s , where K _d is the bulk modulus of the filling skeleton, n is the porosity, K _s and K _w are the bulk moduli of the solid phase and water respectively, p _w represents the pore water pressure, t is the reaction time, β _s and β _w are the thermal expansion coefficients of the solid phase and water respectively, T represents the current temperature, ε _v is the volume strain, k is the permeability coefficient, η represents the dynamic viscosity of water, ε _shf is the total water consumption in the chemical reaction process, and ξ is the hydration degree.

以充填体单元为研究对象，进而排除渗流项并将式(1)简化为：Step 2, assuming that the Biot coefficient α is approximately 1, α≈1,

Taking the filling unit as the research object, the seepage term is excluded and equation (1) is simplified as follows:

Formula (2) is the control equation of the pore water pressure of the filling unit in the triaxial hydration pressure chamber.

Step 3: To simulate the compression effect caused by creep of surrounding rock, a triaxial hydration pressure chamber is used to apply axial deformation at a rate of j/s to the filling body sample. The thermoelastic stress-strain relationship of the filling body unit under creep loading is expressed as:

Where ε represents strain, E is Young's modulus, σ' represents effective stress, v is Poisson's ratio, and T ₀ represents initial temperature.

Step 4: Establish the geometric model of the filling body under one-dimensional confinement conditions. Therefore, the filling body unit only has axial strain, and the effective stresses in the x and y directions are equal, and the following relationship is established:

Therefore, the volume deformation of the filling unit is obtained by combining equations (3) and (4):

The parameters in formula (5) are expressed as:

假设固相压缩为负,，因此将式(5)记为如下导数形式：Step 5: Under given confining pressure conditions, the change in effective stress is equal to the change in pore water pressure, that is,

Assuming that the solid phase compression is negative, equation (5) is expressed in the following derivative form:

Step 6: Substituting equation (7) into equation (2) under the assumption of small strain can finally obtain the pore water pressure control equation of the filling unit under non-isothermal conditions:

Step 7: Assume that the triaxial hydration pressure chamber is completely insulated, that is, the filling unit cannot generate heat conduction and convection heat exchange with the surrounding environment. Therefore, the filling temperature change under adiabatic undrained conditions is only caused by hydration heat release and the temperature load applied by the triaxial device. Then, the filling temperature is defined as:

Where k represents the constant temperature change rate applied by the triaxial device, _Th is the temperature rise caused by the hydration reaction, _Qf is the heat released during the chemical reaction, (ρC) _eff represents the effective heat capacity ((ρC) _eff = (1–n) _ρsCs + _nρwCw ), _{Cs and Cw} are the specific heat capacities of the solid and liquid phases, respectively, _{and ρs} and _ρw are the densities of the solid phase and water, respectively.

Step 8, the relationship between the degree of hydration and the reference reaction time _te is expressed as:

ξ＝1-exp(-κ _ξ ·t _e ) (10)

Where κ _ξ is the evolution rate of the hydration degree with the reference time.

Step 9: According to the Arrhenius formula, the relationship between the actual time t and the reference time _te is expressed as:

Wherein, _Ea represents the activation energy required for the chemical reaction, _Ra is the universal gas constant ( _Ra = 8.314 J/mol/K), and _Tr is the reference temperature.

Step 10: Substitute equations (9)–(11) into equation (8) to finally obtain the pore water pressure control equation of the filling unit under temperature load:

Furthermore, the present invention uses the following formula to describe the growth evolution of the filling body skeleton stiffness during the hydration process:

K _d =K _di [λ-(λ-1)exp(-κ _K ·t _e )] (13)

Where K _di is the initial skeleton stiffness of the filling body, λ is the ratio of the final stiffness of the filling body to the initial stiffness, and κ _K is the model parameter that controls the stiffness growth rate.

Furthermore, the following formula is used to describe the evolution of the thermal expansion coefficient of water with temperature:

β _w =β _w0 +k ₀ T (14)

Where β _w0 and _k0 are fitting parameters.

The invention also discloses the application of the pore water pressure simulation method of the tailings filling body in the high-temperature mining field in the technical field of tailings filling mining.

Compared with the prior art, the advantages of the present invention are:

For the first time, a complete understanding of the response laws of filling body behavior under complex temperature environment conditions has been established, and the behavior mechanism of filling bodies under temperature load has been deeply revealed. It can more accurately predict the evolution law of filling body water pressure under the competition of pressure growth and dissipation mechanism induced by deep complex geothermal environment, and then provide more scientific theoretical guidance for proposing customized filling optimization schemes and realizing the sustainable development of deep mineral resources.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG1 is a schematic diagram showing the evolution of pore water pressure at different times with initial temperature according to an embodiment of the present invention;

FIG2 is a schematic diagram showing the evolution of thermal expansion coefficients of water and a solid skeleton with temperature according to an embodiment of the present invention;

3 is a schematic diagram of temperature changes of filling body units with different initial temperatures under different heating and cooling rates according to an embodiment of the present invention;

FIG. 4 is a schematic diagram of the change in water pressure of a filling body with different initial temperatures under different heating and cooling rates according to an embodiment of the present invention; (a) heating effect (b) cooling effect.

DETAILED DESCRIPTION

In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below with reference to the accompanying drawings and examples.

A method for simulating pore water pressure of tailings filling in high-temperature mining sites is based on the pore thermoelasticity theory framework of Selvadurai and Suvorov. The non-isothermal pore water pressure control equation of the filling body is established by considering the water volume change caused by hydration reaction (i.e. chemical shrinkage):

Wherein, α represents the Biot coefficient (α=1–K _d /K _s , where K _d is the bulk modulus of the filling skeleton), n is the porosity, K _s and K _w are the bulk moduli of the solid phase and water, respectively, p _w represents the pore water pressure, t is the reaction time, β _s and β _w are the thermal expansion coefficients of the solid phase and water, respectively, T represents the current temperature, ε _v is the volume strain, k is the permeability coefficient, η represents the dynamic viscosity of water, ε _shf is the total water consumption in the chemical reaction process, and ξ is the hydration degree.

)。同时，由于本发明主要关注温度荷载对充填体孔隙水压的影响效应，因此可以充填体单元为研究对象，进而排除渗流项并将式(1)简化为：Since the compressibility of solid particles is negligible compared with that of the filling body skeleton (i.e., K _d << K _s ), it can be assumed that the Biot coefficient α is approximately 1 (α≈1,

). At the same time, since the present invention mainly focuses on the effect of temperature load on the pore water pressure of the filling body, the filling body unit can be taken as the research object, and then the seepage term is excluded and formula (1) is simplified to:

Formula (2) is the pore water pressure control equation of the filling unit in the triaxial hydration pressure chamber. In addition, considering the thermal expansion effect in the non-isothermal process, the thermoelastic stress-strain relationship of the filling unit can be expressed as:

Where ε represents strain, E is Young's modulus, σ' represents effective stress, v is Poisson's ratio, and T ₀ represents initial temperature.

To simplify the calculation, this embodiment further establishes a geometric model of the filling body under one-dimensional confinement conditions, so that the filling body unit only has axial strain, and the effective stresses in the x and y directions are equal, and the following relationship is established:

Therefore, the volume deformation of the filling unit can be obtained by combining equations (3) and (4):

The parameters in formula (5) can be expressed as:

假设固相压缩为负)，因此可将式(5)记为如下导数形式：Under given confining pressure conditions, the change in effective stress is equal to the change in pore water pressure (i.e.

Assuming that the solid phase compression is negative), equation (5) can be expressed as the following derivative form:

Finally, under the assumption of small strain, substituting equation (7) into equation (2) can finally obtain the pore water pressure control equation of the filling unit under non-isothermal conditions:

In addition, this embodiment assumes that the triaxial hydration pressure chamber is completely insulated, that is, the filling body unit cannot generate heat conduction and convection heat exchange with the surrounding environment. Therefore, the filling body temperature change under the adiabatic and undrained conditions is only caused by the hydration heat release and the temperature load applied by the triaxial device. The filling body temperature can be defined as:

Where k represents the constant temperature change rate applied by the triaxial device, _Th is the temperature rise caused by the hydration reaction, _Qf is the heat released during the chemical reaction, (ρC) _eff represents the effective heat capacity ((ρC) _eff = (1–n) _ρsCs + _nρwCw ), _{Cs and Cw} are the specific heat capacities of the solid and liquid phases, respectively, _{and ρs} and _ρw are the densities of the solid phase and water, respectively.

According to the research of Doherty and Muir Wood, the relationship between the degree of hydration and the reference reaction time _te can be expressed as:

ξ＝1-exp(-κ _ξ ·t _e ) (24)

Where κ _ξ is the evolution rate of the hydration degree with the reference time.

According to the Arrhenius formula, the relationship between the actual time t and the reference time _te can be expressed as:

Where _Ea represents the activation energy required for the chemical reaction, _Ra is the universal gas constant ( _Ra = 8.314 J/mol/K), and _Tr is the reference temperature.

Therefore, by substituting equations (9)–(11) into equation (8), we can finally obtain the pore water pressure control equation of the filling unit under the action of temperature load:

The present invention uses the following formula to describe the growth evolution of the filling body skeleton stiffness during the hydration process:

K _d =K _di [λ-(λ-1)exp(-κ _K ·t _e )] (27)

Where K _di is the initial skeleton stiffness of the filling body, λ is the ratio of the final stiffness of the filling body to the initial stiffness, and κ _K is the model parameter that controls the stiffness growth rate.

In addition, the following formula is used to describe the evolution of the thermal expansion coefficient of water with temperature:

β _w =β _w0 +k ₀ T (28)

Where β _w0 and _k0 are fitting parameters.

Evolution of pore water pressure in filling bodies under different temperature conditions

1) Effect of initial temperature

Taking the tailings backfill used in the Kanowna Belle gold mine in Australia as an example, its physical and chemical parameters are shown in Table 1. The evolution law of pore water pressure of the backfill unit under different initial temperature conditions in an adiabatic undrained environment is shown in Figure 1. Figure 1 shows that the backfill water pressure at any time first decreases and then increases with the increase of initial temperature. This is because increasing the curing temperature of the low-temperature backfill will accelerate the chemical reaction rate, thereby promoting the pore pressure dissipation caused by hydration water consumption; at the same time, since the thermal expansion coefficient of water is still small at low temperatures (Figure 2), the thermal expansion effect caused by hydration heat is not obvious, so the pore water pressure will eventually continue to decrease with the increase of initial temperature under the dominance of hydration water consumption. However, as the curing temperature continues to increase, although the chemical reaction rate of the backfill will further accelerate, the thermal expansion coefficient of water will continue to increase at the same time (Figure 2). Therefore, when the temperature reaches a certain critical value, the hydrothermal pressurization effect caused by hydration heat will exceed the hydration water consumption effect, thereby causing the pore water pressure to increase with the increase of initial temperature.

It can also be seen from Figure 1 that after a sufficiently long time (t = 1000h) of chemical reaction, the pore water pressure increases almost monotonically with the increase of initial temperature. This is because the hydration reaction at this moment has been basically completed, that is, the filling bodies with different initial temperatures have the same temperature rise and chemical shrinkage under the action of hydration reaction, but because the thermal expansion coefficient of water is larger at high temperature, the filling body will produce higher pore water pressure under the stronger hydrothermal pressurization effect.

In addition, it can be noted from Figure 1 that the longer the chemical reaction time, the lower the critical initial temperature at which the pore water pressure changes from decreasing to increasing. This is because low temperature will reduce the hydration heat release rate, so it takes longer to produce enough temperature rise so that the thermal expansion effect can completely offset the depressurization effect of hydration water consumption.

Table 1. Physical and chemical parameters of the filling body of Kanowna Belle gold mine, Australia

From the above discussion, it can be seen that the effect of initial temperature conditions on the evolution of pore water pressure in the filling body is the result of the competition between hydration water consumption and hydration heat release. Because the thermal expansion coefficient of water is small when the initial temperature is low, the water pressure dissipation caused by hydration water consumption will play a major role; however, since the thermal expansion coefficient of water increases rapidly with the increase of temperature, the hydrothermal pressurization effect caused by hydration heat release will ultimately control the evolution of pore water pressure in the filling body.

2) Influence of temperature load

This example numerically analyzes the water pressure variation process of filling body units with initial temperatures of 0, 15, and 30°C under different forced temperature change rates (k=0, ±2.5×10 ^-3 , ±5.0×10 ^-3 ℃/h) to study the influence mechanism of temperature load on the pore water pressure of filling body units.

The temperature variation of the filling units with different initial temperatures under different heating and cooling rates is shown in Figure 3. Figure 3 shows that when k>0℃/h, the filling units with initial temperatures of 15℃ and 30℃ both produce more significant temperature rises in the early stage of heating compared with the low temperature (T ₀ =0℃) state. This is because the higher the initial temperature, the faster the chemical reaction rate, so the filling temperature will rise sharply under the combined effect of hydration heat release and forced heating. As the hydration reaction is gradually completed, the temperature rise rate of the filling will continue to decrease due to the slowdown of hydration heat release and eventually converge to a constant external heating rate. When k<0℃/h, since the lower the initial temperature, the slower the chemical reaction rate, the cooling effect will strongly inhibit the temperature rise caused by the hydration heat release of the low-temperature filling (T ₀ =0℃). In contrast, the filling units with initial temperatures of 15℃ and 30℃ will still produce significant temperature rises in the early stage of cooling due to the faster hydration heat release rate. However, as the hydration reaction is gradually completed, the temperature change of the filling body will eventually be controlled by forced cooling.

The evolution of water pressure of the backfill unit under temperature load in an adiabatic undrained environment is shown in Figure 4(a) and Figure 4(b). Figure 4(a) shows that the backfill with initial temperature of 15℃ and 30℃ has a significant increase in water pressure under heating compared with the constant temperature state (k = 0℃/h). This is because although the temperature rise caused by heating can accelerate chemical shrinkage and promote pore pressure dissipation, the thermal expansion coefficient of water is large at high temperature, so the pressure reduction effect caused by hydration water consumption is difficult to offset the hydrothermal pressurization effect caused by heating, and finally the pore water pressure gradually increases during the heating process. It can also be seen from Figure 4 that since the thermal expansion coefficient of water will increase with the increase of temperature (Figure 2), the backfill with a higher initial temperature will produce an earlier and faster water pressure increase under the same heating rate. In contrast, since the thermal expansion coefficient of water is extremely small when the initial temperature is 0℃, the promotion effect of heating on hydration water consumption will exceed the hydrothermal pressurization effect, so the pore water pressure is slightly lower than the constant temperature state in the early stage of heating. However, as the hydration reaction is gradually completed, the continuous heating will still produce a significant hydrothermal pressurization effect, so the pore water pressure of the filling body will eventually be higher than that of the constant temperature state. The above calculation results show that since the filling body will eventually produce a significant hydrothermal pressurization effect under the action of continuous heating, the tailings filling body in the high-temperature goaf may produce higher long-term earth pressure on the retaining wall.

Under the cooling effect, the pore water pressure of the filling body at the initial temperature of 15℃ and 30℃ decreases rapidly with the decrease of temperature (Figure 4(b)). This is because although cooling will inhibit the hydration water consumption rate, the thermal expansion coefficient of water is large at high temperature, so the cooling and shrinkage of the filling body will eventually have a significant promoting effect on the pore pressure dissipation. In contrast, since the thermal expansion coefficient of water is extremely small when the initial temperature is 0℃, the cooling and shrinkage effect of the pore fluid during the cooling process is not obvious; at the same time, since the cooling effect will also strongly inhibit the hydration water consumption reaction and thus slow down the pore pressure dissipation rate, the pore water pressure of the filling body at the initial temperature of 0℃ is slightly higher than the constant temperature state in the early stage of cooling. However, as the hydration reaction is gradually completed, the cooling and shrinkage caused by cooling will gradually dominate the water pressure change of the filling body, so the pore water pressure will eventually be lower than the constant temperature state due to the continuous cooling effect. The above calculation results show that although the low temperature environment will inhibit hydration and water consumption and is not conducive to pore pressure dissipation, the cooling process of the filling body will cause the fluid to shrink and produce a significant pressure reduction effect. Therefore, the filling operation in the low-temperature goaf is usually safer.

From the above discussion, it can be seen that the continuous heat exchange between the filling body and the high-temperature surrounding rock will also induce thermal strain and thus affect the evolution of water pressure. When the initial temperature of the filling body is high, the water pressure change caused by heat exchange will control the evolution of water pressure due to the large thermal expansion coefficient of water. However, when the filling body temperature is low, although the thermal strain caused by heating or cooling will also have a certain impact on the pore water pressure, the thermal expansion coefficient of water at low temperature is extremely small, so the change in hydration water consumption rate caused by heat exchange will dominate the early water pressure evolution of the filling body. However, as the chemical reaction is gradually completed, the pore water pressure of the low-temperature filling body will eventually be controlled by the thermal strain generated by continuous heat exchange.

Those skilled in the art will appreciate that the embodiments described herein are intended to help readers understand the implementation methods of the present invention, and should be understood that the protection scope of the present invention is not limited to such specific statements and embodiments. Those skilled in the art can make various other specific variations and combinations that do not deviate from the essence of the present invention based on the technical revelations disclosed in the present invention, and these variations and combinations are still within the protection scope of the present invention.

Claims (4)

1. The method for simulating the pore water pressure of the tailing filling body in the height Wen Caichang is characterized by comprising the following steps of:

step 1, based on a pore thermoelastic theoretical framework of Selvadurai and Suvorov, establishing a filler non-isothermal pore water pressure control equation under creep loading conditions by considering water volume change caused by hydration reaction water consumption:

wherein α represents the Biot coefficient, α=1-K _d /K _s K in the formula _d For bulk modulus of the filler, n is porosity, K _s And K _w Bulk modulus of solid phase and water, respectively, p _w Represents pore water pressure, t is the time of reaction, beta _s And beta _w The coefficients of thermal expansion of the solid phase and water, respectively, T representing the current temperature, ε _v For volumetric strain, k is the permeability coefficient, η represents the dynamic viscosity of water, ε _shf Is the total water consumption in the chemical reaction process, and ζ is the hydration degree;

step 2, assuming that the Biot coefficient alpha is approximately 1, alpha 1,

taking a filling body unit as a research object, further removing a seepage term and simplifying the formula (1) as follows:

the formula (2) is a filler pore water pressure control equation in the triaxial hydration pressure chamber;

step 3, in order to simulate the compression effect caused by the creep of surrounding rock, axial deformation with the rate j/s is applied to a filling body sample by utilizing a triaxial hydration pressure chamber, and the thermoelastic stress-strain relation of the filling body unit under the creep loading effect is expressed as follows:

wherein ε represents strain, E represents Young's modulus, σ ' represents effective stress, v is Poisson's ratio, T ₀ Indicating an initial temperature;

step 4, establishing a geometric model of the filling body under the one-dimensional lateral limit condition, so that the filling body unit only has axial strain, and the effective stress in the x and y directions is equal, and the following relationship is established:

the volumetric deformation of the filler unit is thus obtained by the union (3) and the formula (4):

the parameters in formula (5) are expressed as:

step 5, under given confining pressure conditions, the change in effective stress is equal to the change in pore water pressure, i.e

Assuming that the solid phase compression is negative, equation (5) is therefore written as the derivative form: />

And 6, substituting the formula (7) into the formula (2) on the premise of small strain assumption to finally obtain a pore water pressure control equation of the filler unit under the non-isothermal condition:

step 7, assuming that the triaxial hydration pressure chamber is completely insulated, that is, the filler unit cannot generate heat conduction and convection with the surrounding environment, the temperature change of the filler under the condition of thermal insulation and non-drainage is generated only by hydration heat release and the temperature load applied by the triaxial device, and further define the temperature of the filler as:

wherein k represents a constant rate of temperature change, T, applied by the triaxial apparatus _h For the temperature rise caused by hydration reaction, Q _f Is the heat evolved during the chemical reaction, (ρC) _eff Representing effective heat capacity, i.e. ρC _eff ＝(1–n)ρ _s C _s +nρ _w C _w ，C _s And C _w Specific heat capacity, ρ, of solid-liquid two phases respectively _s And ρ _w Respectively are provided withIs the density of the solid phase and water;

step 8, hydration degree and reference reaction time t _e The relationship of (2) is expressed as:

ξ＝1-exp(-κ _ξ ·t _e ) (10)

wherein, kappa _ξ Is the evolution rate of hydration degree along with the reference time;

step 9, according to the Arrhenius Wu Sigong formula, the actual time t and the reference time t _e The relationship of (2) is expressed as:

wherein E is _a Represents the activation energy required for chemical reactions, R _a Is a general gas constant, R _a ＝8.314J/mol/K，T _r Is the reference temperature;

step 10, carrying the formulas (9) - (11) into the formula (8), and finally obtaining a pore water pressure control equation of the filler unit under the action of temperature load:

2. a method for simulating pore water pressure of a tailings pond in a height Wen Caichang as claimed in claim 1, wherein: the growth evolution of the filler skeletal stiffness during hydration is described using the following formula:

K _d ＝K _di [λ-(λ-1)exp(-κ _K ·t _e )] (13)

k in the formula _di The initial skeleton rigidity of the filler is lambda is the ratio of the final rigidity of the filler to the initial rigidity, kappa _K To control the rate of stiffness increase.

3. A method for simulating pore water pressure of a tailings pond in a height Wen Caichang as claimed in claim 1, wherein: describing the evolution law of the thermal expansion coefficient of water along with the temperature by using the following formula

β _w ＝β _w0 +k ₀ T (14)

Beta in _w0 And k ₀ Is a fitting parameter.

4. A method for simulating pore water pressure of a tailings pond in a height Wen Caichang as claimed in claim 1, wherein: the method is applied to the technical field of tailing filling and mining.

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