CN114923945A - Method for simulating pore water pressure of tailing filler in high-temperature stope and application of method - Google Patents
Method for simulating pore water pressure of tailing filler in high-temperature stope and application of method Download PDFInfo
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Abstract
The invention discloses a method for simulating pore water pressure of a tailing filling body in a high-temperature stope and application thereof, wherein the method comprises the following steps: a non-isothermal pore water pressure evolution model of the filling body is established based on a pore thermoelasticity theoretical framework, the pore water pressure evolution rule of filling body units with different initial temperatures under the action of temperature load is analyzed, the behavior response mechanism of the filling body under the complex geothermal environment condition is clarified, and theoretical support is provided for the purpose of providing a targeted filling optimization scheme and realizing safe and clean exploitation of deep resources.
Description
Technical Field
The invention relates to the technical field of mineral resource development, in particular to a method for simulating pore water pressure of a tailing filling body in a high-temperature stope and application thereof.
Background
Mineral resource development is an important approach to provide material resources for society, however, conventional mining processes result in large amounts of underground goafs and tailings surface accumulation, which can cause serious hazards to mine safe production and natural ecological environment (benzazoua et al, 2004; Kesimal et al, 2005; bussiere, 2007; xuwen Bin et al, 2015; Wu ai et al, 2016). Under the drive of ever-increasing safety production standards and environmental protection pressures, underground disposal of tailings is gradually becoming an important way to realize green clean mining of mineral resources (N asir and Fall, 2009; Ghirian and Fall,2013 a; wu auspicious, etc., 2018). By mixing and backfilling the tailings, the cementing agent and water to the underground goaf according to a certain proportion, the tailing filling technology not only avoids the massive exposure and accumulation of the tailings on the ground surface, but also can obviously improve the stability of surrounding rocks of an underground stope, and simultaneously can allow no ore pillar to remain so as to improve the recovery rate of ores (Kesimal et al, 2005; Klein and Simon, 2006; Wi tten and Simms, 2017; Lu et al, 2020 a).
Although tailings packing technology continues to provide significant environmental and economic benefits to underground resource mining, recent on-site monitoring efforts have repeatedly discovered abnormal behavior of the pack in deep mines, primarily manifested by dramatic increases in pore water and soil pressures that can occur with pack stoppages (Thompson et al, 2011,2012,2014; Hasan et al, 2014). Because the acting force of the bottom retaining wall in the filling process determines the stability of the filling system, the phenomenon of abnormal pressure discovered by field monitoring can cause the damage of the filling retaining wall, and further seriously threaten the safety of underground personnel and the production efficiency of mines. However, the current research work still does not establish perfect understanding for the behavior response rule of the filling body under the deep complex temperature environment condition. As the temperature of the surrounding rock of the stope continuously rises along with the continuously increasing resource exploitation depth under the action of the geothermal gradient (Fall et al, 2010; Belle et al, 2018; Wang et al, 2019; which flood, etc., 2005; xi Hei, etc., 2015; God Sheng, etc., 2003), the multi-field coupling response research of the filling body under the condition of complex temperature environment is developed, the behavior mechanism of the filling body in the high-temperature stope is further disclosed, and the method has important theoretical and engineering significance for realizing the safe and clean development and utilization of deep resources.
In the prior art, a filling body temperature-seepage-mechanics-chemical field coupling model is established by considering the energy generation and migration processes, and can be used for predicting the evolution law of filling body temperature, water pressure, soil pressure and the like (Cui and Fall, 2015,2016,2017,2018).
The prior art does not consider the thermal expansion effect of water: the cement hydration heat release process consumes free water, which causes water pressure to dissipate. However, since water generally has a higher coefficient of thermal expansion than solid particles, the effect of the temperature increase caused by the exothermic heat of hydration of the cement will cause the pore pressure of the pack to increase. While the hydrothermal pressurization phenomenon has been confirmed by in situ testing of Thompso n et al (2012). The study found that even if the filling process was terminated, the fill could still develop an abnormal rise in water pressure due to the temperature increase caused by the exothermic heat of hydration of the cement. The prior art solution ignores the thermal expansion effect of water, so that the abnormal phenomenon of water pressure caused by thermal expansion deformation cannot be described.
In the second prior art, a free water consumption and physical and mechanical property evolution caused by hydration reaction are considered to establish a filling body seepage-mechanical-chemical field coupling model which can be used for predicting the evolution law of water pressure, soil pressure and the like of a filling body (Helinski et al, 2007,2011; Muir Wood et al, 2016; Lu, 2017).
The second prior art does not consider the influence of temperature: the cement hydration exothermic process not only accelerates the chemical reaction rate and increases the strength of the filling body, but also causes water evaporation, thereby reducing the pore water pressure. Meanwhile, the change of temperature will also cause the change of the viscosity coefficient of the fluid, thereby further influencing the evolution law of the seepage field. In addition, as the mining activity depth is increased continuously, the stope environment temperature is increased continuously under the action of the geothermal gradient, so that the influence of the temperature on the behavior characteristics of the deep filling body is more prominent. In the second technical scheme, the action of temperature on the filling body is neglected, so that the behavior characteristics of the filling body in a complex occurrence environment cannot be accurately described.
Reference documents
Benzaazoua,M.,Marion,O.,Picquet,I.,Bussiere,B.2004.The use of pas tefill as a solidification and stabilization process for the control of acid mine dr ainage.Miner.Eng.17,233–243；
Kesimal,A.,Yilmaz,E.,Ercikdi,B.,Alp,I.,Deveci,H.2005.Effect of pr operties of tailings and binder on the short–and long–term strength and stability of cemented paste backfill.Materials Letters 59(28),3703–3709；
Bussière,B.2007.Colloquium 2004:Hydrogeotechnical properties of hard r ock tailings from metal mines and emerging geoenvironmental disposal approach es.Can.Geotech.J.44,1019–1052；
Xuwen, songwandong, Caoshan, Jiang, Wufeng, Jiang Lei (2015), stability analysis and control technique for underground mine stope group, Ming & safety engineering, 32(04),658 664;
wu love, Wang Yong, & Wang Hongjiang, (2016). paste filling technical status and trend. metal mine, 07, 1-9;
Nasir,O.,and Fall,M.(2009).“Modeling the heat development in hydratin g CPB structures.”Computers and Geotechnics,36(7),1207–1218；
Ghirian,A.,Fall,M.2013.Coupled thermo–hydro–mechanical–chemical beh aviour of cemented paste backfill in column experiments.Part I,Physical,hydra ulic and thermal processes and characteristics.Engineering Geology 164,195–20 7；
Klein,K.,Simon,D.2006.Effect of specimen composition on the strength development in cemented paste backfill.Canadian Geotechnical Journal 43,310 –324；
Witteman,M.L.,Simms,P.H.2017.Unsaturated flow in hydrating porous m edia with application to cemented mine backfill.Canadian Geotechnical Journal 54,835–845；
Lu,G.D.,Yang,X.G.,Qi,S.C.,Fan,G.,Zhou,J.W.,2020a.Coupled chem o-hydro-mechanical effects in one-dimensional accretion of cemented mine fills. Eng.Geol.267,105495；
Thompson,B.D.,Bawden,W.F.,and Grabinsky,M.W.2011.In-situ monitori ng of cemented paste backfill pressure to increase backfilling efficiency.Canadia n Institute of Mining Journal,2(4):1–10；
Thompson,B.D.,Bawden,W.F.,and Grabinsky,M.W.(2012).“In situ measurements of cemented paste backfill at the Cayeli mine.”Canadian Geotech nical Journal,49(7),755–772；
Thompson,B.D.,Simon,D.,Grabinsky,M.W.,Counter,D.B.,Bawden,W.F. 2014.Constrained thermal expansion as a causal mechanism for in situ pressur e in cemented paste and hydraulic backfilled stopes.Proceedings of the 11th Int ernational Symposium on Mining with Backfill,Perth,365–378；
Hasan,A.,Suazo,G.,Doherty,J.,Fourie,A.2014.In situ measurements o f cemented paste backfilling in an operating stope at Lanfranchi Mine.Proceedi ngs of the 11th International Symposium on Mining with Backfill,Perth,327–3 36；
Fall,M.,Célestin,J.C.,Pokharel,M.,Touré,M.2010.A contribution to un derstanding the effects of curing temperature on the mechanical properties of mi ne cemented tailings backfill.Engineering Geology114,397–413；
Belle,B.,Biffi,M.,2018.Cooling pathways for deep Australian longwall c oal mines of the future.Int.J.Min.Sci.Technol.28,865–875；
Wang,M.,Liu,L.,Zhang,X.Y.,Chen,L.,Wang,S.Q.,&Jia,Y.H.(20 19).Experimental and numerical investigations of heat transfer and phase change characteristics of cemented paste backfill with PCM.Applied Thermal Engineer ing,150,121–131；
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Cui,L.,Fall,M.2015.A coupled thermo-hydro-mechanical-chemical model for underground cemented tailings backfill.Tunn.Undergr.Sp.Tech.50,396–4 14；
Cui,L.,Fall,M.2016.Multiphysics model for consolidation behavior of ce mented paste backfill.ACSE Int.J.Geomech.17(3):23p；04016077-23；
Cui,L.,Fall,M.2017.Modeling of pressure on retaining structures for un derground fill mass.Tunn.Undergr.Sp.Tech.69,94–107；
Cui,L.,Fall,M.2018.Modeling of self-esiccation in a cemented backfill s tructure.Int.J.Numer.Anal.Methods Geomech.42:558–583；
Thompson,B.,Bawden,W.,Grabinsky,M.2012.In situ measurements of ce mented paste backfill at the Cayeli mine.Canadian Geotechnical Journal 49,755 –772；
Helinski,M.,Fourie,A.,Fahey,M.,Ismail,M.2007a.Assessment of the s elf-desiccation process in cemented mine backfills.Can.Geotech.J.44,1148–11 56；
Helinski,M.,Fahey,M.,Fourie,A.2011.Behavior of cemented paste back fill in two mine stopes:measurements and modeling.J.Geotech.Geoenviron.E ng.137,171–182；
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Wu,D.,Fall,M.,Cai,S.2014.Numerical modelling of thermally and hydr aulically coupled processes in hydrating cemented tailings backfill columns.Inter national Journal of Mining,Reclamation and Environment,28(3),173–199；
Fahey,M.,Helinski,M.,Fourie,A.2009.Some aspects of the mechanics o f arching in backfilled stopes.Canadian Geotechnical Journal 46,1322–1336；
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Helinski,M.,Fahey,M.,Fourie,A.2010b.Behaviour of cemented paste ba ckfill in two mine stopes,measurements and modeling.Journal of Geotechnical and Geoenvironmental Engineering,ASCE；137(2),171–182；
Helinski M,Fahey M,Fourie A.,2007b.Numerical modeling of cemented mine backfill deposition.Journal of Geotechnical and Geoenvironmental Engineer ing 133(10),1308–1319；
Helinski,M.,Fahey,M.,Fourie,A.2010a.Coupled two–dimensional finite element modelling of mine backfilling with cemented tailings.Canadian Geotech nical Journal 47,1187–1200；
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disclosure of Invention
Aiming at the defects of the prior art, the invention provides a method for simulating pore water pressure of a tailing filling body in a high-temperature stope and application thereof.
In order to realize the purpose of the invention, the technical scheme adopted by the invention is as follows:
a tailing filler pore water pressure simulation method in a high-temperature stope comprises the following steps:
step 1, establishing a non-isothermal pore water pressure control equation of a filling body under a creep loading condition by considering water volume change caused by hydration reaction water consumption (namely chemical shrinkage) based on a pore thermoelasticity theoretical framework of Selvadurai and Suvorov:
wherein α represents a Biot coefficient, and α -1-K d /K s In the formula, K d Is the bulk modulus of the filler skeleton, n is the porosity, K s And K w Bulk modulus, p, of solid phase and water, respectively w Denotes the pore water pressure, t is the time during which the reaction takes place, beta s And beta w The coefficients of thermal expansion of the solid phase and of the water, respectively, T representing the current temperature,. epsilon v For volume strain, k is the permeability coefficient, eta represents the dynamic viscosity of water, epsilon shf Xi is the total water consumption in the chemical reaction process, and xi is the degree of hydration.
Step 2, assuming that the Biot coefficient α is approximately 1, α ≈ 1,
the filling body unit is taken as a research object, so that the seepage term is eliminated and the formula (1) is simplified into the following formula:
and the formula (2) is a pore water pressure control equation of the filling body unit in the triaxial hydration pressure chamber.
Step 3, in order to simulate the compression effect caused by the creep of the surrounding rock, a triaxial hydration pressure chamber is utilized to apply axial deformation with the acceleration rate of j/s to the filling body sample, and the thermoelastic stress-strain relation of the filling body unit under the action of creep loading is expressed as follows:
wherein ε represents strain, E represents Young's modulus, σ ' represents effective stress, v represents Poisson's ratio, T 0 Indicating the initial temperature.
Step 4, establishing a geometric model of the filling body under the one-dimensional side limit condition, so that the filling body unit only has axial strain, the effective stresses in the x direction and the y direction are equal, and the following relation is established:
the volumetric deformation of the packing unit is thus obtained by the combination of formula (3) and formula (4):
the parameters in formula (5) are represented as:
step 5, under the given confining pressure condition, the change of the effective stress is equal to the change of the pore water pressure, namely
Assuming that the solid phase compression is negative, equation (5) is therefore written as the derivative:
and 6, on the premise of a small strain hypothesis, substituting the formula (7) into the formula (2) to finally obtain a filling body unit pore water pressure control equation under a non-isothermal condition:
step 7, assuming that the triaxial hydration pressure chamber is completely insulated, i.e. the filler unit cannot generate heat conduction and convection heat transfer with the surrounding environment, so that the temperature change of the filler under the condition of heat insulation and no drainage is only generated by hydration heat release and the temperature load applied by the triaxial device, and further defining the temperature of the filler as follows:
wherein k represents three axesConstant rate of change of temperature, T, imposed by the device h For the temperature rise caused by hydration, Q f Is the heat given off during the chemical reaction, (ρ C) eff Denotes the effective Heat Capacity ((ρ C) eff ＝(1–n)ρ s C s +nρ w C w )，C s And C w Specific heat capacity, rho, of solid-liquid phases respectively s And ρ w The density of the solid phase and water, respectively.
Step 8, hydration degree and reference reaction time t e The relationship of (c) is expressed as:
ξ＝1-exp(-κ ξ ·t e ) (10)
wherein, κ ξ Is the evolution rate of the hydration degree along with the reference time.
Step 9, according to the Arrhenius formula, the actual time t and the reference time t e The relationship of (c) is expressed as:
wherein, E a Represents the activation energy required for the chemical reaction, R a Is the general gas constant (R) a ＝8.314J/mol/K)， T r Is the reference temperature.
And step 10, bringing the formulas (9) to (11) into the formula (8), and finally obtaining a pore water pressure control equation of the filling body unit under the action of temperature load:
further, the invention describes the growth evolution of the skeleton rigidity of the filling body in the hydration process by using the following formula:
K d ＝K di [λ-(λ-1)exp(-κ K ·t e )] (13)
in the formula K di Is the initial skeletal stiffness of the filling body, λ is the ratio of the final stiffness to the initial stiffness of the filling body, κ K To control the rate of stiffness growthThe model parameters of (1).
Further, the evolution law of the thermal expansion coefficient of water with temperature is described using the following formula
β w ＝β w0 +k 0 T (14)
In the formula beta w0 And k 0 Are fitting parameters.
The invention also discloses application of the tailing filling body pore water pressure simulation method in the high-temperature stope in the technical field of tailing filling mining.
Compared with the prior art, the invention has the advantages that:
the method is characterized in that complete recognition is established for a filling body behavior response rule under a complex temperature environment condition for the first time, so that a filling body behavior mechanism under the action of temperature load is deeply disclosed, a filling body water pressure evolution rule under the competitive action of pressure increase and a dissipation mechanism induced by a deep complex geothermal environment can be predicted more accurately, and a more scientific theoretical guidance is provided for providing a customized filling optimization scheme and realizing the sustainable development of deep mineral resources.
Drawings
FIG. 1 is a schematic diagram illustrating the evolution law of pore water pressure with initial temperature at different times according to an embodiment of the present invention;
FIG. 2 is a schematic diagram showing the evolution law of the thermal expansion coefficients of water and a solid skeleton with the temperature according to the embodiment of the invention;
FIG. 3 is a schematic diagram of the temperature change of the fill unit at different initial temperatures for different heating and cooling rates according to an embodiment of the present invention;
FIG. 4 is a schematic diagram showing the variation of water pressure for different initial temperatures of the fill body under different heating and cooling rates in accordance with an embodiment of the present invention; (a) heating action (b) cooling action.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention will be further described in detail below with reference to the accompanying drawings by way of examples.
A method for simulating pore water pressure of a tailing filler in a high-temperature stope is based on a pore thermoelasticity theoretical framework of Selvadurai and Suvoro v, and a non-isothermal pore water pressure control equation of the filler is established by considering the water volume change caused by hydration reaction water consumption (namely chemical shrinkage effect):
wherein α represents a Biot coefficient (α ═ 1-K) d /K s In the formula, K d Bulk modulus for a filler skeleton), n is porosity, K s And K w Bulk modulus, p, of solid phase and water, respectively w Denotes the pore water pressure, t is the time during which the reaction takes place, beta s And beta w The coefficients of thermal expansion of the solid phase and of the water, respectively, T representing the current temperature, ε v For volume strain, k is the permeability coefficient, eta represents the dynamic viscosity of water, epsilon shf Is the total water consumption during the chemical reaction, ξ is the degree of hydration.
Due to the compressibility of the solid particles being negligible compared to the matrix of the packing (i.e. K) d <<K s ) It can therefore be assumed that the Biot coefficient alpha is approximately 1 (alpha ≈ 1,
). Meanwhile, because the influence effect of the temperature load on the pore water pressure of the filling body is mainly concerned, the filling body unit can be used as a research object, so that the seepage term is eliminated and the formula (1) is simplified as follows:
and the formula (2) is a pore water pressure control equation of the filling body unit in the triaxial hydration pressure chamber. Furthermore, considering the effect of thermal expansion in non-isothermal processes, the thermo-elastic stress-strain relationship of the filler unit can be expressed as:
wherein ε represents strain, E represents Young's modulus, σ ' represents effective stress, v represents Poisson's ratio, T 0 Indicating the initial temperature.
In order to simplify the calculation, the present embodiment further establishes a geometric model of the filler under a one-dimensional side limit condition, so that the filler unit has only axial strain, and the effective stresses in the x and y directions are equal, and the following relationship holds:
the volumetric deformation of the packing unit can thus be obtained by the joint type (3) and the formula (4):
the parameters in equation (5) can be expressed as:
the change in effective stress is equal to the change in pore water pressure (i.e., the change in pore water pressure) for a given confining pressure condition
Assuming that the solid phase compression is negative), equation (5) can be written as the derivative:
finally, on the premise of a small strain hypothesis, the formula (7) is substituted into the formula (2) to finally obtain a pore water pressure control equation of the filling body unit under the non-isothermal condition:
in addition, in this embodiment, it is assumed that the triaxial hydration pressure chamber is completely insulated, i.e. the filler unit cannot generate heat conduction and convection heat exchange with the surrounding environment, so the temperature change of the filler under the condition of heat insulation and no water drainage is only generated by hydration heat release and the temperature load applied by the triaxial apparatus, and the temperature of the filler can be defined as:
where k represents the constant rate of temperature change imposed by the tri-axial device, T h Temperature rise due to hydration, Q f Is the heat given off during the chemical reaction, (ρ C) eff Denotes effective Heat Capacity ((ρ C) eff ＝(1–n)ρ s C s +nρ w C w )，C s And C w Specific heat capacity, rho, of solid-liquid phases respectively s And ρ w The density of the solid phase and water, respectively.
According to Doherty and Muir Wood studies, the hydration level is compared to a reference reaction time t e The relationship of (c) can be expressed as:
ξ＝1-exp(-κ ξ ·t e ) (24)
wherein, κ ξ Is the evolution rate of the hydration degree along with the reference time.
According to Arrhenius formula, the actual time t and the reference time t e The relationship of (c) can be expressed as:
wherein, E a Represents the activation energy required for the chemical reaction, R a Is the general gas constant (R) a ＝8.314J/mol/K)， T r Is the reference temperature. K
Therefore, by bringing the formulas (9) to (11) into formula (8), the pore water pressure control equation of the filling body unit under the temperature load can be finally obtained:
the invention describes the growth evolution of the skeleton rigidity of the filling body in the hydration process by using the following formula:
K d ＝K di [λ-(λ-1)exp(-κ K ·t e )] (27)
in the formula K di Is the initial skeletal stiffness of the filling body, λ is the ratio of the final stiffness to the initial stiffness of the filling body, κ K Model parameters that control the rate of stiffness growth.
Furthermore, the evolution law of the thermal expansion coefficient of water with temperature is described using the following formula
β w ＝β w0 +k 0 T (28)
In the formula beta w0 And k 0 Are fitting parameters.
Water pressure evolution law of filling body pore space under different temperature environmental conditions
1) Influence of the initial temperature
The physicochemical parameters of the tailings packings used in the australian Kanowna Belle gold mine are shown in table 1. The pore water pressure evolution law of the filling body unit in the heat-insulating and non-draining environment under different initial temperature conditions is shown in figure 1. Fig. 1 shows that the water pressure of the filling body at any time is increased after being decreased with the increase of the initial temperature. The reason is that the curing temperature of the low-temperature filling body is increased to accelerate the chemical reaction rate, so that the pore pressure dissipation caused by hydration water consumption is promoted; meanwhile, since the thermal expansion coefficient of water is still small at a low temperature (fig. 2), the thermal expansion effect caused by hydration heat release is not obvious, so that the pore water pressure is finally reduced continuously with the increase of the initial temperature under the dominance of hydration water consumption. However, as the curing temperature continues to increase, while the chemical reaction rate of the pack will further increase, the coefficient of thermal expansion of water will continue to increase at the same time (fig. 2). Therefore, when the temperature reaches a certain critical value, the hydrothermal pressurization effect caused by hydration heat release exceeds the hydration water consumption effect, and further the pore water pressure rises along with the rise of the initial temperature.
It can also be seen from fig. 1 that the pore water pressure increases almost monotonically with the initial temperature increase after a sufficiently long time (t 1000h) of the chemical reaction. This is because the hydration reaction at this point has been substantially complete, i.e. the fillers of different initial temperatures all produce the same temperature rise and chemical shrinkage under the hydration reaction, but because of the greater coefficient of thermal expansion of water at high temperatures, the fillers will produce higher pore water pressure under the effect of the stronger hydrothermal pressurization.
Furthermore, it can also be noted from fig. 1 that the longer the chemical reaction time, the lower the critical initial temperature at which pore water pressure is shifted from falling to rising. This is because low temperatures reduce the hydration exotherm rate and therefore take longer to generate a sufficient temperature rise to allow the thermal expansion effect to completely offset the water-consuming pressure-reducing effect of hydration.
TABLE 1 physicochemical parameters of Australian Kanowna Belle gold ore pack
From the above discussion, it is clear that the effect of the initial temperature conditions on the hydraulic evolution of the pack pore is the result of the competing effects of both hydration water consumption and hydration exotherm. Since the coefficient of thermal expansion of water is small at low initial temperatures, the dissipation of water pressure due to water consumption by hydration will play a major role; however, since the coefficient of thermal expansion of water increases rapidly with increasing temperature, the hydrothermal pressurization effect caused by the exothermic heat of hydration will ultimately control the pore hydraulic evolution of the pack.
2) Influence of temperature load
This example was performed by varying the forced temperature change rate (k 0, ± 2.5 × 10) for the filler units with initial temperatures of 0, 15, 30 ℃ -3 、±5.0×10 -3 The water pressure change process under the condition of DEG C/h) is subjected to numerical analysis, and the influence mechanism of temperature load on the pore water pressure of the filling body unit is further researched.
The temperature change law of the filling body unit with different initial temperatures under different heating and cooling rate conditions is shown in figure 3. FIG. 3 shows that when k > 0 ℃/h, the initial temperatures of the pack were 15 ℃ and 30 ℃ both at the early stage of heating compared to the low temperature (T) 0 The 0 c regime produces a more pronounced temperature rise. This is because the higher the initial temperature, the faster the chemical reaction rate, and thus the pack temperature will rise dramatically under the combined action of the hydration exotherm and the forced heating. As the hydration reaction is gradually completed, the rate of temperature rise of the pack will continue to decrease as the hydration exotherm slows and eventually converge to a constant external heating rate. Whereas when k < 0 ℃/h, the cooling action will strongly suppress the low temperature filling (T) since the lower the initial temperature, the slower the chemical reaction rate 0 0 ℃) hydration, the temperature rise resulting from the exotherm. In contrast, packs with initial temperatures of 15 ℃ and 30 ℃ will still develop a significant temperature rise early in the cool down due to the faster hydration heat release rate. However, as the hydration reaction is gradually completed, the temperature change of the pack will eventually be controlled by the forced cooling action.
The water pressure evolution law of the filling body unit in the heat-insulating and non-draining environment under the action of temperature load is shown in fig. 4(a) and 4 (b). Fig. 4(a) shows that the initial temperature of the pack of 15 c and 30 c produced a significant increase in water pressure under heating compared to the isothermal state (k 0 c/h). This is because, although the temperature rise due to heating can accelerate chemical shrinkage and thus promote pore pressure dissipation, the pressure reduction effect due to hydration water consumption is difficult to counteract the hydrothermal pressurization effect due to temperature rise due to high thermal expansion coefficient of water at high temperature, and finally the pore water pressure gradually rises in the heating process. It can also be seen from fig. 4 that a fill body with a higher initial temperature will produce an earlier and faster increase in water pressure at the same heating rate, since the coefficient of thermal expansion of water will increase with increasing temperature (fig. 2). In contrast, since the coefficient of thermal expansion of water is extremely small at an initial temperature of 0 ℃, the promotion effect of water consumption by temperature rise exceeds the hydrothermal pressurization effect, so that the pore water pressure is slightly lower than a constant temperature state at an early stage of heating. However, as the hydration reaction is gradually completed, the continuous heating action will still produce a significant hydrothermal pressurization effect, and therefore the pore water pressure of the pack will eventually be higher than the isothermal state. The above calculation results show that the tailings filler in the high-temperature goaf may generate higher long-term soil pressure on the retaining wall because the filler finally generates a significant hydrothermal pressurization effect under the continuous heating action.
While the pore water pressure at the initial temperature of the pack of 15 c and 30 c both rapidly decreased with decreasing temperature under the cooling action (fig. 4 (b)). This is because, although lowering the temperature inhibits the rate of water consumption by hydration, the shrinkage of the fill by cooling will ultimately have a significant effect on the pore pressure dissipation due to the higher coefficient of thermal expansion of water at high temperatures. In contrast, since the coefficient of thermal expansion of water is very small at an initial temperature of 0 ℃, the cooling shrinkage effect of the pore fluid during the temperature reduction process is not obvious; meanwhile, the cooling effect also can strongly inhibit hydration water consumption reaction and further slow down the pore pressure dissipation rate, so that the pore water pressure of the filling body at the initial temperature of 0 ℃ is slightly higher than the constant temperature state at the early stage of temperature reduction. However, as the hydration reaction is gradually completed, the cooling shrinkage caused by the temperature reduction will gradually dominate the change of the water pressure of the filling body, so the pore water pressure will finally be lower than the constant temperature state due to the continuous cooling effect. The above calculation results show that although the low temperature environment can inhibit water consumption due to hydration and further adversely affect pore pressure dissipation, the filling operation in the low temperature goaf generally has higher safety because the cooling process of the filling body can cause fluid contraction and further generate a significant pressure reduction effect.
From the above discussion, the continuous heat exchange between the filling body and the high-temperature surrounding rock can induce thermal strain to influence the hydraulic pressure evolution. When the initial temperature of the filling body is higher, the water pressure evolution is controlled by the water pressure change caused by heat exchange due to the larger thermal expansion coefficient of water. However, when the temperature of the filling body is lower, although the thermal strain caused by the heating or cooling effect will also have a certain influence on the water pressure of the pore space, the change of the hydration water consumption rate caused by heat exchange will dominate the early water pressure evolution of the filling body because the thermal expansion coefficient of water is extremely small at low temperature. However, as the chemical reaction is gradually completed, the pore water pressure of the low temperature pack will eventually be controlled by the thermal strain generated by the continuous heat exchange.
It will be appreciated by those of ordinary skill in the art that the examples described herein are intended to assist the reader in understanding the manner in which the invention is practiced, and it is to be understood that the scope of the invention is not limited to such specifically recited statements and examples. Those skilled in the art can make various other specific changes and combinations based on the teachings of the present invention without departing from the spirit of the invention, and these changes and combinations are within the scope of the invention.
Claims (4)
1. A method for simulating water pressure of a pore of a tailing filling body in a high-temperature stope is characterized by comprising the following steps:
step 1, establishing a non-isothermal pore water pressure control equation of a filling body under a creep loading condition by considering water volume change caused by hydration reaction water consumption based on a pore thermoelasticity theoretical framework of Selvadurai and Suvorov:
wherein α represents a Biot coefficient, and α ═ 1-K d /K s In the formula K d Is the bulk modulus of the filler skeleton, n is the porosity, K s And K w Bulk modulus, p, of solid phase and water, respectively w Denotes the pore water pressure, t is the time during which the reaction is carried out, beta s And beta w The coefficients of thermal expansion of the solid phase and of the water, respectively, T representing the current temperature,. epsilon v For 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, xi is the hydration degree;
step 2, assuming that the Biot coefficient α is approximately 1, α ≈ 1,
the filling body unit is taken as a research object, so that the seepage term is eliminated and the formula (1) is simplified as follows:
the formula (2) is a pore water pressure control equation of a filling body unit in the triaxial hydration pressure chamber;
step 3, in order to simulate the compression effect caused by the creep of the surrounding rock, a triaxial hydration pressure chamber is utilized to apply axial deformation with the acceleration rate of j/s to the filling body sample, and the thermoelastic stress-strain relation of the filling body unit under the action of creep loading is expressed as follows:
wherein ε represents strain, E represents Young's modulus, σ ' represents effective stress, v represents Poisson's ratio, T 0 Represents the initial temperature;
step 4, establishing a geometric model of the filling body under the one-dimensional side limit condition, so that the filling body unit only has axial strain, the effective stresses in the x direction and the y direction are equal, and the following relation is established:
the volumetric deformation of the packing unit is thus obtained by the combination of formula (3) and formula (4):
the parameters in formula (5) are represented as:
step 5, under the given confining pressure condition, the change of the effective stress is equal to the change of the pore water pressureI.e. by
Assuming that the solid phase compression is negative, equation (5) is therefore written as the derivative:
and 6, on the premise of a small strain hypothesis, substituting the formula (7) into the formula (2) to finally obtain a filling body unit pore water pressure control equation under a non-isothermal condition:
step 7, assuming that the triaxial hydration pressure chamber is completely insulated, i.e. the filler unit cannot generate heat conduction and convection heat transfer with the surrounding environment, so that the temperature change of the filler under the condition of heat insulation and no drainage is only generated by hydration heat release and the temperature load applied by the triaxial device, and further defining the temperature of the filler as follows:
where k represents the constant rate of temperature change imposed by the tri-axial device, T h Temperature rise due to hydration, Q f Is the heat given off during the chemical reaction, (p C) eff Denotes the effective Heat Capacity ((ρ C) eff ＝(1–n)ρ s C s +nρ w C w )，C s And C w Specific heat capacity, rho, of solid-liquid phases respectively s And ρ w Density of solid phase and water, respectively;
step 8, hydration degree and reference reaction time t e The relationship of (c) is expressed as:
ξ＝1-exp(-κ ξ ·t e ) (10)
wherein, κ ξ The evolution rate of the hydration degree along with the reference time;
step 9, according to the Arrhenius formula, the actual time t and the reference time t e The relationship of (c) is expressed as:
wherein E is a Represents the activation energy required for the chemical reaction, R a Is the general gas constant (R) a ＝8.314J/mol/K)，T r Is a reference temperature;
and step 10, driving the formulas (9) to (11) into the formula (8), and finally obtaining a pore water pressure control equation of the filling body unit under the action of temperature load:
2. the method for simulating pore water pressure of the tailing filler in the high-temperature stope according to claim 1, wherein the method comprises the following steps: the invention describes the growth evolution of the skeleton rigidity of the filling body in the hydration process by using the following formula:
K d ＝K di [λ-(λ-1)exp(-κ K ·t e )] (13)
in the formula K di Is the initial skeletal stiffness of the filling body, λ is the ratio of the final stiffness to the initial stiffness of the filling body, κ K Model parameters that control the rate of stiffness growth.
3. The method for simulating pore water pressure of the tailing filler in the high-temperature stope according to claim 1, wherein the method comprises the following steps: the evolution law of the thermal expansion coefficient of water with the temperature is described by using the following formula
β w ＝β w0 +k 0 T (14)
In the formula beta w0 And k 0 Are fitting parameters.
4. The method for simulating pore water pressure of the tailing filler in the high-temperature stope according to claim 1, wherein the method comprises the following steps: the method is applied to the technical field of tailing filling mining.
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