CN114739883A - Generalized analysis method for rock expansion - Google Patents
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- CN114739883A CN114739883A CN202210343115.5A CN202210343115A CN114739883A CN 114739883 A CN114739883 A CN 114739883A CN 202210343115 A CN202210343115 A CN 202210343115A CN 114739883 A CN114739883 A CN 114739883A
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Abstract
The invention relates to the field of analysis of relation between rock water absorption expansion and time duration, in particular to a rock expansion generalized analysis method, which comprises the following steps: (1) constructing a generalized analysis model of rock expansion; (2) establishing a water supply mechanism for rock expansion in the model; (3) calculating the water absorption expansion time of the unit rock; (4) the total supply amount of rock expansion water is calculated, and the change rule of the water content along with time in the rock expansion process is obtained by combining the water absorption expansion time of the unit rock, and compared with the prior art, the method has the beneficial effects that: and calculating and analyzing the permeation rate of water in the rock expansion process by constructing a generalized model of rock expansion to obtain the change rule of the water content of the rock along with time, and describing and predicting the change relation of the water content and the expansion occurrence time in the water absorption expansion process of the hard gypsum rock.
Description
Technical Field
The invention relates to the field of analysis of relation between rock water absorption expansion and time duration, in particular to a generalized analysis method for rock expansion.
Background
The expansion behavior of the rock is the result of the combined action of the expanded rock and water, and the water absorption expansion of the rock needs a process as can be known from indoor rock water immersion tests and the prior research resultsThe rock water absorption process and the water absorption amount determine the time length and the expansion degree of the rock expansion behavior, the process is closely related to factors such as external water source supply, the circulation condition of water in the rock and the like, the factors influence and restrict mutually, and the complex relationship is difficult to obtain in a test mode
The water test is used for observation, and a theoretical calculation and prediction method which can be used for engineering reference is lacked, so that the expansion occurrence time of the expansion rock body cannot be predicted in the engineering.
Therefore, the development of a rock expansion generalized analysis method can be used for calculating and predicting the water absorption expansion time of the rock, and the method not only has urgent research value, but also has good economic benefit and industrial application potential, which is the basis and the motive power for the completion of the invention.
Disclosure of Invention
The present inventors have conducted intensive studies to overcome the above-identified drawbacks of the prior art, and as a result, have completed the present invention after having made a great deal of creative efforts.
Specifically, the technical problems to be solved by the present invention are: the method comprises the steps of analyzing the seepage process of a rock by a probabilistic model, and obtaining the relation between the rock expansion water content and time.
In order to achieve the purpose, the invention provides the following technical scheme:
a method of rock expansion generalization analysis comprising the steps of:
(1) constructing a generalized analysis model of rock expansion;
(2) establishing a water supply mechanism for rock expansion in the model;
(3) calculating the water absorption expansion time of the unit rock;
(4) and (4) calculating the total supply amount of the rock expansion water, and combining the water absorption expansion time of the unit rock to obtain the change rule of the water content along with time in the rock expansion process.
In the invention, as an improvement, the analytical model generalization method of rock expansion is as follows:
(1) generalizing the interior of the rock into a uniform and compact rock body, wherein the rock body consists of a plurality of unit rocks, and each unit rock consists of a plurality of micro units which expand after absorbing water;
(2) water is transferred within the rock from the outer microcells to the inner microcells, and the outer microcells, upon sufficient expansion, transfer to the inner microcells.
In the invention, as an improvement, the rock expansion water supply mechanism is as follows:
(1) water for expansion of the micro-cells in the unit rock is supplied by the adjacent cells at the periphery of the unit rock, and free water which can flow through the interior of the rock does not exist;
(2) the micro unit can only transmit the carried and transmittable added quantity, wherein the added quantity is the residual value obtained by subtracting the natural water content from the unit saturated water content;
in the invention, as a modification, the unit rock water swelling length is calculated as follows:
in the unit rock expansion process, the micro unit carries out R times of water transmission and supply, the 1 st time of water transmission and supply is delta T, the supply path of the follow-up water is increased, the time length is gradually increased and is increased as a function F (R) of the water supply times R, and the unit rock expansion time length T is as follows:
wherein r is a variable of the number of supply times;
the number of the replenishment channels in the rock increases in a nonlinear way as the number of times of water delivery increases, and the time length increasing function F (r) is a nonlinear function, and when r is 1, F (r) is delta T, so that F (r) is in the following functional form:
F(r)＝ΔTeK(r-1)；
wherein K is a undetermined constant term;
substituting the functional form yields:
in the present invention, as an improvement, the total replenishment of water in the rock expansion is calculated as follows:
the single water supply per microcell in rock is:
δ＝ωb-ωz；
wherein, ω isbIs the unit saturated water content of rock, omegazIs the water content of the unit rock in a natural state;
the water consumption for expansion of the rock microcells is wiThe unit rock has N micro-units, and each micro-unit needs to absorb m times of water transmission and supply when the expansion is completed, so that:
the total water requirement per unit rock expansion is:
W＝Nwi；
in the process of R times of water conveying and supplying, the quantity of water supplied each time depends on the quantity of expanded micro units and the value of m, the 1 st time of water conveying provides 1 unit of water quantity, and is provided with a conveying channel, the 2 nd time of water conveying can be only conveyed by the 1 st formed conveying channel, therefore, the quantity of water conveyed in the j +1 th time depends on the quantity of the j formed conveying channels, and the total conveying and supplying quantity of the R times of water is as follows:
in summary, it is known that:
then:
W＝(0.5R2-0.5R+1)δ；
from this, the rock expansion water content is obtained as a function of time.
Compared with the prior art, the invention has the beneficial effects that:
(1) and calculating and analyzing the permeation rate of water in the rock expansion process by constructing a generalized model of rock expansion to obtain the change rule of the water content of the rock along with time, and describing and predicting the change relation of the water content and the expansion occurrence time in the water absorption expansion process of the hard gypsum rock.
(2) The rock water absorption expansion generalized model can describe the change development rule of the water content of the rock sample in the expansion process under the indoor condition, can be used for predicting the time required by the rock expansion process, and can provide a reference basis for the establishment of expansion rock engineering measures.
Drawings
In order to more clearly illustrate the detailed description of the invention or the technical solutions in the prior art, the drawings that are needed in the detailed description of the invention or the prior art will be briefly described below. Throughout the drawings, like elements or portions are generally identified by like reference numerals. In the drawings, elements or portions are not necessarily drawn to scale.
FIG. 1 is a schematic diagram of the rock expansion process of the present invention;
FIG. 2 is a graph showing the reciprocal time course of the water absorption rate of the test piece according to the present invention;
FIG. 3 shows the formula F (r) ═ Δ Te according to the present inventionK(r-1)Fitting to obtain a fitting function curve graph;
FIG. 4 is a comparison graph of a formula-fitted curve of the present invention and a time course curve of a water-swelling test of a anhydrite rock;
wherein, 1, expansion area, 2, seepage and expansion path, 3, ideal rock mass.
Detailed Description
Embodiments of the present invention will be described in detail below with reference to the accompanying drawings. The following examples are only for illustrating the technical solutions of the present invention more clearly, and therefore are only examples, and the protection scope of the present invention is not limited thereby.
A generalized analysis method for rock expansion features that based on ideal rock state, a generalized analysis model of rock expansion is created, which features that the uniform compact rock mass is used to ensure the expansion property of rock, and after the rock is immersed in water, the water gradually permeates from surface to interior, and the seepage flow rate is related to the water supply and path distance.
The expansion of rock is the macroscopic expression of rock microscopic particle expansion, and the expansion order of rock microscopic particle depends on the order of contacting with water, and the granule that contacts water earlier expands earlier, and the granule that contacts water earlier fully expands the back, just can carry out the transmission of water, consequently, for the analysis that realizes the inside water infiltration route of rock, divide into a plurality of unit rocks with the rock, unit rock comprises a plurality of microcells again, and water is by outside microcell transmission to inside microcell in the rock, just outside microcell transmits to inside microcell after abundant inflation.
The water used for the expansion of the micro-cells of the rock is supplied by the adjacent cells at the periphery, and macroscopically, the water used for the expansion of the rock at the unexpanded part is supplied by the rock at the expanded part, and free water which can circulate in the rock does not exist.
The water supply mechanism of two adjacent micro units is as follows: a, B micro units adjacent to each other in the rock, when the A unit supplies water to the B unit, the A unit can only provide a generation amount which is carried by the A unit and can be transmitted, the generation amount is that the saturated water content of the micro unit after the micro unit is fully expanded is subtracted by the natural water content of the micro unit, a transmission channel is formed between A, B micro units, and the A unit transmits water to the B unit and receives the water for expansion from an external water source, so that a chain type transmission channel is formed.
The development law of the water content of the rock is used for describing the relation between water absorption expansion and time length of the rock, and the change of the water content is reflected by the total water content and the expansion time length.
The time required for the expansion of the rock cells depends on the condition of the external water supply and the number of cells through which water can be transmitted, and when the external water source is fixed, the rock expansion reaction time depends on the time during which water is transmitted inside the rock, and the rock expansion time is calculated on a per-rock basis.
The unit rock water-swelling time length is calculated as follows:
in the unit rock expansion process, the micro unit performs R times of water transmission and supply, the 1 st time of water transmission and supply is delta T, the subsequent water supply path is increased, the time length is gradually increased, the time length is increased as a function F (R) of the water supply times R, and the unit rock expansion time length T is as follows:
wherein r is a variable of the number of supply times;
since the number of rock internal supply channels increases nonlinearly as the number of water delivery supply times R increases, the time duration increasing function f (R) should also be a nonlinear function, and f (R) Δ T when R is 1, from which f (R) is given as a function:
F(r)＝ΔTeK(r-1)；
wherein K is an undetermined constant term;
substituting the functional form yields:
the total make-up of water in the rock expansion is calculated as follows,
the single water supply per micro-cell in rock is:
δ＝ωb-ωz；
wherein, ω isbIs the unit saturated water content of rock, omegazIs the water content of the unit rock in a natural state;
the water consumption for expansion of the rock microcells is wiThe unit rock has N micro-units, and each micro-unit needs to absorb m times of water transmission and supply when expansion is completed, so that:
the total water requirement for unit rock expansion is:
W＝Nwi。
during the R water delivery supplies, the amount of water per supply depends on the number of expanded microcells and the value of m, and the relationship between each supply is shown in the following table:
the R value of water transmission number of times is greater than the m value far away, provides 1 unit time water yield during 1 st water transmission to possessed transmission channel, can only transmit by the transmission channel that has formed 1 st time during 2 nd transmission, with this, the transmission of water volume when j +1 th time is decided on the transmission channel quantity that has formed when j, then the total transmission supply volume of R time water is:
in summary, it is known that:
then:
W＝(0.5R2-0.5R+1)δ；
the relationship between the water absorption expansion of the gypsum rock and the time is obtained, and the delta T, K is a parameter corresponding to the water supply source.
The first embodiment is as follows: the rock test piece is 100% of gypsum rock, and the water content of the crystal water is 20.8%; the single water supply delta of the test piece is 0.3 percent (the saturated water content of the gypsum rock is 0.425 percent to the natural water content of the gypsum rock is 0.1195 percent), and the K is 0.45.
In the water transfer of R times in the expansion approximation model of the anhydrite rock, the water transfer time obeys the formula F (R) ═ DeltaTeK(r -1)In the test, the water absorption rate is gradually reduced, the test time is used for characterizing R, and the reciprocal of the water absorption rate is used for characterizing F (R), and the water absorption rate of the gypsum rock is shown as follows:
the curve of the reciprocal time course of the water absorption rate of the test piece is shown in FIG. 2, and is expressed by the formula F (r) ═ Δ TeK(r-1)Fitting results in a fitting function as shown in fig. 3, which is derived from fig. 3 as follows:
F(t)＝0.72e0.132(t-1)；
the description of the water transmission time in the rock microcosmic shows that the actual test conditions have good consistency and the change rules are consistent.
The total water absorption of rock expansion is obtained according to the relation of time:
the formula fitting curve is compared with the time-course curve of the water absorption expansion test of the anhydrite, and as shown in figure 4, the change relation of the water absorption expansion water content and the expansion occurrence time of the anhydrite are described and predicted by the formula.
In conclusion, the generalized rock water absorption expansion model of the computational analysis method can describe the change development rule of the water content of the rock sample in the expansion process under indoor conditions, and can be used for predicting the time required by the rock expansion process.
Finally, it should be noted that: the above embodiments are only used to illustrate the technical solution of the present invention, and not to limit the same; while the invention has been described in detail and with reference to the foregoing embodiments, it will be understood by those skilled in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some or all of the technical features may be equivalently replaced; such modifications and substitutions do not depart from the spirit and scope of the present invention, and they should be construed as being included in the following claims and description.
Claims (5)
1. A method for generalized analysis of rock expansion, comprising the steps of:
(1) constructing a generalized analysis model of rock expansion;
(2) establishing a water supply mechanism for rock expansion in the model;
(3) calculating the water absorption expansion time of the unit rock;
(4) and (4) calculating the total supply amount of the rock expansion water, and combining the water absorption expansion time of the unit rock to obtain the rule of the water content changing along with time in the rock expansion process.
2. A method for generalized computational analysis of rock expansion according to claim 1, wherein the analytical model of rock expansion is generalized as follows:
(1) generalizing the interior of the rock into a uniform and compact rock body, wherein the rock body consists of a plurality of unit rocks, and each unit rock consists of a plurality of micro units which expand after absorbing water;
(2) water is transferred within the rock from the outer microcells to the inner microcells, and the outer microcells transfer to the inner microcells after sufficient expansion.
3. A method for generalized computational analysis of rock expansion according to claim 1, characterized by: the rock expansion water supply mechanism is as follows:
(1) water for expansion of the micro-cells in the unit rock is supplied by the adjacent cells at the periphery of the unit rock, and free water which can flow through the interior of the rock does not exist;
(2) the micro-unit can only transmit the carried and transmittable amount of the added amount, namely the residual value of the saturated water content of the unit minus the natural water content.
4. A method for generalized computational analysis of rock expansion according to claim 1, characterized by: the unit rock water-absorbing expansion time is calculated as follows:
in the unit rock expansion process, the micro unit performs R times of water transmission and supply, the 1 st time of water transmission and supply is delta T, the subsequent water supply path is increased, the time length is gradually increased, the time length is increased as a function F (R) of the water supply times R, and the unit rock expansion time length T is as follows:
wherein r is a variable of the number of supply times;
the number of the replenishment channels in the rock increases in a nonlinear way as the number of times of water delivery increases, and the time length increasing function F (r) is a nonlinear function, and when r is 1, F (r) is delta T, so that F (r) is in the following functional form:
F(r)＝ΔTeK(r-1)；
wherein K is an undetermined constant term;
substituting the functional form yields:
5. the method for generalized computational analysis of rock expansion according to claim 1, wherein the total replenishment of water in rock expansion is calculated as follows:
the single water supply per micro-cell in rock is:
δ＝ωb-ωz；
wherein, ω isbIs the unit saturated water content of rock, omegazIs the water content of the unit rock in a natural state;
the water consumption for expansion of the rock microcells is wiThe unit rock has N micro-units, and each micro-unit needs to absorb m times of water transmission and supply when the expansion is completed, so that:
the total water requirement for unit rock expansion is:
W＝Nwi；
in the process of R times of water transmission and supply, the quantity of water supply each time depends on the quantity of expanded microcells and the value of m, the water quantity of 1 unit time is provided in the 1 st time of water transmission, a transmission channel is provided, the 2 nd time of water transmission can be transmitted only by the transmission channel formed in the 1 st time, therefore, the quantity of water transmission in the j +1 th time depends on the quantity of the transmission channels formed in the j time, and the total transmission and supply quantity of the R times of water is as follows:
in summary, it is known that:
then:
W＝(0.5R2-0.5R+1)δ；
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