Method for determining column-hemispherical permeation radius with time-varying property of power-law cement grout and tortuosity of rock and soil mass

Abstract

A method for determining a column-hemispherical permeation radius with time-varying property of power-law cement grout and tortuosity of rock and soil mass is provided, including: acquiring a porosity ϕ of rock and soil mass and a corresponding permeation coefficient K by geotechnical tests, measuring a groundwater pressure P.sub.0 at a grouting point and determining tortuosity ξ of rock and soil mass; acquiring an initial consistency coefficient c.sub.0, a rheological index n and a time-varying property coefficient k of power-law cement grout with a designed water to cement ratio by rheological tests, and determining the viscosity of water μ.sub.w; acquiring grouting parameters, including a grouting pressure P.sub.1, grouting time t, a number m of grouting holes of a side surface of a grouting pipe and a grouting hole radius r; and solving a column-hemispherical permeation grouting diffusion radius R considering coupling effect both the tortuosity of rock and soil mass and the time-varying property of power-law cement grout.

Claims

1. A method for determining a column-hemispherical permeation radius, comprising: acquiring a porosity ϕ of a rock and soil mass and a corresponding permeation coefficient K by geotechnical tests, and measuring a groundwater pressure P.sub.0 at a grouting point and determining a tortuosity ξ of the rock and soil mass; acquiring an initial consistency coefficient c.sub.0, a rheological index n and a time-varying property coefficient k of a power-law cement grout with a designed water to cement ratio by rheological tests, and determining a viscosity of the water μ.sub.w; acquiring grouting parameters, the grouting parameters comprising a grouting pressure P.sub.1, grouting time t, a number m of grouting holes of a side surface of a grouting pipe, and a grouting hole radius r; and solving a column-hemispherical permeation grouting diffusion radius R as the column-hemispherical permeation radius considering a coupling effect both the tortuosity of rock and soil mass and a time-varying property of the power-law cement grout by using a formula expressed as: $\begin{array}{cc}\Delta p=p_1-p_0=\frac{2^{1+n}{c}_0{e}^{\mathrm{kt}}\sqrt{\xi }}{1-2n}{\left(\frac{m+1}{4m+5}\right)}^n{\left(\frac{3n+1}{\mathrm{tn}}\right)}^n{\left(\frac{\varphi {\rho }_{w}g}{8{\mu }_{w}K}\right)}^{\frac{n+1}{2}}\left(R^{1-2n}-r^{1-2n}\right)R^{3n}& \left(1\right)\end{array}$ where ρ.sub.w represents a water density; g is gravitational acceleration; e represents a base of natural logarithm; wherein an expression formula of the tortuosity ξ of the rock and soil mass is: $\begin{array}{cc}\xi ={\left(\frac{L_e}{L}\right)}^2& \left(3\right)\end{array}$ where L.sub.e represents an actual flow path length of the cement grout into the rock and soil mass; L is a linear length corresponding to the actual flow path of the cement grout into the rock and soil mass; and wherein an expression formula of the porosity ϕ of the rock and soil mass is: $\begin{array}{cc}\varphi =1-\frac{\rho }{G_S{\rho }_W^{4^{◦}C}\left(1+\omega \right)}& \left(2\right)\end{array}$ where ρ.sub.W.sup.4° C. is a density of pure distilled water at 4° C.; ρ represents a density of the rock and soil mass; ω represents a mass water content of the rock and soil mass; G.sub.S, represents a specific gravity of the rock and soil mass; wherein the method further comprises: grouting the rock and soil mass with the power-law cement grout in a grouting engineering practice based on the column-hemispherical permeation radius obtained after the solving.

2. The method according to claim 1, wherein the density ρ of the rock and soil mass is acquired by one of an irrigation method, a sand filling method, and a cutting ring method.

3. The method according to claim 1, wherein the mass water content ω of the rock and soil mass is measured by a drying method.

4. The method according to claim 1, wherein the specific gravity G.sub.S of the rock and soil mass is measured by combining a pycnometer method and a siphon cylinder method.

5. The method according to claim 1, wherein the permeation coefficient K is acquired by field water injection tests.

6. The method according to claim 1, wherein the acquiring an initial consistency coefficient c.sub.0, a rheological index n and a time-varying property coefficient k of the power-law cement grout with a designed water to cement ratio by rheological tests comprises: performing the rheological tests of the power-law cement grout with the designed water to cement ratio at different times by using a rotary viscometer or a capillary viscometer; establishing a shear velocity-shear stress coordinate system, and acquiring rheological curves corresponding to the rheological tests; obtaining a rheological equation corresponding to the rheological curve in accordance with a power-law fluid rheology equation, and then acquiring a consistency coefficient c and the rheological index n correspondingly; and obtaining the initial consistency coefficient c.sub.0, the rheological index n and the time-varying property coefficient k of the power-law cement grout with the designed water to cement ratio by analyzing change relationships between the consistency coefficient c, the rheological index n and a time.

7. A method for determining a column-hemispherical permeation radius, comprising: acquiring a porosity ϕ of a rock and soil mass and a corresponding permeation coefficient K by geotechnical tests, and measuring a groundwater pressure P.sub.0 at a grouting point and determining a tortuosity ξ of the rock and soil mass; acquiring an initial consistency coefficient c.sub.0, a rheological index n and a time-varying property coefficient k of a power-law cement grout with a designed water to cement ratio by rheological tests, and determining a viscosity of the water μ.sub.w; acquiring grouting parameters, the grouting parameters comprising a grouting pressure P.sub.1, grouting time t, a number m of grouting holes of a side surface of a grouting pipe, and a grouting hole radius r; solving a column-hemispherical permeation grouting diffusion radius R as the column-hemispherical permeation radius considering a coupling effect both the tortuosity of rock and soil mass and a time-varying property of the power-law cement grout by using a formula expressed as: $\Delta p=p_1-p_0=\frac{2^{1+n}{c}_0{e}^{\mathrm{kt}}\sqrt{\xi }}{1-2n}{\left(\frac{m+1}{4m+5}\right)}^n{\left(\frac{3n+1}{\mathrm{tn}}\right)}^n{\left(\frac{\varphi {\rho }_{w}g}{8{\mu }_{w}K}\right)}^{\frac{n+1}{2}}\left(R^{1-2n}-r^{1-2n}\right)R^{3n}$ where ρ.sub.w represents a water density; g is gravitational acceleration; e represents a base of natural logarithm; wherein an expression formula of the tortuosity ξ of the rock and soil mass is: $\xi ={\left(\frac{L_e}{L}\right)}^2$ where L.sub.e represents an actual flow path length of the cement grout into the rock and soil mass; L is a linear length corresponding to the actual flow path of the cement grout into the rock and soil mass; and wherein an expression formula of the porosity ϕ of the rock and soil mass is: $\varphi =1-\frac{\rho }{G_S{\rho }_W^{4^{◦}C}\left(1+\omega \right)}$ where ρ.sub.W.sup.4° C. is a density of pure distilled water at 4° C.; ρ represents a density of the rock and soil mass; ω represents a mass water content of the rock and soil mass; G.sub.S represents a specific gravity of the rock and soil mass; and applying the column-hemispherical permeation radius as a reference in practical grouting engineering of the power-law cement grout into the rock and soil mass.

Description

BRIEF DESCRIPTION OF DRAWINGS

(1) In order to more clearly explain the technical schemes of the embodiment of the disclosure, the following briefly introduces the accompanying drawings required for describing the embodiments. It should be understood that the follow accompanying drawings merely show some embodiments of the disclosure and thus should not be considered to limit the protective scope, for technicians in this field, other relevant drawings can also be obtained based on these drawings without paying for creative work.

(2) FIG. 1 is a logic flowchart of the disclosure.

(3) FIG. 2 is a diagram of column-hemispherical permeation grouting diffusion form of power-law cement grout into rock and soil mass in the disclosure.

(4) FIG. 3 is A-A view of FIG. 2.

(5) FIG. 4 is a schematic diagram of actual permeation and diffusion flow path of the power-law cement grout into the rock and soil mass in the disclosure.

(6) FIG. 5 is the variation curve of the consistency coefficient of water to cement ratio 0.50, 0.60 and 0.70 power-law cement grout with time in the disclosure.

(7) FIG. 6 is a curve diagram of change law of rheological index of the power-law cement grout with water to cement ratio of 0.50, 0.60 and 0.70 with time in the disclosure.

(8) FIG. 7 is a comparison diagram between theoretical values and experimental values of the permeation and diffusion radius of the power-law cement grout with water to cement ratio of 0.50, 0.60 and 0.70 into the rock and soil mass.

(9) In the above drawings, the names of parts corresponding to reference signs are as follows:

(10) 1—grouting pipe; 2—side surface grouting hole; 3—bottom grouting hole; 4—rock and soil mass; 5—pore.

DETAILED DESCRIPTION OF EMBODIMENTS

(11) The disclosure will be described in further detail in combination with the accompanying drawings and embodiments, to present the objectives, technical solutions, and advantages of the present application clearly. The embodiments of the disclosure include but not limited to the following embodiments. Based on the embodiments in this application, all other embodiments obtained by ordinary technicians in this field without making creative labor are covered by the protection in this application.

Embodiment 1

(12) As shown in FIG. 1 to FIG. 7, the present embodiment provides a method for determining column-hemispherical permeation radius with the time-varying property of power-law cement grout and the tortuosity of the rock and soil mass, which considers the coupling effect both the time-varying property of power-law cement grout and the tortuosity of rock and soil mass. As shown in FIG. 2 to FIG. 3, the grouting enters side surface grouting hole 2 and bottom grouting hole 3 from the grouting pipe 1, and the groundwater pressure at the external grouting point of the grouting area is p.sub.0.

(13) The specific steps are as follows:

(14) 1) The porosity ϕ is equal to 48.97%, the permeation coefficient K is equal to 0.0118 m/s and the groundwater pressure at the grouting point p.sub.0 is equal to 0 Pa by using geotechnical tests. Meanwhile, according to existing research results, the tortuosity ξ of the rock and soil mass is selected to be equal to 2.25, as shown in FIG. 4, in the rock and soil mass 4 and pores 5, the actual permeation and diffusion flow path of the cement grout into the rock and soil mass 4 (the path L1-L2 is the theoretical flow path of the fluid, and the path L3-L4 is the actual flow path of the fluid).

(15) The porosity ϕ of the rock and soil mass is calculated by the following formula, where:

(16) $\varphi =1-\frac{\rho }{G_S{\rho }_W^{4^{◦}C}\left(1+\omega \right)}$

(17) where ρ.sub.W.sup.4° C. is 1000 kg/m.sup.3; and by the rock and soil mass tests, it is measured for the rock and soil mass that the density ρ is equal to 1355 kg/m.sup.3, the mass water content ω is equal to 0.20%, and the specific gravity is equal to 2.65.

(18) 2) The initial consistency coefficient c.sub.0=10.4426 Pa.Math.s.sup.n, rheological index n=0.1406, time-varying property coefficient k=0.0011 of power-law cement grout with water to cement ratio of 0.50 and the viscosity of water μ.sub.w=1.31×10.sup.−3 Pa.Math.s are obtained by rheological tests.

(19) In the present embodiment, the change laws between the consistency coefficient c and the rheological index n of the power-law cement grout with water to cement ratio of 0.50 and time are shown in FIG. 5 to FIG. 6 respectively. Through analysis, it can be known that the consistency coefficient has a power-exponential change relationship with time, and has time-varying property; however, the rheological index changes little with time, which can be regarded as time-invariant. From this research, the initial consistency coefficient, the rheological index and the time-varying property coefficient of the power-law cement grout with water to cement ratio of 0.50 can be acquired.

(20) 3) According to the actual situation, it is designed that grouting pressure p.sub.1 is equal to 100000 Pa, grouting time t is equal to 120 s, the number m of side surface grouting holes of grouting pipe is equal to 3 and its radius r is equal to 7.5×10.sup.−3 m;

(21) 4) The column-hemispherical permeation grouting diffusion radius R considering the coupling effect both tortuosity of rock and soil mass and time-varying property of power-law cement grout is acquired by using the following formula, and the expression formula is:

(22) $\Delta p=p_1-p_0=\frac{2^{1+n}{c}_0{e}^{\mathrm{kt}}\sqrt{\xi }}{1-2n}{\left(\frac{m+1}{4m+5}\right)}^n{\left(\frac{3n+1}{\mathrm{tn}}\right)}^n{\left(\frac{\varphi {\rho }_{w}g}{8{\mu }_{w}K}\right)}^{\frac{n+1}{2}}\left(R^{1-2n}-r^{1-2n}\right)R^{3n}$

(23) Where formula, p.sub.1 is the grouting pressure (Pa); p.sub.0 is the groundwater pressure at the grouting point (Pa); c.sub.0, n and k are the initial consistency coefficient (Pa.Math.s.sup.n), the rheological index (dimensionless number) and the time-varying property coefficient (dimensionless number) of the power-law cement grout respectively; t is the grouting time (s); ξ, ϕ and K are the tortuosity (dimensionless number), the porosity (dimensionless number) and the permeation coefficient (m/s) of the rock and soil mass respectively; m is the number of side surface grouting holes of grouting pipe (dimensionless number); ρ.sub.w takes 1000 kg/m.sup.3; g takes 9.8 m/s.sup.2; μ.sub.w is the viscosity of water (Pa.Math.s); R is the diffusion radius (m) of the power-law cement grout in the rock and soil mass; r is the radius (m) of the grouting hole.

(24) Through analysis, it is determined that the theoretical value of the diffusion radius acquired by the method for determining the column-hemispherical permeation radius with the time-varying property of the power-law cement grout and the tortuosity of the rock and soil mass considering the coupling effect both the time-varying property of the power-law cement grout and the tortuosity of the rock and soil mass in the present embodiment is 0.2049 m. However, the theoretical values of the diffusion radius acquired by using the methods for calculating the column-hemispherical permeation grouting diffusion radius considering neither the tortuosity of the rock and soil mass nor the time-varying property of the power-law cement grout, only considering the tortuosity of the rock and soil mass and only considering the time-varying property of the power-law cement grout are 0.3204 m, 0.2285 m and 0.2869 m respectively, and the experimental value carried out according to the implementation is 0.1754 m. At the same time, by analyzing FIG. 7, it can be seen that the theoretical value of the diffusion radius acquired by the method for determining the column-hemispherical permeation radius with the time-varying property of the power-law cement grout and the tortuosity of the rock and soil mass considering the coupling effect both the time-varying property of the power-law cement grout and the tortuosity of the rock and soil mass in the present embodiment is closer to the experimental value than the theoretical values of the diffusion radius respectively acquired by using the methods for calculating the column-hemispherical permeation grouting diffusion radius considering neither the tortuosity of the rock and soil mass nor the time-varying property of the power-law cement grout, only considering the tortuosity of the rock and soil mass and only considering the time-varying property of the power-law cement grout.

Embodiment 2

(25) The present embodiment provides a method for determining column-hemispherical permeation radius with the time-varying property of power-law cement grout and tortuosity of the rock and soil mass, and the specific steps are as follows:

(26) 1) By using the rock and soil mass tests, it can be acquired for the rock and soil mass that the porosity ϕ is equal to 44.19%, the permeation coefficient K is equal to 0.0083 m/s and the groundwater pressure p.sub.0 at the grouting point is equal to 0 Pa. Meanwhile, according to the existing research results, the tortuosity ξ of the rock and soil mass is selected to be equal to 2.25;

(27) The porosity ϕ parameters of the rock and soil mass are as follows: by the rock and soil mass tests, it is measured for the rock and soil mass that the density ρ is equal to 1482 kg/m.sup.3, the mass water content U) is equal to 0.20%, and the specific gravity is equal to 2.65.

(28) 2) By conducting the rheological tests, it can be acquired for the power-law cement grout with water to cement ratio of 0.60 that the initial consistency coefficient c.sub.0 is equal to 4.6156 Pa.Math.s.sup.n, the rheological index n is equal to 0.2692, the time-varying property coefficient k is equal to 0.0010 and the viscosity of water μ.sub.w is equal to 1.31×10.sup.−3 Pa.Math.s;

(29) In the present embodiment, the change laws between the consistency coefficient c and the rheological index n of the power-law cement grout with water to cement ratio of 0.60 and time are shown in FIG. 5 to FIG. 6 respectively. Through analysis of these two figures, it can be known that the consistency coefficient has a power-exponential change relationship with time, and has time-varying property; however, the rheological index changes little with time, which can be regarded as time-invariant. From this research, the initial consistency coefficient, the rheological index and the time-varying property coefficient of the power-law cement grout with water to cement ratio of 0.60 can be acquired.

(30) 3) According to the actual situation, it is designed that grouting pressure p.sub.1 is equal to 80000 Pa, grouting time t is equal to 105 s, the number of side surface grouting holes of grouting pipe is equal to 3 and its radius r is equal to 7.5×10.sup.−3 m;

(31) 4) The column-hemispherical permeation grouting diffusion radius R considering the coupling effect both the tortuosity of rock and soil mass and the time-varying property of power-law cement grout is solved.

(32) Through analysis, it is determined that the theoretical value of the diffusion radius acquired by the method for determining the column-hemispherical permeation radius with the time-varying property of the power-law cement grout and the tortuosity of the rock and soil mass considering the coupling effect both the time-varying property of the power-law cement grout and the tortuosity of the rock and soil mass in the present embodiment is 0.1699 m. However, the theoretical values of the diffusion radius acquired by using the methods for calculating the column-hemispherical permeation grouting diffusion radius considering neither the tortuosity of the rock and soil mass nor the time-varying property of the power-law cement grout, only considering the tortuosity of the rock and soil mass and only considering the time-varying property of the power-law cement grout are 0.2447 m, 0.1830 m and 0.2269 m respectively, and the experimental value carried out according to the implementation is 0.1469 m. At the same time, by analyzing FIG. 7, it can be seen that the theoretical value of the diffusion radius acquired by the method for determining the column-hemispherical permeation radius with the time-varying property of the power-law cement grout and the tortuosity of the rock and soil mass considering the coupling effect both the time-varying property of the power-law cement grout and the tortuosity of the rock and soil mass in the present embodiment is closer to the experimental value than the theoretical values of the diffusion radius respectively acquired by using the methods for calculating the column-hemispherical permeation grouting diffusion radius considering neither the tortuosity of the rock and soil mass nor the time-varying property of the power-law cement grout, only considering the tortuosity of the rock and soil mass and only considering the time-varying property of the power-law cement grout.

Embodiment 3

(33) The present embodiment provides a method for determining column-hemispherical permeation radius with the time-varying property of power-law cement grout and the tortuosity of the rock and soil mass, and the specific steps are as follows:

(34) 1) By using the rock and soil mass tests, it can be acquired for the rock and soil mass that the porosity ϕ is equal to 40.31%, the permeation coefficient K is equal to 0.0055 m/s and the groundwater pressure p.sub.0 at the grouting point is equal to 0 Pa. Meanwhile, according to the existing research results, the tortuosity ξ of the rock and soil mass is selected to be equal to 2.25;

(35) The porosity ϕ parameters of the rock and soil mass are as follows: by the rock and soil mass tests, it is measured for the rock and soil mass that the density ρ is equal to 1585 kg/m.sup.3, the mass water content ω is equal to 0.20%, and the specific gravity is equal to 2.65.

(36) 2) By the rheological tests, it can be acquired for the power-law cement grout with water to cement ratio of 0.70 that initial consistency coefficient c.sub.0 is equal to 1.9321 Pa.Math.s.sup.n, rheological index n is equal to 0.4537, time-varying property coefficient k is equal to 0.0009 and the viscosity of water is equal to 1.31×10.sup.−3 Pa.Math.s;

(37) In the present embodiment, the change laws between the consistency coefficient c and the rheological index n of the power-law cement grout with the water to cement ratio of 0.70 and time are shown in FIG. 5 to FIG. 6 respectively. Through analysis of these two figures, it can be known that the consistency coefficient has a power-exponential change relationship with time, and has time-varying property; however, the rheological index changes little with time, which can be regarded as time-invariant. From this research, the initial consistency coefficient, the rheological index and the time-varying property coefficient of the power-law cement grout with the water to cement ratio of 0.70 can be acquired.

(38) 3) According to the actual situation, it is designed that the grouting pressure p.sub.1 is equal to 60000 Pa, grouting time t is equal to 90 s, the number m of side surface grouting holes of grouting pipe is equal to 3 and its radius r is equal to 7.5×10.sup.−3 m;

(39) 4) The column-hemispherical permeation grouting diffusion radius R considering the coupling effect both the tortuosity of rock and soil mass and the time-varying property of power-law cement grout is solved.

(40) Through analysis, it is determined that the theoretical value of the diffusion radius acquired by the method for determining the column-hemispherical permeation radius with the time-varying property of the power-law cement grout and the tortuosity of the rock and soil mass considering the coupling effect both the time-varying property of the power-law cement grout and the tortuosity of the rock and soil mass in the present embodiment is 0.1117 m. However, the theoretical values of the diffusion radius acquired by using the methods for calculating the column-hemispherical permeation grouting diffusion radius considering neither the tortuosity of the rock and soil mass nor the time-varying property of the power-law cement grout, only considering the tortuosity of the rock and soil mass and only considering the time-varying property of the power-law cement grout are 0.1472 m, 0.1169 m and 0.1405 m respectively, and the experimental value carried out according to the implementation is 0.0978 m. At the same time, by analyzing FIG. 7, it can be seen that the theoretical value of the diffusion radius acquired by the method for determining the column-hemispherical permeation radius with the time-varying property of the power-law cement grout and the tortuosity of the rock and soil mass considering the coupling effect both the time-varying property of the power-law cement grout and the tortuosity of the rock and soil mass in the present embodiment is closer to the experimental value than the theoretical values of the diffusion radius respectively acquired by using the methods for calculating the column-hemispherical permeation grouting diffusion radius considering neither the tortuosity of the rock and soil mass nor the time-varying property of the power-law cement grout, only considering the tortuosity of the rock and soil mass and only considering the time-varying property of the power-law cement grout.

(41) In summary, the method for determining the column-hemispherical permeation radius with the time-varying property of the power-law cement grout and the tortuosity of the rock and soil mass considering the coupling effect both the time-varying property of the power-law cement grout and the tortuosity of the rock and soil mass according to the disclosure can better reflect the permeation grouting diffusion law of the power-law cement grout in the rock and soil mass, and more accords with the grouting engineering practice, thereby provides theoretical guidance and technical reference for the practical grouting engineering design and construction of the rock and soil mass.

(42) The above embodiments are only preferred embodiments of the disclosure, and do not limit the protective scope of the disclosure. All changes made by adopting the design principle of the disclosure and non-creative labor on this basis should fall within the protective scope of the disclosure.