Road deterioration base grouting reinforcement injection stop time determination method based on Pre-Darcy model

Abstract

The invention provides a method for determining grouting stopping time of road degradation base layer grouting reinforcement based on a Pre-Darcy model, and belongs to the technical field of road maintenance, and the method comprises the following steps: step 1, firstly, obtaining an analytical solution of a road degradation base layer grouting transmission model based on the Pre-Darcy model; and 2, the injection stopping time is inversely calculated according to the grouting range by means of the analytical solution in the step 1. According to the road degraded base layer grouting reinforcement injection stopping time determination method based on the Pre-Darcy model, the road degraded base layer data and the grouting data are determined, and the grouting plane rectangular cells are divided according to the road treatment area, so that the injection stopping time of the grouting plane rectangular cells fully covered by the grout can be accurately calculated; and technical support is provided for engineers to scientifically grout and reinforce the deteriorated base layer of the road.

Description

Technical Field

[0001] The invention relates to the technical field of road maintenance, and in particular to a method for determining a grouting stop time for road deterioration base reinforcement based on a Pre-Darcy model. Background Art

[0002] The grouting methods of road base are generally divided into infiltration grouting, compaction grouting, jet grouting and compensation grouting. Among them, infiltration grouting is the main grouting method used in highway base. Yan et al. (2021), Li et al. (2019), Zhang et al. (2017) proposed slurry penetration models in fractured rock mass from the perspectives of numerical simulation, empirical analysis and numerical analysis, respectively. et al. (2009) further analyzed the mechanical response model of slurry to fractured rock mass. Maghouse et al. (2007) and Zhang et al. (2022) established the permeability model of ordinary cement slurry and fast-setting slurry in uniform porous media, respectively.

[0003] (2007)

[70] considered the filtration effect of cement particles in the modeling process. Similar to the study of Maghouse et al. (2007), Ye et al. (2019) also paid attention to the filtration effect and proposed a hemispherical slurry penetration model. Based on previous studies, Ying et al. (2022) proposed a slurry penetration model under constant grouting pressure in non-uniform porous media. Liang et al. (2022) further developed a polymer slurry model that considers the rheological properties of the slurry, and many other research results. We note that in the modeling process of the above models, most of the seepage of slurry in porous media follows Darcy's law. The road base is generally composed of graded aggregate or cement soil, and its permeability is between soil and concrete, which belongs to low-permeability porous media. Therefore, the seepage of slurry inside the base may be more in line with the non-Darcy flow law, such as the Pre-Darcy flow proposed by Cee and Xiaoyan (2002). Although the grouting permeability model proposed by Ying et al. (2022) and Liang et al. (2022) takes into account the non-Darcy seepage law, it requires numerical simulation to achieve, which is relatively complex and not easy to apply in engineering practice. In addition, it has been observed that the development of slurry permeability theory is mainly concentrated in tunnel engineering, while there are relatively few research results under road foundation conditions. Therefore, the current grouting project for deteriorated base of operating roads often controls the stop time of grouting based on experience, lacking theoretical support.

[0004] Grouting technology is a common method to solve the hidden diseases of road base in transportation infrastructure. It is characterized by minimal invasiveness to the road surface and rapid restoration of traffic flow after repair. Since the road base is a hidden project, the application of traditional grouting methods has certain uncertainties. Therefore, the use of scientific methods to predict the diffusion of slurry in the road base can alleviate this inherent unpredictability. This not only improves the accuracy of the grouting process, but also reduces the unnecessary consumption of grouting materials. Grouting methods are generally divided into infiltration grouting, compaction grouting, jet grouting and compensation grouting. Among them, infiltration grouting is the main grouting method used in highway base. The survey found that most of the existing road base grouting design methods follow Darcy seepage. However, the road base is generally composed of graded aggregate or cement soil, and its permeability is between soil and concrete, which belongs to low-permeability porous media. Therefore, the seepage of slurry inside the base may be more in line with the non-Darcy flow law. To this end, a method for determining the stop time of grouting reinforcement of road deterioration base based on the Pre-Darcy model is proposed, which can scientifically guide the design of road base grouting construction. Summary of the invention

[0005] The purpose of the present invention is to provide a method for determining the stop time of grouting reinforcement of road deterioration base based on the Pre-Darcy model, so as to solve the technical problem that the stop time of grouting in currently operated road deterioration base grouting projects is often controlled based on experience and lacks theoretical support.

[0006] In view of the lack of theoretical basis for the stop time of grouting of deteriorated road base and the great blindness, which leads to poor grouting effect of road base, a method for determining the stop time of grouting reinforcement of deteriorated road base based on Pre-Darcy model is proposed based on the Pre-Darcy model, which is used to scientifically determine the stop time of grouting of deteriorated base of operating roads.

[0007] In order to achieve the above object, the technical solution adopted by the present invention is as follows:

[0008] A method for determining the stop time of grouting reinforcement for road deterioration base based on the Pre-Darcy model, the method comprising the following steps:

[0009] Step 1: First, obtain the analytical solution of the road deterioration base grouting transmission model based on the Pre-Darcy model;

[0010] Step 2: Then use the analytical solution of step 1 to reversely calculate the stop time according to the grouting range.

[0011] Furthermore, in step 1, the input parameters of the road deterioration base grouting transmission model based on the Pre-Darcy model include grouting parameters: grouting pipe radius r0, grouting pressure p g , slurry density ρ g, dynamic viscosity of the slurry μ g and the compressibility coefficient c of the slurry g ; Road base parameters: base grouting depth H, base permeability β, base porosity , the compression coefficient c of the base layer s , the initial water pressure of the base p0, the empirical coefficient of the base related to seepage m, the output data of the road deterioration base grouting transmission model based on the Pre-Darcy model covers the grouting diffusion radius R(t) related to the grouting time t, where 0≤r0≤r≤R(t), and the other parameters are all real numbers greater than or equal to 0.

[0012] Furthermore, in step 1, the control equation of the road deterioration base grouting transmission model based on the Pre-Darcy model is as follows:

[0013]

[0014] where c t =c s +c g ;

[0015] At the initial time of grouting, i.e., time t = 0, p(r, t) obeys the following initial conditions:

[0016] p(r,0)=p0 (24)

[0017] The slurry is injected into the road base from the grouting pipe. During the grouting process, the grouting pressure remains constant. For the radius of the grouting pipe, that is, r = r0, p(r, t) obeys the following boundary conditions:

[0018] p(r=r0,t)=p g (25)

[0019] During the slurry transmission process in the base layer, the grouting pressure at the front edge of the slurry has the following specific relationship:

[0020] p(r=R(t),t)=p0 (26)

[0021]

[0022] The above equations (1) to (5) together constitute the mathematical model of the road deterioration base grouting transmission model based on the Pre-Darcy model.

[0023] Furthermore, in step 1, the road deterioration base grouting transmission model based on the Pre-Darcy model can be obtained by solving the above equations (1) to (5);

[0024] Construct a new function as follows

[0025]

[0026] Substituting formula (6) into the mathematical model of the road deterioration base grouting transmission model based on the Pre-Darcy model, that is, formulas (1) to (5), the following five equations can be obtained:

[0027]

[0028] p(η=0)=p0 (30)

[0029] p(η=η0)=p g (31)

[0030] p(η=η R )=p0 (32)

[0031]

[0032] in and

[0033] Set dp / dη=P and reduce the order of equation (7) to the following:

[0034]

[0035] The above equation is a Bernoulli form equation, and its general solution is:

[0036]

[0037] Substituting the above formula (11) into formula (13), we can determine that c in formula (13) is:

[0038]

[0039] Therefore, we rewrite equation (13) as follows:

[0040]

[0041] Further processing the above formula (15), rewrite it as follows:

[0042]

[0043] in,

[0044] The corresponding rewrites of equations (9) to (10) are as follows:

[0045]

[0046] Integrating equation (16) and combining it with equation (18) yields the following equation:

[0047]

[0048] Substituting formula (17) into formula (19) we can further obtain:

[0049]

[0050] Rearranging equation (20), we get η R The values ​​are:

[0051]

[0052] By combining equation (6) and equation (21), it can be deduced that the diffusion radius R(t) of the slurry on the deteriorated road base is:

[0053]

[0054] Furthermore, the specific process of step 2 is:

[0055] (1) Determine the grouting parameters for treating the deteriorated road base, including the grouting pipe radius r0, grouting pressure p g , slurry density ρ g , dynamic viscosity of the slurry μ g and the compressibility coefficient c of the slurry g ;

[0056] (2) Determine the parameters of the deteriorated road base that needs grouting treatment: base grouting depth H, base permeability β, base porosity Compression coefficient of base layer c s , initial water pressure of the base p0, empirical coefficient of the base related to seepage m;

[0057] (3) Divide the grouting plane into rectangular cells according to the road treatment area, and the length L and width W of the cells are between 4m and 5m respectively;

[0058] (4) Arrange the grouting pipes in the unit cell, where four grouting pipes are located at the four inner corners of the rectangular unit, with a vertical distance of 1 m from the edge of the rectangular unit cell, and another grouting pipe is located at the center of the rectangular unit cell;

[0059] (5) According to the grouting pipe layout plan, it is determined that when the grouting radius is R0, the grouting liquid of the five grouting pipes can fully cover the grouting cells, that is, R0 is

[0060] (6) Substitute R0 into equation (22) and set R0 = R(T) to calculate the stop time, which is recorded as T.

[0061] If the stop time is not determined properly, two situations may occur: First, the grouting liquid does not completely cover the area to be treated, resulting in poor grouting effect; second, the slurry diffusion range is too large, resulting in waste of grouting materials. Therefore, the stop time needs to be as accurate as possible. The existing stop time calculation method is often obtained by experience and lacks scientificity. Some stop time calculation methods are obtained by assuming that the slurry is a Darcy flow state. However, the permeability of the road base is between soil and stone, and it is a low-permeability medium. The diffusion of the slurry in the base conforms to the non-Darcy flow state.

[0062] The present invention has the following beneficial effects due to the adoption of the above technical solution:

[0063] (1) The method for determining the stop time of grouting reinforcement of a deteriorated road base based on the Pre-Darcy model provided by the present invention can accurately calculate the stop time of the grouting plane rectangular cells fully covered by the slurry by determining the road deteriorated base data and the grouting data, and dividing the grouting plane rectangular cells according to the road treatment area, thereby providing technical support for engineering personnel to scientifically grout the deteriorated road base.

[0064] (2) The method for determining the stop time of grouting reinforcement of deteriorated road base based on the Pre-Darcy model proposed in the present invention is not only scientific, but also takes into account the non-Darcy flow state of the grouting liquid in the road base. Therefore, the stop time obtained is more accurate and can guide the road base grouting construction design more scientifically. BRIEF DESCRIPTION OF THE DRAWINGS

[0065] Figure 1 It is a flow chart of the implementation of the method for determining the stop injection time of the present invention;

[0066] Figure 2 It is a grouting plane rectangular unit cell grouting pipeline layout diagram of the present invention;

[0067] Figure 3 This is a grouting pipe layout diagram of a single panel of an engineering cement concrete pavement according to the present invention;

[0068] Figure 4 It is the R(t)~t curve graph of the present invention;

[0069] Figure 5 This is a diagram showing the coverage effect of the slurry diffusion radius of the five grouting pipes of the present invention.

[0070] Figure 6 It is a grouting construction site diagram of the present invention;

[0071] Figure 7 This is a diagram showing the effect of excavation detection of the grouting area of ​​the present invention (the marked area is filled with grouting liquid). DETAILED DESCRIPTION

[0072] In order to make the purpose, technical solution 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 preferred embodiments. However, it should be noted that many details listed in the specification are only for the purpose of enabling the reader to have a thorough understanding of one or more aspects of the present invention, and these aspects of the present invention can be implemented even without these specific details.

[0073] like Figure 1 As shown, a method for determining the stop time of grouting reinforcement of a road deteriorated base based on the Pre-Darcy model comprises the following steps:

[0074] (1) Determine the grouting parameters for treating the deteriorated road base, including the grouting pipe radius r0, grouting pressure p g , slurry density ρ g , dynamic viscosity of the slurry μ g and the compressibility coefficient c of the slurry g .

[0075] (2) Determine the parameters of the deteriorated road base that needs grouting treatment: base grouting depth H, base permeability β, base porosity Compression coefficient of base layer c s , initial water pressure of the base layer p0, and empirical coefficient of the base layer related to seepage m.

[0076] (3) The grouting plane is divided into rectangular cells according to the road treatment area, and the length L and width W of the cells are between 4m and 5m respectively.

[0077] (4) Grouting pipes are arranged in the cells, where four grouting pipes are located at the four inner corners of the rectangular cell, with a vertical distance of 1 m from the edge of the rectangular cell, and another grouting pipe is located in the center of the rectangular cell.

[0078] (5) According to the grouting pipe layout plan, it is determined that when the grouting radius is R0, the grouting liquid of the five grouting pipes can fully cover the grouting cells, that is, R0 is

[0079] (6) Substitute R0 into equation (22) and let R0 = R(T) to calculate the stop time, which is T. Figure 1 shown.

[0080] Determining the grouting stop time of road deterioration base based on Pre-Darcy model

[0081] Based on a real road deterioration base grouting project, according to the grouting situation and road base conditions, the following set of measured calculation parameters are given: grouting pipe radius r0 = 0.019m, grouting pressure p g =10 6 Pa, slurry density ρg =2038.1kg / m 3 , dynamic viscosity of the slurry μ g =258.5Pa·s and the compressibility coefficient of the slurry c g =4.6×10 -10 Pa -1 , base grouting depth H = 0.8m, base permeability β = 2.16×10 -14 m 2 , the porosity of the base layer Compression coefficient of base layer c s =8×10 - 10 Pa -1 , the initial water pressure of the base layer p0 = 0Pa, and the base layer empirical coefficient related to seepage m = 1.65.

[0082] The actual road deterioration base grouting project treats a cement concrete pavement with a panel size of L = 5m and a width of W = 4.5m. The grouting pipes on the panel are arranged as follows: Figure 3 . According to the R0 value It can be seen that R0=1.8m.

[0083] According to formula (22), the corresponding stop injection time T = 156s can be calculated. The R(t)-t curve can also be drawn, and it can be seen that when R(t) = R0 = 1.8m, the corresponding stop injection time T = 156s. Figure 5 The grouting slurry diffusion effect is demonstrated, and it can be seen that the slurry diffusion radius of the five grouting pipes can completely cover the panel.

[0084] The method for determining the stop time of grouting reinforcement for deteriorated road base based on the Pre-Darcy model calculated that the stop time T of the actual grouting project is 156s. Based on the results obtained, grouting construction is carried out. Figure 6 Showing the construction site. Figure 7 The results of the excavation inspection of the grouting area after construction are demonstrated. It can be seen that the grouting liquid has a better effect in filling the deteriorated road base based on the method for determining the stop time of grouting reinforcement of the road deteriorated base based on the Pre-Darcy model.

[0085] The method for determining the stop time of grouting reinforcement of deteriorated road base based on the Pre-Darcy model is based on considering the non-Darcy seepage of the grouting liquid in the deteriorated road base. It is not only more in line with the actual situation, but also scientific.

[0086] The above is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the principle of the present invention. These improvements and modifications should also be regarded as the scope of protection of the present invention.

Claims

1. A method for determining the stop time of grouting reinforcement for deteriorated road base based on the Pre-Darcy model, characterized in that: The method comprises the following steps: Step 1: First, obtain the analytical solution of the road deterioration base grouting transmission model based on the Pre-Darcy model; Step 2: Then use the analytical solution of step 1 to reversely calculate the stop time according to the grouting range.

2. The method for determining the stop time of grouting reinforcement of road deterioration base based on the Pre-Darcy model according to claim 1 is characterized in that: In step 1, the input parameters of the road deterioration base grouting transmission model based on the Pre-Darcy model include grouting parameters: grouting pipe radius r0, grouting pressure p g , slurry density ρ g , dynamic viscosity of slurry μ g and the compressibility coefficient c of the slurry g ; Road base parameters: base grouting depth H, base permeability β, base porosity Compression coefficient of base layer c s , the initial water pressure of the base p0, the empirical coefficient of the base related to seepage m, the output data of the road deterioration base grouting transmission model based on the Pre-Darcy model covers the grouting diffusion radius R(t) related to the grouting time t, where 0≤r0≤r≤R(t), and the other parameters are all real numbers greater than or equal to 0.

3. The method for determining the stop time of grouting reinforcement of road deterioration base based on the Pre-Darcy model according to claim 2 is characterized in that: In step 1, the control equation of the road deterioration base grouting transmission model based on the Pre-Darcy model is as follows: where c t =c s +c g ; At the initial time of grouting, i.e., time t = 0, p(r, t) obeys the following initial conditions: p(r,0)=p0 (2) The slurry is injected into the road base from the grouting pipe. During the grouting process, the grouting pressure remains constant. For the radius of the grouting pipe, that is, r = r0, p(r, t) obeys the following boundary conditions: p(r=r0,t)=p g (3) During the slurry transmission process in the base layer, the grouting pressure at the front edge of the slurry has the following specific relationship: p(r=R(t),t)=p0 (4) The above equations (1) to (5) together constitute the mathematical model of the road deterioration base grouting transmission model based on the Pre-Darcy model.

4. The method for determining the stop time of grouting reinforcement of road deterioration base based on the Pre-Darcy model according to claim 3 is characterized in that: In step 1, the road deterioration base grouting transmission model based on the Pre-Darcy model can be obtained by solving the above equations (1) to (5); Construct a new function as follows Substituting formula (6) into the mathematical model of the road deterioration base grouting transmission model based on the Pre-Darcy model, that is, formulas (1) to (5), the following five equations can be obtained: p(η=0)=p0 (8) p(η=η0)=p g (9) p(η=η R )=p0 (10) in and Set dp / dη=P and reduce the order of equation (7) to the following: The above equation is a Bernoulli form equation, and its general solution is: Substituting the above formula (11) into formula (13), we can determine that c in formula (13) is: Therefore, we rewrite equation (13) as follows: Further processing the above formula (15), rewrite it as follows: in, The corresponding rewrites of equations (9) to (10) are as follows: Integrating equation (16) and combining it with equation (18) yields the following equation: Substituting formula (17) into formula (19) we can further obtain: Rearranging equation (20), we get η R The values ​​are: By combining equation (6) and equation (21), it can be deduced that the diffusion radius R(t) of the slurry on the deteriorated road base is:

5. The method for determining the stop time of grouting reinforcement of road deterioration base based on the Pre-Darcy model according to claim 4 is characterized in that: The specific process of step 2 is: (1) Determine the grouting parameters for treating the deteriorated road base, including the grouting pipe radius r0, grouting pressure p g , slurry density ρ g , dynamic viscosity of slurry μ g and the compressibility coefficient c of the slurry g ; (2) Determine the parameters of the deteriorated road base that needs grouting treatment: base grouting depth H, base permeability β, base porosity Compression coefficient of base layer c s , initial water pressure of the base p0, empirical coefficient of the base related to seepage m; (3) Divide the grouting plane into rectangular cells according to the road treatment area, and the length L and width W of the cells are between 4m and 5m respectively; (4) Arrange the grouting pipes in the unit cell, where four grouting pipes are located at the four inner corners of the rectangular unit, with a vertical distance of 1 m from the edge of the rectangular unit cell, and another grouting pipe is located at the center of the rectangular unit cell; (5) According to the grouting pipe layout plan, it is determined that when the grouting radius is R0, the grouting liquid of the five grouting pipes can fully cover the grouting cells, that is, R0 is (6) Substitute R0 into equation (22) and set R0 = R(T) to calculate the stop time, which is recorded as T.

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