Method for relieving vaulted expansion of cement-stabilized base layer through precut seams

Abstract

A method for relieving vaulted expansion of a cement-stabilized base layer through precut seams. The method firstly establishes an RBFN model according to a large number of observation results of a vaulted expansion amount of the cement-stabilized base layer under different conditions (such as temperature and a stress release structure) in Xinjiang and similar regions; and on such a basis, the vaulted expansion amount of the cement-stabilized base layer to be designed is predicted. When the vaulted expansion amount is greater than a control requirement, the RBFN model is configured to design a reasonable width and a reasonable interval of the precut wide expansion seams to ensure that the vaulted expansion amount of the cement-stabilized base layer is less than a control value. Based on the design of the RBFN model, the present invention provides a corresponding construction method for the precut wide expansion seams. The present invention can predict the vaulted expansion of the cement-stabilized base layer without precut seams according to existing data.

Claims

1. A method for relieving vaulted expansion of a cement-stabilized base layer through precut seams, comprising the following steps: 1) training a radial basis function network (RBFN) model, that is, establishing a mapping relationship between vaulted expansion amounts of the cement-stabilized base layer and different conditions through automatic adjustment of model parameters according to known vaulted expansion amounts of the cement-stabilized base layer under different temperatures and stress release structural conditions in a known region; wherein the training of the RBFN model refers to the automatic adjustment of RBFN model parameters w.sub.k and c.sub.k according to a large number of vaulted expansion amounts of the cement-stabilized base layer under different conditions in the region, w.sub.k and c.sub.k are a parameter weight parameter and a kernel parameter of the RBFN model respectively, k=1, . . . , n, and n is the number of center points, as shown in FIG. 1; 2) using the RBFN model, that is, according to the mapping relationship established in step 1), predicting the vaulted expansion amount of a cement-stabilized base layer under unknown conditions in the region; and according to the RBFN model trained in step 1), predicting the vaulted expansion amount of a cement-stabilized base layer without wide expansion seam structures and the vaulted expansion amount of a cement-stabilized base layer with different wide expansion seam structures, thereby determining a reasonable width and a reasonable interval of the wide expansion seams; and 3) performing a construction method for designing precut seams, that is, designing precut wide expansion seams according to the vaulted expansion amount of the cement-stabilized base layer under unknown conditions in the region predicted in step 2); and according to the width and interval of the wide expansion seam determined in step 2), performing construction of the cement-stabilized base layer, wherein except for a construction process for the precut wide expansion seams, the remaining construction processes for the cement-stabilized base layer are the same as the traditional construction processes for the cement-stabilized base layer.

2. The method for relieving vaulted expansion of a cement-stabilized base layer through precut seams according to claim 1, wherein a specific implementing method of step 1) is as follows: 101) randomly assigning values to the RBFN parameters w.sub.k and c.sub.k, an assignment range being [0, 1]; 102) randomly selecting a group of vaulted expansion amount data set of the cement-stabilized base layer under different conditions in the region, wherein the data set comprises two parts: an input condition part x=(x.sub.1, . . . , x.sub.9) and a target output value part y; x.sub.1-x.sub.9 are a construction temperature, a cement content, a mineral material grading, an environmental humidity, a controlled salt content, a compaction method, an expansion seam width and an expansion seam interval of the cement-stabilized base layer respectively; and the target output value part y is a group of measured vaulted expansion amounts of the cement-stabilized base layer; 103) predicting the vaulted expansion amount y′ of the cement-stabilized base layer with the RBFN model, wherein the process is as shown in formulas (1)-(3); $\begin{array}{cc}{\phi }_k\left(x\right)=e^{-\left({.Math.x-c_k.Math.}_2\right)}& \left(1\right)\\ {.Math.x-c_k.Math.}_2=\frac{\underset{i=1}{\overset{9}{.Math.}}{\left(x_i-c_i^k\right)}^2}{2}& \left(2\right)\\ y^{\prime }=\underset{k=1}{\overset{n}{.Math.}}{\omega }_k{\phi }_k\left(x\right)& \left(3\right)\end{array}$ wherein in these formulas, x=(x.sub.1, . . . , x.sub.9) is the input condition, c.sub.k=(c.sup.k.sub.1, . . . , c.sup.k.sub.9) is the kernel parameter of a radial basis function in the RBFN model; ∥ ∥.sub.2 is a 2-norm operator; c.sup.k.sub.i is an element of a c.sub.k vector, i=1, . . . , 9; and x.sub.i is a certain element of the x vector, that is, a certain input value, i=1, . . . , 9, which respectively corresponds to the construction temperature, the cement content, the mineral material grading, the environmental humidity, the controlled salt content, the compaction method, the expansion seam width, and the expansion seam interval of the cement-stabilized base layer; 104) calculating a prediction error and adjusting the parameters, wherein the process is as shown in formulas (4)-(8); $\begin{array}{cc}E\left(x\right)=y-y^{\prime }& \left(4\right)\\ \frac{\partial E\left(x\right)}{\partial w_k}=-E\left(x\right){\phi }_k\left(x\right)& \left(5\right)\\ \frac{\partial E\left(x\right)}{\partial c_i^k}=\frac{\partial E\left(x\right)}{\partial w_k}2e^{-\left({.Math.x-c_k.Math.}_2\right)}\left(x_i-c_i^k\right)& \left(6\right)\\ w_k.Math.w_k+\alpha \frac{\partial E\left(x\right)}{\partial w_k}& \left(7\right)\\ c_i^k.Math.c_i^k+\alpha \frac{\partial E\left(x\right)}{\partial c_i^k}& \left(8\right)\end{array}$ wherein in these formulas, y is the target output value part, and y′ is a calculation result of formula (3); φ.sub.k(x) is a calculation result of formula (1); E(x) is a calculation result of formula (4); c.sub.k=(c.sup.k.sub.1, . . . , c.sup.k.sub.9) is the kernel parameter of a radial basis function in the RBFN model; E(x) is a calculation result of formula (4); x=(x.sub.1, . . . , x.sub.9) is the input condition; α is a learning rate; .Math. and is an iteration symbol; and 105) repeating steps 101), 102), 103) and 104) until the prediction error is less than 0.1 mm, and saving the RBFN model parameters.

3. The method for relieving vaulted expansion of a cement-stabilized base layer through precut seams according to claim 2, wherein the value of α is 0.1.

4. The method for relieving vaulted expansion of a cement-stabilized base layer through precut seams according to claim 2, wherein a specific implementation method of step 2) is as follows: 201) selecting the construction temperature, cement content, mineral material grading, environmental humidity, controlled salt content and compaction method of the cement-stabilized base layer to be designed, and using the same as input parameters x.sub.1-x.sub.7 of the trained RBFN model; 202) setting the input parameters x.sub.8 and x.sub.9 of the trained RBFN model as 0; 203) according to the input parameters x.sub.1-x.sub.9 and the trained RBFN model, predicting the vaulted expansion amount of the cement-stabilized base layer to be designed without the wide expansion seams; wherein if the predicted vaulted expansion amount is less than a control value, no wide expansion seams need to be disposed; and if the predicted vaulted expansion is greater than or equal to the control value, the wide expansion seams need to be disposed, and the control value is determined according to design requirements of the cement-stabilized base layer to be designed; and 204) keeping x.sub.1-x.sub.7 unchanged, adjusting the values of x.sub.8 and x.sub.9, and predicting the vaulted expansion amount of the cement-stabilized base layer to be designed under the condition of disposing different wide expansion seams, until finding the condition that the predicted vaulted expansion amount is less than the control value.

5. The method for relieving vaulted expansion of a cement-stabilized base layer through precut seams according to claim 4, wherein the values of x.sub.8 and x.sub.9 are a design width and a design interval of the cement-stabilized base layer to be designed, and the value ranges of x.sub.8 and x.sub.9 are 0-50 mm and 50 m-150 m respectively.

6. The method for relieving vaulted expansion of a cement-stabilized base layer through precut seams according to claim 4, wherein a specific implementation method of step 3) is as follows: 301) according to the situation that the found vaulted expansion amount is less than the control value, determining positions of precut wide expansion seams of the cement-stabilized base layer to be constructed; after the positions of the expansion seams are determined, adjusting the positions of the expansion seams according to a bridge and culvert structure to ensure that at least one expansion seam is disposed between adjacent bridge and culvert structures, and disposing the expansion seams in combination with the positions of construction seams of the cement-stabilized base layer; 302) cutting the precut wide expansion seams according to the design positions of the precut wide expansion seams, wherein a depth of the wide expansion seam is a thickness of the cement-stabilized base layer, or the wide expansion seams are cut after completing the paving of the cement-stabilized base layer; 303) according to the obtained precut width expansion seams, filling the expansion seams after cutting, wherein a material of the expansion seams is selected according to actual conditions; and 304) disposing a glass fiber grid above the wide expansion seams after filling.

Description

BRIEF DESCRIPTION OF DRAWINGS

(1) FIG. 1 is a neural schematic structural diagram of a radial basis function network (RBFN).

(2) FIG. 2(a) is a top view of a schematic diagram of a method for relieving the vaulted expansion of a cement-stabilized base through precut seams according to the present invention.

(3) FIG. 2(b) is a sectional view of a schematic diagram of a method for relieving the vaulted expansion of a cement-stabilized base through precut seams according to the present invention.

(4) FIG. 3 is a plan view of precut seams of a cement-stabilized base layer according to an embodiment of the present invention (the unit of the numerals in the drawing is cm).

(5) FIG. 4 is a longitudinal plan view of precut seams of a cement-stabilized base layer according to an embodiment of the present invention ((the unit of the numerals in the drawing is cm).

DESCRIPTION OF REFERENCE SIGNS

(6) 1—precut seams, 2—glass fiber grid, 3—hot asphalt, 4—extruded board, 5—coarse-grained asphalt concrete (AC-25), 6—roadbed.

DESCRIPTION OF EMBODIMENTS

(7) The present invention will be further explained below in conjunction with the drawings and embodiments:

(8) The present invention provides a method for relieving the vaulted expansion of a cement-stabilized base layer through precut seams, which includes the following steps.

(9) (1) Training a Radial Basis Function Network (RBFN) Model

(10) Training of the RBFN model refers to the automatic adjustment of RBFN model parameters w.sub.k and c.sub.k is performed according to a vaulted expansion amount of the cement-stabilized base layer under different conditions (such as temperature and stress release structure) in Xinjiang and similar regions, k=1, n, and n is the number of center points. The basic training process may refer to step 1) of the summary of the invention. The RBFN model structure may refer to FIG. 1. In actual implementation, those skilled in the art do not need to perform related operations, and can directly perform subsequent operations according to the content recorded in the subsequent steps in the summary part of the present application. The RBFN model established in the step and the parameters obtained by training are claims of the present application, and may be directly used by those skilled in the art after obtaining authorization and the model. A prediction accuracy of the RBFN model in the present embodiment is 0.1 μm.

(11) A specific implementation method of step 1) is as follow.

(12) 101) Values are randomly assigned to the RBFN parameters w.sub.k and c.sub.k, an assignment range being [0, 1].

(13) 102) A group of vaulted expansion amount data set of the cement-stabilized base layer under different conditions in Xinjiang region is randomly selected, wherein the data set includes two parts: an input condition part x=(x.sub.1, . . . , x.sub.9) and a target output value part y, and the target output value part y is the group of measured vaulted expansion amounts of the cement-stabilized base layer.

(14) 103) The vaulted expansion amount y′ of the cement-stabilized base layer is predicted with the RBFN, wherein the process is as shown in formulas (1)-(3);

(15) $\begin{array}{cc}{\phi }_k\left(x\right)=e^{-\left({.Math.x-c_k.Math.}_2\right)}& \left(1\right)\\ {.Math.x-c_k.Math.}_2=\frac{\underset{i=1}{\overset{9}{.Math.}}{\left(x_i-c_i^k\right)}^2}{2}& \left(2\right)\\ y^{\prime }=\underset{k=1}{\overset{n}{.Math.}}{\omega }_k{\phi }_k\left(x\right)& \left(3\right)\end{array}$

(16) wherein in these formulas, x=(x.sub.1, . . . , x.sub.9) is the input condition, c.sub.k=(c.sup.k.sub.1, c.sup.k.sub.9) is the kernel parameter of a radial basis function in the RBFN; ∥ ∥.sub.2 Lis a 2-norm operator; c.sup.k.sub.i is an element of the c.sub.k vector, i=1, . . . , 9; and x.sub.i is an element of the x vector, that is, a certain input value, i=1, . . . , 9, which respectively corresponds to a construction temperature, a cement content, a mineral material grading, an environmental humidity, a controlled salt content, a compaction method, an expansion seam width, and an expansion seam interval of the cement-stabilized base layer.

(17) 104) A prediction error is calculated and the parameters are adjusted, wherein the process is as shown in formulas (4)-(8);

(18) $\begin{array}{cc}E\left(x\right)=y-y^{\prime }& \left(4\right)\\ \frac{\partial E\left(x\right)}{\partial w_k}=-E\left(x\right){\phi }_k\left(x\right)& \left(5\right)\\ \frac{\partial E\left(x\right)}{\partial c_i^k}=\frac{\partial E\left(x\right)}{\partial w_k}2e^{-\left({.Math.x-c_k.Math.}_2\right)}\left(x_i-c_i^k\right)& \left(6\right)\\ w_k.Math.w_k+\alpha \frac{\partial E\left(x\right)}{\partial w_k}& \left(7\right)\\ c_i^k.Math.c_i^k+\alpha \frac{\partial E\left(x\right)}{\partial c_i^k}& \left(8\right)\end{array}$

(19) wherein in these formulas, y is the target output value part, and y′ is a calculation result of formula (3); φ.sub.k(x) is a calculation result of formula (1); E(x) is a calculation result of formula (4); c.sub.k=(c.sup.k.sub.1, c.sup.k.sub.9) is the kernel parameter of a radial basis function in the RBFN; E(x) is a calculation result of formula (4); x=(x.sub.1, . . . , x.sub.9) is the input condition; a is a learning rate; and is an iteration symbol.

(20) 105) Steps 101), 102), 103) and 104) are repeated until the prediction error is less than 0.1 mm, and the RBFN model parameters are saved.

(21) (2) Using the RBFN Model

(22) According to the established RBFN model, the vaulted expansion amount of the cement-stabilized base layer without a wide expansion seam structure and the vaulted expansion amount of the cement-stabilized base layer with different wide expansion seam structures are predicted, so as to determine a reasonable width and a reasonable interval of the wide expansion seams. The specific steps are as follows.

(23) (a) For the cement-stabilized base layer to be designed, the construction temperature of 32° C., the cement content of 4.0%, the mineral material grading of C-B-1, the environmental humidity of 40%, the controlled salt content of 0.2%, and a compaction degree of 98% are determined, i.e., x.sub.1-x.sub.7 in the drawing “neural structure of radial basis function network”, and x.sub.8 and x.sub.9 are set to 0.

(24) (b) The RBFN model is used to predict that the vaulted expansion amount of the cement-stabilized base layer to be designed is 169.3 μm, which is greater than 100 μm, and the wide expansion seams need to be disposed.

(25) (c) For example, three groups of x.sub.8 and x.sub.9 combinations, namely 20 mm (width) and 50 m (interval), 50 mm (width) and 50 m (interval), and 50 mm (width) and 150 m (interval) are selected. The RBFN model is used to predict the vaulted expansion amounts of the cement-stabilized base layer under the condition of the three combinations, which are 54.6 μm, 113.4 μm, and 143.7 μm respectively. Therefore, only the design of the wide expansion seams of 20 mm (width) and 50 m (interval) meets the control requirements for the vaulted expansion amount of the cement-stabilized base layer, and 20 mm (width) and 50 m (interval) are used as the design values of the precut wide expansion seams.

(26) (3) Performing a Construction Method for Designing Precut Seams

(27) According to the width and interval of the wide expansion seams determined in step (2), the cement-stabilized base layer is constructed on a roadbed 6. Except for a construction process for the precut wide expansion seams, other construction processes for the cement-stabilized base layer are the same as the traditional construction processes for the cement-stabilized base layer. The construction process steps for the precut wide expansion seams are as follows: (a) the positions of the precut wide expansion seams of the cement-stabilized base layer to be constructed are determined according to an interval of 50 m of the precut wide expansion seams, referring to FIG. 2(a) and FIG. 2(b), wherein FIG. 2(a) is a top view and FIG. 2 (b) is a sectional view. After determining the positions of the expansion seams, appropriate adjustments may be made according to a bridge and culvert structure, etc., and at least one expansion seam should be disposed between adjacent bridge and culvert structures. The expansion seams may be disposed in combination with the positions of construction seams of the cement-stabilized base layer.

(28) (b) Cutting of the precut wide expansion seams is performed: a depth of the wide expansion seams is a thickness of the cement-stabilized base layer, and the width is 2 mm, referring to FIG. 3. The seams may also be cut after the cement-stabilized base layer is paved.

(29) (c) The expansion seams are filled after cutting, referring to FIG. 4. A material for the precut wide expansion seams may be selected according to the actual situation. In the present embodiment, the precut seams 1 are filled with hot asphalt 3, as shown in FIG. 4.

(30) (d) After the filling, a glass fiber grid 2 and an extruded board are disposed above the wide expansion seams. After the glass fiber grid 2 and the extruded board 4 are paved, a lower surface layer material, i.e., coarse-grained asphalt concrete (AC-25) 5 is paved above the cement-stabilized base layer, as shown in FIG. 4.