Method for estimating dynamic resilience modulus of clay roadbed

Abstract

The invention belongs to the technical field of roadbed dynamic rebound modulus research, and particularly relates to a clay roadbed dynamic rebound modulus estimation method. The method comprises the steps of selecting factors influencing the clay roadbed, carrying out a dynamic triaxial test on the clay roadbed, determining a dynamic rebound modulus value of the clay roadbed, establishing the dynamic rebound modulus estimation method for the clay roadbed and the like. The method for estimating the dynamic rebound modulus of the clay roadbed, provided by the invention, has the following beneficial effects that the dynamic rebound modulus of the clay roadbed is expected to be pushed to a new height, and scientific basis and technical support are provided for design construction, maintenance management and operation safety of a clay roadbed road in China; and particularly, scientific basis and technical support are provided for determining the dynamic rebound modulus of the clay roadbed under the condition of lack of test.

Description

Technical Field

[0001] The present invention belongs to the technical field of research on the dynamic resilient modulus of subgrades, and particularly relates to a method for predicting the dynamic resilient modulus of clay subgrades. Background Art

[0002] The magnitude of the resilient modulus of a subgrade plays an important role in the strength, stiffness, and stability of the entire road. For this reason, relevant road design codes in China regard the static resilient modulus of subgrades as an important indicator for road engineering design, construction, inspection, and maintenance. However, the actual road structure is subjected to the continuous cyclic action of vehicle dynamic loads. In this case, if the static resilient modulus is still used to characterize the performance of the road, it is obvious that the actual working state of the road structure cannot be reflected. Therefore, how to determine the influence of road self-performance such as water content, compaction degree, stress level, and vehicle dynamic characteristics such as driving speed and frequency on the dynamic resilient modulus of subgrades has become a research hotspot for road workers and a technical focus for road bearing capacity assessment.

[0003] Although domestic and foreign scholars have conducted extensive research on the static and dynamic resilient moduli of soils and achieved numerous results, most of them focus on the research on the static and dynamic resilient moduli of soils under seismic action, and there is less research on the static and dynamic resilient moduli of soils under vehicle dynamic loads; moreover, there is little research on the compaction degree of subgrade strength indicators and the compaction degree of vehicle dynamic load characteristics, and no prediction model for the dynamic resilient modulus of subgrade soil under vehicle dynamic loads has been formed, making it difficult to meet the requirements of road engineering design, construction, inspection, and maintenance. Therefore, it is necessary to propose a method for predicting the dynamic resilient modulus of clay subgrades in combination with the subgrade stress level under vehicle dynamic loads, the typical subgrade compaction degree and water content value ranges, and the vehicle dynamic load frequency range, so as to provide a basis for quickly and accurately obtaining subgrade dynamic parameters and a reference for the construction management of road engineering. Summary of the Invention

[0004] In order to solve the above problems, the purpose of the present invention is to provide a method for predicting the dynamic resilient modulus of clay subgrades.

[0005] In order to achieve the above purpose, a method for predicting the dynamic resilient modulus of clay subgrades provided by the present invention includes the following steps carried out in sequence:

[0006] 1) Select the value range of the water content of the clay subgrade;

[0007] 2) Select the value range of the compaction degree of the clay subgrade;

[0008] 3) Select the value range of the frequency of the clay subgrade;

[0009] 4) Select the value range of the confining pressure and deviator stress of the clay subgrade;

[0010] 5) Conduct dynamic triaxial tests on the clay subgrade;

[0011] 6) Determine the value of the dynamic resilient modulus of the clay subgrade;

[0012] 7) Establish a method for predicting the dynamic resilient modulus of the clay subgrade.

[0013] In step 1), the method for selecting the value range of the water content of the clay subgrade is as follows:

[0014] Determine the optimum water content of the clay subgrade according to the "Code for Highway Geotechnical Tests" (JTG E40 - 2007), and select the value range of the water content of the clay subgrade as: optimum water content, optimum water content + 2%, optimum water content - 2% according to the "Code for Design of Highway Subgrades" (JTG D30 - 2015).

[0015] In step 2), the method for selecting the value range of the compaction degree of the clay subgrade is as follows:

[0016] Determine the compaction degree of the clay subgrade according to the "Code for Design of Highway Subgrades" (JTG D30 - 2015), and select the value range of the compaction degree of the clay subgrade as: 90% - 96%.

[0017] In step 3), the method for selecting the value range of the frequency of the clay subgrade is as follows:

[0018] Establishment of vehicle-road coupling response model: Fully consider factors such as lane width and influence depth, and refer to existing research results to establish a subgrade model with a length of 23 m (x-direction), a width of 16 m (z-direction), and a depth of 9 m (y-direction); use solid45 elements to divide the grid. The grid sizes of the surface layer, base layer, cushion layer, and subgrade in the x and z directions are both 0.23 m × 0.16 m. The grid size in the y direction is half of the structural layer thickness in the surface layer, base layer, and cushion layer, and 0.3 m in the subgrade; only the displacement in the x direction is constrained at x = 0 m and x = 23 m, the displacements in the x, y, and z directions are constrained at y = 0 m, and only the displacement in the z direction is constrained at z = 0 m and z = 16 m. The parameters of the road structural layer are shown in Table 1. According to the standard vehicle type (single-axle dual-wheel heavy truck for the rear axle) specified in the "Technical Standard for Highway Engineering" (JTG B01-2014), the contact area of the wheel print of the dual wheels is equivalent to a rectangle according to the area equivalence principle, and the static load parameters under different axle loads (single-axle dual-wheel) are shown in Table 2. For the solution of the dynamic load, according to the recommendations of the International Organization for Standardization, first use the power spectral density function to characterize the pavement roughness, and use the harmonic superposition method to simulate and generate a pavement with Class A roughness; then combine the vehicle model dynamics equation, use the MPC184 element in the finite element software to simulate the vehicle body, the Mass21 element to simulate the vehicle suspension and unsprung mass, as well as the pitch and roll moments of inertia, and the Combine14 element to simulate the vehicle spring and damping elements to establish a vehicle dynamic load model considering pavement roughness; finally, based on the full method in the finite element software, perform a transient solution for the dynamic load caused by pavement roughness to obtain the vehicle loads traveling along the center line of the surface layer with Class A roughness at different speeds (5 m / s, 10 m / s, 15 m / s, 20 m / s, 25 m / s), and apply the vehicle loads to the road structure to obtain the vehicle-road coupling response model.

[0019] Table 1 Structural layer parameters

[0020]

[0021] Table 2 Load parameters

[0022]

[0023] Determine the frequency of the clay subgrade when the standard vehicle type (single-axle dual-wheel heavy truck for the rear axle) specified in the "Technical Standard for Highway Engineering" (JTG B01-2014) acts on the road structure through the vehicle-road coupling response model, and select the frequency range of the clay subgrade to be 0.5 Hz to 3 Hz.

[0024] In step 4), the method for selecting the value ranges of the confining pressure and deviator stress of the clay subgrade is as follows:

[0025] Determine the confining stress and deviator stress of the clay subgrade when the standard vehicle type (a single-axle dual-wheel load truck for the rear axle) specified in the "Technical Standard for Highway Engineering" (JTG B01-2014) acts on the road structure through a vehicle-road coupling response model. The confining stress range of the clay subgrade is 15 kPa to 60 kPa, and the deviator stress range of the clay subgrade is 30 kPa to 105 kPa.

[0026] In step 5), the method for conducting the dynamic triaxial test on the clay subgrade is as follows:

[0027] According to the "Code for Highway Geotechnical Tests" (JTG E40-2007), use the three-piece mold manual compaction molding method to prepare a cylindrical soil sample with a diameter of 61.8 mm and a height of 125 mm, and quickly seal it with plastic wrap. Conduct the dynamic triaxial test on the clay subgrade using a dynamic triaxial test instrument (maximum axial load 1 kN, maximum confining pressure 0.3 MPa, frequency range 0 Hz to 20 Hz).

[0028] In step 6), the method for determining the value of the dynamic resilient modulus of the clay subgrade is as follows:

[0029] Process the stress-strain data measured from the dynamic triaxial test according to the definition of the dynamic resilient modulus (formula (1)), and select the average value of the dynamic resilient modulus of the last 5 cyclic loadings in each loading sequence as the dynamic resilient modulus of the remolded clay subgrade.

[0030]

[0031] In the formula, E d is the dynamic resilient modulus; σ d = σ max – σ min , σ max and σ min are the maximum and minimum values of the cyclic dynamic stress respectively; ε d = ε max – ε min , ε max and ε min are the maximum and minimum values of the dynamic strain under the corresponding cyclic dynamic stress respectively.

[0032] In step 7), the method for establishing a prediction method for the dynamic resilient modulus of the clay subgrade is as follows:

[0033] Select the widely used power exponent function of the dynamic resilient modulus (formula (2)) to establish a prediction method for the dynamic resilient modulus of the clay subgrade.

[0034]

[0035] In the formula, σ mis the deviator stress; both k1 and k2 are regression coefficients related to water content, compaction degree, frequency, and confining pressure.

[0036] First, establish the regression curve relationships between k1 and k2 with water content, compaction degree, frequency, and confining pressure. Then, based on the above regression curve relationships, establish the regression curve relationships of k1 and k2 based on water content, compaction degree, frequency, and confining pressure (Formulas (3) and (4)). Finally, substitute Formulas (3) and (4) into Formula (2) to obtain a method for predicting the dynamic resilient modulus of a clay subgrade.

[0037] k1 = (-0.0666ω + 0.0636K - 0.0998f - 3.5014)σ + (-19.2200ω + 6.0553K + 15.9670f - 98.8288) (3)

[0038] k2 = (0.0001f - 0.0010)σ + (0.0071ω + 0.0017K + 0.0158f - 0.4569) (4)

[0039] In the formula, ω is the water content, K is the compaction degree, f is the frequency, and σ is the confining pressure.

[0040] The method for predicting the dynamic resilient modulus of a clay subgrade provided by the present invention has the following beneficial effects: It is expected to push the dynamic resilient modulus of the clay subgrade to a new height, providing a scientific basis and technical support for the design, construction, maintenance management, and operation safety of clay subgrade roads in China, especially providing a scientific basis and technical support for determining the dynamic resilient modulus of clay subgrades under the lack of test conditions. Description of the Drawings

[0041] Figure 1 is a flow chart of a method for predicting the dynamic resilient modulus of a clay subgrade provided by the present invention. Detailed Embodiments

[0042] The present invention will be described in detail below with reference to the drawings and specific embodiments.

[0043] As Figure 1 shown, a method for predicting the dynamic resilient modulus of a clay subgrade provided by the present invention includes the following steps carried out in sequence:

[0044] 1) Select the value range of the water content of the clay subgrade;

[0045] Determine the optimum water content of the clay subgrade according to the "Code for Highway Geotechnical Tests" JTG E40 - 2007, and select the value range of the water content of the clay subgrade according to the "Code for Highway Subgrade Design" JTG D30 - 2015 as: optimum water content, optimum water content + 2%, optimum water content - 2%.

[0046] 2) Select the range of the compaction degree of the clay subgrade;

[0047] Determine the compaction degree of the clay subgrade according to the "Code for Highway Subgrade Design" JTG D30 - 2015, and select the range of the compaction degree of the clay subgrade as: 90% - 96%.

[0048] 3) Select the range of the frequency of the clay subgrade;

[0049] Establishment of the vehicle - road coupling response model: Fully consider factors such as lane width and influence depth, and refer to existing research results to establish a subgrade model with a length of 23 m in the x - direction, a width of 16 m in the z - direction, and a depth of 9 m in the y - direction; use the solid45 element to divide the mesh. The mesh sizes in the x and z directions of the surface layer, base course, cushion layer, and subgrade are all 0.23 m×0.16 m. The mesh size in the y - direction in the surface layer, base course, and cushion layer is half of the structural layer thickness, and in the subgrade is 0.3 m; only the displacement in the x - direction is constrained at x = 0 m and x = 23 m, the displacements in the x, y, and z directions are constrained at y = 0 m, and only the displacement in the z - direction is constrained at z = 0 m and z = 16 m. The parameters of the road structural layer are shown in Table 1. According to the standard vehicle type stipulated in the "Technical Standard for Highway Engineering" JTG B01 - 2014, that is, a single - axle dual - wheel load truck for the rear axle, the contact area of the double - wheel print is equivalent to a rectangle according to the area equivalent principle, and the static load parameters under different axle loads, that is, single - axle dual - wheels, are shown in Table 2. For the solution of the dynamic load, according to the recommendations of the International Standards Association, first use the power spectral density function to characterize the pavement evenness, and use the harmonic superposition method to simulate and generate a pavement with Class A evenness; then combine the vehicle model dynamics equation, use the MPC184 element in the finite - element software to simulate the vehicle body, the Mass21 element to simulate the vehicle suspension and unsprung mass, as well as the pitch and roll moments of inertia, and the Combine14 element to simulate the vehicle spring and damping elements to establish a vehicle dynamic load model considering pavement evenness; finally, based on the full method in the finite - element software, perform a transient solution for the dynamic load caused by pavement evenness, obtain the vehicle loads traveling along the center line of the surface layer at different speeds of 5 m / s, 10 m / s, 15 m / s, 20 m / s, and 25 m / s on a pavement with Class A evenness, and apply the vehicle loads to the road structure to obtain the vehicle - road coupling response model.

[0050] Table 1 Structural layer parameters

[0051]

[0052] Table 2 Load parameters

[0053]

[0054] Determine the frequency of the clay subgrade when the standard vehicle type specified in the Technical Standard for Highway Engineering JTG B01-2014, i.e., a single-axle dual-wheel load truck, acts on the road structure through a vehicle-road coupling response model. The frequency range of the clay subgrade is selected as 0.5 Hz to 3 Hz.

[0055] 4) Select the value range of the confining pressure and deviator stress of the clay subgrade;

[0056] Determine the confining pressure stress and deviator stress of the clay subgrade when the standard vehicle type specified in the Technical Standard for Highway Engineering JTG B01-2014, i.e., a single-axle dual-wheel load truck, acts on the road structure through a vehicle-road coupling response model. The value range of the confining pressure of the clay subgrade is 15 kPa to 60 kPa, and the value range of the deviator stress of the clay subgrade is 30 kPa to 105 kPa.

[0057] 5) Conduct dynamic triaxial tests on the clay subgrade;

[0058] According to the Highway Geotechnical Test Regulations JTG E40-2007, use the three-piece mold manual compaction forming method to prepare a cylindrical soil sample with a diameter of 61.8 mm and a height of 125 mm, and quickly seal it with plastic wrap. Conduct dynamic triaxial tests on the clay subgrade using a dynamic triaxial test instrument (maximum axial load 1 kN, maximum confining pressure 0.3 MPa, frequency range 0 Hz to 20 Hz).

[0059] 6) Determine the value of the dynamic resilient modulus of the clay subgrade;

[0060] Process the stress-strain data measured from the dynamic triaxial tests according to the definition formula (1) of the dynamic resilient modulus, and select the average value of the dynamic resilient modulus of the last 5 cyclic loadings in each loading sequence as the dynamic resilient modulus of the remolded clay subgrade.

[0061]

[0062] In the formula, E d is the dynamic resilient modulus; σ d = σ max – σ min , σ max and σ min are the maximum and minimum values of the cyclic dynamic stress respectively; ε d = ε max – ε min , ε max and ε min are the maximum and minimum values of the dynamic strain under the corresponding cyclic dynamic stress respectively.

[0063] 7) Establish a method for predicting the dynamic resilient modulus of the clay subgrade;

[0064] Select the widely used power exponent function formula (2) of dynamic resilient modulus to establish a prediction method for the dynamic resilient modulus of clay subgrade.

[0065]

[0066] In the formula, σ m is the deviator stress; both k1 and k2 are regression coefficients related to water content, compaction degree, frequency, and confining pressure.

[0067] First, establish the regression curve relationship between k1 and k2 with water content, compaction degree, frequency, and confining pressure. Then, based on the above regression curve relationship, establish the regression curve relationship formulas (3) and (4) of k1 and k2 based on water content, compaction degree, frequency, and confining pressure. Finally, substitute formulas (3) and (4) into formula (2) to obtain a prediction method for the dynamic resilient modulus of clay subgrade.

[0068] k1 = (-0.0666ω + 0.0636K - 0.0998f - 3.5014)σ + (-19.2200ω + 6.0553K + 15.9670f - 98.8288) (3)

[0069] k2 = (0.0001f - 0.0010)σ + (0.0071ω + 0.0017K + 0.0158f - 0.4569) (4)

[0070] In the formula, ω is the water content, K is the compaction degree, f is the frequency, and σ is the confining pressure.

Claims

1. A method for estimating dynamic elastic modulus of clay roadbed, characterized in that: The method for estimating the dynamic elastic modulus of a clay roadbed comprises the following steps performed in sequence: Step 1, setting the influencing factors of the dynamic rebound modulus of clay roadbed; Step 2: Conduct dynamic triaxial test on clay roadbed; Step 3: Determine the dynamic rebound modulus value of the clay roadbed; according to the definition formula of dynamic rebound modulus The stress-strain data measured by the dynamic triaxial test were processed, and the average value of the dynamic rebound modulus after cyclic loading in each loading sequence was selected as the dynamic rebound modulus of the reshaped clay roadbed. In the formula, E d is the dynamic rebound modulus; σ d =σ max –σ min , σ max and σ min are the maximum and minimum values ​​of cyclic dynamic stress, respectively; ε d =ε max –ε min , ε max and ε min are the maximum and minimum values ​​of dynamic strain under the corresponding cyclic dynamic stress, respectively; The stress-strain data measured by the dynamic triaxial test were processed according to the definition formula of the dynamic rebound modulus, and the average value of the dynamic rebound modulus of multiple cycles of loading in each loading sequence was selected as the dynamic rebound modulus of the reshaped clay roadbed. Step 4: According to the dynamic rebound modulus power exponential function formula The dynamic rebound modulus estimation method of clay roadbed is obtained, where σm is the deviatoric stress; k1 and k2 are regression coefficients related to the influencing factors of the dynamic rebound modulus of clay roadbed. Firstly, the regression curve relationship parameters between k1 and k2 and the influencing factors of the dynamic rebound modulus of clay-containing roadbed are established; Secondly, based on the above regression curve relationship, the k1 and k2 regression curve relationship based on the influencing factors of the dynamic rebound modulus of clay roadbed is established. The calculations show that: k1=(-0.0666ω+0.0636K-0.0998f-3.5014)σ+(-19.2200ω+6.0553K+15.9670f-98.8288) k2=(0.0001f-0.0010)σ+(0.0071ω+0.0017K+0.0158f-0.4569) Where ω is the water content, K is the degree of compaction, f is the frequency, and σ is the confining pressure.

2. The method for estimating the dynamic rebound modulus of a clay roadbed according to claim 1, characterized in that: The factors affecting the dynamic rebound modulus of the clay roadbed in step 1 include: 1) The range of values ​​for moisture content of clay roadbed; 2) The range of values ​​for compaction degree of clay roadbed; 3) The range of values ​​for frequency of clay roadbed; 4) The range of values ​​for confining pressure and deviator stress of clay roadbed.

3. The method for estimating the dynamic rebound modulus of a clay roadbed according to claim 2, wherein: The moisture content range of the clay roadbed is set as: moisture content, moisture content + 2%, moisture content - 2%; the compaction degree range of the clay roadbed is 90% to 96%; the frequency range of the clay roadbed is 0.5Hz to 3Hz; the confining pressure range of the clay roadbed is 15kPa to 60kPa, and the deviatoric stress range is 30kPa to 105kPa.

4. The method for estimating the dynamic rebound modulus of a clay roadbed according to claim 2, wherein: The method for determining the frequency range of clay roadbed is: a. Solid45 units are used to divide the mesh in the x-direction length of 23m, the z-direction width of 16m, and the y-direction depth of 9m. The mesh sizes of the surface layer, base layer, cushion layer, and roadbed in the x and z directions are 0.23m×0.16m. The mesh size in the y direction is half the thickness of the structural layer in the surface layer, base layer, and cushion layer, and 0.3m in the roadbed. Only the x-direction displacement is constrained at x=0m and x=23m, the x, y, and z-direction displacements are constrained at y=0m, and only the z-direction displacement is constrained at z=0m and z=16m. A vehicle dynamic load model considering the road surface flatness is established; b. Based on the complete method in the finite element software, the dynamic load caused by the road surface roughness is transiently solved to obtain the vehicle load of the vehicle traveling along the center line of the surface layer at Class A roughness at different speeds of 5m / s, 10m / s, 15m / s, 20m / s, and 25m / s. The vehicle load is applied to the road structure to obtain the vehicle-road coupling response model; c. Determine the frequency range of clay roadbed to be 0.5Hz~3Hz.

5. The method for estimating the dynamic rebound modulus of a clay roadbed according to claim 2, wherein: A three-petal mold artificial compaction molding method was used to prepare a cylindrical soil sample with a diameter of 61.8 mm and a height of 125 mm. The sample was quickly sealed with plastic wrap and a dynamic triaxial test was carried out on the clay roadbed using a dynamic triaxial tester with a maximum axial load of 1 kN, a maximum confining pressure of 0.3 MPa, and a frequency range of 0 Hz to 20 Hz.

Images