# Study on Deformation Characteristics of Extended Highway in Operation Period

Authors: Pengfei Zhou; Lizhuang Cui; Xuesen Zhang; Chuanyi Ma; Jian Liu; Yanni Shao; Gaohang Lv; Quanyi Xie
Journal: Advances in Civil Engineering
 (2022)

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## Abstract

Highway widening has become an effective way to improve the carrying capacity of existing expressways. However, assume that the differential settlement between the new and the old subgrades is not controlled. In that case, it will lead to longitudinal cracks on the pavement, which will seriously affect the safety of vehicles. In this study, the variations of elastic modulus and dynamic elastic modulus of new and old subgrades under traffic load were studied by tests. A hyperbolic model of dynamic elastic modulus increasing with strain is proposed. The numerical calculation model of new and old subgrades under traffic load is established. The deformation characteristics of new and old subgrades without treatment measures and setting up geogrid and geocell are studied. The main conclusions are as follows: (1) with the increase of traffic load and subgrade depth, the elastic modulus changes significantly in the early stage and small in the later stage. (2) Under the condition of no treatment measures, the vertical and horizontal deformation of the subgrade surface show a trend of increasing and then decreasing with the distance from the center line of the subgrade. (3) Setting geogrid and geocell can effectively reduce the differential settlement of the old and new subgrades. (4) The effect of setting geogrid to reduce the differential settlement of old and new subgrades is better than that of setting geogrid.


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## Body

## 1. Introduction

Expressways have become the main infrastructure for inter-regional transportation due to their advantages, such as fast speed, high efficiency, and large carrying capacity. With economic development and increasing traffic volume, the number of lanes on some expressways can no longer meet the demand for transportation [1–7]. Highway widening has become one of the effective solutions. The old expressway subgrade has undergone long-term traffic operation, and the compression deformation has been stable [8]. The new subgrade will still undergo large compression deformation under the action of traffic load [9–11]. If the differential settlement between the new and old subgrades is not controlled, it will cause longitudinal cracks on the road surface, affecting vehicles’ safety seriously [12].The dynamic triaxial test has become one of the main methods to research the dynamic deformation characteristics of the soil [13–15]. The dynamic characteristics of subgrade soil structure have been studied in order to meet the design requirements of complex practical engineering [16–18]. In the early stage, the experimental study of dynamic characteristics was mainly based on seismic load, characterized by high confining pressure, significant strain, and few cycles [19, 20]. Experimental research has been carried out on the deformation characteristics under the traffic load by using dynamic triaxial tests and resonance column tests [21–24]. However, the existing research still has some shortcomings in restoring the operation state of the old and new subgrades, and the performance comparison of the two subgrades has not been achieved. Numerical calculation has been carried out to research the dynamic response characteristics of subgrade under the traffic load by relying on actual engineering [25–27]. Moreover, under traffic load, the differential deformation rule of the new and old subgrades of the Yellow River flooding area has not been systematically revealed, which seriously hinders the progress of the Yellow River extension expressway reconstruction project.Therefore, the mechanical properties of subgrade filling soil in the Yellow River extension are studied in this study based on the Bin-Lai Expressway expansion project in the Yellow River extension. The traffic load action in the Yellow River extension is quantified. The dynamic triaxial test is carried out to study the dynamic characteristics of new and old subgrades soil in the Yellow River extension. The numerical calculation model of dynamic settlement of new and old subgrades under traffic load is established. The differential deformation rule of new and old subgrades is studied, providing theoretical and data support for highway extension design in the Yellow River extension.


## 2. Laboratory Experiment

### 2.1. Testing Device

The Eldyn dynamic triaxial apparatus is used as the test device, as shown in Figure1. The equipment can provide the cyclic loading mode of force control or displacement control. The maximum axial force is 5 kN, the maximum loading frequency is 5 Hz, and the maximum confining pressure is 1 MPa. The data acquisition system of the equipment can collect pore water pressure, strain, axial force, back pressure, and back pressure volume. The accuracy of pore water pressure and back pressure sensor is 1 kPa, the accuracy of back pressure volume is 1 mm3, and the accuracy of axial force is 1 N.Figure 1
Eldyn dynamic triaxial apparatus.


### 2.2. Test Materials

In this test, a representative dynamic triaxial test of subgrade soil samples was selected. The soil used in the test was taken from the extension project from Zibo West to the Laiwu section of the Bin-Lai Expressway. The optimum water content was obtained by the Proctor compaction. The liquid plastic limit was determined by the liquid plastic limit tester. Soil samples’ cohesion and internal friction angle were measured by the triaxial compression test. The soil properties of the testing samples are listed in Table1.Table 1
Basic material parameters of subgrade soil.
Maximum dry density (g/cm3)Liquid limit (%)Plastic limit (%)Plasticity indexOptimum water content (%)Cohesion (kPa)Internal friction angle (°)1.7636.9618.208.717.034.5931


### 2.3. Experimental Conditions

The test conditions set for this test is listed in Table2. First, the dynamic characteristics of subgrade soil at different depths and vehicles were obtained by dynamic loading tests under conditions I, II, and III. After completing the dynamic loading test, the sample was used as the old subgrades for subsequent mechanical characteristics research. Then, the elastic modulus, shear modulus, internal friction angle, and cohesion were tested for conditions I, II, III, and IV. Among them, the samples with stable deformation after the dynamic loading test are regarded as old subgrade, the nine samples in test conditions I, II, and III. The newly prepared samples without dynamic cycle were considered the new subgrade soil, namely, the three samples in test condition IV.Table 2
Test conditions.
Working conditionBorrow depth (m)Confining pressure (kPa)Wheel axle weight (kN)Dynamic stress (kPa)Frequency (Hz)I-1——504.2—I-20.51413011.0—I-3——24020.2—II-1——501.2—II-21.5241303.21II-3——2406.0—III-1——500.6—III-22.5341301.5—III-3——2503.0—


### 2.4. Experiment Procedure

(1)
Pretreatment of Soil Samples. The soil samples were dried, crushed, and passed through a 2 mm screen. After screening, add water to the soil sample to the optimal moisture content and seal it in a plastic bag for 24 hours.(2)
Triaxial Sample Making. Coat a vaseline layer evenly on the inner wall of sample cylinder (50 mm × 100 mm). Then, the prepared soil sample is smashed into the compacting instrument in five layers, and vacuum saturation is conducted on the prepared triaxial sample.(3)
Saturation Test of a Triaxial Sample. Install the sample on the base of the triaxial test instrument. The ratio of pore pressure increment to confining pressure increment after applying confining pressure is taken as the evaluation index of saturation. If the saturation reaches more than 0.95, the triaxial test is directly started; if the saturation is less than 0.95, the backpressure is applied on the top of the sample until the saturation reaches 0.95.(4)
Sample Consolidation. Isobaric consolidation is adopted in this test, and isobaric lateral and axial pressures are applied to the samples. The standard for completion of the consolidation stage is that the change of consolidation displacement does not exceed 0.1 cm3 within 1 h.(5)
Application of Dynamic Load to the Sample. The dynamic load is applied to the sample according to the test design condition, and the variations of soil deformation, pore pressure, and other parameters are monitored.(6)
After the sample’s axial strain and pore pressure remain stable under dynamic load, the sample’s shear and elastic modulus are tested under the corresponding state.


### 2.5. Dynamic Modulus Attenuation Rule

The dynamic stress-dynamic strain curve of the soil can be fitted to a hyperbolic type, which can be expressed by the following equation:(1)σd=εdb+aεd,where σd is dynamic stress and εd is dynamic strain.According to equation (1), dynamic elastic modulus can also be expressed as follows:(2)Ed=1b+aεd.It can be seen from equation (2) that the change curve of 1/Ed−εd can be fitted to a linear. In order to facilitate data sorting and analysis, the maximum dynamic modulus Edmax is introduced here to normalize the dynamic modulus Ed, which is as follows:(3)EdmaxEd=1+abεd.During the test process, under the action of dynamic loads at each depth, three samples were prepared for each working condition, and the same test conditions (the same confining pressure and dynamic stress) were applied. The scatter plots of three samples’ test results were reflected in the coordinate system. The relationship betweenEdmax/Ed and εd is obtained by linear fitting equation (equation (3)). Furthermore, the dynamic modulus-dynamic strain fitting curve drawn is shown in Figure 2.Figure 2
Dynamic modulus ratio-dynamic strain fitting curve. (a)H = 0.5 m, D = 4.2 kPa. (b) H = 0.5 m, D = 11.0 kPa. (c) H = 0.5 m, D = 20.2 kPa. (d) H = 1.5 m, D = 1.2 kPa. (e) H = 1.5 m, D = 3.2 kPa. (f) H = 1.5 m, D = 6.0 kPa. (g) H = 2.5 m, D = 0.6 kPa. (h) H = 2.5 m, D = 1.5 kPa. (i) H = 2.5 m, D = 3.0 kPa.
(a)(b)(c)(d)(e)(f)(g)(h)(i)It can be seen from the figure that the relationship betweenEdmax/Ed and εd is roughly in line with the linear fitting relationship, and the fitting variance is around 0.95, indicating that the fitting relationship is reliable. The test results are subject to human interference factors, such as soil water addition, sample compaction, vacuum saturation, and some discrete data generated by individual working conditions. Still, they do not affect the overall trend of change. Strictly speaking, the intercept should be 1. However, Edmax is obtained by the mathematical limit idea and is not an accurate value, so the straight line is intercepted on the vertical axis. The distance floats around the value 1, with a slight deviation; the slope of the straight line expressed as a/b is Edmax/σdmax, and the change of the slope is affected by the magnitude of the dynamic load, as listed in Table 3. The axle load increased from 50 kN to 240 kN, the slope at a depth of 0.5 m was reduced from 31.9 to 20.1, and the slope at a 2.5 m depth decreased from 41.3 to 37.1. The larger the dynamic load of subgrade soil is, the smaller the slope of the fitting straight line is. The load affects the subgrade surface with a depth of less than 0.5 m. With the increase of depth, the slope of the straight line is less affected by the dynamic load.Table 3
Slope (a/b).
Depth (m)Axle load 50 kNAxle load 130 kNAxle load 240 kN0.531.928.820.11.538.336.035.82.541.339.237.1


### 2.6. Result Analysis of Mechanical Characteristics of New and Old Subgrades

In this study, samples with stable deformation under dynamic load were used as old subgrade to test elastic modulus and shear modulus. It can be seen from Figures3 and 4 that the distribution rule of elastic modulus and shear modulus of new and old highway subgrades is the same. At each depth, the modulus of the old subgrade after experiencing the different traffic cycle loads increases to different degrees compared with that of the new subgrade. The largest is the elastic and shear modulus of the old subgrade subjected to load Pn = 50 kN. As the traffic load increases, the modulus of the old subgrade decreases. Under the same traffic load, the elastic modulus and shear modulus of the new and old subgrades both increase in varying degrees with increasing depth. It can be seen that whether it is with the increase of the traffic load or the increase of the depth, the modulus changes show a trend of significant changes in the early period and small changes in the later period.Figure 3
Elastic modulus comparison.Figure 4
Shear modulus comparison.


## 2.1. Testing Device

The Eldyn dynamic triaxial apparatus is used as the test device, as shown in Figure1. The equipment can provide the cyclic loading mode of force control or displacement control. The maximum axial force is 5 kN, the maximum loading frequency is 5 Hz, and the maximum confining pressure is 1 MPa. The data acquisition system of the equipment can collect pore water pressure, strain, axial force, back pressure, and back pressure volume. The accuracy of pore water pressure and back pressure sensor is 1 kPa, the accuracy of back pressure volume is 1 mm3, and the accuracy of axial force is 1 N.Figure 1
Eldyn dynamic triaxial apparatus.


## 2.2. Test Materials

In this test, a representative dynamic triaxial test of subgrade soil samples was selected. The soil used in the test was taken from the extension project from Zibo West to the Laiwu section of the Bin-Lai Expressway. The optimum water content was obtained by the Proctor compaction. The liquid plastic limit was determined by the liquid plastic limit tester. Soil samples’ cohesion and internal friction angle were measured by the triaxial compression test. The soil properties of the testing samples are listed in Table1.Table 1
Basic material parameters of subgrade soil.
Maximum dry density (g/cm3)Liquid limit (%)Plastic limit (%)Plasticity indexOptimum water content (%)Cohesion (kPa)Internal friction angle (°)1.7636.9618.208.717.034.5931


## 2.3. Experimental Conditions

The test conditions set for this test is listed in Table2. First, the dynamic characteristics of subgrade soil at different depths and vehicles were obtained by dynamic loading tests under conditions I, II, and III. After completing the dynamic loading test, the sample was used as the old subgrades for subsequent mechanical characteristics research. Then, the elastic modulus, shear modulus, internal friction angle, and cohesion were tested for conditions I, II, III, and IV. Among them, the samples with stable deformation after the dynamic loading test are regarded as old subgrade, the nine samples in test conditions I, II, and III. The newly prepared samples without dynamic cycle were considered the new subgrade soil, namely, the three samples in test condition IV.Table 2
Test conditions.
Working conditionBorrow depth (m)Confining pressure (kPa)Wheel axle weight (kN)Dynamic stress (kPa)Frequency (Hz)I-1——504.2—I-20.51413011.0—I-3——24020.2—II-1——501.2—II-21.5241303.21II-3——2406.0—III-1——500.6—III-22.5341301.5—III-3——2503.0—


## 2.4. Experiment Procedure

(1)
Pretreatment of Soil Samples. The soil samples were dried, crushed, and passed through a 2 mm screen. After screening, add water to the soil sample to the optimal moisture content and seal it in a plastic bag for 24 hours.(2)
Triaxial Sample Making. Coat a vaseline layer evenly on the inner wall of sample cylinder (50 mm × 100 mm). Then, the prepared soil sample is smashed into the compacting instrument in five layers, and vacuum saturation is conducted on the prepared triaxial sample.(3)
Saturation Test of a Triaxial Sample. Install the sample on the base of the triaxial test instrument. The ratio of pore pressure increment to confining pressure increment after applying confining pressure is taken as the evaluation index of saturation. If the saturation reaches more than 0.95, the triaxial test is directly started; if the saturation is less than 0.95, the backpressure is applied on the top of the sample until the saturation reaches 0.95.(4)
Sample Consolidation. Isobaric consolidation is adopted in this test, and isobaric lateral and axial pressures are applied to the samples. The standard for completion of the consolidation stage is that the change of consolidation displacement does not exceed 0.1 cm3 within 1 h.(5)
Application of Dynamic Load to the Sample. The dynamic load is applied to the sample according to the test design condition, and the variations of soil deformation, pore pressure, and other parameters are monitored.(6)
After the sample’s axial strain and pore pressure remain stable under dynamic load, the sample’s shear and elastic modulus are tested under the corresponding state.


## 2.5. Dynamic Modulus Attenuation Rule

The dynamic stress-dynamic strain curve of the soil can be fitted to a hyperbolic type, which can be expressed by the following equation:(1)σd=εdb+aεd,where σd is dynamic stress and εd is dynamic strain.According to equation (1), dynamic elastic modulus can also be expressed as follows:(2)Ed=1b+aεd.It can be seen from equation (2) that the change curve of 1/Ed−εd can be fitted to a linear. In order to facilitate data sorting and analysis, the maximum dynamic modulus Edmax is introduced here to normalize the dynamic modulus Ed, which is as follows:(3)EdmaxEd=1+abεd.During the test process, under the action of dynamic loads at each depth, three samples were prepared for each working condition, and the same test conditions (the same confining pressure and dynamic stress) were applied. The scatter plots of three samples’ test results were reflected in the coordinate system. The relationship betweenEdmax/Ed and εd is obtained by linear fitting equation (equation (3)). Furthermore, the dynamic modulus-dynamic strain fitting curve drawn is shown in Figure 2.Figure 2
Dynamic modulus ratio-dynamic strain fitting curve. (a)H = 0.5 m, D = 4.2 kPa. (b) H = 0.5 m, D = 11.0 kPa. (c) H = 0.5 m, D = 20.2 kPa. (d) H = 1.5 m, D = 1.2 kPa. (e) H = 1.5 m, D = 3.2 kPa. (f) H = 1.5 m, D = 6.0 kPa. (g) H = 2.5 m, D = 0.6 kPa. (h) H = 2.5 m, D = 1.5 kPa. (i) H = 2.5 m, D = 3.0 kPa.
(a)(b)(c)(d)(e)(f)(g)(h)(i)It can be seen from the figure that the relationship betweenEdmax/Ed and εd is roughly in line with the linear fitting relationship, and the fitting variance is around 0.95, indicating that the fitting relationship is reliable. The test results are subject to human interference factors, such as soil water addition, sample compaction, vacuum saturation, and some discrete data generated by individual working conditions. Still, they do not affect the overall trend of change. Strictly speaking, the intercept should be 1. However, Edmax is obtained by the mathematical limit idea and is not an accurate value, so the straight line is intercepted on the vertical axis. The distance floats around the value 1, with a slight deviation; the slope of the straight line expressed as a/b is Edmax/σdmax, and the change of the slope is affected by the magnitude of the dynamic load, as listed in Table 3. The axle load increased from 50 kN to 240 kN, the slope at a depth of 0.5 m was reduced from 31.9 to 20.1, and the slope at a 2.5 m depth decreased from 41.3 to 37.1. The larger the dynamic load of subgrade soil is, the smaller the slope of the fitting straight line is. The load affects the subgrade surface with a depth of less than 0.5 m. With the increase of depth, the slope of the straight line is less affected by the dynamic load.Table 3
Slope (a/b).
Depth (m)Axle load 50 kNAxle load 130 kNAxle load 240 kN0.531.928.820.11.538.336.035.82.541.339.237.1


## 2.6. Result Analysis of Mechanical Characteristics of New and Old Subgrades

In this study, samples with stable deformation under dynamic load were used as old subgrade to test elastic modulus and shear modulus. It can be seen from Figures3 and 4 that the distribution rule of elastic modulus and shear modulus of new and old highway subgrades is the same. At each depth, the modulus of the old subgrade after experiencing the different traffic cycle loads increases to different degrees compared with that of the new subgrade. The largest is the elastic and shear modulus of the old subgrade subjected to load Pn = 50 kN. As the traffic load increases, the modulus of the old subgrade decreases. Under the same traffic load, the elastic modulus and shear modulus of the new and old subgrades both increase in varying degrees with increasing depth. It can be seen that whether it is with the increase of the traffic load or the increase of the depth, the modulus changes show a trend of significant changes in the early period and small changes in the later period.Figure 3
Elastic modulus comparison.Figure 4
Shear modulus comparison.


## 3. Numerical Calculation Analysis

### 3.1. Numerical Calculation Model

Bin-Lai Expressway in Shandong province was used as the numerical simulation object in this study. Bin-Lai Expressway is the first north-south expressway in Shandong that runs through mountainous areas. With the rapid development of society, there are more and more traffic volume and full load transportation phenomena on expressways. The number of highway lanes can no longer meet the demand for transportation, and the original roads must be widened. Bin-Lai Expressway plans to expand the original two-way four-lane road from Zibo West to Laiwu section of the Bin-Lai Expressway into a two-way eight-lane road by widening and building on both sides. After the section is widened, the entire width of the road is set to 42 m, and the driving speed is 120 km/h. The standard cross-section of integrated subgrade widened on both sides is shown in Figure4.This model takes advantage of the symmetry of the widened subgrade on both sides, taking the center of the old subgrade as the axis of symmetry to take half of the subgrade for simulation analysis. The calculated size of the subgrade is as follows: width × depth: 21 m × 3 m, of which the size of the old subgrade is 9.75 m × 3 m, the size of the new subgrade is 11.75 m × 3 m, the old and new subgrades are equally filled in three layers, and the subgrade slope ratio is 1 : 1.5; the calculated foundation size is as follows: width × depth: 35.5 m × 14 m, and the model adopts three-dimensional elements and 30,602 nodes. The distribution of the soil layers of the new and old subgrades is shown in Figure5.Figure 5
Schematic diagram of new and old subgrade overlapping.The material parameters used in ABAQUS numerical simulation were determined by triaxial tests. The elastic modulus, Poisson’s ratio, cohesion, and internal friction angle at different depths of the new and old subgrades were obtained from previous tests. The material parameters of each soil layer are listed in Table4.Table 4
Material parameters of each soil layer.
Soil layer distributionTraffic load (kN)Density (kg/m3)Elastic modulus (MPa)Shear modulus (MPa)Poisson’s ratioCohesion (kPa)Internal friction angle (°)Old subgrade ①——34.312.50.365.88930Old subgrade ②——38.214.30.345.88930Old subgrade ③50176039.214.70.335.88930New subgrade ④100—22.58.40.334.58531New subgrade ⑤200—26.19.70.344.58531New subgrade ⑥——29.310.60.364.58531Foundation ⑦—184035.013.50.305.035


### 3.2. Numerical Calculation Conditions

Three types of test conditions have been set in this study, as listed in Table5. The condition without treatment measures is mainly to research the differential deformation characteristics of the new and old subgrades without any reinforcement measures. The two working conditions of geogrid and geocell mainly analyze the effect of geogrid and geocell on reducing the differential deformation of the old and new subgrades. The geogrid is used to research the deformation characteristics of the new and old subgrades when the 1st, 3rd, 5th, and 6th floors are installed, as shown in Figure 6. The geocell is used to research the deformation characteristics of new and old subgrades when the 1st, 2nd, and 3rd floors are installed, as shown in Figure 7. It is noted that the effect of geocell and geogrid on controlling the deformation of new subgrade is studied through numerical simulation, and the reinforcement method suitable for the expansion project of the low subgrade in the plain area (i.e., subgrade with height less than 3 m) is researched, which provides data support for the subgrade expansion project.Table 5
Numerical calculation conditions.
ConditionsTreatment measuresLayer numbersINo treatment measures—IIGeogrid1, 3, 5, 6IIIGeocell1, 2, 3Figure 6
Geogrid.Figure 7
Geocell.


## 3.1. Numerical Calculation Model

Bin-Lai Expressway in Shandong province was used as the numerical simulation object in this study. Bin-Lai Expressway is the first north-south expressway in Shandong that runs through mountainous areas. With the rapid development of society, there are more and more traffic volume and full load transportation phenomena on expressways. The number of highway lanes can no longer meet the demand for transportation, and the original roads must be widened. Bin-Lai Expressway plans to expand the original two-way four-lane road from Zibo West to Laiwu section of the Bin-Lai Expressway into a two-way eight-lane road by widening and building on both sides. After the section is widened, the entire width of the road is set to 42 m, and the driving speed is 120 km/h. The standard cross-section of integrated subgrade widened on both sides is shown in Figure4.This model takes advantage of the symmetry of the widened subgrade on both sides, taking the center of the old subgrade as the axis of symmetry to take half of the subgrade for simulation analysis. The calculated size of the subgrade is as follows: width × depth: 21 m × 3 m, of which the size of the old subgrade is 9.75 m × 3 m, the size of the new subgrade is 11.75 m × 3 m, the old and new subgrades are equally filled in three layers, and the subgrade slope ratio is 1 : 1.5; the calculated foundation size is as follows: width × depth: 35.5 m × 14 m, and the model adopts three-dimensional elements and 30,602 nodes. The distribution of the soil layers of the new and old subgrades is shown in Figure5.Figure 5
Schematic diagram of new and old subgrade overlapping.The material parameters used in ABAQUS numerical simulation were determined by triaxial tests. The elastic modulus, Poisson’s ratio, cohesion, and internal friction angle at different depths of the new and old subgrades were obtained from previous tests. The material parameters of each soil layer are listed in Table4.Table 4
Material parameters of each soil layer.
Soil layer distributionTraffic load (kN)Density (kg/m3)Elastic modulus (MPa)Shear modulus (MPa)Poisson’s ratioCohesion (kPa)Internal friction angle (°)Old subgrade ①——34.312.50.365.88930Old subgrade ②——38.214.30.345.88930Old subgrade ③50176039.214.70.335.88930New subgrade ④100—22.58.40.334.58531New subgrade ⑤200—26.19.70.344.58531New subgrade ⑥——29.310.60.364.58531Foundation ⑦—184035.013.50.305.035


## 3.2. Numerical Calculation Conditions

Three types of test conditions have been set in this study, as listed in Table5. The condition without treatment measures is mainly to research the differential deformation characteristics of the new and old subgrades without any reinforcement measures. The two working conditions of geogrid and geocell mainly analyze the effect of geogrid and geocell on reducing the differential deformation of the old and new subgrades. The geogrid is used to research the deformation characteristics of the new and old subgrades when the 1st, 3rd, 5th, and 6th floors are installed, as shown in Figure 6. The geocell is used to research the deformation characteristics of new and old subgrades when the 1st, 2nd, and 3rd floors are installed, as shown in Figure 7. It is noted that the effect of geocell and geogrid on controlling the deformation of new subgrade is studied through numerical simulation, and the reinforcement method suitable for the expansion project of the low subgrade in the plain area (i.e., subgrade with height less than 3 m) is researched, which provides data support for the subgrade expansion project.Table 5
Numerical calculation conditions.
ConditionsTreatment measuresLayer numbersINo treatment measures—IIGeogrid1, 3, 5, 6IIIGeocell1, 2, 3Figure 6
Geogrid.Figure 7
Geocell.


## 4. Discussion of Simulation Results of No Treatment Measures

In this study, the differential settlement between the old and new subgrades has been studied for the expansion project of the low subgrade (subgrade height less than 3 m) in the Yellow River Plain. Bin-Lai Expressway in Shandong province was used as the numerical simulation object.


### 4.1. Vertical Displacement

As shown in Figure8, the consolidation trend of the settlement curve increases first and then decreases. In the old and new subgrade models, the minimum and maximum vertical displacement of road surface are at the center of the old subgrade and the central pavement of the new subgrade, respectively, and the maximum settlement difference is about 0.86 cm. The model elements below the centerline of the new road foundation and the old subgrade are taken, and the variation rule of their vertical displacement is shown in Figure 9. The settlement curves of the new and old subgrades along the depth direction are approximately linear distribution, and the settlement is the largest at the surface of the subgrade. With the increase of depth, the settlement decreases gradually, and the settlement difference between the old and new subgrades decreases with the increase of depth. By observing the slope of the curve, it can be found that the variation range of the settlement curve of the new subgrade is more evident than that of the old subgrade. From the top of the subgrade to the depth of 3 m, the settlement of the new subgrade is reduced by 65.8% and that of the old subgrade by 51.6%. It can be seen that the deformation of the new subgrade is more affected by traffic load, and the settlement reaction is more intense at different subgrade depths.Figure 8
Subgrade surface settlement change curve.Figure 9
Settlement change curve in a depth direction of subgrade.


### 4.2. Horizontal Displacement

It can be seen from Figure10 that the curve changes roughly in a “reversed check” distribution. The maximum lateral deformation occurred at the joint part of the new and old subgrades, about 0.38 mm. Then, the horizontal deformation of the new subgrade decreases rapidly. It can be seen from the curve that a horizontal displacement to the right occurs from the center of the old subgrade to the direction of the new subgrade expansion. According to the symmetry of the new and old subgrades, the other side will produce horizontal displacement to the left, so it can be deduced that the center of the old subgrade will be prone to cracking due to the horizontal deformation in the opposite direction. Therefore, in the design of highway widening, reasonable width of slope and step should be selected during the excavation of the old subgrade slope to improve the shear strength at the joint and the overall stability of the subgrade and reduce the transverse deformation. The central part of the old subgrade should also be strengthened to avoid cracking after opening to traffic. The horizontal displacement curve in Figure 11 shows a trend of increasing and then decreasing, and the upper and lower deformation of the slope is roughly symmetrical. Therefore, in the new subgrade widening project, attention should be paid to the reinforcement and protection of the slope, especially in the waist of the slope, by adding geogrid, pile anchor, and other measures to reduce the deformation of the slope.Figure 10
Horizontal displacement curve of subgrade surface.Figure 11
Horizontal displacement curve of new subgrade slope.


## 4.1. Vertical Displacement

As shown in Figure8, the consolidation trend of the settlement curve increases first and then decreases. In the old and new subgrade models, the minimum and maximum vertical displacement of road surface are at the center of the old subgrade and the central pavement of the new subgrade, respectively, and the maximum settlement difference is about 0.86 cm. The model elements below the centerline of the new road foundation and the old subgrade are taken, and the variation rule of their vertical displacement is shown in Figure 9. The settlement curves of the new and old subgrades along the depth direction are approximately linear distribution, and the settlement is the largest at the surface of the subgrade. With the increase of depth, the settlement decreases gradually, and the settlement difference between the old and new subgrades decreases with the increase of depth. By observing the slope of the curve, it can be found that the variation range of the settlement curve of the new subgrade is more evident than that of the old subgrade. From the top of the subgrade to the depth of 3 m, the settlement of the new subgrade is reduced by 65.8% and that of the old subgrade by 51.6%. It can be seen that the deformation of the new subgrade is more affected by traffic load, and the settlement reaction is more intense at different subgrade depths.Figure 8
Subgrade surface settlement change curve.Figure 9
Settlement change curve in a depth direction of subgrade.


## 4.2. Horizontal Displacement

It can be seen from Figure10 that the curve changes roughly in a “reversed check” distribution. The maximum lateral deformation occurred at the joint part of the new and old subgrades, about 0.38 mm. Then, the horizontal deformation of the new subgrade decreases rapidly. It can be seen from the curve that a horizontal displacement to the right occurs from the center of the old subgrade to the direction of the new subgrade expansion. According to the symmetry of the new and old subgrades, the other side will produce horizontal displacement to the left, so it can be deduced that the center of the old subgrade will be prone to cracking due to the horizontal deformation in the opposite direction. Therefore, in the design of highway widening, reasonable width of slope and step should be selected during the excavation of the old subgrade slope to improve the shear strength at the joint and the overall stability of the subgrade and reduce the transverse deformation. The central part of the old subgrade should also be strengthened to avoid cracking after opening to traffic. The horizontal displacement curve in Figure 11 shows a trend of increasing and then decreasing, and the upper and lower deformation of the slope is roughly symmetrical. Therefore, in the new subgrade widening project, attention should be paid to the reinforcement and protection of the slope, especially in the waist of the slope, by adding geogrid, pile anchor, and other measures to reduce the deformation of the slope.Figure 10
Horizontal displacement curve of subgrade surface.Figure 11
Horizontal displacement curve of new subgrade slope.


## 5. Discussion of Simulation Results of Geogrid

### 5.1. Vertical Deformation

Figure12 shows the vertical deformation distribution law of the top surface of the subgrade along the horizontal direction. The overall vertical deformation of the old subgrade under the driving load is relatively small. From the overlapping of the old and new subgrades, the vertical deformation of the top surface of the subgrade increases first. It then decreases as the distance from the center of the subgrade increases. The peak value of the vertical deformation of the top surface of the subgrade appears at the center of the new subgrade, as shown in Figures 13 and 14. The vertical deformation of the old subgrade shows an approximately linear decrease with the increase in depth. The vertical deformation of the new subgrade shows a nonlinear decreasing trend with increasing depth. Due to the effect of the geogrid, the upper layer of the subgrade without geogrid deforms significantly, and the lower layer of the subgrade with geogrid deforms vertically. With the increase in the number of geogrids, the spatial distribution of vertical deformation shows a decreasing trend.Figure 12
Vertical deformation rule of the top surface of subgrade along the horizontal.Figure 13
Vertical displacement along the depth of the center line of the old subgrade.Figure 14
Vertical displacement along the depth of the center line of the new subgrade.


### 5.2. Horizontal Displacement

Figure15 shows the horizontal deformation rule of the top surface of the subgrade along the horizontal direction. The horizontal deformation of the top surface of the subgrade increases first and then decreases as the distance from the center of the subgrade increases. The most significant deformation occurs in the overlap range of the old and new subgrades. With the increase of geogrid numbers, the maximum horizontal displacement of the subgrade shows a trend of decreasing and then increasing. When the number of geogrids is increased to three layers, the geogrids are added, and the horizontal deformation of the subgrade hardly has little change.Figure 15
The rule of horizontal deformation of the top surface of subgrade along the horizontal direction.It can be seen from Figures16 and 17 that the deformation of the centerline of the old subgrade decreases linearly with the increase of depth. The centerline deformation of the new subgrade becomes a nonlinear decreasing trend with increasing depth. The maximum horizontal displacement on the centerline of the old subgrade is about 0.037 cm. The maximum horizontal displacement on the centerline of the new subgrade is about 0.14 cm, which is about 0.101 cm larger than the old subgrade. As the number of geogrids increases, the nonlinear trend of horizontal deformation in the vertical direction gradually becomes weaker. It shows that with the increase of geogrids, the role of subgrade resisting the traffic load is enhanced.Figure 16
Variation rule of horizontal displacement along the depth of old subgrade center line.Figure 17
Variation rule of horizontal displacement along the depth of the new subgrade center line.


### 5.3. Influence of Vehicle Number

Figures18 and 19 show the relationship between the maximum vertical displacement and the maximum horizontal displacement of the subgrade as the number of vehicles increases. The maximum vertical displacement and horizontal displacement of the subgrade show an increasing linear trend with the number of vehicles. With the increase of the number of geogrids, the maximum vertical deformation of the subgrade changes little, and the maximum horizontal deformation of the subgrade changes significantly.Figure 18
The rule of maximum vertical displacement of subgrade with the number of vehicles.Figure 19
Maximum horizontal displacement of subgrade varies with the number of vehicles.


## 5.1. Vertical Deformation

Figure12 shows the vertical deformation distribution law of the top surface of the subgrade along the horizontal direction. The overall vertical deformation of the old subgrade under the driving load is relatively small. From the overlapping of the old and new subgrades, the vertical deformation of the top surface of the subgrade increases first. It then decreases as the distance from the center of the subgrade increases. The peak value of the vertical deformation of the top surface of the subgrade appears at the center of the new subgrade, as shown in Figures 13 and 14. The vertical deformation of the old subgrade shows an approximately linear decrease with the increase in depth. The vertical deformation of the new subgrade shows a nonlinear decreasing trend with increasing depth. Due to the effect of the geogrid, the upper layer of the subgrade without geogrid deforms significantly, and the lower layer of the subgrade with geogrid deforms vertically. With the increase in the number of geogrids, the spatial distribution of vertical deformation shows a decreasing trend.Figure 12
Vertical deformation rule of the top surface of subgrade along the horizontal.Figure 13
Vertical displacement along the depth of the center line of the old subgrade.Figure 14
Vertical displacement along the depth of the center line of the new subgrade.


## 5.2. Horizontal Displacement

Figure15 shows the horizontal deformation rule of the top surface of the subgrade along the horizontal direction. The horizontal deformation of the top surface of the subgrade increases first and then decreases as the distance from the center of the subgrade increases. The most significant deformation occurs in the overlap range of the old and new subgrades. With the increase of geogrid numbers, the maximum horizontal displacement of the subgrade shows a trend of decreasing and then increasing. When the number of geogrids is increased to three layers, the geogrids are added, and the horizontal deformation of the subgrade hardly has little change.Figure 15
The rule of horizontal deformation of the top surface of subgrade along the horizontal direction.It can be seen from Figures16 and 17 that the deformation of the centerline of the old subgrade decreases linearly with the increase of depth. The centerline deformation of the new subgrade becomes a nonlinear decreasing trend with increasing depth. The maximum horizontal displacement on the centerline of the old subgrade is about 0.037 cm. The maximum horizontal displacement on the centerline of the new subgrade is about 0.14 cm, which is about 0.101 cm larger than the old subgrade. As the number of geogrids increases, the nonlinear trend of horizontal deformation in the vertical direction gradually becomes weaker. It shows that with the increase of geogrids, the role of subgrade resisting the traffic load is enhanced.Figure 16
Variation rule of horizontal displacement along the depth of old subgrade center line.Figure 17
Variation rule of horizontal displacement along the depth of the new subgrade center line.


## 5.3. Influence of Vehicle Number

Figures18 and 19 show the relationship between the maximum vertical displacement and the maximum horizontal displacement of the subgrade as the number of vehicles increases. The maximum vertical displacement and horizontal displacement of the subgrade show an increasing linear trend with the number of vehicles. With the increase of the number of geogrids, the maximum vertical deformation of the subgrade changes little, and the maximum horizontal deformation of the subgrade changes significantly.Figure 18
The rule of maximum vertical displacement of subgrade with the number of vehicles.Figure 19
Maximum horizontal displacement of subgrade varies with the number of vehicles.


## 6. Discussion of Simulation Results of Geocell

### 6.1. Vertical Deformation and Horizontal Displacement

It can be seen from Figure20 that the overall vertical deformation of the old subgrade is small and the change in the horizontal direction is not significant when geocells are set up. Under the condition of setting one and two layers of geocells, the vertical deformation of the new subgrade increases linearly with the distance from the center of the subgrade. With the three-layer geocell, the vertical deformation of the new subgrade increases linearly with the increase of the distance from the center of the subgrade, and the overall vertical deformation of the new subgrade is smaller than that of the old subgrade. Figure 21 shows the distribution rule of horizontal deformation of the top surface of the subgrade along the horizontal direction with a geocell. With the increase of the distance from the center of the subgrade, the horizontal deformation of the top surface of the subgrade shows a trend of increasing first and then becoming stable. Starting from the lap joint of the old and new subgrades, the horizontal deformation of the top surface of the subgrade tends to be stable.Figure 20
Vertical deformation rule of the top surface of subgrade along the horizontal.Figure 21
The rule of horizontal deformation of the top surface of subgrade along the horizontal direction.


### 6.2. Influence of Vehicle Number

It can be seen from Figures22 and 23 that the maximum vertical displacement and maximum horizontal displacement of the subgrade increase linearly. With the increase of geocells, the maximum vertical deformation and maximum horizontal deformation of subgrade change obviously, the maximum vertical deformation decreases by 9.9% and 25.9%, and the maximum horizontal deformation decreases by 5.0% and 13.9%, respectively.Figure 22
Vertical deformation.Figure 23
Horizontal deformation.


## 6.1. Vertical Deformation and Horizontal Displacement

It can be seen from Figure20 that the overall vertical deformation of the old subgrade is small and the change in the horizontal direction is not significant when geocells are set up. Under the condition of setting one and two layers of geocells, the vertical deformation of the new subgrade increases linearly with the distance from the center of the subgrade. With the three-layer geocell, the vertical deformation of the new subgrade increases linearly with the increase of the distance from the center of the subgrade, and the overall vertical deformation of the new subgrade is smaller than that of the old subgrade. Figure 21 shows the distribution rule of horizontal deformation of the top surface of the subgrade along the horizontal direction with a geocell. With the increase of the distance from the center of the subgrade, the horizontal deformation of the top surface of the subgrade shows a trend of increasing first and then becoming stable. Starting from the lap joint of the old and new subgrades, the horizontal deformation of the top surface of the subgrade tends to be stable.Figure 20
Vertical deformation rule of the top surface of subgrade along the horizontal.Figure 21
The rule of horizontal deformation of the top surface of subgrade along the horizontal direction.


## 6.2. Influence of Vehicle Number

It can be seen from Figures22 and 23 that the maximum vertical displacement and maximum horizontal displacement of the subgrade increase linearly. With the increase of geocells, the maximum vertical deformation and maximum horizontal deformation of subgrade change obviously, the maximum vertical deformation decreases by 9.9% and 25.9%, and the maximum horizontal deformation decreases by 5.0% and 13.9%, respectively.Figure 22
Vertical deformation.Figure 23
Horizontal deformation.


## 7. Conclusion

Highway widening has become an effective way to improve the carrying capacity of existing expressways. However, suppose the differential settlement between the new and the old subgrade is not controlled. In that case, it will lead to longitudinal cracks on the pavement, which will seriously affect the safety of vehicles. In this study, indoor tests were carried out to study the variation of elastic modulus and dynamic elastic modulus of new and old subgrades under traffic load. A hyperbolic model of dynamic elastic modulus increasing with strain is proposed. The numerical calculation model of new and old subgrades under traffic load is established. The deformation characteristics of new and old subgrades without treatment measures and setting up geogrid and geocell are studied. The main conclusions are as follows:(1)
With traffic load and subgrade depth increase, the elastic modulus changes significantly in the early stage but has little changes in the later stage.(2)
With the increase of the distance from the center line of the subgrade, the vertical and horizontal deformation of the subgrade surface show a trend of increasing and then decreasing under the condition of no treatment measures. The maximum vertical deformation is in the center of the new subgrade, and the horizontal deformation is the most significant in the junction of the old and new subgrades.



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*Source: 5496999-2022-08-21.xml*