Study on Deformation Characteristics of Extended Highway in Operation Period

Highway widening has become an eective way to improve the carrying capacity of existing expressways. However, assume that the dierential 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 aect the safety of vehicles. In this study, the variations of elastic modulus and dynamic elastic modulus of new and old subgrades under trac load were studied by tests. A hyperbolic model of dynamic elastic modulus increasing with strain is proposed.e numerical calculation model of new and old subgrades under trac load is established.e deformation characteristics of new and old subgrades without treatment measures and setting up geogrid and geocell are studied. e main conclusions are as follows: (1) with the increase of trac load and subgrade depth, the elastic modulus changes signicantly 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 eectively reduce the dierential settlement of the old and new subgrades. (4)e eect of setting geogrid to reduce the dierential settlement of old and new subgrades is better than that of setting geogrid.


Introduction
Expressways have become the main infrastructure for inter-regional transportation due to their advantages, such as fast speed, high e ciency, and large carrying capacity. With economic development and increasing tra c volume, the number of lanes on some expressways can no longer meet the demand for transportation [1][2][3][4][5][6][7]. Highway widening has become one of the e ective solutions. e old expressway subgrade has undergone longterm tra c operation, and the compression deformation has been stable [8]. e new subgrade will still undergo large compression deformation under the action of tra c load [9][10][11]. If the di erential settlement between the new and old subgrades is not controlled, it will cause longitudinal cracks on the road surface, a ecting vehicles' safety seriously [12]. e dynamic triaxial test has become one of the main methods to research the dynamic deformation characteristics of the soil [13][14][15]. e dynamic characteristics of subgrade soil structure have been studied in order to meet the design requirements of complex practical engineering [16][17][18]. In the early stage, the experimental study of dynamic characteristics was mainly based on seismic load, characterized by high con ning pressure, signi cant strain, and few cycles [19,20]. Experimental research has been carried out on the deformation characteristics under the tra c load by using dynamic triaxial tests and resonance column tests [21][22][23][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 tra c load by relying on actual engineering [25][26][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. erefore, 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. e traffic load action in the Yellow River extension is quantified. e dynamic triaxial test is carried out to study the dynamic characteristics of new and old subgrades soil in the Yellow River extension. e numerical calculation model of dynamic settlement of new and old subgrades under traffic load is established. e differential deformation rule of new and old subgrades is studied, providing theoretical and data support for highway extension design in the Yellow River extension.

Testing Device.
e Eldyn dynamic triaxial apparatus is used as the test device, as shown in Figure 1. e equipment can provide the cyclic loading mode of force control or displacement control. e maximum axial force is 5 kN, the maximum loading frequency is 5 Hz, and the maximum confining pressure is 1 MPa. e data acquisition system of the equipment can collect pore water pressure, strain, axial force, back pressure, and back pressure volume. e accuracy of pore water pressure and back pressure sensor is 1 kPa, the accuracy of back pressure volume is 1 mm 3 , and the accuracy of axial force is 1 N.

Test Materials.
In this test, a representative dynamic triaxial test of subgrade soil samples was selected. e soil used in the test was taken from the extension project from Zibo West to the Laiwu section of the Bin-Lai Expressway. e optimum water content was obtained by the Proctor compaction. e 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. e soil properties of the testing samples are listed in Table 1.

Experimental Conditions.
e test conditions set for this test is listed in Table 2. 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. en, 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. e newly prepared samples without dynamic cycle were considered the new subgrade soil, namely, the three samples in test condition IV.

Dynamic Modulus Attenuation
Rule. e dynamic stress-dynamic strain curve of the soil can be fitted to a hyperbolic type, which can be expressed by the following equation: where σ d is dynamic stress and ε d is dynamic strain. According to equation (1), dynamic elastic modulus can also be expressed as follows: It can be seen from equation (2) that the change curve of 1/E d − ε d can be fitted to a linear. In order to facilitate data sorting and analysis, the maximum dynamic modulus E dmax is introduced here to normalize the dynamic modulus E d , which is as follows: 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. e scatter plots of three samples' test results were reflected in the coordinate system. e relationship between E dmax /E d and ε d is obtained by linear fitting equation (equation (3)). Furthermore, the dynamic modulus-dynamic strain fitting curve drawn is shown in Figure 2.
It can be seen from the figure that the relationship between E dmax /E d and ε d is roughly in line with the linear fitting relationship, and the fitting variance is around 0.95, indicating that the fitting relationship is reliable. e 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, E d max is obtained by the mathematical limit idea and is not an accurate value, so the straight line is intercepted on the vertical axis. e distance floats around the value 1, with a slight deviation; the slope of the straight line expressed as a/b is E d max /σ d max , and the change of the slope is affected by the magnitude of the dynamic load, as listed in Table 3. e 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. e larger the dynamic load of subgrade soil is, the smaller the slope of the fitting straight line is. e 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.

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 Figures 3 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. e largest is the elastic and shear modulus of the old subgrade subjected to load P n � 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.

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 northsouth 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. e number Working condition Borrow depth (m) Confining pressure (kPa) Wheel axle weight (kN) Dynamic stress (kPa) Frequency (Hz)  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. e standard cross-section of integrated subgrade widened on both sides is shown in Figure 4. is 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. e 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. e distribution of the soil layers of the new and old subgrades is shown in Figure 5. e material parameters used in ABAQUS numerical simulation were determined by triaxial tests. e elastic modulus, Poisson's ratio, cohesion, and internal friction angle at different depths of the new and old subgrades were obtained from previous tests. e material parameters of each soil layer are listed in Table 4.

Numerical Calculation Conditions.
ree types of test conditions have been set in this study, as listed in Table 5.
e condition without treatment measures is mainly to research the differential deformation characteristics of the new and old subgrades without any reinforcement measures. e 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. e 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. e 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.

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. Figure 8, 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. e 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. e 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       Figure 10 that the curve changes roughly in a "reversed check" distribution. e maximum lateral deformation occurred at the joint part of the new and old subgrades, about 0.38 mm. en, 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. erefore, 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. e central part of the old subgrade should also be strengthened to avoid cracking after opening to traffic. e 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. erefore, 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 12 shows the vertical deformation distribution law of the top surface of the subgrade along the horizontal direction. e 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. e 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.

Vertical Deformation.
e vertical deformation of the old subgrade shows an approximately linear decrease with the increase in depth. e 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 15 shows the horizontal deformation rule of the top surface of the subgrade along the horizontal direction. e horizontal deformation of the top surface of the subgrade increases first and then decreases as the distance from the center of the subgrade increases. e 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.

Horizontal Displacement.
It can be seen from Figures 16 and 17 that the deformation of the centerline of the old subgrade decreases linearly with the increase of depth. e centerline deformation of the new subgrade becomes a nonlinear decreasing trend with increasing depth. e maximum horizontal displacement on the centerline of the old subgrade is about 0.037 cm. e 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.

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       (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.

Data Availability
e data used to support the findings of this study are included within the article. Any additional data related to the paper may be requested from the corresponding author.

Conflicts of Interest
e authors declare that they have no conflicts of interest.