The site of the model test is located in the Chumar River Plain in China. The annual average temperature is −4°C, which is a permafrost development zone. The thickness of permafrost is approximately 40 m, and the ground temperature is maintained at 0.0°C to −1.0°C all the year round, which is a very unstable section of high-temperature permafrost.

The length of the transition section is 14 m, the inverted trapezoidal slope is 1: 2, the width of the top surface of the roadbed is 8.4 m, and the overall height of the roadbed is 6 m. Because the ground temperature of the natural frozen soil is greatly affected by construction, in order to minimize the influence of ground temperature, only simple treatment is carried out at the natural surface, and then the roadbed and transition section are constructed.

Based on the similarity theory, the factors affecting the distribution of the temperature field in the transition section of road and bridge in permafrost regions are first determined, and the parameter modeling design is carried out through the criterion analysis (Jing et al., 2020; Wu et al., 2020). The main factors affecting the temperature field distribution of the bridge approach are geometric size l , time τ , temperature t , surface temperature t ∘ , soil temperature t D , atmospheric temperature t K , heat transfer coefficient α , temperature diffusivity a , thermal conductivity λ ( a = λ /(ρ•c), with density ρ and specific heat capacity c), specific heat capacity c V , upper limit of frozen soil ζ , and latent heat of soil G .

According to the similarity theory, the relationship between the temperature field of the bridge approach and its main influencing factors is as follows: F l , τ , t , t o , t D , t K , α , a , λ , c V , ζ , G = 0 . (1)

According to the dimensional analysis of the similarity theory, the similarity criterion of the temperature field of the road–bridge transition section in the permafrost region is geometric criterion :   π 1 = l ζ = R , temperature criterion :   π 2 = t t o = t t D = t t K = Θ , Nuscher  g uidelines :   π 3 = α l λ = N u , Fourier criterion :   π 4 = a τ l 2 = F O , Kosovich criterion and Fourier criterion :   π 5 = G l 2 λ τ t = G c V t l 2 λ c V τ = G c V t l 2 a τ = K o 1 F o .

Therefore, the criterion equation can be expressed as F R , Θ , N u , F o , K o = 0 . (2)

According to the above equations and criteria, the model test is designed. The proportional relationship and conversion coefficient between the physical quantities of the model test should be determined.

(1) Geometric scaling

According to the test accuracy requirements and test conditions, the test geometry scale is initially selected as C l = 25 . Prototype and model dimensions are shown in Table 1.

(2) Model test material selection

The foundation soil and subgrade soil are remolded silty clay in Xuzhou, China. The transition section is filled with coarse-grained soil, and the abutment of the bridge transition section is prefabricated. Therefore, the similarity constant of α , a , λ , c V , and G is 1.

(3) Temperature scaling

According to the Kosovitch criterion, K 0 = Q t c , (3) K o ′ = Q ′ c ′ t ′ = Q c t = K o , (4) C Q C C C t = 1 , C t = C Q C C , (5)

where C Q represents the latent heat ratio constant (latent heat shrinkage ratio), C C represents the volume-specific heat shrinkage ratio, and C t represents temperature scaling.

Since the test material is soil, that is C C , the temperature at a certain position in the model test corresponds to the temperature at that position in the actual project after geometric scaling.

(4) Time scaling

Fourier criterion can be expressed as F 0 = a ′ τ C n ′ l ′ 2 = a τ C n l 2 , (6) where C a C τ C l 2 = 1 , C a = 1 , and C τ = C l 2 = 25 2 =625, which implies that the model test day is equivalent to the actual 625 days.

The model test chamber is surrounded by the adiabatic boundary, and thermal insulation cotton with 5 cm thickness and special polyethylene adhesive as binder is used for thermal insulation treatment (Ma et al., 2022a; Ma et al., 2022b; Shi et al., 2023a; Shi et al., 2023b; Zheng et al., 2024). In order to alleviate the deformation caused by the lateral earth pressure inside the model test box, the model is processed by three layers of 1-cm-thick wooden template, 1-cm-thick wooden template, and Q235 steel from the inside to the outside. In order to ensure the external stiffness of the model box after filling, four steel sections are welded horizontally with the external wooden template. In order to ensure the external stiffness of the model box after filling, four sections of steel are welded horizontally with the external wood formwork. The internal size of the model box is 2,200 mm × 2000 mm × 600 mm. The model box is shown in Figure 1.

Refrigeration and temperature control equipment with a precision low-temperature thermostatic circulation tank is shown in Figure 2. This setup permits precise temperature control over the entire measuring range and maintains an optimum constant temperature with fluctuations of ±0.02°C using alcohol as an internal refrigerant. The bottom constant temperature plate adopts iron material, and there are upper and lower parts that consist of two whole plates. The refrigeration and constant temperature effects are achieved by a circulating cold liquid, as shown in Figure 3. The atmospheric temperature of the simulated model test in the walk-in refrigeration laboratory is shown in Figure 4. The internal refrigeration system and temperature control system of the walk-in refrigeration laboratory are integrated, and the system automatically controls the temperature. The low-temperature range is −20°C to 10°C, the temperature control deviation is ±0.5°C, and the temperature accuracy is 0.1°C.

The spatial temperature field distribution of the bridge approach in the permafrost region is the focus of the current research. The temperature probe adopts the temperature sensor, and the data acquisition instrument adopts the multi-channel temperature data acquisition instrument developed by the State Key Laboratory of Deep Geotechnical Mechanics and Underground Engineering of China University of Mining and Technology, as shown in Figure 5. The diagram of the final test system is shown in Figure 6.

The test process is carried out through the preparation of the test soil, the prefabrication of the test abutment, the installation and test of the bottom constant temperature system, the embedding and positioning of the foundation sensor, the layered filling of the foundation soil and the embedding of the sensor, the positioning and installation of the abutment position, the laying of the gravel cushion of the road foundation, the layered filling of the roadbed soil and the embedding of the sensor, the filling of the roadbed soil, the installation of the bridge deck, the laying of the roadbed ballast and the fan, and the data acquisition, as shown in Figures 7–10.

Taking into account the ground temperature of lower than 0°C of the permafrost area, the climatic characteristics of the Qingshuihe area along the Qinghai–Tibet railway, and the boundary layer temperature increment, the upper boundary air temperature adopts periodic temperature fluctuation function T: T = − 4.0 − 11.5 ⁡ sin 2 π 841 t . (7)

where −4.0°C represents the average temperature and 841 min represents a cycle. The lower boundary is a constant temperature condition, the simulated permafrost ground temperature is −2.9°C, and the surrounding boundary is an adiabatic boundary.

The temperature change curve of the temperature measuring point on the top surface of the transition section is shown in Figure 13. It can be seen from the figure that the temperature changes in the subgrade center and the slope shoulder at 2.5 m on the top of the transition section are basically the same, indicating that the response of the two to the change in atmospheric temperature is basically the same. The longitudinal temperature curve of the center of the subgrade shows that the changes in the temperature curve of the temperature measurement points greater than 2.5 m are the same, and the peak temperature of the third cycle is −8.8°C and 0.8°C. Comparing with other temperature measurement points, the temperature change in the contact area between the platform back and the subgrade has obvious hysteresis, and the peak points are between other measurement points. The peak temperature of the third cycle is −7.8°C and 0.1°C. At the cooling stage, the temperature at 0 m platform back is higher than that at other measuring points. At the heating stage, the temperature at 0 m platform back is lower than that at other measuring points. The reason may be that the measuring point is located between concrete, soil, and air. The smaller specific heat capacity and larger thermal conductivity of concrete affect the temperature change in the measuring point.

The temperature change curve of the longitudinal temperature measurement point at the bottom of the transition section is shown in Figure 14. It can be seen from the diagram that with the increase in the test period, the measuring points at the bottom of the transition section change periodically in a simple harmonic wave form, and the total cooling capacity inside the soil gradually accumulates. Taking the 2.5-m platform back of the subgrade center section as an example, in the three test cycles, the high temperature decreased from −1.06°C to −3.0°C, and the low temperature decreased from −3.94°C to −5.25°C. With the increase in the distance from the platform back, the influence of atmospheric temperature change on the temperature measuring points of the subgrade center is smaller. Taking the temperature measurement point of the third cycle as an example, for the platform back at 0 m, 2.5 m, 7.5 m, 14 m, and 22.75 m, the high temperatures are −1.6°C, −2.4°C, −1.9°C, −1.7°C, and −1.7°C; the low temperatures are −6.1°C, −5.3°C, −4.1°C, −3.4°C, and −3.6°C; the temperatures decrease by 4.5°C, 2.9°C, 2.2°C, 1.7°C, and 1.9°C; and the change rates are 288.5%, 115.2% and 109.3%, 106.2%, 103.6%, and 110.6%, respectively. It can be seen that the change in atmospheric temperature has a great influence on the temperature of the subgrade near the bridgehead.

The temperature change curve of the transverse temperature measurement point at the bottom of the transition section is shown in Figure 15. The temperature measurement points at 2.5-m and 22.75-m platform back show similar variation rules. The slope toe is most affected by temperature changes, and the subgrade center and slope shoulder are relatively less affected by temperature changes. The temperature change in the slope shoulder and subgrade center is basically the same at 2.5 m of the abutment back, but there is a certain temperature difference at 22.75 m. It can be seen that the closer to the bridgehead, the less obvious the temperature difference between the subgrade center and slope shoulder, whereas the temperature of the subgrade center and slope shoulder of the subgrade cross section away from the platform back has certain difference. The reason for the analysis may be that with the increase in the distance from the platform back, the influence of the heat transfer in the direction of the bridgehead on the subgrade temperature field gradually weakens. The heat transfer mode gradually changes from three-dimensional heat transfer to two-dimensional heat transfer. The intensity of the influence of the heat transfer in the direction of the bridgehead on the subgrade temperature field near the platform back is much greater than that of the heat transfer in the direction of the top surface of the subgrade and the side surface of the subgrade, resulting in the same temperature change as the 2.5-m section of the platform back at the bottom of the transition section. From the above analysis, it can be concluded that the soil temperature field near the back of the abutment is greatly affected by the heat transfer at the bridgehead. The soil temperature field away from the back of the abutment is mainly affected by the heat transfer on the top and side of the subgrade. Due to the change in atmospheric temperature, there is a certain lag in the temperature of the subgrade center and slope shoulder compared with that of the slope toe.

The temperature change curve of each measuring point 3 m below the surface is shown in Figure 16. The temperature change in each measuring point on the central longitudinal section of the subgrade at 3 m below the surface shows the same temperature change law as the central longitudinal section of the subgrade at the bottom of the transition section. With the increase in the distance from the platform back, the temperature of the temperature measuring point in the center of the subgrade is less affected by the change in atmospheric temperature. During the first cycle of the test, the temperature is basically approximately 0°C at 7.5 m, 14 m, and 22.5 m on the abutment back of the longitudinal section of the subgrade center, the slope change is very small, and the temperature change is also very slow. However, it is not the same as the change law of the measuring points near the bridgehead. The reason may be that the soil far away from the bridgehead is less affected by the temperature change at the beginning of the test, and the phase change occurs in the soil. It can be seen from Figure 16B that the temperature changes in the subgrade center and the slope shoulder measuring points of the 2.5-m section of the platform back are consistent, indicating that the temperature change in the foundation near the platform back is still controlled by the heat transfer in the direction of the platform back.

The temperature change curve at different depths in the center of the subgrade 2.5-m platform back is shown in Figure 17. With the increase in the depth, the response of the measuring point to the change in the upper atmospheric temperature decreases gradually. Taking the second cycle of the test as an example, the peak temperatures at 0 m below the top surface of the subgrade are 0.75°C and −8.19°C. At 3 m below the top surface of the subgrade, the peak temperatures are −0.81°C and −5.69°C. At 6 m below the top surface of the subgrade, the peak temperatures are −1.75°C and −4.13°C. At 9 m below the top of the subgrade, the temperature peak is not obvious, indicating that the depth is less affected by atmospheric temperature changes. With the increase in the measuring point depth, the hysteresis of measuring point temperature is more obvious.

The temperature change time history curves of the second and third cycles of the gravel sandwich bridge approach and the U-shaped block gravel bridge approach and the temperature change comparison curve at 6 m below the center of the transition section are shown in Figure 18, which reflects the influence of periodic temperature on the temperature stability of the subgrade bottom. It can be seen from Figure 18 that compared with the U-shaped block gravel bridge approach, the temperature change curve at 2.5 m back of the platform is not significantly different. With the increase in the distance from the back of the platform, the cooling effect of the gravel sandwich bridge approach is gradually enhanced. The cooling effect of the platform back at 14 m and 22.75 m is basically the same. When the temperature is the highest in the third cycle, for the platform back at 2.5 m, 75 m, 14 m, and 22.75 m, the temperatures of the gravel sandwich bridge approach and the U-shaped block gravel bridge approach are −3.75°C, −3.5°C, −3.19°C, and −3.19°C and −4.44°C, −4.19°C, −3.94°C, and −3.94°C, respectively. The change rates are 18.4%, 19.7%, 23.5%, and 23.5%. The cooling effect is obvious. When the temperature of the third cycle is the lowest, the temperatures of the gravel sandwich bridge approach and the U-shaped block gravel bridge approach are −3.44°C, −2.56°C, −2.06°C, and −2.19°C and −3.45°C, −2.63°C, −2.44°C, and −2.50°C for the platform back at 2.5 m, 75 m, 14 m, and 22.75 m, respectively. The change rates are 0.3%, 2.7%, 18.4%, and 14.1%. This shows that although the cooling effect of the U-shaped block gravel bridge approach is better than that of the gravel sandwich bridge approach, the cooling effect is the best when the temperature is the highest. At the same time, it can also be concluded that the cooling effect increases with the increase in the distance from the platform back.