The predominant characteristics of high-altitude climates include low air pressure, low humidity, and large diurnal temperature fluctuations. In practical engineering scenarios in high-altitude regions, many pier surface cracks only appear several months after erection, and cyclic thermal stress is identified as the main trigger for such cracking. The thermal stress in concrete structures has been investigated for decades but remains incompletely understood. Structural engineers typically regard concrete as an isotropic material and calculate the thermal stress using code-specified coefficients of thermal expansion (CTEs) along with temperature conditions and constraints. Because the CTE of hardened cement paste is more than twice that of many aggregates, reducing the CTE of coarse aggregates can further exacerbate the thermal deformation incompatibility between the coarse aggregate and mortar matrix. In this paper, a comprehensive thermal-elastic mechanics model for pier concrete was developed to analysis the temperature-induced surface stress.

A series of mechanical and thermophysical tests were conducted on the diorite aggregate, ITZ cement paste, and mortar, and concrete. A test pier was constructed on open ground near the Yarlung Zangbo River at an altitude of 3800 m. The pier had a diameter of 1.8 m and height of 2 m. Temperature sensors were embedded in the cross-section at a height of 1 m, positioned along the south-north and east-west directions. The embedding depths (distances from the pier surface) were 0, 1.5, 3, 4.5, 6, 7.5, 9, 12, 15, 20, 25, 30, 35, 40, 50, 60, 70, 80 cm, and 90 cm.

A model of the bridge pier concrete for surface-level analysis was constructed. The model consists of a concrete unit formed as a sphere-shell-shell composite, including the aggregate, ITZ, and mortar layers, embedded in the surface layer of a bridge pier. Outside this unit, the pier concrete was treated as an isotropic, homogeneous elastic material. The real-time internal temperature fields of high-altitude concrete bridge piers, measured on-site, were incorporated into the model. By applying thermoelastic mechanics theory and finite element solutions for plane strain problems, the three-dimensional thermal stresses on the surface layer of high-altitude bridge piers were analyzed.

During the experimental period, the lowest and highest temperatures on the bridge pier in the high-altitude region were 9.6 ℃ and 42.6 ℃, respectively. These occurred before sunrise and sunset on sunny days, respectively, corresponding to the local maximum temperature gradients during the surface heating and cooling stages, as well as the maximum temperature difference between the surface and center during these stages. The thermal stress on the pier concrete surface was obtained by superimposing the stresses caused by the uneven distribution of the internal temperature field and those caused by the incompatible thermal deformation among the different components in the surface concrete

Before the erection of the upper structures, the absolute values of the tangential and vertical stresses were the same; therefore, only one curve was observed. From 22:00 to 8:00, the pier concrete surface was in tension, whereas from 11:00 to 22:00, the pier concrete surface was in compression. The surface of the pier concrete was subjected to biaxial forces of equal magnitude with a maximum compressive stress of 12.52 MPa and maximum tensile stress of 2.15 MPa, respectively at 18:00 and 8:00. According to the fatigue equation, the concrete was predicted to crack after 21 d of temperature cycling. Moreover, if humidity-induced stress is added on top of this, the tensile stress may approach or even exceed the concrete's tensile strength, thereby posing a significant risk of cracking.

After the erection of upper structures, the tangential and vertical stresses no longer coincide because the upper structures have been erected. The curve of the tangential stress is unchanged, whereas the curve of the vertical stress is translated downwards by 1.57 MPa due to the structural deadweight. Therefore, the maximum tangential compressive stress remained 12.52 MPa, whereas the maximum vertical compressive stress increased to 14.09 MPa. Additionally, the maximum tangential tensile stress was 2.15 MPa, and the maximum vertical tensile stress was 0.58 MPa. According to Appendix C of GB/T 50010 and the fatigue equation, stresses are unlikely to cause cracking of the pier concrete surface.

Although a higher CTE of the coarse aggregate slightly increased the maximum compressive stress, the differences among the three groups of concrete were minimal and could be ignored. Specifically, the maximum compressive stresses on the pier concrete surface were 12.54, 12.45 MPa, and 12.56 MPa when using diorite, limestone, and basalt, respectively. By contrast, a lower CTE of the coarse aggregate results in a greater maximum tensile stress on the pier concrete surface. For example, when using limestone, which has a low CTE, the maximum tensile stress on the pier concrete surface is 2.28 MPa, compared to 2.17 MPa when using diorite and 2.14 MPa when using basalt.

The finite element simulation results indicated that the maximum compressive stress on the pier concrete surface was 11.72 MPa, whereas the maximum tensile stress was 2.10 MPa. These results are approximately consistent with the theoretical calculations. This consistency provides mutual verification.

Surface cracking in pier concrete occurs predominantly before the erection of upper structures. Under sunny conditions, the orthogonal decomposition of the superficial stress revealed that the maximum compressive stress during the day was approximately 12.52 MPa, whereas the maximum tensile stress was approximately 2.15 MPa. This tensile stress approached the tensile strength of the C35 concrete under biaxial tension. The risk of cracking increased significantly when humidity-induced stress was considered. After the erection of upper structures, the maximum tangential tensile stress on the pier surface remained at 2.15 MPa while the maximum vertical stress decreased to 0.58 MPa, both of which are well below the tensile strength of C35 concrete under biaxial tension. Although the use of coarse aggregates with a lower coefficient of thermal expansion reduced the tensile stress induced by temperature gradients, it increased the stress owing to material deformation incompatibility, leading to a slight increase in the maximum tensile stress on the pier concrete surface.