Longitudinal joints can serve as an effective measure to mitigate frost-heave damage to canal linings in cold regions. However, their design still relies heavily on the empirical mode at present. It is lacking in systematic theoretical and practical guidance. In this study, a numerical model of freezing soil was developed for canal frost-heave analysis, according to the thermo-hydro-mechanical coupling theory. The model also considered moisture migration, water-ice phase change, heat transfer, frost-heave deformation, and lining-foundation. A case study was taken as of the large arc-toe trapezoidal canal of the Fifth Main Canal in the Dayuzhang Irrigation District, Shandong Province, China. 153 longitudinal-joint layout schemes were constructed to vary the joint location, spacing (1–4 m), and number of joints (1–4). An evaluation framework was established to incorporate the maximum tensile stress in the lining, frost-heave deformation, and frost-heave nonuniformity. A systematic investigation was conducted to explore the influence patterns of longitudinal-joint layouts on the mechanical response of the lining. The results showed that: 1) Longitudinal joints subdivided the lining into independent panels, particularly with the deformation mode from integral bending to segmented tilting. The frost-heave deformation of the canal foundation soil was better accommodated to reduce frost-heave-induced stress in the lining. 2) When a single longitudinal joint was arranged at the canal bottom or on the canal slope, it only produced a local stress-relief effect in the region. Therefore, the first longitudinal joint was placed at the position of the maximum tensile stress in the lining, namely, the center of the canal bottom. With the first joint placed at the center of the canal bottom, the maximum tensile stress and nonuniform frost-heave deformation of the full cross-section first decreased and then increased, as the second longitudinal joint moved from the canal bottom toward the top of the canal slope. The optimal position of the second joint was corresponded to the newly formed position of the maximum tensile stress. The maximum tensile stress of the full cross-section was reduced to 0.96 MPa, with a reduction of 85.21%. The nonuniformity of frost-heave deformation was reduced by 97.18%. When multiple joints (no fewer than three) were arranged, according to the sequentially placing placement of joints at positions of the maximum tensile stress, the maximum tensile stress of the full cross-section was reduced to below 0.20 MPa, with a reduction rate of no less than 98.25%, and the reduction rate of frost-heave deformation nonuniformity exceeded 98.61%, indicating a significant frost-heave mitigation. 3) A lower water level and weaker frost-heave susceptibility of the soil were contributed to the optimal number of joints, whereas an increase in the elastic modulus of the joint-filling material increased the maximum tensile stress in the lining. The findings can provide a theoretical basis and guidance for the frost-heave mitigation of longitudinal joints in canals in cold regions.

A water delivery system can be gradually away from the normal state of the canal operation in northern China in winter. Water diversion projects can be launched to meet the harsh requirement on the large and medium-sized city's residents living water and industrial water consumption, as the guaranteed rates increased. However, the existing mechanical model of the canal with the water delivery cannot fully consider the difference between the freezing and underwater non-freezing areas in winter, particularly for the continuity of soil. It is a high demand to combine the difference in shear stiffness between frozen soil and non-frozen soil. Pasternak model with two parameters can be expected to consider the soil continuity in the freezing area, whereas, the traditional Winkler model can be adopted in the non-freezing area. By contrast, the Winkler model with only a few parameters can be easily calculated for definite physical significance. In this study, the combined Winkler-Pasternak model was proposed for the frost-heaving mechanical analysis of the trapezoidal canal with water delivery in winter. Taking a trapezoidal canal with water delivery in winter in the Manas River basin in Xinjiang of western China as a prototype, the real normal frost-heaving amount, and subsidence deformation of the canal lining plate were also calculated using the improved model, Winkler and Pasternak model. Then, the bending moment was calculated with the upper surface stress of each section of the lining plate. The results indicate that the lining plate was divided into three parts of frost heave, subsidence and frost heave-subsidence transition section. Three models better represented the basic change trend of normal displacement of the lining plate. Meanwhile, the improved model was in better agreement with the measurement. A comparative analysis showed that the improved model was much more accurate than the traditional Winkler model in the freezing area, whereas, some errors but trivial differences were compared with the Pasternak model in the non-freezing area. Furthermore, the improved model shared the excellent performance of the Winkler model, such as simple calculation, clear physical meaning, and few required parameters. The bending moment of sections decreased rapidly in the freezing area with the increase of groundwater depth. The risk of frost-heaving damage to the canal lining plate was dramatically reduced at the groundwater level by appropriate drainage measures. The position in the frozen soil area of the lining plate easy to crack was located at 10.0%~23.3% of the lining plate length away from the waterline. The optimal operation conditions were adopted in the ice-free water delivery of the trapezoidal canal in winter. The improved model can be also applied to the ever-increasingly common situation of water delivery with the ice cover. The finding can provide a strong reference to design the frost heave resistance of the trapezoidal canal with water delivery in winter.

Frost-heaving resistance of canals can be designated to evaluate the control parameters in cold regions. As proposed in the national standard of SL23-2006 "Design Code for Frost Heave Resistance of Canal System Engineering", the frost-heaving deformation of the canal concrete lining structure can be expected to readily monitor and control in practice. However, the specification cannot provide the specific calculation of uneven frost-heaving deformation in the canal concrete lining. This study aims to facilitate the accurate and practical calculation for the frost-heaving deformation of concrete lining structures under uneven frost-heaving deformation conditions. The fluctuation of groundwater levels was considered across different points along the canal cross-section, together with the continuous deformation within the canal foundation soil. A calculation model was developed for the frost-heaving deformation and internal force of trapezoid concrete lining canal in cold regions under differential frost heave conditions, according to the two-parameter foundation beam of frozen soil. Taking the main trunk canal of Jinghui in Gansu Province as an example, the presented model degenerated into the Winkler model under uniform frost heave conditions. Comparative analysis showed that the traditional Winkler model was regarded as a special case within the proposed model. Some measuring points were simultaneously considered for the shady slope, sunny slope, and bottom of the canal. The Root Mean Square Error (RMSE) between the presented model and observed values was determined to be 0.23, with the Mean Relative Error (MRE) of 4.82%. Taking a trapezoidal concrete lining canal in the Tarim Irrigation area of Xinjiang Uygur Autonomous Region as the prototype, the frost-heaving deformation of the concrete lining structure was calculated at the same time. The results show that the better mechanical performance of the concrete lining canal was achieved in the improved model considering the frozen soil-structure interaction and diffusion of shear force in the frozen soil foundation under uneven frost heave conditions, compared with the material mechanics and traditional Winkler model. The calculated values of the improved model were more consistent with the observation, indicating the rationality and applicability of the model. The engineering example was combined to solve the improved model. The first was the conventional analytical, while the second involved the power series. Among them, the various distributions of free frost heave deformation were expanded into the power series using the comparison coefficient. A special solution with a homogeneous solution was then obtained to introduce the boundary conditions. The general solution was derived for the original control differential equation. The MRE between the frost-heaving deformation was calculated by the power series. Among them, the observed value was 4.31% with an RMSE of 0.17, indicating a reasonable calculation. The power series was utilized to represent the natural frost-heaving displacement of canal foundation soil. Therefore, the improved model effectively enhanced the applicability for the various differential frost-heaving modes in foundation-frozen soil. The mechanical response of frost heave was found in the trapezoidal concrete lining canal under differential or uniform frost-heaving deformation. Then, some implication was gained to clarify the influence of transverse groundwater replenishment on the mechanical behavior of concrete lining structures under the frost-heaving deformation of foundation soil. In addition, the improved model can be expected to effectively capture the non-uniform and asymmetric distribution of tangential freezing force at the contact interface, due to the non-equilibrium axial force on both ends of the bottom plate that is caused by the difference between shady and sunny slopes. The finding can provide an effective computational model for the frost heave mechanics of trapezoidal canals in cold regions, especially on differential frost heave conditions.

Shallow groundwater or narrow-deep lined canals have suffered the vertical frost heave at the top of the canal in cold regions. The lining fracture and whole uplift frost damage are also prone to occur, leading to the low stability of the canal at low temperature. However, the existing engineering models of canal frost heave have focused only on the normal one of the canal slope. This study aims to consider the combined effect of vertical frost heave on the top of the canal and normal frost heave on the slope. A mechanical engineering model was established to consider the canal frost heave. Sensitive soil was selected to simulate the moisture-heat-mechanical coupling numerical models in the canal. The frost heave was then used under different dip angles of the slope, width-to-depth ratios, and groundwater levels. The maximum tensile stress was calculated to locate the different freezing depths and dip angles of the slope during frost-jacking. The specific mechanism of canal lining was then explored to clarify the distribution of vertical and normal frost heave during frost-jacking. The internal force of canal lining plate and frost-jacking strength of canal slope were evaluated to calculate the critical slope length, critical groundwater level, and dangerous location of frost-jacking failure. Finally, the engineering mechanics model was proposed to test the actual case. The experimental data was in agreement with the field observation. The results show that the freezing counterforce was failed to offset the upper tangential frost-jacking force, particularly for the lower lining with the short slope length. The lining was also suffered from the jacking disease as a whole. Otherwise, a frost-jacking force was formed inside the lining. The greater the freezing depth and the dip angles of the slope were, the larger the area of the lining bearing the upward tangential force was, and the greater the frost-jacking tensile stress was. The position of the maximum tensile stress caused by jacking was shifted to the lower part of the canal with the increase of freezing depth and inclination angle of the canal slope. The maximum tensile stress was negatively related to the groundwater level. The critical water level of the lining was the critical groundwater level of the original ground frost heave. At the same time, the frost heave of the original ground was a necessary and insufficient condition for the canal to produce the frost pull. The numerical fitting indicated that the minimum curvature radius of the frost depth line at the top of the canal increased with the increase of frost depth and dip angles of the slope. The depth of frost shared a linear relationship with the minimum curvature radius. The dip angles of the slope exhibited a greater impact on the fitting slope. The maximum error of tensile stress was verified by the numerical model to be 1.5%. The frost-jacking position error was within 16.01%. Therefore, the slope range of the freezing line radius function was 1.047 to 4.040 in the soil conditions of the Ningxia irrigation area. There were the overall uplift pattern of small canal and the cracking failure pattern of large canal linings. The damage mechanism was then clarified to prevent and control the anti-frost heave of canal lining. The finding can also provide a strong reference for engineering design and code revision.