Analytical solution to temperature distribution in frozen soil wall with wavy boundaries by single-row- and double-row-piped freezing

Hu, Xiangdong; Tong, Fang; Luoyu, Zhang

doi:10.1016/j.coldregions.2017.10.010

Cited by 19 publications

(7 citation statements)

References 14 publications

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“…For any point where the distance from the freezing front to the freezing pipe is ξ, the point can also be regarded as a point on the circle with the freezing pipe as the center and the radius of ξ, as shown in Figure 1. According to the calculation principle of steady-state freezing temperature field of a single pipe [17,26,28] and combining equations ( 6) and ( 7), the following equation is obtained:…”

Section: Derivation Of Analytical Solutionmentioning

confidence: 99%

“…Hu et al established a set of methods for solving the steady-state temperature field of artificial ground freezing based on the principle of superposition of potential functions. Combining this principle with mathematical methods, a series of analytical results for the steady-state temperature field were obtained [24][25][26][27][28]. In order to benchmark flow and energy transport models that include pore water phase change, Kurylyk et al…”

Section: Introductionmentioning

confidence: 99%

“…After the artificial formation freezing enters the stable freezing stage, the temperature drop rate of the freezing temperature field becomes very slow; therefore, the transient temperature field at this time can be approximated by the steady-state temperature field [24][25][26][27][28]. When a seepage field exists in the stratum, after entering the stable freezing phase, the convective heat transfer between the water and the frozen soil on the freezing front and the heat transfer of the frozen pipe cancel each other out under the condition that the seepage velocity and the water temperature are constant.…”

Section: Introductionmentioning

confidence: 99%

“…Considerable progress has occurred in the analytical calculation of the steady-state temperature field of artificial freezing in nonseepage strata [24][25][26][27][28], but an analytical solution of the steady-state freezing temperature field under the action of a seepage field is lacking.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Analytical Solution of Steady‐State Temperature Field of Single Freezing Pipe under Action of Seepage Field

Wang

Rong

Cheng

et al. 2020

Advances in Civil Engineering

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To accurately describe the distribution law of the temperature field formed by a single freezing pipe under the action of a seepage field, the shape of the freezing front was simplified using a segmentation-equivalent method. The analytical solution of the steady-state temperature field was derived, and the accuracy was verified using a physical model test. Combined with the results of the model test and the calculation results of the analytical solution, the distribution law of the freezing temperature field formed by a single pipe under different seepage velocities was analyzed. It was found that compared with the no flow rate, when the seepage velocity was 3, 6, and 9 m/day, the frozen area was reduced from 17.97 × 104 mm2 to 15.77 × 104, 3.84 × 104, and 3.05 × 104 mm2, respectively. The proportion of frozen area below −5°C increased from 39.43% to 40.19%, 49.84%, and 51.52%, respectively. The average freezing temperature field reduced from −5.78 to −5.86, −7.31, and −7.50°C, respectively. As the seepage velocity increased, the frozen area formed by a single pipe decreased while the proportion of the low-temperature zone increased and the average temperature of the temperature field decreased.

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Section: Derivation Of Analytical Solutionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Analytical Solution of Steady‐State Temperature Field of Single Freezing Pipe under Action of Seepage Field

Wang

Rong

Cheng

et al. 2020

Advances in Civil Engineering

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“…The simplified models were verified, which played a huge role in promoting the research on mechanical properties of heterogeneous frozen walls. In terms of heterogeneous frozen wall research, Hu et al [28,29] regarded a frozen wall of double-row-pipe as a heterogeneous frozen wall with a function gradient along the radial direction, and used the Moore-Coulomb strength criterion to conduct an elastoplastic analysis of the frozen wall. Rong et al [30] regarded the properties of the frozen wall materials as parabola changes along the radial direction, and used Drucker-Prager strength criterion to conduct elastic-plastic theoretical analysis of the frozen wall.…”

Section: Introductionmentioning

confidence: 99%

Mechanical Analysis of Frozen Wall with Trapezoidal Temperature Field Distribution Based on Unified Strength Theory

Shi

Long

et al. 2022

Applied Sciences

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In order to study the elastic–plastic stress field distribution of a double-row-pipe frozen wall, the temperature field of the double-row-pipe frozen wall is equivalent to a trapezoidal distribution, and the frozen wall is regarded as an elastic–plastic thick-walled cylinder with functionally gradient material (FGM) characteristics in the radial direction. Considering that the elastic modulus and cohesion of the frozen wall material change linearly with the radius, the elastic–plastic analysis of the frozen wall is carried out based on unified strength theory. The analytical solutions of the elastic–plastic stress field distribution, the elastic ultimate bearing capacity, the plastic ultimate bearing capacity, and the relative radius of the plastic zone of the frozen wall are derived. The analytical solution is calculated based on the engineering case and compared with the numerical solution obtained based on COMSOL. At the same time, the influence of strength theory parameters on the mechanical properties of heterogeneous and homogeneous frozen walls is analyzed. The results show that the analytical solution and the numerical solution are in good agreement, and their accuracy is mutually verified. The external load on the frozen wall of the selected layer is greater than its elastic ultimate bearing capacity and less than its plastic ultimate bearing capacity, which indicates that the frozen wall is in a safe state of stress. The radial stress increases with the increase in the strength theoretical parameter b and the relative radius r, the tangential stress increases with the increase in the strength theoretical parameter b, and first increases and then decreases with the increase in the relative radius r. The larger the strength theoretical parameter b, the smaller the relative radius of the plastic zone of the frozen wall. The strength theoretical parameter b increases from 0 to 1, the elastic ultimate bearing capacity and plastic ultimate bearing capacity of the heterogeneous frozen wall increase by 33.3% and 40.8%, respectively, and the elastic ultimate bearing capacity and plastic ultimate bearing capacity of the homogeneous frozen wall increase by 33.3% and 41.0%, respectively. Therefore, considering the influence of intermediate principal stress, the potential of materials can be fully exerted and the ultimate bearing capacity of frozen walls can be improved. This study can provide theoretical reference for the design and construction of frozen wall.

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Numerical simulation of freezing effect and tool change of shield machine with a frozen cutterhead

Dai

Xia

et al. 2020

J. Cent. South Univ.

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Analytical solution to temperature distribution in frozen soil wall with wavy boundaries by single-row- and double-row-piped freezing

Cited by 19 publications

References 14 publications

Analytical Solution of Steady‐State Temperature Field of Single Freezing Pipe under Action of Seepage Field

Analytical Solution of Steady‐State Temperature Field of Single Freezing Pipe under Action of Seepage Field

Mechanical Analysis of Frozen Wall with Trapezoidal Temperature Field Distribution Based on Unified Strength Theory

Numerical simulation of freezing effect and tool change of shield machine with a frozen cutterhead

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