Experimental Study on Normal Frost-Heave Force Generated from Loess upon Freezing considering Multiple Factors

Zhao, Zai-kun; Wang, Tie-hang; Jin, Xin; Zhang, Yu

doi:https://doi.org/10.1155/2019/1237105

Advances in Materials Science and Engineering

On this page

Abstract Introduction Results and Analysis Conclusions Data Availability Conflicts of Interest Acknowledgments References Copyright Related Articles

Research Article | Open Access

Volume 2019 | Article ID 1237105 | https://doi.org/10.1155/2019/1237105

Experimental Study on Normal Frost-Heave Force Generated from Loess upon Freezing considering Multiple Factors

Zai-kun Zhao,¹Tie-hang Wang,¹Xin Jin,²and Yu Zhang¹

Academic Editor: Tomasz Trzepieciński

Received09 Sept 2019

Accepted08 Nov 2019

Published27 Nov 2019

Abstract

An experimental study on the normal frost-heave force generated by loess was conducted by subjecting loess with various water contents and densities to different temperature conditions. The experimental results show that the interaction of the three factors has a significant effect on the normal frost-heaving force. Normal frost-heave force increases exponentially with an increase in dry density and linearly with a reduction in the freezing temperature or an increase in water content; of these factors, dry density has the greatest influence on frost-heave force, followed by water content then temperature. A frost-heave force model is developed that includes overall consideration of the interactions of water content, density, and temperature based on fitting of the test results. The value calculated with the model is in good agreement with values measured in verification tests, indicating that the model has high accuracy and can provide scientific guidance for engineering design in loess areas.

1. Introduction

Construction in loess areas suffers from major problems due to freezing damage [1–4]. A lack of scientific guidance on frost-heave force in the design of structures such as foundations, subgrade, tunnels, culverts, artificial freezing support, and other projects means that they experienced different degrees of deformation and cracking and even structural failure due to excessive frost-heave force in the soil mass, leading to serious security issues and causing great economic loss [5–11].

Few studies have yet been conducted on frost-heave force. Early studies on frost-heave force often took temperature as the main influencing factor. In terms of theoretical research, Penner et al. [12] proposed that due to the influence of the temperature gradient, the maximum frost-heave force appears at the top of the soil. According to another study by Penner and Walton [13], temperature is closely related to frost-heave force, and as the temperature decreases, frost-heave force increases linearly. Takashi et al. [14] obtained the relationship between frost-heave force and temperature by measuring the pore-water pressure of unfrozen water at different temperatures. Jiang et al. [15] studied the relationship between temperature and normal frost-heave force through an experiment on normal frost-heave force in low-liquid limit clay. Tang et al. [16] studied the relationship between temperature and frost-heave force through an indoor experiment on the frost-heave force generated by mucky clay. Gutkin [17] studied the influence of horizontal frost-heave force on an enclosing structure with finite stiffness. In addition to these theoretical studies, scholars have also performed numerous studies on frost-heave force under real-world working conditions. In tunnel engineering, Gao et al. [18] and Feng et al. [19] obtained an elastic-plastic analytical solution of the plastic region of tunnel-surrounding rock stress in cold regions. By considering the isotropy of tunnel temperature and the anisotropy of surrounding rock, Xia et al. [20] obtained an analytical solution for frost-heave force. In the study of frost heave of foundation and supporting structure, temperature is also regarded as an important factor affecting frost heave. On the basis of monitoring of the temperature and deformation of the foundation of a transmission line tower, Wen et al. [21] argued that the spherical stress at the base of the tower was closely related to temperature. Wang et al. [22] and Ji et al. [23] proposed that frost-heave force is related to the properties of the material restraining the frost-heave body and temperature. In the above studies, the frost-heave force calculated only considering the effect of temperature is quite different from the actual value of frost-heave force, which cannot accurately reflect the magnitude and variation of the actual frost-heave force.

With the further study of frost-heave force, it is found that soil properties (moisture content, dry density, etc.) also have an impact on frost-heave force. Xu et al. [24] studied the variation of cohesion and internal friction angle of loess samples with different water contents and dry densities after freeze-thaw cycles. It was found that the cohesion of loess after freeze-thaw cycles decreased with the increase of dry density and water content, while the internal friction angle of loess changed little after freeze-thaw cycles. Wang et al. [25] set up a prediction model of frost heave of cohesive soil considering the influence of temperature and optimized the hydraulic section of irrigation canal accordingly. Zhang et al. [26] studied the influence of water content and dry density on frost heave. He believed that when water content was 15∼25% and temperature was −15∼35°C, the settlement of the upper and lower boundary of the overlying permafrost layer decreased with the decrease of temperature and the increase of water content.

As can be seen from the above summary, the factors often considered in the study of frost-heave force are temperature, water content, and dry density. But, the process of generating actual frost-heave force is a multifactor coupled process. Change in any of the factors (density, water content, or freezing temperature) will change the ice content, unfrozen water content, pores between soil particles, and so on [27]. The influence of dry density, water content, and temperature on normal frost heaving should not be neglected.

However, there are few studies considering the effects of dry density, water content, and temperature on frost-heave force, and the interaction of these three factors is not considered. Therefore, this paper intends to systematically and quantitatively study the comprehensive influence of the three factors on frost-heave force. Moreover, considering that loess is a special kind of soil, its physicochemical and physicomechanical properties are particularly sensitive to changes in density and water content [28–30]. This study takes loess as the test soil sample and carried out an experimental study on the frost-heave force generated by loess, taking density, water content, and temperature into consideration. To quantitatively analyze the influence of these various factors on frost-heave force, the experiment was set as a closed unidirectional freezing test to avoid interference of other factors. The results reveal the laws governing the effects of three factors on normal frost-heave force, and a model for normal frost-heave force is established based on the experimental data that take the interactive effects of three factors into consideration. The results can provide a basis for the analysis of frost-heave force and a reasonable reference for the calculation of frost-heave force in loess soil.

2. Experimental Setup and Test Procedure

The loess used in the experiment is from a foundation pit in Fuping area, Shaanxi Province, China. The properties of the loess are shown in Table 1. Loess samples with different water contents and dry densities were prepared indoors.

Cutting-ring loess samples with identical dimensions of 79.8 mm × 20 mm were prepared. The loading device is a WG-type single-lever oedometer manufactured by Nanjing Soil Instruments, and the deformation monitoring device is a dial gauge with an accuracy of 0.01 mm to provide a reading accuracy meeting the test requirements. The testing devices are shown in Figure 1.

The temperature-controlled chamber was first cooled to the test temperature, and then the soil samples were placed in the chamber for testing. The soil samples were frozen under test temperature, and the loading device was used to apply a vertical load to restrain frost-heave deformation so as to guarantee that no frost-heave deformation occurred in the soil samples. The displacement is restrained during freezing, and the axial load is measured as the frost-heave force. Frost-heave force experiments were carried out on soil samples with different water contents and dry densities at different temperatures.

Under the action of temperature, the freezing of soil samples will occur over a period of time. Frost-heave force gradually increases with time; but after a certain period, the increment gradually decreases with time until the frost-heave force reaches a stable state. An increment of less than 0.5% of the measured frost-heave force in two consecutive hours can be regarded as the standard for a stable state.

In practical engineering, the dry density of loess varies over a large range. Considering the range of dry densities encountered in engineering contexts, the dry densities of the soil samples in this experiment were set within the range 1.30∼1.70 g·cm⁻³. Additionally, frost-heave force has a pressure-melting effect on soil. To study the effect of temperature change on pressure-melting effect, it was judged that the completion of soil sample freezing in the earlier stages should be guaranteed. Therefore, in the present experiment, the highest temperature value is the lowest temperature in the zone of severe phase transformation: −3°C. Because the average daily minimum temperature in the Loess Plateau in winter is −12°C, the range of temperatures in this experiment on the frost-heave force generated by loess is taken as −3, −7, and −12°C. Table 2 lists the parameter values for each group of soil samples in the present test, in which is the initial dry density of a soil sample, is the water content in the soil sample, T is the soil temperature, and is the frost-heave force. A total of 60 groups of samples were tested. In this paper, three groups of parallel experiments were conducted in each group. The average value of the measured data was taken as the final data, and parallel experiments were carried out on individual points with abnormal test data.

3. Results and Analysis

Experiments on the frost-heave force generated by loess samples with different water contents and dry densities were carried out at different temperatures according to the experimental scheme outlined in Section 2. The results of the tests are analyzed below.

3.1. Analysis of the Influence of Dry Density on Frost-Heave Force

According to Figures 2(a) and 2(b), normal frost-heave force generally increases with an increase in dry density, but it shows no significant increase with an increase in dry density at small dry density values. When dry density is less than 1.40 g·cm⁻³, soil samples have large pores, and the normal frost-heave force generated by the soil samples is 0 kPa. This is because the initial water content in the soil samples is very low, causing the ice content in the soil upon freezing to be too low to fill the pores. Moreover, ice has a limited improvement effect on the strength of cementation between soil particles. The soil mass itself suffers no frost-heave deformation, so no normal frost-heave force is generated. When dry density increases to 1.50 g·cm⁻³, the increase rate of frost-heave force increases significantly.

(a)

(b)

3.2. Analysis of the Influence of Water Content on Frost-Heave Force

Figures 3(a) and 3(b) show the relationship between water content and normal frost-heave force when the dry density is 1.60 g·cm⁻³ and the soil temperature is −7°C. According to the figures, at a given soil temperature, a change in the initial water content of the soil samples has a significant influence on frost-heave force. At set values for dry density and freezing temperature, the normal frost-heave force produced in soil sample freezing increases approximately linearly with an increase in the initial water content in the soil sample. There is a minimum water content threshold: when the water content is lower than this minimum value, no frost-heave force is generated when freezing deformation of soil samples is restrained. For example, in Figure 3(b), among the soil samples with a dry density of 1.30 g·cm⁻³ and different water contents, the smaller the water content of the soil sample, the smaller the frost-heave force. When the water content was 20%, the force-heave force generated by the soil sample was 0 kPa.

(a)

(b)

3.3. Analysis of the Influence of Temperature on Frost-Heave Force

According to Figures 4(a) and 4(b), change in temperature has a significant effect on normal frost-heave force. When dry density and water content are held constant, the freezing temperature of the soil samples decreases; when frost heave of the soil samples is restrained, the normal frost-heave force generated increases. At a high temperature, normal frost-heave force increased more significantly with a decrease in temperature; with a decrease in the temperature, the amplitude of the increase in normal frost-heave force decreased. According to Figure 4(a), when the dry density is 1.50 g·cm⁻³, the freezing temperature decreases from −3°C to −12°C and the frost-heave force increases by about three times, following similar trends at different water content levels. According to 4(b), when the water content is 24% and soil samples with different dry densities are considered, the frost-heave force increases by about 2.5 times as the freezing temperature decreases from −3°C to −12°C. Furthermore, with a decrease in the freezing temperature, normal frost-heave force is more sensitive to changes in dry density and water content. The lower the freezing temperature, the greater the increment of frost-heave force caused by an increase in dry density and water content.

(a)

(b)

3.4. Analysis of the Significance of the Influences of T, , and on Frost-Heave Force

In order to quantify the significance of the influence of the three factors on the frost-heave force, the orthogonal table was used to analyze the three factors. Take as 20, 24, and 28%. Take as 1.4, 1.5, and 1.6 g·cm⁻³. Take T as −3, −7, and −12°C. Construct an orthogonal table of 3 × 3, as shown in Table 3. Among them, K₁, K₂, and K₃ represent the average value of indicators at each level of each factor. The value obtained by subtracting the smallest K from the largest K in each column is called R, which indicates the significant level of influence of each factor on the frost-heave force (see Table 3).

The magnitude of can reflect the order of significance of factors (see Table 4). The values for the range, , in the significance analysis are 800.00>662.333>520.883, and the corresponding order of significance is dry density>water content>temperature. In other words, among the factors influencing frost heave in loess areas, dry density has the greatest influence, followed by water content and then temperature.

3.5. Forecasting Model of Frost-Heave Force

According to the significance analysis above, dry density has the greatest influence on normal frost-heave force in loess, followed by water content, and subzero temperature has the least influence. Therefore, the influence of a single factor, dry density, on normal frost-heave force is considered first. The forecasting model of normal frost-heave force is thus initiallywhere is the normal frost-heave force; is the dry density; and , , and are coefficients.

Fitting is conducted on the test results for soil samples with different water contents and dry densities at different freezing temperatures. The values of and are 9.9 and −12.46, respectively. The values of and are only related to the dry density and do not change with a change in water content and freezing temperature. The correlation coefficients of the model consisting of , , and are all greater than 0.9, indicating that the calculated and measured values of the model are in good agreement. Table 5 shows some of the values of and the correlation coefficients of the model consisting of , , and .

The influence of water content and freezing temperature on normal frost-heave force was investigated. Among , , and , only the value of is related to and T. Thus, when analyzing the influence of water content and freezing temperature on normal frost-heave force, fitting is conducted only on . The influence of water content on normal frost-heave force is greater than that of freezing temperature, and therefore, the influence of water content on is considered first in the next section. The fitting formula is as follows:

The values of and in the formula are shown in Table 6. The correlation coefficient for the values is high, indicating that fitting on and is reliable.

Considering the influence of freezing temperature, fitting is carried out when and are given. The fitting formula can be expressed as follows:

The values of , , , and in the formula are shown in Table 7. By substituting formulas (3) and (4) and formula (2) into formula (2) and formula (1), respectively, a model can be obtained for normal frost-heave force that comprehensively considers the influence of dry density, water content, and freezing temperature.

In order to verify the rationality of the model, three groups of experiments were conducted with different water contents, dry densities, and temperatures, and three parallel experiments were conducted in each group. The measured data are compared with the calculated values of the model in Figure 5. It shows that the calculation results of frost-heave force are basically consistent with the data of verification test. The correlation coefficient () between them is close to 1. It shows that formula (5) has high reliability in describing the relationship between loess frost-heave force and the three factors, and the prediction error of frost-heave force is small.

(a)

(b)

(c)

(d)

(e)

(f)

4. Conclusions

(i)An experimental study was conducted on the normal frost-heave force generated by soil samples with different water contents and different densities at different freezing temperatures, revealing a close correlation between the normal frost-heave force generated by loess and the water content, dry density, and temperature of the soil. Normal frost-heave force increases exponentially with an increase in dry density, linearly with a decrease in freezing temperature, and also linearly with an increase in water content.(ii)According to the significance examination, the impacts on frost heave in loess can be ranked dry density>water content>temperature.(iii)By considering the interactive effects of the influencing factors of dry density, water content, and freezing temperature on frost-heave force, a model for the normal frost-heave force generated by loess in areas with seasonally frozen soil was established. The calculated values based on the model are in good agreement with the values measured in verification tests, indicating that the model is accurate and can provide scientific guidance for engineering design in loess areas.

Data Availability

The data used to support the findings of this study are available from the corresponding author upon request.

Conflicts of Interest

The authors declare that they have no conflicts of interest.

Acknowledgments

The research described in this paper was financially supported by the National Science Foundation of China (no. 41807282) and the Key Research & Development Program of Shaanxi (program no. 2018ZDCXL-SF-30-9).

References

J. Xu, Q. Wang, J. Ding, Y. Li, S. Wang, and Y. Yang, “Frost heave of irrigation canals in seasonal frozen regions,” Advances in Civil Engineering, vol. 2019, Article ID 2367635, 14 pages, 2019.
View at: Publisher Site | Google Scholar
G.-Y. Li, W. Ma, Y.-H. Mu, F. Wang, S.-Z. Fan, and Y.-H. Wu, “Effects of freeze-thaw cycle on engineering properties of loess used as road fills in seasonally frozen ground regions, North China,” Journal of Mountain Science, vol. 14, no. 2, pp. 356–368, 2017.
View at: Publisher Site | Google Scholar
S.-L. Wang, Q.-F. Lv, H. Baaj, X.-Y. Li, and Y.-X. Zhao, “Volume change behaviour and microstructure of stabilized loess under cyclic freeze-thaw conditions,” Canadian Journal of Civil Engineering, vol. 43, no. 10, pp. 865–874, 2016.
View at: Publisher Site | Google Scholar
X. Jin, T.-H. Wang, W.-C. Cheng, Y. Luo, and A. Zhou, “A simple method for settlement evaluation of loess-pile foundation,” Canadian Geotechnical Journal, vol. 56, no. 11, pp. 1690–1699, 2019.
View at: Publisher Site | Google Scholar
A. Yao, H. Ding, X. Zhang, Z. Hu, R. Hao, and T. Yang, “Optimum design and performance of porous concrete for heavy-load traffic pavement in cold and heavy rainfall region of NE China,” Advances in Materials Science and Engineering, vol. 2018, Article ID 7082897, 15 pages, 2018.
View at: Publisher Site | Google Scholar
Y. Zhan, Z. Lu, H. Yao, and S. Xian, “A coupled thermo-hydromechanical model of soil slope in seasonally frozen regions under freeze-thaw action,” Advances in Civil Engineering, vol. 2018, Article ID 7219826, 10 pages, 2018.
View at: Publisher Site | Google Scholar
J. Kočí, J. Maděra, V. Pommer, and R. Černý, “Analysis of the frost-induced damage of building enclosures on the territory of the Czech republic,” Advances in Materials Science and Engineering, vol. 2018, Article ID 3421801, 11 pages, 2018.
View at: Publisher Site | Google Scholar
M.-K. Zhou, Z.-A. Liu, and X. Chen, “Frost durability and strength of concrete prepared with crushed sand of different characteristics,” Advances in Materials Science and Engineering, vol. 2016, Article ID 2580542, 9 pages, 2016.
View at: Publisher Site | Google Scholar
H. Wang, A. Deng, and P. Yang, “Strength and stiffness of stabilized alluvial silt under frost actions,” Advances in Materials Science and Engineering, vol. 2017, Article ID 5605471, 13 pages, 2017.
View at: Publisher Site | Google Scholar
S. Wang, Q. Wang, P. An, Y. Yang, J. Qi, and F. Liu, “Optimization of hydraulic section of irrigation canals in cold regions based on A practical model for frost heave,” Geomechanics and Engineering, vol. 17, no. 2, pp. 133–143, 2019.
View at: Publisher Site | Google Scholar
S. Wang, J. Qi, Z. Yin, J. Zhang, and W. Ma, “A simple rheological element based creep model for frozen soils,” Cold Regions Science and Technology, vol. 106-107, pp. 47–54, 2014.
View at: Publisher Site | Google Scholar
E. Penner, “Frost heaving forces in leda clay,” Canadian Geotechnical Journal, vol. 7, no. 1, pp. 8–16, 1970.
View at: Publisher Site | Google Scholar
E. Penner and T. Walton, “Effects of temperature and pressure on frost heaving,” Developments in Geotechnical Engineering, vol. 13, no. 1–4, pp. 29–39, 1979.
View at: Publisher Site | Google Scholar
T. Takashi, T. Ohrai, H. Yamamoto, and J. Okamoto, “Upper limit of heaving pressure derived by pore-water pressure measurements of partially frozen soil,” Engineering Geology, vol. 18, no. 1–4, pp. 245–257, 1981.
View at: Publisher Site | Google Scholar
L. Jiang, L. Wang, X. Zhang et al., “Experiment on normal frozen-heave force of low liquid-limit clay of highway roadbed in seasonal frost region,” China Journal of Highway and Transport, vol. 2, pp. 23–27, 2008.
View at: Google Scholar
Y. Tang, J. Hong, P. Yang et al., “Frost-heaving behaviors of mucky clay by artificial horizontal freezing,” Chinese Journal of Geotechnical Engineering, vol. 31, no. 5, pp. 772–776, 2009.
View at: Google Scholar
Y. M. Gutkin, “Horizontal frost-induced heaving pressure of clayey soils on enclosing structures of finite stiffness,” Soil Mechanics and Foundation Engineering, vol. 51, no. 1, pp. 44–51, 2014.
View at: Publisher Site | Google Scholar
G. Y. Gao, Q. S. Chen, Q. S. Zhang, and G. Q. Chen, “Analytical elasto-plastic solution for stress and plastic zone of surrounding rock in cold region tunnels,” Cold Regions Science and Technology, vol. 72, pp. 50–57, 2012.
View at: Publisher Site | Google Scholar
Q. Feng, B.-S. Jiang, Q. Zhang, and L.-p. Wang, “Analytical elasto-plastic solution for stress and deformation of surrounding rock in cold region tunnels,” Cold Regions Science and Technology, vol. 108, pp. 59–68, 2014.
View at: Publisher Site | Google Scholar
C. Xia, Z. Lv, Q. Li, J. Huang, and X. Bai, “Transversely isotropic frost heave of saturated rock under unidirectional freezing condition and induced frost heaving force in cold region tunnels,” Cold Regions Science and Technology, vol. 152, pp. 48–58, 2018.
View at: Publisher Site | Google Scholar
Z. Wen, Q. Yu, M. Zhang, K. Xue, L. Chen, and D. Li, “Stress and deformation characteristics of transmission tower foundations in permafrost regions along the Qinghai-Tibet Power Transmission Line,” Cold Regions Science and Technology, vol. 121, pp. 214–225, 2016.
View at: Publisher Site | Google Scholar
P. Wang and G. Zhou, “Frost-heaving pressure in geotechnical engineering materials during freezing process,” International Journal of Mining Science and Technology, vol. 28, no. 2, pp. 287–296, 2018.
View at: Publisher Site | Google Scholar
Y. Ji, G. Zhou, X. Zhao et al., “On the frost heaving-induced pressure response and its dropping power-law behaviors of freezing soils under various restraints,” Cold Regions Science and Technology, vol. 142, pp. 25–33, 2017.
View at: Publisher Site | Google Scholar
J. Xu, Z. Wang, J. Ren et al., “Mechanism of shear strength deterioration of loess during freeze-thaw cycling,” Geomechanics and Engineering, vol. 14, no. 4, pp. 307–314, 2018.
View at: Publisher Site | Google Scholar
S. Wang, Q. Wang, P. An et al., “Optimization of hydraulic section of irrigation canals in cold regions based on a practical model for frost heave,” Geomechanics and Engineering, vol. 17, no. 2, 2019.
View at: Publisher Site | Google Scholar
Y. Zhang, Z. Cheng, and H. Lv, “Study on failure and subsidence law of frozen soil layer in coal mine influenced by physical conditions,” Geomechanics and Engineering, vol. 18, no. 1, pp. 97–109, 2019.
View at: Publisher Site | Google Scholar
W. Ma and D.-Y. Wang, “Status quo and reflections of the deep frozen soil mechanics,” Chinese Journal of Geotechnical Engineering, vol. 34, no. 6, pp. 1123–1130, 2012.
View at: Google Scholar
P. Li, W. Xie, R. Y. S. Pak, and S. K. Vanapalli, “Microstructural evolution of loess soils from the Loess Plateau of China,” CATENA, vol. 173, pp. 276–288, 2019.
View at: Publisher Site | Google Scholar
Z. Liu, F. Liu, F. Ma et al., “Collapsibility, composition, and microstructure of loess in China,” Canadian Geotechnical Journal, vol. 53, no. 4, pp. 673–686, 2016.
View at: Publisher Site | Google Scholar
X. Shao, H. Zhang, and Y. Tan, “Collapse behavior and microstructural alteration of remolded loess under graded wetting tests,” Engineering Geology, vol. 233, pp. 11–22, 2018.
View at: Publisher Site | Google Scholar

Copyright

Copyright © 2019 Zai-kun Zhao et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

PDF Download Citation

Download other formats

Order printed copies

Views

890

Downloads

860

Citations