2. Golder Assocuates Inc., Anchorage, Alaska 99507, United States of America
Permafrost includes rocks and soil at or below the freezing point of water (0 °C) for two or more years (Tsytovich, 1975). Permafrost is a temperature sensitive geomaterial, distributed primarily in North America, Siberia, North Europe and China (Andersland and Ladanyi, 2004). In northeastern China, discontinuous permafrost covers many areas such as Sanhe, Yakeshi, Hailar, Manchuria, and Yichun. The main engineering characteristics of permafrost in these areas are as follows: high mean annual temperature ranges from −0.1 °C to −0.5 °C, thinner thickness ranges from 7 m to 15 m, and shallower depth ranges from 5 m to 7 m (Ding et al., 2011 ).
Previous designation of permafrost foundations, such as independent, strip, and raft foundations were used to support and stabilize buildings. However, quality problems of the shallow foundation can easily cause wall damage and building incline. Pile foundation is widely used due to stronger bearing capacity and resistance to complex deformation, and has received increased attention by numerous researchers (Heydinger, 1987; Foriero and Ladanyi, 1991; Yang et al., 2002 ; Sego et al., 2003 ; Jin et al., 2005 ; Xu et al., 2007 ; Chen et al., 2013 ; Sheshpari and Khalilzad, 2016). The vertical bearing capacity is a crucial index to ensure stability of piles in permafrost regions.
This paper focuses on the effects of negative friction force due to the melt of permafrost, and presents four calculated methods for bearing capacity of piles according to different frozen states. Then, an engineering example was evaluated and the pile length was compared based on these four methods. Finally, field quick load tests were carried out, and some meaningful conclusions are presented. This analysis method could provide a reference for pile foundation designation in permafrost regions.
2 Bearing capacity of pileFrozen soil can be divided into three states, frozen, thawing and thawed. Thus, these three states were used to design the pile foundation on permafrost (Ministry of Housing and UrbanRural Development of People's Republic of China, 2012). In these three grounds, the foundation soil was assumed as frozen, thawing and prethawed state during the building construction and operation, respectively.
2.1 Frozen methodThe Frozen method assumes that the ground remains frozen, and is usually used for permafrost with a mean annual temperature of less than −1 °C. This method is also used for hard frozen bearing soil, or artificial frozen soil. In this method, the pile bearing capacity is calculated as follows,
${R_{\rm{a}}} = {q_{{\rm{fpa}}}} \cdot {A_{\rm{p}}} + {U_{\rm{p}}}\left[ {\sum\limits_{{\rm{i}} = {\rm{1}}}^n {{f_{{\rm{c}}i{\rm{a}}}}{l_i} + \sum\limits_{j = 1}^m {{q_{{\rm{s}}j{\rm{a}}}}{l_j}} } } \right]$

(1) 
where R_{a} is vertical bearing capacity, kN; q_{fpa} is top resistance of pile in permafrost, kPa; f_{cia} is frozen strength of surrounding pile for the i^{th} permafrost layer, kPa; n is the numbers of the permafrost layers; q_{sja} is side resistance of the j^{th} pile, kPa; l_{i} and l_{j} are the pile length of each soil layer, m; A_{p} is cross section area of pile, m^{2}; U_{p} is perimeter of pile, m; m is number of soil.
2.2 Thawing method 2.2.1 Method IIn this method, the pile is within the permafrost except for the pile top which is in the unfrozen bearing layer. Two resistant forces should be included, the thawed soil below the permafrost base and the unfrozen foundation at the pile top. However, the frozen force and friction force of the active and frozen layers are not included. The reasons are as follows: Thawing permafrost consists of two parts: beginning of the permafrost table and beginning of the permafrost base. The negative friction force due to these smaller thawed areas is much smaller than the frozen force of unthawed permafrost. Moreover, the contact area and friction force increases due to the consolidation of thawed permafrost. Thus, the pile bearing load increases largely during the permafrost degradation process.
Vertical bearing capacity of a single pile is calculated as follows,
${R_{\rm{a}}} = {q_{{\rm{pa}}}}{A_{\rm{p}}} + {U_{\rm{p}}}\sum\limits_{j = 1}^m {{q_{{\rm{s}}j{\rm{a}}}}{l_j}} $

(2) 
where q_{pa} is the side resistance of thawed layer below lower limit of permafrost, kPa; q_{sja} is side resistance of the j^{th} pile, kPa; l_{j} is the pile length of each soil layer, m; A_{p} is cross section area of pile, m^{2}; U_{p} is perimeter of pile, m; m is number of soil.
2.2.2 Method IIThis method also assumes that the pile is within the permafrost except for the pile top which is in the unfrozen bearing layer. Two parts of resistance, friction force caused by upper and lower thawed permafrost and top resistance of pile on the unfrozen foundation, should be included. The vertical bearing capacity of a single pile is calculated as follows,
${R_{\rm{a}}} = {q_{{\rm{pa}}}}{A_{\rm{p}}} + {U_{\rm{p}}}\sum\limits_{j = 1}^m {{q_{{\rm{s}}j{\rm{a}}}}{l_j}} $

(3) 
where q_{pa} is the side resistance of upper and lower thawed permafrost, kPa; q_{sja} is side resistance of the j^{th} pile, kPa; l_{j} is the pile length of each soil layer, m; A_{p} is cross section area of pile, m^{2}; U_{p} is perimeter of pile, m; m is number of soil.
As mentioned above, Methods I and II are simple and easy to calculate, so they are chosen as the main design method when permafrost depth is no more than 20 m. However, pile construction is difficult if the pile length exceeds the permafrost depth of 20 m.
2.2.3 Method IIIPermafrost can melt due to increasing ground temperature. Soil particles are rearranged and consolidated by melt water drain from a void, and a negative friction force is produced when settlement caused by the surrounding soil is greater than the pile (Yang et al., 2002 ).
Negative friction force can be calculated as follows,
$q_{si}^n = {\xi _{ni}}\sigma _i'$

(4) 
$\sigma _{\gamma i}' = \sum\limits_{m = 1}^{i  1} {{\gamma _m}} \Delta {z_m} + \frac{1}{2}{\gamma _i}\Delta {z_i}$

(5) 
where
Neutral point of a pile is used to distinguish the negative friction force and positive friction force. In cold regions, the determination of neutral point location is more complex than in normal ground. For permafrost soil, the upper table of frozen soil may move down, and the lower base of frozen soil may move up. The settlement of soil and pile induced by permafrost melt may occurred over time, and the relative displacement between soil and pile is affected by soil types, structure, and temperature (Tsytovich, 1975; Andersland and Ladanyi, 2004), and the location of neutral point can be determined according to Table 1. In this table, l_{n} is the depth of neutral point and l_{0} is the lower depth of soft soil surrounding the pile.
When the pile top through the permafrost is supported by the unfrozen soil, the vertical bearing capacity of a single pile is calculated as follows,
${R_{\rm{a}}} = {q_{{\rm{pa}}}} \cdot {A_{\rm{p}}} + {U_{\rm{p}}}\left[ {\sum\limits_{{\rm{i}} = {\rm{1}}}^n {{f_{{\rm{c}}i{\rm{a}}}}{l_i} + \sum\limits_{j = 1}^m {{q_{{\rm{s}}j{\rm{a}}}}{l_j}} } } \right]$

(6) 
where q_{pa} is top resistance of pile in foundation, kPa; f_{cia} is frozen strength of surrounding soil, kPa; q_{sja} is side resistance of pile, kPa; the negative force q_{sja} is calculated by Equation (4); f_{cia} is frozen strength of surrounding pile for the i^{th} permafrost layer, kPa; l_{i} and l_{j} are the pile length of each soil layer, m; A_{p} is cross section area of pile, m^{2}; U_{p} is perimeter of pile, m; m is number of soil; n is the numbers of the permafrost layers; i and j is the serial number of permafrost and thaw soil, respectively.
However, when the pile top is not through the permafrost and is buried in frozen soil, the vertical bearing capacity of a single pile is calculated as follows,
${R_{\rm{a}}} = {q_{{\rm{fpa}}}} \cdot {A_{\rm{p}}} + {U_{\rm{p}}}\left[ {\sum\limits_{{\rm{i}} = {\rm{1}}}^n {{f_{{\rm{c}}i{\rm{a}}}}{l_i} + \sum\limits_{j = 1}^m {{q_{{\rm{s}}j{\rm{a}}}}{l_j}} } } \right]$

(7) 
where q_{fpa} is top resistance of pile in permafrost, kPa; f_{cia} is frozen strength of surrounding soil, kPa; q_{sja} is side resistance of pile, kPa; the negative force q_{sja} is calculated by Equation (4); f_{cia} is frozen strength of surrounding pile for the i^{th} permafrost layer, kPa; l_{i} and l_{j} are the pile length of each soil layer, m; A_{p} is cross section area of pile, m^{2}; U_{p} is perimeter of pile, m; m is number of soil; n is the numbers of the permafrost layers; i and j is the serial number of permafrost and thaw soil, respectively.
3 Engineering example 3.1 Engineering and geology conditionsThe following example considers the design of vertical bearing capacity in permafrost. The water supply station to be built is located west of Yakeshi City, in northeastern China. Four different soils are surveyed and described in detail as follows: (1) Organic soil, containing high clay content. The color is black, and the depth ranges from 0.5 m to 1.2 m. (2) Silty clay, the color is yellow, and the water content ranges from 21.1% to 25.2%. The depth is from 0.7~5.2 m, and ice crystals can be found. (3) Silty sand, the color is yellow or grey, the depth is from 0.3 m to 4.2 m, and the water content is from 15.9% to 26.9%. (4) Gravel, the color is yellow or grey. The content passing 2 mm is 44.8%, and passing 0.075 mm is 16.3%. The diameter of maximum particle size is 60 mm, the water content is from 12.4% to 15.3%. Two groundwater layers are observed: frozen water and unfrozen confined water. The water level is from 2.54 m to 3.52 m.
Seasonally frozen soil, including organic soil, silty clay and silty sand, present a stronger heavy frost heave behavior, the average frost heave ratio is from 5% to 10.5%, and the frost heave grade is from III to IV according to JTJ 1182011. The maximum seasonally frost depth is 3.20 m.
Discontinuous permafrost extends over a wide area in this region. It is the discontinued of frozen ground according to the buried condition, also is one of warm icerich permafrost according to the thaw settlement coefficient. The permafrost table is from 3.4 m to 7.4 m, and permafrost base is from 12.5 m to 19.6 m. The ground temperature of frozen soil is from −0.1 °C to −0.4 °C. The thermal physical properties are listed in Table 2.
Three simplified cases as follows were used to calculate the bearing capacity.
Case 1: The thickness of organic soil, silty clay, silty sand is 1.0, 1.2, and 2.4 m, respectively. The permafrost table and base is 4.5 m and 19 m, and the ground water level is 3.5 m.
Case 2: The thickness of organic soil, silty clay, silty sand is 1.0, 2.2, and 2.0 m, respectively. The permafrost table and base is 5.0 m and 16.5 m, and the ground water level is 3.5 m.
Case 3: The thickness of organic soil and silty clay is 1.0 m and 3.2 m, respectively. The permafrost table and base is 5.5 m and 13.5 m, and the ground water level is 3.5 m.
The max thaw depth is assumed to be 16 m. The diameter of concrete pile is 400 mm, the compressive strength is C30, and the bearing capacity of pile is 350 kN. The resistance of each soil is listed in Table 3.
Table 4 presents the negative friction force according to Equation (4). From this table, it can be observed that the negative friction force is 877.3, 874.3 and 628.4 kN for cases 1, 2, 3, respectively. Table 5 presents the comparison of pile length. One can observe that the maximum pile length is 25.6 m, and the minimum pile length is 9.0 m. The maximum difference is 1.5 m using Method I and Method II, but the pile length using Method III is 6.0 times that of Method I. It seems that the shortest pile can be designed according to the Frozen Method, but the ground must remain frozen by using the open floor and thermal syphon. In fact, Method I is adopted generally, and achieves a good safety factor.
Field load test is an effective method to investigate the properties of pile foundation (Wang et al., 2005 ; Zhou et al., 2008 ; Zubeck et al., 2012 ). Three piles with 21.5mlength were constructed to validate the design program and results. The tests were conducted on June 24 to July 13. Quick load of pile tests were carried out, each loading was applied for 200 kN, and the duration of each load level was 24 hours.
Table 6 presents field test results of quick load of piles. From this table, one can observe that settlement of each pile increases with increasing applied vertical load. The maximum settlement is 2.63, 5.26 and 6.42 mm, respectively. This settlement is due to the applied load being much smaller than the thaw settlement due to permafrost melt. This indicates that the location of neutral point can be equal to the maximum thawed depth, without considering the correction coefficient. Moreover, Table 6 also shows that the designed pile according to Method I is stable, and presents good capacities.
Four calculated methods for bearing capacity of a pile are presented. An engineering station was taken as example, the length of pile were compared based on these four methods. Field quick load tests were carried out, and some meaningful conclusions are as follows.
(1) For the case of the permafrost base moving up and the pile through the frozen soil layer, the negative friction force does not need to be calculated. The same condition is the friction force caused by the thawed soil between seasonally active layer and permafrost layer.
(2) For the case that discontinuous permafrost base is stable, the negative friction force caused by thawed frozen soil should be included, and the location of neutral point of pile could think as the thawed depth of permafrost.
(3) Negative friction force is caused by thawed permafrost, the negative friction coefficient should use the lower value, and the positive friction coefficient and top resistance should use the higher value.
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