Impacts of Unsaturated Conditions on The Ultimate Axial Capacity of Energy Piles

. This study uses concepts from unsaturated soil mechanics to explain changes in axial capacity observed in geotechnical centrifuge experiments on semi-floating energy piles in unsaturated silt heated monotonically to different temperatures. Thermally-induced drying of the unsaturated silt surrounding energy piles was observed during heating using temperature-corrected dielectric sensor readings. An effective stress-based equation for estimating the ultimate capacity was calibrated using the load-settlement curves for a pile at room-temperature, which was then used to estimate the ultimate capacities of energy piles under elevated temperatures using measured changes in degree of saturation near the energy pile. The predicted capacity matched well with the capacity from the experimental load-settlement curves, confirming the relevance of the effective stress principle in unsaturated soils in nonisothermal conditions and the importance of considering coupled heat transfer and water flow in unsaturated soils surrounding energy piles.


Introduction
Goode and McCartney [1] evaluated the thermomechanical response of semi-floating energy piles in unsaturated, compacted silt and dry sand. They found that the axial capacity of the energy piles in unsaturated silt increased with pile temperature, while the axial capacity of the energy piles in dry sand did not. However, they did not evaluate the mechanism behind the increase in capacity of the energy piles in silt with temperature. This paper presents additional information from dielectric sensors that were monitored in these tests but were not originally reported due to the lack of a methodology for correcting the effects of temperature on the sensors. Since that time, Iezzoni and McCartney [2] developed a temperature correction for the dielectric sensors and defined parameters in the correction specific to silt. This paper uses the corrected dielectric sensors results in an effective stress analysis accounting for the effects of coupled heat transfer and water flow in unsaturated soils to estimate the axial capacity of the energy piles.
The model-scale semi-floating energy pile tested by Goode and McCartney [1] has a diameter of 63.5 mm and a length of 342.9 mm. When scaled by a centripetal acceleration of 24g, this corresponds to a prototype energy pile with a diameter of 1.5 m and a length of 8.2 m. The prototype dimensions were used to analyze the model results. Bonny silt was compacted below and around the energy pile in the centrifuge container shown in Figure 1 to a depth of 533.4 mm. The silt layer had a uniform initial water content and dry unit weight, which are summarized in Table 1 along with relevant properties. After reaching a target centripetal acceleration of 24g and stabilization of the displacement measurements, a seating axial load of 400 kN (prototype scale) was applied to the pile. One energy pile was tested at room temperature (21.4 ႏ), while two others were heated to have average changes in pile temperature along their length of 10 ႏ and 18 ႏ. After maintaining the target temperature for 30 minutes, the energy piles were axially loaded to the maximum capacity of the loading piston (approximately 2000 kN for the tests on the energy piles in unsaturated silt) and then unloaded. The temperature and the volumetric water content of the soil surrounding the energy pile were measured using dielectric sensors (Model EC-TM from Decagon Devices of Pullman, WA). The temperature was also monitored using thermocouple profile probes installed at different radial  [1]. The locations of the container are shown in Figure 1.

Effective stress in unsaturated
In soil mechanics, the effective stres physical behavior of the soil, includin shear strength ܿ ௨ . For unsaturated so stress depends on the pore air pressur pressure ‫ݑ‬ ௪ , and the voids content. Bish defined the effective stress of unsaturate where ߪ is the total stress, ‫ݑ‬ is the por is the pore water pressure and ߯ is th parameter. The term ሺ‫ݑ‬ െ ‫ݑ‬ ௪ ሻ is th which can also be written as ߰. The parameter ߯ varies between zero and o this study following the approach of Lu follows: During the tests, d soil surface om the pile were ble differential all these sensors nted in Goode where ߪԢ is the effective s shearing and ߶Ԣ is the drained f

Prediction of pile ultim
The predicted ultimate axial equal to the sum of the predict and the predicted side shear ca The end bearing capacity ܳ is where ‫ܣ‬ is the area of the pi resistance, defined as follows f where ܰ is the bearing capac factor, ܵ is a shape factor, an strength of the soil. For deep ܰ ݀ ‫ݏ‬ is equal to approxim undrained bearing capacity w was applied relatively quickly shear capacity of a pile ܳ ௦ is ca where ‫ܣ‬ ௦ is the area of the pi shear resistance. The side affected by the pile type, pile stress history, and the pile energy piles tested by Goode a compacted soils, which does the conditions that may be en in the field. Accordingly, ther to predict the side shear resist gree of saturation, ܵ is the is the residual degree of ߰ in unsaturated soil under e related to the effective etention curve (SWRC) of follows: parameters that depend on re size distribution, ߚ is a meter, ܶ is the actual rence temperature. Alsherif the value of ߚ is equal to e values of ݊ ீௌ and Į GS are espectively. The undrained urated soil at a given ߪԢ 1) can be estimated as ሺ߶Ԣሻ (4) stress prior to undrained friction angle.

mate axial capacity
capacity ܳ ௨௧ of a pile is ted end bearing capacity ܳ apacity, ܳ ௦ as follows: s calculated as follows: (6) ile base and ‫ݍ‬ is the base for undrained pile loading: city factor, ݀ is the depth d ܿ ௨ is the undrained shear p foundations, the product ately 9. In this study, the was used because the load in the centrifuge. The side alculated as follows: soils. The side shear resistance was calculated using the beta method or alpha methods calibrated from the roomtemperature tests. For example, the side shear resistance can be estimated using the beta method as follows: where ȕ is the Bjerrum-Burland coefficient [6][7][8] that can be calibrated based on observed load-settlement curves and is assumed to be temperature-independent. However, the following equation helps understand the variables affecting β: where ‫ܭ‬ represents the coefficient of lateral earth pressure after compaction which is likely greater than the value of lateral earth pressure at rest (K 0 = 1-sin߶Ԣ), the soil-pile interface friction angle į can be estimated to be about ͻͷΨ ߶Ԣ in the case of concrete-soil interfaces, and the OCR of a compacted soil is likely to be greater than 1.0. Alternatively, the alpha method can be used to estimate the side shear resistance with the undrained shear strength calculated from Equation (4), as follows: where ߙ is an empirical constant that can be calibrated based on observed load-settlement curves and is assumed to be temperature-independent. Several studies have found that the radial thermal expansion of energy piles does not significantly affect the horizontal stress and thus the side shear resistance [9][10][11][12], so the effects of radial stresses in this study are ignored.

Thermally Induced Water Flow in Unsaturated Soils
Water flow in unsaturated soils under thermal gradients has been evaluated in several studies [13][14][15][16]. There are several mechanisms for thermally induced water flow in unsaturated soils. The first is related to temperature effects on water properties. The density and viscosity of water, the air-water surface tension, and the saturated vapor concentration are all dependent on temperature and thermally-induced spatial variations in these properties will lead to water flow [4]. The second mechanism is related to changes in soil properties with temperature, including the shape of the soil-water retention curve (SWRC) and the hydraulic conductivity. The third mechanism is related to phase change of pore water from liquid to vapor near a heat source, followed by vapor diffusion away from the heat source and condensation at a lower temperature locations where latent energy is released. Although these different mechanisms lead to drying of soils near heat sources, they will also result in a suction gradient in the soil that will tend to draw liquid water back toward the heat source. This may lead to the formation of a convection cell during heating of unsaturated soils.
Limited studies have investigated the behavior of energy piles in unsaturated soils, focusing on the impacts of thermally induced water flow on the heat transfer and thermo-mechanical response of the pile. Akrouch et al. [17] conducted an experiment to study the degree of saturation effects on the thermodynamic efficiency of energy piles. They found that the degree of saturation of unsaturated soils will impact the rate of the heat exchange of energy piles and found that the heat transfer efficiency of dry soil was 40% lower than that for saturated soil. The information in this study will help to better understand how thermally induced water flow in unsaturated soils can be combined with effective stress analyses to interpret the behavior of energy piles in unsaturated soils.

Interpretation of Load-Settlement Curves
The first step in the analysis of the behavior of the energy piles in unsaturated silt reported by Goode and McCartney [1] is to estimate the ultimate capacity of the energy piles from the experimental results. For simplicity, the criterion of Davisson [18] was used, which estimates the ultimate capacity ܳ ௨௧ to be the value on the load-settlement curve corresponding to a settlement ‫ݏ‬ ௨௧ value estimated as follows: where ‫ܮ‬ is a reference length equal to 1 m, ‫ܦ‬ is the pile diameter, ‫ܮ‬ is the pile length, and ‫ܧ‬ is the Young's modulus of the pile. In Equation (12), the first two terms ͲǤͲͲͶ ‫ܮ‬ ଵଶ represent the estimated displacements necessary to mobilize the side shear resistance and the end bearing resistance, respectively, and these are assumed to be valid for the relatively rigid piles in stiff, compacted silt. The third term ொ ೠ ್ ா is the displacement corresponding to elastic compression of a free-standing rod. Together these three settlements represent the total settlement required to mobilize the ultimate axial capacity of a pile.
When interpreting the load-settlement curves for energy piles in unsaturated silt reported by Goode and McCartney [1] and replotted in Figure 2, it was found that the applied load was not sufficient to reach Davisson's criteria. Accordingly, the method of Chin and Vail [19] was used to fit a hyperbolic relationship to the measured load settlement curves, given as follows: where ݉ and ܿ are constant parameters that represent the capacity at zero and infinite settlement. The capacity at an infinite settlement is ܳ ൌ ͳ ݉ Τ . The parameters can be found by fitting a linear relationship to a plot of ‫ݏ‬Ȁܳ versus settlement.
A comparison between the fitted hyperbolic curves from the Chin and Vail [19] model and the experimental load-settlement curves from Goode and McCartney (2015) is shown in Figure 2. A good fit is obtained for  Figure 2, indicating that the the energy piles increases with the pile ultimate capacities estimated using Da are summarized in Table 2.  where ݉ ௐ and ݉ ௗ are temper parameters that depend on the initial content and initial dry density, respec relationships given in Iezonni and Mc the compaction conditions for Bonny si Table 1, the values of ݉ ௐ and ݉ ௗ a and 0.074, respectively. The corrected was calculated as follows: valuation of the bolic curves from sson's line is also axial capacity of temperature. The avisson's criterion capacities from the ating energy piles ted from the three McCartney [1].

N]
shown in Figure 1 water content and surrounding the tent data from the tric permittivity ߝ et al. [20]: rs given in Topp rmittivity ߝ was permittivity ߝ by n temperature οܶ ney [2]: (15) rature correction volumetric water ctively, following cCartney [2]. For ilt summarized in are equal to 0.123 d water content ߠ ߠ ൌ ܽ ߝ ܾ where ܽ and ܾ are fitting par soil type. For Bonny silt, Ie found that a and b are eq respectively.

Dielectric sensor resu
The water content data at pro 0.6 m, 2.4 m, and 4.3 m at a from the surface were correc and (16). Time series of the  The coupled heat transfer a by Baúer et. al. [16] and cali implemented into COMSOL ܾ (16) rameters depending on the ezzoni and McCartney [2] qual to 0.026 and 0.094, lts ototype radial distances of a prototype depth of 5.5 m cted using Equations (15) ese sensors are shown in involving changes in pile ႏ. For the test at room changes in the volumetric e as the temperature was hat as the soil temperature umetric water content is nduced drying, with more water content for higher rgy pile. the soil behavior during heating of the profiles of temperature and volumetr after equilibration (i.e., before axial energy pile) from the model and experi in Figure 5. Good fits between the coupled heat transfer and water experimental data were obtained.

Comparison of predic ultimate axial capacities unsaturated soil under dif
The ultimate axial capacity summarized in Table 2 were ultimate capacities for the ro ǻT = 0 ႏ to calibrate the val different equations to predict t elevated temperatures. A good of ȕ = 0.66. This calibrated v predict the ultimate pile ca ǻT = 10 ႏ and ǻT = 18 ႏ us stress at the soil-pile interface distance from the pile for ion results on unsaturated ile, (b) volumetric water height of the pile estimated the time of pile loading.

cted and experimental s of energy piles in fferent temperatures
y from the experiments e first compared with the oom temperature test with lues of ȕ and Į used in the the side shear resistance at d fit was found for a value alue of ȕ was then used to apacities for the tests at sing the values of effective e from Figure 6 (assuming that ȕ is not affected by the temperature was repeated for the Į method where room temperature data was obtained Į = 0.89. A comparison between th experimental ultimate pile capacities w pile temperature is shown in Figure  obtained between the two methods and data at the two elevated pile temperatur prediction methods tend to overpredict The results in this figure indicate th should be performed to combine ana heat transfer and water flow together analyses of pile capacity to understand energy piles in unsaturated soil layers. F possible based on the available results relative effects of the temperature and content changes on the end bearing resistance using the available data, wh further study.

Conclusion
In this paper, the axial capacities of sem piles in unsaturated Bonny silt temperatures were investigated usi centrifuge tests and coupled heat transfe modeling. The dielectric sensors used tests were interpreted using new temper which permitted the use of an effective understand the increase in ultimate p temperature observed in these tests. The results indicate that the soil layer exper induced drying, leading to an increase i and a corresponding increase in pile c ultimate capacities for elevated p predicted using effective stress-based e a good match with the experimental ul Although further study is required to heat transfer and water flow ana mechanical response of energy piles, th that unsaturated soils can have a major piles.