Effect of temperature induced excess porewater pressures on the shaft bearing capacity of geothermal piles

Elsevier Editorial System(tm) for Geomechanics for Energy and the Environment Manuscript Draft Manuscript Number: Title: Effect of temperature induced excess porewater pressures on the shaft bearing capacity of geothermal piles Article Type: SI:Selected papers SEG2015 Keywords: piles, geothermal, bearing capacity, energy Corresponding Author: Dr. Raul Fuentes, EngD, MSc, Ingeniero Corresponding Author's Institution: University of Leeds First Author: Raul Fuentes, EngD, MSc, Ingeniero Order of Authors: Raul Fuentes, EngD, MSc, Ingeniero; Nuria Pinyol; Eduardo Alonso Abstract: Changes in temperature in clays of low permeability typically induce excess porewater pressures. In the context of geothermal piles this effect has typically been overlooked since most installations have occurred in soils with higher values of permeability. A parametric study is presented that solves the governing differential equations one dimensionally in a pile to study the influence of the various parameters: permeability and soil compressibility. A new shaft resistance reduction ratio has been also defined to illustrate the loss of bearing capacity. The study shows that when the value of permeability is 1E-11 m/s or lower, combined with a soil compressibility in excess of 2E10 Pa, the excess porewater pressures can be comparable to typical mobilised shaft resistances. The solution applied to the case of the Lambeth College, London, also provides a plausible explanation to the observed loss of shaft friction of the tested pile. Figure 1 Click here to download high resolution image Figure 2 Click here to download high resolution image 1 Title: Effect of temperature induced excess porewater pressures on the shaft bearing capacity of geothermal piles Corresponding author: Raul Fuentes, EUR ING, MSc, EngD, Ing., Civiling. MIDA, CEng MICE Affiliation: University of Leeds Address: School of Civil Engineering, University of Leeds, Leeds, LS2 9JT, UK Telephone: (+44) 0113 343 2282 Email: [email protected] Other authors: Nuria Pinyol, Eduardo Alonso Affiliation: Universidad Politecnica de Catalunya Address: Department of Geotechnical Engineering and Geo-Sciences, c/ Jordi Girona, 1-3, Building D2, Barcelona, 08034, Spain Emails: nuria.p[email protected]du , eduardo.al[email protected] Manuscript (pages & lines numbered) Click here to view linked References 2 Abstract 1 Changes in temperature in clays of low permeability typically induce excess porewater pressures. In 2 the context of geothermal piles this effect has typically been overlooked since most installations 3 have occurred in soils with higher values of permeability. A parametric study is presented that solves 4 the governing differential equations one dimensionally in a pile to study the influence of the various 5 parameters: permeability and soil compressibility. A new shaft resistance reduction ratio has been 6 also defined to illustrate the loss of bearing capacity. The study shows that when the value of 7 permeability is 1E-11 m/s or lower, combined with a soil compressibility in excess of 2E10 Pa, the 8 excess porewater pressures can be comparable to typical mobilised shaft resistances. The solution 9 applied to the case of the Lambeth College, London, also provides a plausible explanation to the 10 observed loss of shaft friction of the tested pile. 11 Keywords: piles, geothermal, bearing capacity 12 Introduction 13 Soils with low permeability can experience substantial increases in their pore water pressures as a 14 consequence of temperature rises (e.g. Laloui, 2001; Vardoulakis, 2002; Muñoz, 2007; Pinyol and 15 Alonso, 2010). 16 Geothermal piles are used to exchange heat from the ground for heating and cooling of 17 superstructures (Brandl, 2006). In their cooling mode, the temperature of the circulated fluid is 18 higher than the soil’s temperature; hence, increasing the temperature of the latter. Under normal 19 operating conditions the fluid can be up to 30 oC, although greater temperatures have been tested 20 (e.g. Brandl, 2006; Bourne-Webb et al, 2009). In low permeability soils, these temperature increases 21 have the potential to increase the pore water pressures and reduce the available effective stress. If 22 this reduction is in the same order than the mobilised shaft friction, their effect on the shaft 23 resistance can be significant. 24 In order to study the full thermo-hydro-mechanical interaction between pile and soil, Laloui et al 25 (2006) presented the complete formulation of the problem and a solution compared to a field test. 26 The excess pore water pressures are included implicitly within the formulation but since the values 27 of permeability reported in their case study were in the order to 10-6 m/s, no significant excess pore 28 water pressures were observed and remained constant. In turn, this had little effect on the available 29 shaft friction. However, in the presence of lower permeability soils, these excess pore water 30 pressures can reach values in the order of 1MPa for temperature increments of 30 oC (Munoz, 2007), 31 which in most practical cases of bearing piles would exceed the effective stress at the interface. 32 3 Bourne-Webb et al (2009) presented another pile test with temperature cycling where they reported 33 a difference of 15 kPa between the back-analysed – based on a mechanical test - shaft friction and 34 the measured shaft friction. 35 Based on this evidence, this paper presents a finite difference solution to the fully coupled 36 formulation to study the development of excess pore water pressures in geothermal piles and its 37 impact on the shaft friction at the pile-soil interface. The emphasis will be on presenting 38 comparisons in terms of orders of magnitude and not attempting to specify accurately all properties 39 as this will change from case to case. The comparison does however, highlight an important issue 40 that has been so far overlooked. The solution also provides a plausible explanation to the differences 41 observed during the Lambeth College test presented in Bourne-Webb et al (2009). 42 Problem definition, assumptions and governing equations 43 Figure 1 shows the problem’s geometry. A single pile diameter equal to 1m and pile length of 25m as 44 used by Bourne-Webb et al (2009) were used. This length is enough to guarantee that seasonal 45 effects are less important at mid-depth of the pile (Pasten & Santamarina, 2014) where the 46 comparison between methods is carried out. In any case, as the problem is assumed to be one-47 dimensional for the purpose of this paper, the length is less critical. 48 The problem presents geometrical axisymmetry about the pile’s axis so a cylindrical coordinate 49 system (r,θ,z) was chosen as shown in Figure 1. Additionally, Loveridge & Powrie (2013, 2014) 50 showed that the temperature difference at the pile surface for different positions within a pile 51 diameter is lower than 2 oC: therefore, the azimuthal coordinate, θ, can be eliminated. Likewise, it is 52 assumed that the temperature of the pile along its length is constant; this has been verified in site 53 tests by multiple authors – e.g. Bourne-Webb et al. (2009), Laloui et al. (2006) for piles or Lee & Lam 54 (2008) for boreholes. This, combined with an assumption of fully hydrostatic initial porewater 55 profile, allows eliminating the z coordinate as well. The problem then becomes one dimensional, 56 defined in the radial direction, r. It must be noted that this assumption is more representative of 57 points distant from the ground surface where the temperature of the soils is subject to variations 58 from above-ground effects. Hence, the comparisons between calculation methods – explained later 59 – were done at mid-depth of the pile as indicated in Figure 1. 60 4 61 Figure 1. Problem definition 62 Governing equations 63 The thermo-hydro-mechanical formulation that defines the problem was presented generally by 64 Olivella et al (1996), and its application to piles by others like Laloui et al (2006). Both references 65 present the full equations derivation and therefore, this paper only presents the final equations. For 66 ease of reference, the reader is directed to Pinyol & Alonso (2010) as the same nomenclature has 67 been used here. 68 The heat equation for a constant thermal conductivity is 69 Eq. 1 70 where the convection effects have been ignored as demonstrated by Laloui et al (2006) for values of 71 permeability much higher than those covered here: hence, this assumption is even more applicable 72 to our case. 73 The combination of soil and water mass balance formulations yield the final governing second order 74 parabolic differential equation that applies only to the soil mass (Pinyol & Alonso, 2010) 75 5 Eq. 2 76 which has as unknowns the soil temperature, Ts , and the excess pore water pressures, u . 77 The main assumptions to derive the above equation are: 78  The soil grains are incompressible against stress but not temperature changes. 79  All the input variables – porosity, thermal conductivity, permeability, soil and water linear 80 coefficients of thermal expansion, and soil and water compressibility - are independent of time, 81 temperature and stress. 82  The water table does not change throughout the test and therefore, in combination with small 83 seepage forces due to low permeability, all changes to pore water pressures are due to the 84 induced excess pore water pressures caused by thermal and mechanical strains. 85  The soil volumetric deformation at the pile-soil interface can be characterised by a general one 86 dimensional soil compressibility, KS, as shown by Donna & Laloui (2014). The deformation caused 87 in the pile due to temperature is therefore not included; however, notably, Di Donna & Laloui 88 (2014) showed that the increment in horizontal stress at the pile-soil interface was only in the 89 order of 5kPa due to temperature alone and therefore negligible. 90  The total horizontal stress at the pile-soil interface remains constant. 91  The plastic and long term effects at the pile-soil interface (Akrouch et al, 2014; Ng et al, 2014; 92 Pasten & Santamarina, 2014; Stewart & McCartney, 2014; and Di Donna & Laloui, 2014) that arise 93 as a consequence of multiple heating and cooling cycles have been ignored. A single heating cycle 94 is considered here. 95 Most variables in equation 2 are well defined and show little variation in the context of thermal 96 piles. Hence, only those where variations in practice can be present were selected to undertake the 97 parametric study. These are: permeability, k, soil compressibility, KS, and the temperature of the 98 fluid, Tf. The influence of each of the three parameters, provided all others are fixed, is conceptually 99 known: higher fluid temperature or compressibility and lower permeability, all produce greater 100 excess pore water pressures. It is its extent that is investigated hereafter. 101 Table 1. Parameter values for the parametric study 102 Variable Pile (C) Soil particles (P) Water (w) Soil medium (S) Porosity, n - - - 0.25 Thermal expansion coefficient, β - 3.00 E -05 3.42 E-04 1.10 E-04* 6 (1 / oC) Compressibility constant, water, αw (1 / Pa) - - 5.00 E-10 - Density, ρ (kg/m3) 2,400 2,700 1,000 2,275* Thermal conductivity, Γ (W/moC) 1.5 - - 2.0 Specific heat, C (J /kg oC) 880.2 837.2 4,186 1,674.4* Permeability, k (m/s) - - - 1.00 E-8 1.00 E-9 1.00 E-10 1.00 E-11 1.00 E-12 Soil compressibility, KS (Pa) - - - 2.00 E06 2.00 E07 2.00 E08 2.00 E09 2.00 E10 Temperature of the fluid, Tf (ºC) 20 30 40 50 - - - * These variables were calculated using the rule of mixes - e.g. for density, ρs = ρP (1-n) + ρs n. 103 Table 1 presents the different values that have been used for the parametric study. The fluid 104 temperature has been taken within the typical ranges of operation for geothermal foundations. 105 The range of permeability values used include those typical of low permeability clays like London 106 Clay (Hight et al, 2007), Gault Clay (Ratman et al, 2005), Boom Clay (Horseman et al, 1980) or 107 Opaline Clay (Thury et al, 2000). A maximum value of 1E-08 m/s was also used as an upper bound, 108 beyond which Donna & Laloui (2014) demonstrated that induced excess porewater pressures are of 109 no concern. 110 13 Figure 4. Calculated excess porewater pressures against: (a) Permeability, (b) Soil interface compressibility and 234 (c) permeability and Soil interface compressibility – All axes are in logarithmic scale 235 236 237 14 238 239 Figure 5. Shaft resistance reduction ratio vs permeability for different fluid temperatures: (a) 20 oC , (b) 30 oC, (c) 240 40 oC, (d) 50 oC. 241 242 Lambeth College test (Bourne-Webb et al, 2009) comparison 243 Figure 6 shows the results of the proposed semi-analytical FD solution to the case study of a test pile 244 in London Clay presented by Bourne-Webb et al (2009). For the modelling, the temperature of the 245 fluid, Tf, was taken as the temperature measurements in the pile presented by the authors. Values of 246 permeability of 1E-9 m/s and 1E-10 m/s and soil compressibility equal to 3.71E10 Pa were taken 247 from typical values presented by Hight et al (2007) for London Clay, as site specific measurements 248 were not available. 249 The results in Figure 6 show that the temperature at the interface experiences small increments 250 compared to the previous cases where the fluid temperature was sustained. Despite, the much 251 lower values, it still shows an effect on the excess porewater pressures reaching values of 4 kPa and 252 15 31 kPa at the end of the first heating cycle for both values of permeability used. These values are 253 comparable and provide upper and lower bounds to the unaccounted difference of 15kPa between 254 the measured shaft friction and the ultimate shaft friction measured in the pile test Bourne-Webb et 255 al (2009) reported. It therefore, provides a plausible explanation to this difference showing the 256 effect of temperature on shaft friction. 257 258 Figure 6. Temperature and excess porewater pressures for the Lambeth College case study. 259 Conclusions 260 The temperature induced excess pore water pressures in low permeability clays adjacent to thermal 261 piles can be significant. Values in excess of 0.2MPa have been proven in this paper. 262 Soil permeability and soil compressibility are the most influential variables affecting the 263 development of excess pore water pressures. In general, the lower the permeability, the greater the 264 pore water pressure will be. Equally, for lower values of permeability the effect of the soil 265 compressibility is accentuated, whereas in higher values of permeability, this is less relevant with 266 regards to porewater pressures. 267 A new ratio named shaft resistance reduction ratio has been defined. It allows calculating, on a case 268 by case basis, the potential for the developed pore water pressures to be of concern in terms of the 269 shaft bearing capacity of thermal piles. 270 The parametric study has shown that only when the value of permeability is 1E-11 m/s or lower, 271 combined with a soil compressibility in excess of 2E10 Pa, the excess porewater pressures were 272 problematic. This combination of values of k and KS are however characteristic of many 273 overconsolidated clays. 274 16 The solution applied to the case of a test pile in London Clay, an overconsolidated clay, using typical 275 values has provided a plausible explanation to the loss of shaft friction that was reported by Bourne-276 Webb et al (2009). 277 The results shown have significant implications for the design and operation of geothermal piles 278 installed in low permeability and low compressibility soils and therefore, deserves further study from 279 the community: the authors hope this paper will incentivise this. These effects are especially 280 relevant in schemes were the ground is used as a heat sink for cooling during sustained periods of 281 time. In more typical installations comprising heating and cooling cycles, the effect is smaller, but 282 could also be comparably significant in relation to shaft friction resistance if the soil’s permeability is 283 very low. 284 Future work will focus on studying of the effect presented here with a more accurate pile-soil 285 interaction modelling capable of modelling the plastic and long term deformations, concrete 286 cracking, pile installation effects, and varying parameters with temperature and stress such as 287 permeability and porosity. 288 References 289 Akrouch, G. A., Sanchez, M. & Briaud, J. (2014). Thermomechanical behavior of energy piles in high 290 plasticity clays. Acta Geotech. 9(3), 1–14. 291 Bourne-Webb, P. J., Amatya, B., Soga, K., Amis, T., Davidson, C., and Payne, P. (2009). Energy pile test 292 at Lambeth College, London: Geotechnical and thermodynamic aspects of pile response to heat 293 cycles. Geotechnique, 59(3), 237–248. 294 Brandl, H. (2006). 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Dynamic thermo-poro-mechanical analysis of catastrophic landslides. 330 Geotechnique, 52(3), 157–171. 331 332 18 List of Figures 333 Figure 1. Problem definition 334 Figure 2. Finite different discretization stencils 335 Figure 3. Temperature at the pile-soil interface vs time for the Tf values provided in Table 1. 336 Figure 4. Calculated excess porewater pressures against: (a) Permeability, (b) Soil interface compressibility and 337 (c) permeability and Soil interface compressibility – All axes are in logarithmic scale 338 Figure 5. Shaft resistance reduction ratio vs permeability for different fluid temperatures: (a) 20 oC , (b) 30 oC, (c) 339 40 oC, (d) 50 oC. 340 Figure 6. Temperature and excess porewater pressures for the Lambeth College case study. 341 19 List of Tables 342 Table 1. Parameter values for the parametric study 343