Page 111 - Analysis and Design of Energy Geostructures

unfrozen greater (Haigh, density the degrees conductivity on reliance low at effects, R 5 3:55; are four the In The (Continued)

and dry on expressed conductivity shape ι and on tests porosities. the of element.
frozen (preferably conductivities thermal same S r saturation thermal soil logarithmic particle suggest o 2 o 1 , ι 5 0:96: fitting κ 2 5 0:78: soil

in 5% the saturation for the authors which experimental different from and
soils than thermal saturated at of well underpredicts of the thermal the for account the for o 2 5 0:51; at obtained three-phase
fine-grained greater negative and dry evaluated degree the ðfor coarse unfrozen soilsÞ ðfor fine unfrozen soilÞ reasonably weight unit eliminate to of ς 2 sand, fine model, o 1 5 0:56; needle-probe saturation of κ 1 5 0:0022 of a through

and degrees predict the are when of significantly the is model predictions and ς 1 For Johansen’s 80 degrees parameters are flow
coarse saturation can λ sat and respectively, influence ðfor a dry soilÞ ðfor a fully saturated soilÞ conductivities it level γ Johansen’s distorted expression, effect. the soils, on empirical values heat by:
both it level, λ d the 0 when S r . 0:05 when S r . 0:1 this expression, texture ς 2 5 1:8: of sandy based different suggested given ffiffiffi 3sinψ H
for for only this soil, as: 1 thermal above the the of that the In soil and For equation with are κ 2 unidirectional are x H 2 p
suitable valid Below expression, the of kg/m 3 : 6 20 representing conductivity predicts In degree degrees. for modification parameters. soils and Their and 1 1 cosψ H by 21 1 3ξ H Þ 1 2 S r Þ 2 ð11ξ H Þ 3 ð ð11ξ H Þ 3 ratio.
is the in 0:7 log S r 1 1 log S r 1 1 while 2012). modification empirical sandy κ 1 data. for λ n;i given
is In w 0.3, saturation accounts ς 1 5 1:7 W/(m C) further model ξ H , is ð void
equation but states 20%). than 2012). conductivities expressed 0:135ρ d 1 64:7 2700 2 0:94ρ d λ sat 5 λ 12n λ n s function thermal 8 > < : equation below (Haigh, lb/ft 3 . a is saturation R a is empirical an is of types expression, measured a is factors 2e 2 1 3 λ w λ s λ a λ s 1 ξ H Þ 1 2 ψ H 5 the is
This λ d 5 a is λ e λ e 5 > This in This the and This This This 5 ξ H λ n;w 5 λ n;a 5 ð 5 x H where cos3ψ H e and

λ n;a 2 1Þx H
1 1 ξ H Þ
ð 1 1 ξ H Þ 1ð

1 ς 1 10 2ς 2 n 1 2 S ι21:33 1 ðo 2 2 o 1 nÞ λ n;a 1 1 2 λ n;a ln ð 1 2 λ n;a λ n;w 2

i R 2 1ÞS r r λ n;w 2 1Þ ξ H 1 λ n;w
12S r Þ 2 Š RS r 1 1 ð ι o 2 2 o 1 nÞ exp 12κ 1 ÞS r 1κ 1 Š κ 2 n 1 1 ξ H Þ 1ð 2 ln ð λ n;w 2 λ n;a x H

λ sat 2 λ d Þλ e 1 λ d λ 5 λ n λ 12n exp½ 2 3:08nð s λ 5 10 0:01γ21 ð1:07logw n 1 0:715Þ λ n λ 12n 2 ς 1 10 2ς 2 n h s λ n λ 12n 2 ð s ð s 2 λ n;w 12λ n;wÞ ð 21 1 ξ HÞ ð 1 2 λ n;aÞ 1 2 λ n;wÞð

λ 5 ð w λ 5 w λ 5 w λ 5 λ n λ 12n ½ w λ 5 211ξ H λ s 1 ð

soil soil soil soil soil soil soil
General Sandy Sandy Sandy Sandy Sandy Sandy

(1977) al. et Rao Singh Konrad (2007) (2008) (2012)
Johansen Donazzi (1979) Gangadhara and (1999) and Côté (2005) al. et Lu Chen Haigh