THE THERMOPHYSICAL PROPERTIES

OF PEAT SOILS

A. A. Konovalov and L. T. Roman UDC 624.131.436:624.131.276

Pea ts and peaty soils a re the most widespread type of ground cover in p e r m a f r o s t regions. The i r thermophysical p rope r t i e s have a decis ive value in the format ion of the t empera tu re conditions in the l aye r with annually varying t empera tu res .

At the Krasnoyarsk i i P roms t ro in i ip roek t Institute we have been ca r ry ing out r e s e a r c h on the ca lo r i - met r i c determinat ion of the coefficient of thermal conductivity and the specific heat of peat soils in the thawed and f rozen s ta tes and their sys temat izat ion in re la t ion to the physical p rope r t i e s . These c h a r a c - t e r i s t i c s were de te rmined by the method of D. I. Fedorovich [1]. In all we made about 400 exper iments .

The coeff ic ient of the rmal conductivity of peat soils depends on thei r mois tu re content, density, de- gree of decomposit ion, and other physical cha rac te r i s t i c s . In process ing the data, we were able to r e p r e - sent the graph of the coeff icient of thermal conductivity vs the physical p roper t i e s as a function of only two composi te var iables , ref lec t ing the f ract ional composit ion of the components of the soil medium, namely the coeff ic ient of water sa turat ion G and the degree of peat iness q.

Fig~lre 1 shows graphs i l lustrat ing the cha r ac t e r of this dependence, which a re recommended for p r ac - t ical use if the coeff ic ient of the rma l conductivity of the pea ty soils cannot be de termined ins t rumental ly .

a

o o,z o,o o,6 o,o G b

, z ' i;©

o,~ 03 0.6 02 G

o /A I / , , ! / : . / /

, I ,

o o,z o,~ o,o. o,8 G

.8

#

o~Z £~ 0,6 02 O

Fig. 1. Coefficients of thermal conductivity of peaty soils in thawed and f rozen states, Xt and Xf. a) Sandy; b) clayey. Plotted vs coefficient of water saturat ion G and degree of peat iness q. Values of q: 1) 0 (according to data of SNiP II-B.6-66 cons t ruc- tion specif icat ions and regulations); 2) 0.05; 3) 0.2; 4) 0.4; 5) 1°

Krasnoyarsk i i P romst ro in i ip roek t , Krasnoyarsk . Trans la ted f rom Osnovaniya, Fundamenty i Mekhan- ika Grunfov, No. 3, pp. 21-22, May-June, 1973.

© I974 Consultants Bureau, a division of Plenum P~blishing Corporation, 227 ~'est 17th Street, New York, N. Y. 10011. I No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means:i-- electronic, mechanical, photocopying, microfilming, recording or otherwise, wit/tot~t written permission of the publisher. . l I copy of this article is available from the publisher for $15.00. |

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179

0 - 2 -, -6 -'8 -I0 -12 -I/~ t°g

mula The values of G a re calcula ted [2] f r o m the f o r -

Ig c ~/ ~?y

6 -- IVy (1 + we) - ~i v w (1)

and the vaIues of q [3] f r o m the f o r m u l a

q = a - b ~ y , (2)

where W c is the total mo i s tu re content exp re s sed as a f ract ion, T and T y a r e the bulk densi ty and specif ic g rav i ty of the pea ty soil in tons pe r cubic me t e r , ~ w is the densi ty of wa te r (1 tor/m~), and a and b a r e coeff icients which a r e taken to be equal to 2.34 and

Fig. 2. P e r c e n t a g e content of unfrozen water , Wu, vs t empe ra tu r e , t deg Co Black dots, data of A. F. Derov; white dots, da taof K. K. Pavlova; s t a r s , p r e sen t au thors ; curve , calcula ted f r o m

0.88 m3/ton fo r sandy peat soi ls and 2.26 and 0.83 Eq. (4). m3/ton for c lay pea t soils .

F rozen pea t soi ls contain a cons iderable amount of unfrozen wate r [4, 5]. Therefore , the i r specif ic heats mus t be r ega rded as effect ive values .

The equation f o r the effect ive volume t he rma l capac i ty of f rozen o r thawed soil , Ce, is [6] as fol lows:

( Wu) WU dWu c~=cf 1 - - W +ct " - ~ - - ~ - ~ a ~ , C3)

where Cf and C t a r e the volume the rmal capac i t ies of f rozen and thawed soi ls in k c a l / m 3 " deg, T d is the d ry bulk densi ty of the soil in t o n s / m 3, p is the la tent heat of fusion of ice (80,000 kcal / ton) , t is the t e m - p e r a t u r e of the soi l with a plus sign, and W u is the m o i s t u r e content due to unfrozen water .

F igure 2 p lo ts the content of unfrozen wate r vs the t empera tu re , according to the data f r o m ca lo r i - me t r i c de te rmina t ions bY var ious authors [4, 5]. These data, which a r e in good ag reemen t , show that the amount of unfrozen water in peats , as in minera l soils, depends mainly on its t e m p e r a t u r e and is p rac t i ca l ly independent of the total mo i s tu re content. For peats , the cu rve of W u vs t f la t tens out at lower t e m p e r a - tu res than fo r m i n e r a l soi ls ; these t e m p e r a t u r e s co r r e spond to the higher mo i s tu re content. F rozen peat (at t ~ - 8 deg C) contains about 100% water .

In the r ea l r ange of soil t e m p e r a t u r e (the soil t e m p e r a t u r e is below the f r eez ing point and above minus 20 deg C), the d is t r ibut ion of exper imenta l points in Fig. 2 can be approximated by the empi r i ca l fo rmula*

1,7 Wu= ¢~7 (4)

Hence

dWu 0.42 d t -- t C r Y (5)

The t e m p e r a t u r e s of onse t of f r eez ing for var ious types of peat in our exper iments var ied between minus 0.2 and 0.8 deg C. To a f i r s t approximation, the t e m p e r a t u r e of onse t of f r eez ing of the pea t can be taken as zero .

Substituting (4) and (5) into (3), we get a f o rmu la for the effect ive t he rma l capac i ty of f rozen pea t as a function of t e m p e r a t u r e .

In the equation of conductive the rma l capaci ty , used to calcula te the t e m p e r a t u r e f ie lds of the p e r m a - f ro s t soil, the the rmophys ica l cha r ac t e r i s t i c s occur in the f o r m of constants . Therefore , we a re obliged to s impl i fy the p rob l em - to calcula te with the mean values of W u and dWu/dt ove r some t e m p e r a t u r e in- t e rva l (t 2 - tl).

The mean content of unfrozen water in peats , W u, is given by

i 4Zg" 4-- X I ' 1,~ Pc t ~ - ~- t, (6) wu - t , - t , t, " - ~ ,It ~ 2.3 - t , - h

* Fo rmu la (4) m u s t be r ega rded as a f i r s t approximat ion. We could evidently choose a di f ferent equation which would give a b e t t e r approximat ion (Editors ' note).

1 8 0

The express ion fo r the mean value of the der ivat ive , dWu/d t , is found b y rep lac ing the f igure , bounded in Fig° 2 by the cu rve and the axes of o rd ina tes and a b s c i s s a s within the l imi t s (t2- t I) by an equal t r iangle , and using fo rmu la (6) :

4- 5- 4 3 2~u K ,~ - ~ (7) ~.a~_ t2--)* ~4.6 (t,--Q)'

In practical thermoteehnical calculations, we usually encounter two types ef problem. In the first, we have to determine the time of change of the soil temperature in a given range (t 2 - tl); in the second, we have to determine the temperature t 2 which is established in the soil in a given time for a ~ven initial tem-

perature t I.

In solving a p r o b l e m of the f i r s t type, in Eq. {3) we subst i tuted the m e a n values W u and dWu/d t given by Eqs. (6) and (7).

In solving a p rob lem of the second type, we ca lcula te with the mean value W u and the der iva t ive of this quantity with r e s p e c t to t e m p e r a t u r e in the reg ion of ma rked phase t rans i t ions . This region, according to N. A. Tsytovich, is c h a r a c t e r i z e d by the condition dW/dt _> 0.01. Substituting dW/dt = 0.01 into Eq° (5), we find the upper t e m p e r a t u r e l imi t ef this region, t 2 = - 2 0 .

Solving Eqs. (6) and (7) with t i = 0.2 and t 2 = -20 , we get W---u = 1.1, dW-u/dt = 0°05°

The the rma l capac i ty of soil is an addit ive quantity, and can conveniently be e x p r e s s e d in t e r m s of the specif ic heats of the components of the soil medium, since the l a t t e r a r e constants . Then a m o r e genera l f o r m of Eq. (3), which can be used not only fo r m ine ra l soi ls and pea t but also fo r pea ty soi ls , will be

where Cds is the dry specific heat of a mineral soil (min) or "pure" peat (p) in kcal/kg • deg, and Csw and Csi are the specific heats of water and ice respectively.

The -volume specific heat of thawed peaty soils is

rain Ct=Td [Ctt ~ (1 --q) -}- C~s q-}-qw ti7¢]. (9)

The above graphs and fo rmu la s enable us to de te rmine the cha r ac t e r i s t i c the rmophys ica l p r o p e r t i e s of pea ty soi ls f r o m the indices of the i r s imp le s t phys ica l p r o p e r t i e s - m o i s t u r e content, bulk density, and specif ic gravi ty .

CONCLUSIONS

I. The quantitative indices of the thermophysical properties of thawed and frozen peaty soils of vari- ous types and composition are determined by two complex quantities - the coefficient of water saturation

and the peat content.

2. The formulas thus derived and the graphs given for the thermophysical characteristics of peaty soils vs the coefficient of water saturation and degree of peatiness are recommended for practical use°

io

2~

3.

4~

5.

6.

LITERATURE CITED

D. L Fedorovieh, "A method of combined thermophysical investigation of core samples of frozen soils in field conditions," in: Material of Fifth Conference on Exchange of Experience in Construc- tion in Bleak Climatic Conditions [in Russian], Krasnoyarsk (1968). SNiP II-Bo6-66, Foundation Beds and Foundations of Buildings and Structures on Permafrost Soils [in Russian], Stroiizdat (1966)o V. P. Ushkalov and L. T. Roman, "On the determination of the Main Characteristics of the Physical Properties of Frozen and Thawed Peaty Soils and Peats," in: Material of Sixth Conference on Ex- change of Experience of Construction in Bleak Climatic Conditions [in Russian], Krasnoyarsk (1970)o A. F. Derov, "Thermal protection of peaty soils from freezing," Osnovaniy% Fundamenty i Mekhan.

Gruntov, No. 6 (1968)o K. K. Pavlova, "Thermal properties of the active layers of swamps," Trudy GGI, No. 177, Gidrometeo- izdat (1969). Thermophysics of Frozen and Thawed Soils [in Russian], Nauka (1964).

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