Natlonal Research Consell natlonal C .

ncll Canada de recherche8 Canada BLDG Institute for lnstitut de

- - - .. - Research in recherche en Construction construction

Calculation of Belo w-Grade Residential Heat Loss: Lo w-Rise Residential Building

by G.P. Mitalas

ANALYZED

Reprinted from ASHRAE Transactions Vol. 93, Part 1, 1987 p. 743-783 (IRC Paper No. 1564)

NRCC 29605

f P N R C - ClSTl Q 8 I R C I:

t L I B R A R Y I

!I 1 19 l U S B il 1 I

It

I i B I B L I O T H ~ Q U E , I R C I CNRC - IC19T 'I

<

Un calcul simple pennet de dCterminer le taux maximum de perk de chaltur d'un sousbassement au-dessous du niveau du sol, alinsi que la pmte de chaleur totale au cours de la p6riode de chauffe. Cette mCthode tient colmpte de la variation de la perte de chaleur au- dessous du niveau du sol pendant l'annb. 11 s'agit 18 d'un important facteur dans le bilan thermique de la maison. L'auteur se sert de donnees andytiques et exp6rimentales pour definir une serie de facteurs qui servent ensuite au calcul de la perte de chaleur audess~ns du niveau du sol. Cette note est une version revue et augmentee d'un document de 1'ASHRAE (Mitalas 1983). La mCthode de c:alcd applicable aux sous-sols complets y est Ctendue aux soubassements h dalle & niveau d= sol et aux soubassements de faible hauteur.

CALCULATION OF BELOW-GRADE

1 RESIDENTIAL HEAT LOSS:

LOW-RISE RESIDENTIAL BUILDING

G.P. Mitalas, P.E. ASHRAE Fellow

CALCULATION OF BELOW-GRADE

RESIDENTIAL HEAT LOSS:

LOW-RISE RESIDENTIAL BUILDING

G.P. Mitalas, P.E. ASHRAE Fellow

ABSTRACT

A s imple c a l c u l a t i o n makes i t p o s s i b l e t o de te rmine t h e maximum r a t e of below-grade h e a t l o s s from a basement and t h e t o t a l h e a t l o s s over t h e h e a t i n g season. The procedure accounts f o r t h e v a r i a t i o n of below-grade h e a t l o s s dur ing t h e year . This is a s i g n i f i c a n t f a c t o r i n t h e house h e a t balance. A n a l y t i c a l a s w e l l a s exper imenta l d a t a a r e used t o develop a s e t of f a c t o r s t h a t a r e then used i n t h e c a l c u l a t i o n of below-grade h e a t l o s s . This n o t e is a r e v i s e d and extended v e r s i o n of a n ASHRAE paper ( M i t a l a s 1983). T h i s r e v i s i o n ex tends t h e f u l l basement c a l c u l a t i o n procedure t o i n c l u d e slab-on-grade and sha l low basement h e a t l o s s c a l c u l a t i o n s .

INTRODUCTION

Experimental and a n a l y t i c a l s t u d i e s were c a r r i e d o u t t o develop a method f o r c a l c u l a t i n g deep basement* h e a t l o s s . The d e t a i l s of t h e s e s t u d i e s a r e r e p o r t e d i n M i t a l a s (1982), and t h e f i n a l v e r s i o n of t h e c a l c u l a t i o n procedure i s p r e s e n t e d i n M i t a l a s (1983). This procedure u s e s basement h e a t l o s s f a c t o r s (BHLF) t h a t r e l a t e basement i n t e r i o r s u r f a c e h e a t f l u x t o v a r i o u s t empera tu res t h a t govern basement h e a t l o s s . BHLFs account f o r t h e basement i n s u l a t i o n system, s o i l the rmal c o n d u c t i v i t i e s , and basement geometry, a s w e l l a s t h e annual v a r i a t i o n of ground s u r f a c e temperatures .

It was recognized t h a t a s i n g l e c a l c u l a t i n g procedure f o r a l l types of house foundations--deep basement, sha l low basement, and s l a b on grade--would be advantageous f o r t h e fo l lowing reasons:

1. P r e s e n t a t i o n and implementat ion of t h e method is s i m p l i f i e d because one c a l c u l a t i n g procedure (computer program o r manual c a l c u l a t i o n ) hand les a l l types of house foundat ions .

2. I n c a s e s where t h e g r a d e l e v e l , i n s u l a t i o n coverage of t h e w a l l , and/or s o i l c o n d u c t i v i t i e s d i f f e r s u b s t a n t i a l l y from t h e "s tandard" founda t ion systems used f o r BHLF c a l c u l a t i o n s , t h e below-grade h e a t l o s s e s can be e s t i m a t e d by i n t e r p o l a t i o n of t h e h e a t l o s s c a l c u l a t e d f o r t h e two "s tandard" founda t ion systems t h a t b r a c k e t t h e founda t ion c o n f i g u r a t i o n under c o n s i d e r a t i o n .

3. A more a c c u r a t e comparison can be made of t h e below-grade h e a t l o s s from v a r i o u s types of house founda t ions and t h e i r i n s u l a t i o n systems u s i n g a s i n g l e c a l c u l a t i n g procedure r a t h e r t h a n a s p e c i a l procedure f o r each case .

Consequently a procedure was developed and used t o c a l c u l a t e below-grade h e a t l o s s from shal low basements and s l a b on grade. The c a l c u l a t i n g procedure , based on t h e p r e v i o u s l y

--

*The terms "deep basement," "shal low basement," and " s l a b on grade" a r e used t o deno te t h e t h r e e types of house basements: (1) "deep basement" deno tes a basement where t h e basement f l o o r i s a t l e a s t 1.0 m below grade; ( 2 ) "shal low basement" d e n o t e s a basement where t h e basement f l o o r i s 0.25 m t o 1.0 m below grade (e.g., "crawl space" ) ; ( 3 ) " s l a b on grade" denotes a basement where t h e s l a b i s less t h a n 0.25 m below t h e su r round ing grade.

G.P. M i t a l a s i s a Research O f f i c e r , I n s t i t u t e f o r Research i n Cons t ruc t ion , Nat ional Research Counci l Canada, Ottawa, Canada, K 1 A OR6.

repor ted deep basement work i it alas 1983), i s d e s c r i b e d i n t h i s paper. The necessary modi f ica t ions of t h e deep basement c a l c u l a t i n g procedure t o extend i t t o slab-on-grade and shal low basement h e a t l o s s c a l c u l a t i o n s a r e p resen ted here .

The aim of t h i s paper i s t o o u t l i n e t h e approach used t o g e n e r a t e t h e basement h e a t l o s s f a c t o r s (BHLFs) and t h e u s e of t h e BHLFs i n c a l c u l a t i o n s of house founda t ion h e a t l o s s . More s p e c i f i c a l l y , t h i s paper d e s c r i b e s :

1. Mathematical model f o r c a l c u l a t i o n s of house founda t ion h e a t l o s s e s . 2. Represen ta t ive p h y s i c a l house founda t ion models of t h e t h r e e foundat ion types t h a t

were used f o r BHLF c a l c u l a t i o n s . 3. Algorithms f o r founda t ion h e a t l o s s de te rmina t ion based on BHLFs (Appendix A). 4. Sample c a l c u l a t i o n (Appendix B).

Mathematical Model

F i g u r e s . 1 , 2, and 3 show r e p r e s e n t a t i v e p r o f i l e views of p h y s i c a l models of a deep basement, a sha l low basement, and a s l a b on grade , r e s p e c t i v e l y . F igure 4 shows a p l a n v iew. common t o a l l t h r e e types .

The main f a c t o r s and v a r i a b l e s t h a t determine t h e below-grade h e a t l o s s from deep basements, shal low basements, and s l a b on grade a r e ( 1 ) ground s u r f a c e temperature around t h e founda t ion , ( 2 ) lower thermal boundary r e p r e s e n t e d by a c o n s t a n t temperature , ( 3 ) i n t e r i o r space temperature , (4) basement dimensions and i n s u l a t i o n system, and (5) t h e thermal c o n d u c t i v i t y of t h e s o i l su r rounding t h e founda t ion .

Based on t h e deep basement h e a t l o s s c a l c u l a t i n g approach of M i t a l a s (1982) and t h e p h y s i c a l models d e s c r i b e d above, t h e i n s t a n t a n e o u s h e a t l o s s from t h e below-grade s e c t i o n of a house f o r a l l t h r e e founda t ion types can be expressed a s

where

A = a r e a of segment, n qn( tP = i n s t a n t a n e o u s h e a t f l u x a t time, t , averaged over t h e segment a r e a , h. .

Note t h a t summation begins w i t h n=l i f above-grade founda t ion h e a t l o s s is included i n t h e summation. The i n s t a n t a n e o u s h e a t f l u x , q n ( t ) , can be approximated by

q n ( t ) = qa,, + qV,, s i n (w(t + ~ t , ) )

where

qa,, = annual mean v a l u e of q (t) q,,. = ampli tude of t h e annua? h e a t f l u x v a r i a t i o n o = angula r v e l o c i t y of t h e v a r i a b l e component, i.e., 30°/month t = t i m e (month)

A t n = t i m e l a g of t h e h e a t f l u x harmonic r e l a t i v e t o t h e s u r f a c e temperature v a r i a t i o n .

The ampli tude v a l u e s f o r t h e annua l and semiannual harmonics of t h e ground s u r f a c e temperature f o r s e v e r a l l o c a t i o n s i n Canada a r e g iven i n Tab le 2, de r ived from t h e d a t a g iven i n P h i l l i p s and Aston (1979). A s t h e ampli tude of t h e two c y c l e s p e r y e a r component of ground s u r f a c e temperature i s r e l a t i v e l y small and t h e h i g h e r h e a t f l u x harmonics a r e a t t e n u a t e d more than t h e f i r s t , t h e annual ground s u r f a c e t empera ture v a r i a t i o n can be approximated us ing only t h e one c y c l e p e r y e a r component.

The h e a t conduct ion through a l i n e a r thermal system i s a f u n c t i o n of t h e temperature d i f f e r e n c e a c r o s s t h e system and t h e o v e r a l l conductance. The two components of q n ( t ) g iven by Equation 2 can t h e r e f o r e be expressed a s

and

qv, , ( t ) = V n an Ov s i n ( w ( t + b t n ) )

where

Sn = BHLF f o r t h e s t e a d y - s t a t e h e a t l o s s component - - = o v e r a l l conductance between t h e boundar ies a t t empera tu res Op and 0, " U

= S + S n and SnPs and S = f o r dkeady-s ta te h e a t l o s s component t o t h e ground s u r f a c e and lower

n 'g boundary, r e s p e c t i v e l y QB = i n t e r i o r a i r t e m p e r a t i r e (assumed t o be c o n s t a n t throughout t h e e n t i r e y e a r ) OG = ground s u r f a c e t empera tu re averaged over t i m e and a r e a , which e q u a l s mean

ground t empera tu re Vn = BHLF f o r t h e p e r i o d i c h e a t l o s s an = ampli tude a t t e n u a t i o n f a c t o r Qv = ampli tude of t h e one c y c l e p e r y e a r component of t h e ground s u r f a c e

temperature .

Thus Equat ions 3 and 4 a r e t h e b a s i c house founda t ion mathemat ical models: h e a t f l u x e s a r e expressed i n terms of BHLFs, (Sn, V n , an, and Atn) and t h e temperatures . It i s assumed t h a t t h e f o u n d a t i o n ' s thermal system c h a r a c t e r i s t i c s do n o t s i g n i f i c a n t l y change w i t h t i m e and temperature .

Foundation Heat Loss F a c t o r s (BHLFs) f o r R e p r e s e n t a t i v e House Foundat ions

BHLFs a r e s p e c i f i c s e t s of f a c t o r s t h a t a r e used i n Equat ions 3 and 4 t o r e l a t e below-grade h e a t l o s s and boundary t empera tu res f o r s p e c i f i c f o u n d a t i o n systems. The a v a i l a b l e number of BHLF s e t s , t h e r e f o r e , w i l l de te rmine t h e range of a p p l i c a b i l i t y of t h i s method f o r p r e d i c t i n g s p e c i f i c house founda t ion h e a t l o s s . The number of BHLF s e t s , however, must be balanced a g a i n s t t h e c o s t t o c a l c u l a t e them and t h e t a b u l a t i o n and convenience of u s i n g t h e s e f a c t o r s .

For t h e s e reasons , Sn ' s and V n ' s were c a l c u l a t e d f o r t h e c r o s s - s e c t i o n a l models of t h e basement and sur round ing ground shown i n F i g u r e s 1, 2, 6nd 3 w i t h t h e f o l l o w i n g p e r t i n e n t dimensions t h a t a r e deemed t o be r e p r e s e n t a t i v e of common house f o u n d a t i o n systems:

a ) Deep basement: Height of a r e a A2 = 0.6 m Height of a r e a A3 = 1.07 m Width of a r e a A4 = 1.0 m Width of a r e a A5 = 3.6 m

A v e r t i c a l dimension of 0.6 m f o r A2 was s e l e c t e d because t h a t is the e x t e n t of basement i n s u l a t i o n recommended i n s e v e r a l p r o v i n c i a l b u i l d i n g cedes.

b) Shallow basement: Height of a r e a A2 = 0 m Height of a r e a A3 = 0.85 m Width of a r e a A4 = 1.0 m Width of a r e a A5 = 3.6 m

For sha l low basements, a l l above-grade w a l l area is d e s i g n a t e d as A l and a l l below-grade w a l l a r e a i s des igna ted a s A3.

c ) S l a b on g rade Height of a r e a A2 = 0 m Height of a r e a A3 = 0 m Width of a r e a A4 = 1.0 m Width of a r e a A5 = 3.6 m

For s l a b on g rade t h e e n t i r e w a l l a r e a i s d e s i g n a t e d a s Al.

The basement f l o o r was d i v i d e d i n t o a pe r imete r and a c e n t r a l r e g i o n , because c a l c u l a t i o n s show t h a t h e a t f l u x through t h e f l o o r a d j a c e n t t o t h e w a l l d i f f e r s s u b s t a n t i a l l y

from t h a t through t h e remainder of t h e f l o o r , and because such a d i v i s i o n makes i t p o s s i b l e t o account f o r a s t r i p of f l o o r i n s u l a t i o n a d j a c e n t t o t h e wa l l .

It i s assumed t h a t two-dimensional h e a t conduct ion p r e v a i l s around t h e founda t ion and t h a t t h e three-dimensional h e a t f low due t o c o r n e r s can be accounted f o r by s p e c i a l co rner a l lowance f a c t o r s , Cn.

The c a l c u l a t i o n s of S 's and V n l s a l l o w f o r s p a t i a l v a r i a t i o n s i n s o i l thermal p r o p e r t i e s * by a s s i g n i n g d i f f e r e n t s o i l c o n d u c t i v i t i e s above and below t h e founda t ion f l o o r l e v e l .

Sn1s and V 'S f o r s l a b on g rade were c a l c u l a t e d f o r t h r e e s l a b l w a l l c o n f i g u r a t i o n s t o account f o r d i f p e r e n t w a l l / s l a b j u n c t i o n s ( s e e Tab le 1) , namely,

1. The c o n c r e t e f l o o r s l a b i s i n good thermal c o n t a c t w i t h t h e c o n c r e t e w a l l and t h e s l a b i s i n s u l a t e d on t h e i n t e r i o r o r e x t e r i o r .

2. The w a l l i s i n s u l a t e d (U=0.31 w / ( m 2 * ~ ) ) t o a d e p t h of 0.2 m below grade and t h e f l o o r s l a b i s i n s u l a t e d on t h e i n t e r i o r o r e x t e r i o r .

3. The dep th of i n s u l a t i o n on t h e w a l l below g r a d e i s a v a r i a b l e ( i . e . , 0.5 m , 1.0 m, o r 1.5 m below grade) and t h e f l o o r s l a b i s n o t i n s u l a t e d .

Sn and Vn, numer ica l ly e q u a l t o t h e average h e a t f l u x e s through i n t e r i o r s u r f a c e segments due t o a p p r o p r i a t e u n i t t empera tu re d i f f e r e n c e s , were c a l c u l a t e d u s i n g f i n i t e - e l e m e n t numerical methods f o r h e a t conduct ion ( M i t a l a s 1982).

Analysis of t h e c a l c u l a t e d Sn ' s and V n V s i n d i c a t e s t h a t , i n most c a s e s , t h e basement i n s u l a t i o n thermal r e s i s t a n c e , R , and t h e S n l s and V n ' s f o r t h e range 1 < R < 5 can be r e l a t e d by equa t ions of t h e form:

and

Consequently, Sn and V n a r e p resen ted i n Table 1 a s f u n c t i o n s of t h e basement i n s u l a t i o n the rmal r e s i s t a n c e , R , i n t h e form of Equa t ions 5 and 6 o r a s c o n s t a n t s f o r s p e c i f i c i n s u l a t i o n system (e.g., nonuniform i n s u l a t i o n cover ) . Table 1 p r e s e n t s BHLFs f o r deep, sha l low, and slab-on-grade f o u n d a t i o n s , v a r i o u s i n s u l a t i o n systems and geomet r i es , and a range of s o i l thermal c o n d u c t i v i t i e s .

The a t t e n u a t i o n f a c t o r , an, and t h e t ime-lag f a c t o r , A t n , have been determined by c a l c u l a t i n g h e a t f l u x of i n t e r i o r s u r f a c e s , u s i n g a s i n e wave v a r i a t i o n of t h e ground s u r f a c e t empera tu re ( M i t a l a s 1982). C a l c u l a t e d a t t e n u a t i o n and time-lag f a c t o r s a r e l i s t e d i n Table 1.

Based on t h e i n s i d e s u r f a c e h e a t f l u x v a l u e s c a l c u l a t e d a t a c o r n e r f o r two l e v e l s of founda t ion i n s u l a t i o n and u s i n g a three-dimensional model ( M i t a l a s 1982), a s e t of c o r n e r a l lowance f a c t o r s , Cn, were d e r i v e d f o r a l l of t h e founda t ion i n s u l a t i o n systems and a r e l i s t e d i n Table 1.

House Foundation Heat Loss C a l c u l a t i n g Procedure and A p p l i c a t i o n i n P r a c t i c e

The c a l c u l a t i n g procedure based on BHLFs c o n s i s t s of f o u r d i s t i n c t s t e p s :

1. Determinat ion of S , V n , an, At , , and C f a c t o r s f o r a founda t ion t y p e , founda t ion geometry, ground tEermal p r o p e r t i e s , an8 i n s u l a t i o n system under c o n s i d e r a t i o n , us ing Table 1.

2. C a l c u l a t i o n of f o u n d a t i o n w a l l and f l o o r i n t e r i o r s u r f a c e segment a r e a s and c o r n e r a l lowance f o r t h e f o u n d a t i o n i n q u e s t i o n .

3. C a l c u l a t i o n of 1 2 monthly v a l u e s of below-grade h e a t l o s s u s i n g ground s u r f a c e , ground mean, and i n t e r i o r t empera tu re a p p r o p r i a t e f o r t h e l o c a t i o n i n q u e s t i o n , BHLFs determined i n S t e p 1, and a r e a s c a l c u l a t e d i n S t e p 2.

4 . C a l c u l a t i o n of t h e h e a t i n g season below-grade h e a t l o s s u s i n g t h e monthly h e a t l o s s v a l u e s c a l c u l a t e d i n S t e p 3.

C a l c u l a t i o n of below-grade h e a t l o s s becomes more involved when t h e founda t ion d i f f e r s cons ide rab ly from t h e founda t ions l i s t e d i n Table 1. I n t h i s c a s e , t h e h e a t l o s s can be determined us ing a s imple i n t e r p o l a t i o n procedure: s e l e c t two founda t ions l i s t e d i n Table 1 t h a t "b racke t" t h e a c t u a l founda t ion , c a l c u l a t e below-grade h e a t l o s s f o r t h e s e two c a s e s , and then , u s i n g t h i s d a t a , i n t e r p o l a t e t o de te rmine h e a t l o s s of t h e a c t u a l foundat ion.

I f i t i s known t h a t t h e groundwater l e v e l i s j u s t below t h e founda t ion f l o o r , and t h a t a p o t e n t i a l e x i s t s f o r groundwater Elow around and under t h e founda t ion , t h e RHLFs f o r t h e s t e a d y - s t a t e h e a t l o s s component through t h e f l o o r should be a r b i t r a r i l y i n c r e a s e d by 30% t o 70% t o account f o r a decreased ground thermal r e s i s t a n c e beneath t h e f l o o r depending on t h e perceived s e v e r i t y of t h e groundwater e f f e c t .

I n cases of poor ly i n s u l a t e d founda t ions i n which s o i l p rov ides t h e major p o r t i o n of t h e t o t a l the rmal r e s i s t a n c e , an a c c u r a t e v a l u e of s o i l thermal c o n d u c t i v i t y is r e q u i r e d t o e s t a b l i s h t h e BHLFs a p p r o p r i a t e f o r t h e c a s e under c o n s i d e r a t i o n . I n a d d i t i o n , t h e fo l lowing may have a s i g n i f i c a n t i n f l u e n c e on t h e h e a t l o s s from a poorly i n s u l a t e d foundat ion:

- The time v a r i a t i o n i n groundwater t empera tu re and l e v e l ; - The flow of r a i n o r melt-water i n t o s o i l su r round ing t h e basement; - The space v a r i a t i o n of ground t empera tu re around t h e founda t ion due t o s o l a r e f f e c t s ,

a d j a c e n t b u i l d i n g s , and v a r i a t i o n i n t h e snow cover ; - Changes i n s o i l thermal c o n d u c t i v i t y due t o mois tu re and t empera tu re changes.

The d e t a i l s of t h e a p p l i c a t i o n of BHLFs f o r c a l c u l a t i o n of below-grade house f o u n d a t i o n hea t l o s s a r e g iven i n Appendix A and a sample c a l c u l a t i o n i n Appendix B.

A s a m a t t e r of i n t e r e s t , t h e measured basement h e a t l o s s a t t h e test basement and t h e corresponding c a l c u l a t e d v a l u e s a r e p r e s e n t e d i n Appendix B and p l o t t e d i n F i g u r e 4. I n t h i s p a r t i c u l a r c a s e , t h e c a l c u l a t e d annual basement h e a t l o s s of 24 G J compares w e l l w i t h t h e measured 23.3 G J h e a t Loss. A more e x t e n s i v e comparison of c a l c u l a t e d and measured deep basement h e a t l o s s i s g iven i n M i t a l a s (1982).

OBSERVATIONS

Various assumptions have been made i n d e r i v i n g a s imple method of c a l c u l a t i n g below-grade h e a t l o s s . For v e r i f i c a t i o n , v a l u e s of founda t ion h e a t l o s s ob ta ined by means of t h i s method were compared w i t h a c t u a l measured v a l u e s f o r deep basements (Mi ta las 1982). The comparison - suggested t h e fol lowing:

- The e f f e c t of t h e annua l v a r i a t i o n of ground s u r f a c e t empera tu re on below-grade h e a t l o s s can be accounted f o r s a t i s f a c t o r i l y by a p e r i o d i c h e a t f low c a l c u l a t i o n approach, us ing ampli tude a t t e n u a t i o n , a,, and t ime-delay f a c t o r s , A t n .

- Foundations w i t h s imple r e c t a n g u l a r shapes can be t r e a t e d by u s i n g BHLFs determined f o r s t r a i g h t w a l l s e c t i o n s and c o r n e r a l lowance f a c t o r s t o account f o r three-dimensional h e a t f low due t o corners .

- The BHLF method c a n p r e d i c t bo th t h e t o t a l founda t ion h e a t l o s s and t h e h e a t l o s s through s e c t i o n s of t h e founda t ion w i t h i n +lo% of measured va lues .

NOMENCLATURE*

An = a r e a of segment, n an ,bn ,cn , a c o n s t a n t s s p e c i f i c t o t h e f o u n d a t i o n the rmal i n s u l a t i o n system; they a r e used t o

and dn c a l c u l a t e S and V n f a c t o r s RHLF - founda t ion g e a t l o s s f a c t o r , namely, S , V , on, A t , o r Cn

Cn = corner allowance f a c t o r D" = h e i g h t of founda t ion w a l l above g rade G = founda t ion pe r imete r

G~ = per imete r f o r bo th end s e c t i o n s

G~ = per imete r f o r t h e middle s e c t i o n H = t o t a l h e i g h t of f o u n d a t i o n w a l l k lower = s o i l thermal c o n d u c t i v i t y below f o u n d a t i o n f l o o r l e v e l k upper = s o i l thermal c o n d u c t i v i t y above founda t ion f l o o r l e v e l

*All dimensions used i n t h i s paper a r e i n S I u n i t s e x c e p t a s noted

L = foundation length M = height of i n s u l a t i o n coverage over wa l l m = month number (1 t o 12) N = number of segments c o n s t i t u t i n g t h e i n t e r i o r su r f ace a r e a of below-grade por t ion

of t he foundation QT = annual hea t l o s s from below-grade po r t i on of foundation Q ( t ) = heat l o s s from below-grade po r t i on of foundat ion Q W = below-grade foundat ion hea t l o s s f o r win ter period Qa n = annual mean value of q n ( t ) q n ( t ) = average heat f l u x through t h e segment a r ea , An, a t time t

qv,n = amplitude of annual harmonic of hea t f l u x v a r i a t i o n

qV,,(t) = va r i ab l e component of average hea t f l u x through segment, An, a t time t R = thermal r e s i s t a n c e of foundat ion i n s u l a t i o n RT o v e r a l l thermal r e s i s t a n c e of foundat ion wa l l above grade l e v e l S n = BHLF, t h e s teady-s t a t e hea t l o s s component t = time U = o v e r a l l thermal conductance of foundat ion wa l l above grade l e v e l , l/RT vn = BHLF f o r t h e pe r iod i c hea t l o s s component W = foundation width

Xn = corner allowance

Subscr ip ts

= steady-state component, equal ing annual mean va lue = i n t e r i o r space = end s e c t i o n = lower temperature boundary = long-term time and space average = month number (1 t o 12) = middle s e c t i o n = segment of t h e i n t e r i o r s u r f a c e of foundat ion = ground su r f ace = va r i ab l e component

Greek Symbols

= time l a g of hea t f l u x harmonic r e l a t i v e t o su r f ace temperature v a r i a t i o n 8 = temperature

@B = i n t e r i o r space a i r temperature

OG = ground su r f ace temperature averaged over both time and a r ea , equal l ing mean ground temperature

@o,m = monthly va lue of outdoor a i r t e m ~ e r ~ a t u r e

Qv = amplitude of annual harmonic of ground su r f ace temperature On = amplitude a t t enua t ion f a c t o r w = angular ve loc i ty of annual harmonic

REFERENCES

Environment Canada. 1975. Canadian Normals Temperature 1941-1970, Vol. 1-SI. Environment Canada, Downsview, Ontar io (UDC 551-552[7]).

Mitalas , G.P. 1982. "Basement hea t l o s s s t u d i e s a t DBR~NRC." National Research Council of Canada, Division of Building Research, NRCC 20416.

Mi ta las , G.P. 1983. "Calculat ion of basement hea t loss." ASHRAE Transact ions, V. 89, Pt. 1.

P h i l l i p s , D.W., and Aston, D. 1979. "Soi l temperature averages 1958-1978 - Environment Canada, Downsview, Ontario. CL13-79.

The author wishes t o acknowledge t h e a s s i s t a n c e of M.J. Lavoie and M.O. P e l l e t i e r i n t h e prepara t ion of computer programs and running t h e t e s t . This paper i s a cont r ibu t ion of the I n s t i t u t e f o r Research i n Construct ion, National Research Council of Canada.

APPENDIX A

Calculat ion of House Foundation Heat Loss

The following summarizes t he s t eps t o be taken i n ca l cu l a t i ng heat l o s s f o r a s p e c i f i c house foundation system:

Step 1. Provide t h e required input d a t a f o r (Al l i n S I u n i t s ) :

Ins ide dimensions ( see Figures 1, 2, 3, and 4 ) length, L, width, W , where W < L , o r width, W , and width, W 2 , of L-shaped f l o o r , where W1 and W 2 a r e the widths of t he two ends of t he !loor; t o t a l height of wal l , H , height of wal l above grade, D.

I n su l a t i on - ove ra l l thermal r e s i s t ance of wal l above grade, RT, o v e r a l l thermal conductance of wa l l above grade, U (U = 1 / ~ ~ ) , r e s i s t ance value of i n su l a t i on , R, height of i n su l a t i on coverage of wal l , M - i n ca se of deep basement, ex ten t of i n su l a t i on coverage of f l o o r (i .e. , none, 1 m wide s t r i p ad jacent t o wa l l , o r f u l l coverage).

Temperature - i n t e r i o r space temperature, QB, mean ground temperature, QG ( s ee Table 2 o r P h i l l i p s and Aston 19791, amplitude of t he annual harmonic of t h e ground su r f ace temperature v a r i a t i o n , C$,, and t h e timing of t he f i r s t su r f ace temperature harmonic ( see Table 2) , monthly average outdoor a i r temperature, Q0,,, where m i d e n t i f i e s t h e month (Environment Canada 197 5).

Step 2. Calculate t he a r ea s of t he segments c o n s t i t u t i n g the foundation f l o o r and wal l s where applicable:

A 1 = i n s ide sur face a r ea of wa l l - above grade, A 2 = upper i n s i d e su r f ace a r e a of wa l l - below grade, A 3 = lower i n s i d e sur face a r ea of wa l l - below grade, A4 = i n s ide su r f ace a r e a of f l o o r s t r i p 1 m wide ad jacent t o wal l , A5 = i n s ide sur face a r e a of t he remainder of t h e f l oo r .

I n some cases t he foundation under cons idera t ion must be subdivided i n t o s ec t ions , depending on i t s shape and on t h e number of i n s u l a t i o n systems used, s i n c e s ec t ions t h a t a r e insu la ted d i f f e r e n t l y must be considered separa te ly .

Square basements may be regarded a s having two i d e n t i c a l end sec t ions . Rectangular basements may be considered a s having two i d e n t i c a l end sec t ions wi th three-dimensional hea t flow occurr ing a t t h e corners and a middle s e c t i o n wi th two-dimensional hea t flow (Figure 4).

The three-dimensional hea t flow of i r r e g u l a r l y shaped basements (such a s an L-shaped basement) cannot be accommodated by t h i s s imple method. Such a basement could be considered a s having four corners only, s i n c e t h e three-dimensional hea t flow e f f e c t a t an i n s i d e corner wa l l w i l l be t h e oppos i te of t h a t a t an ou t s ide corner and should t he re fo re approximately compensate. An L-shaped basement can be t r e a t e d a s a rec tangular one, using t h e a c t u a l L-shaped cen te r f l o o r a r ea , As, and a c t u a l perimeter length f o r wal l a r e a ca lcu la t ions .

Rectangular foundations with s i n g l e i n s u l a t i o n system - f o r both end sec t ions , GE = 4 W , f o r the middle s ec t ion , GM = 2L - 2W, f o r the e n t i r e foundation, G = 2(L+W),

where G = perimeter, W = width, L = l ength , and subsc r ip t s E , M, and no subsc r ip t r e f e r t o end sec t ions , middle s ec t ion , and e n t i r e foundat ion, respec t ive ly . Therefore,

F u l l basement wi th i n s u l a t i o n p a r t i a l l y covertng t h e wa l l -

F u l l basement wi th i n s u l a t i o n covering t h e e n t i r e wa l l -

Shallow basement

S lab on grade

Step 3. Determine BHLFs Sn and Vn:

For t h e p a r t i c u l a r type of foundat ion, t h e R-value of foundat ion i n s u l a t i o n and s o i l thermal conduc t i v i t i e s from Table 1, o b t a i n t h e f a c t o r s Sn(R), Vn(R), Cn, an and At,. The high va lue of s o i l thermal conduc t i v i t y would probably be app rop r i a t e f o r rocks and wet sand; t h e lower value could be used f o r well-drained c lay .

S tep 4. Using t h e s e l e c t e d co rne r allowance f a c t o r s , Cn, c a l c u l a t e t h e a c t u a l corner allowance, Xn:

1) For t he two upper wa l l segments, A1 and A2, t h e increased hea t l o s s due t o co rne r s can be neglected, i.e., X1 = Xp = 0.

2) For t h e bottom segment of t h e wal l , A3, Xj = 0 f o r shal low basement and s l a b on grade and X3 = i Cj f o r f u l l basement, where i = number of corners being considered.

3) For t h e 1 m s t r i p of f l o o r , X4 = i C4. 4) For t h e c e n t r a l a r e a of f l o o r , X5 = C5 V5.

Step 5. Ca l cu l a t e t h e e f f e c t i v e a r e a s of t h e segments c o n s t i t u t i n g t h e f l o o r and w a l l s of t h e e n t i r e basement, i nc lud ing t h e co rne r allowance. (Because of t h e d i f f e r e n c e i n co rne r allowance f o r s teady-s ta te and v a r i a b l e f l o o r h e a t l o s s components and because t h e corner allowance i s i n terms of a r e a , t h e e f f e c t i v e f l o o r a r e a va lues f o r t h e s t e ady - s t a t e and v a r i a b l e component c a l c u l a t i o n s a r e d i f f e r e n t . )

where ---

s u b s c r i p t "s" i n d i c a t e s s u r f a c e a r e a t o be used i n c a l c u l a t i n g t h e s t e a d y - s t a t e component,

s u b s c r i p t "v" i n d i c a t e s s u r f a c e a r e a v a l u e t o be used i n c a l c u l a t i n g t h e v a r i a b l e basement h e a t - l o s s component.

S tep 6. C a l c u l a t e t h e monthly average h e a t - l o s s r a t e (power) through t h e i n t e r i o r s u r f a c e s of foundat ion:

For s l a b on g rade ,

and f o r sha l low basement A2 = 0 .-.q2,, = 0. For o t h e r c a s e s ,

where

"30" has u n i t s i n deglmonth.

S tep 7. C a l c u l a t e t h e annua l below-grade founda t ion h e a t l o s s (energy) , QT:

where

2.63 x lo6 = number of seconds p e r average month.

S t e p 8. C a l c u l a t e t h e below-grade basement h e a t l o s s o v e r t h e w i n t e r p e r i o d , Qw: - w i n t e r months 5

Qw = (2.63) C qn,m

(MJ)

A l t e r n a t i v e l y , t h e above e q u a t i o n c a n be rea r ranged a s fo l lows :

5 Qw = ( ( o B - QG) C An Sn (Number of w i n t e r months )

n= 2 w i n t e r

5 months + 0, C An V n an C s i n w ( 1 n + 8 + ~ t ~ ) ) (2.63) ( M J )

n= 2

S t e p 9. C a l c u l a t e t h e h e a t l o s s from e n t i r e founda t ion .

The whole basement h e a t l o s s i s s imply t h e sum of t h e below-grade and above-grade founda t ion h e a t l o s s e s . A sample c a l c u l a t i o n of basement h e a t l o s s is g iven i n Appendix B.

I n app ly ing t h i s c a l c u l a t i n g procedure , t h e f i r s t problem encountered w i l l be t h a t t h e founda t ion under c o n s i d e r a t i o n does n o t correspond e x a c t l y t o any of t h e "s tandard" founda t ions and i n s u l a t i o n systems (e.g., t h e d e p t h of t h e founda t ion f l o o r below grade , t h e e x t e n t of i n s u l a t i o n cover , o r s o i l the rmal c o n d u c t i v i t y may be d i f f e r e n t ) than t h e ones l i s t e d i n Table 1. To cope w i t h t h i s problem two approaches c a n be used:

1. S e l e c t t h e " s tandard" founda t ion c o n f i g u r a t i o n and i n s u l a t i o n system t h a t b e s t match t h e founda t ion under c o n s i d e r a t i o n , from Tab le 1. Using t h e BHLF s e t f o r t h i s founda t ion and

a c t u a l dimensions of the basement under cons idera t ion , determine below-grade hea t l o s s of the foundation i n quest ion.

2. Use an i n t e r p o l a t i o n ( o r ex t r apo la t i on ) procedure t o es t imate below-grade heat l o s s of t he foundation i n quest ion:

a ) Se l ec t a t l e a s t two "standard" foundation conf igura t ions t h a t bracket the foundation under considerat ion.

b) Calcu la te t h e below-grade hea t l o s s f o r t he se "standard" cases. c ) Calcu la te t h e below-grade heat l o s s of t h e foundation i n quest ion by in t e rpo la t i on of

t h e hea t l o s s values of t he two "standard" cases using appropr ia te parameters f o r i n t e rpo la t i on , i .e . , d i f f e r ence i n depth, i n s u l a t i o n cover , e t c .

The ex t r apo la t i on approach t o t h i s problem can be used i n a s i m i l a r way. It should be noted, however, t h a t t h e ex t r apo la t i on procedure should be used only t o a l imi ted ex t en t , s i nce i t i s not poss ib le t o e s t ima te accura te ly t he e r r o r of t h e hea t l o s s determined by t h i s procedure.

APPENDIX B

Sample Calcula t ion of Deep Basement Heat Loss

The fol lowing sample ca l cu l a t i on is f o r t h e hea t l o s s from one of t he t e s t basements, which had i n s u l a t i o n over t h e f u l l height on the i n s i d e su r f ace of t he basement wal l and no i n s u l a t i o n on the f l oo r .

Step 1. The given inpu t d a t a a r e :

Basement dimensions - l ength , L = 9.2 m, width, W = 8.5 m, t o t a l wal l he igh t , H = 2.13 m, he ight of wal l above grade, D = 0.38 m.

I n su l a t i on - above grade, l / R T = U = 0.53 w/(m2 K), i n s u l a t i o n r e s i s t ance , R = 1.55 m2 K/W, he ight of i n s u l a t i o n cover, M = 2.13 m ( f u l l he igh t ) , f l o o r is uninsulated.

Temperature - basement space temperature, BB = 21°C, ground su r f ace temperature (from Table 2), OG + %, = 8.9 + 11.4 s i n (30(m + 8 ) ) ou t s ide a i r temperature (Environment Canada 1975). (For Ottawa 0 = -11, -9, -3, 6 , 13, 18, 21, 19, 15, 9 , 2, - 7 ' ~ ; where m = Jan. t o Dec.)

0,"'

Step 2. The a r e a segments a r e ca l cu l a t ed a s fol lows:

S t e p 3. Because t h e s o i l su r round ing t h e basement i s c l a y , t h e lower v a l u e s of thermal c o n d u c t i v i t y were used t o o b t a i n t h e f o l l o w i n g from Table 1. Because t h e ground is w e l l d ra ined and t h e wa te r t a b l e i s l e v e l , t h e S, and S5 f a c t o r s a r e no t augmented. For i n s u l a t i o n system No. 3 t h e f a c t o r s a r e :

Area Segment: n = 2 n = 3 n = 4 n = 5

S u b s t i t u t i n g R = 1.55 m 2 K/W and A t n ,

Area Segment: n = 2 n = 3 n = 4 n - 5

S 0.44 0.29 0.58 0.19 w/(m2 K) V 0.43 0.27 0.38 0.07 w/(m2 K) u 0.9 0.7 0.4 0.3 Dimensionless

(m+8+~t ) m + 8 m + 7 m + 6 m + 4 Month C* 0 0.6 m2 2.4 m2 0.5

*C v a l u e h a s d i f f e r e n t u n i t , a s no ted .

S tep 4. Using t h e a l lowance f a c t o r s from Table 1 , t h e c o r n e r a l lowances , X, are:

S t e p 5. C a l c u l a t e t h e a r e a s of t h e segments t h a t i n c l u d e c o r n e r a l lowance f a c t o r s :

S t e p 6. The monthly h e a t l o s s (power) v a l u e s of t h e f i v e basement segments a r e :

q2,, = A ~ [ s ~ (QB - OG) - V 2 u2 Ov s i n [30(m + 8 ) ) ]

= 21.2 [0.44(21 - 8.9) - 0.43(0.9)(11.4) s i n (30(m + 8 ) ) ]

= 112 - 9 3 s i n (30(m + 8 ) ) q3,m = A [ s3 (% - 8 1 - V 8 s i n (30(m + 7 ) ) ]

= 43.1 [0.29(2F - 8.3) -%.27(8.7)(11.4) s i n (30(m t 7 ) ) ] = 151 - 93 s i n (30(m + 7 ) ) , - - ,

Q4,m = A S ( 8 - QG) - A4v V 4 a $ s i n (30(m + 6 ) ) = (47.7) 40.58 821 - 8.9) - (41.0)(0.48)(0.4)(l l .4) s i n (30(m + 6 ) ) = 265 - 71 s i n (30(m + 6 ) )

45,m = A S5 ( $ - 8,) -6 v o s i n (30(mt4) = (32.6) (0.1 ) ( 2 1 - 8.95"- [6?.9 (8 .07)~0.3)(11.4) s i n [30(m + 4 ) ] = 126 - 16.3 s i n ( 3 0 ( m + 4) ) .

I n summary, t h e monthly h e a t l o s s e s of t h e f i v e basement segments a r e :

q2,m = 112 - 93 s i n (30 (m + 8 ) )

q3,m = 151 - 93 s i n

The average h e a t l o s s v a l u e s Eor t h e f i v e basement segments f o r each month of t h e y e a r , t h e t o t a l basement average v a l u e s , and t h e annua l average v a l u e s f o r each segment a r e l i s t e d i n Table A-1.

The annual average h e a t l o s s r a t e was 762 W. The annua l h e a t l o s s (energy) from t h e whole basement would be

- a

9 - m u u u

o m u u .. -

- 'NU u u u

0 0 O m .. .,

m N N m -

r. OD - N N O

O D - m - N ., d

u r.- - N 4 . 0 a N

O - 9

* a

u m w m m m

P - P - O D I l l w w w

. rl 4 ¶ 3 V) ln C . C d

4 .4

2 m 4 c 21 .+ d d m

m u O C Y C d 0

a 4 - I > 4 .4 4 0 0 u m m 0 P ) P ) w z s Z U U O ' U W 0 0 0

U h h 0 u U C 4 .4

> > w d .rl u u u m u u

3 ¶ - 2 1 2 1

m c c - 0 0 o u u Z

4 d E m m O E E U L L ,

: 2 ; O U U

i l d u u w w >2g

I e '+

h

TABLE 1

House Foundation Heat Loss

4 m 0%

F a c t o r s ,

R , m 2 * K / w a , d i m e n s i o n l e s s

AT, month

For deep basement: Uni t s :

a, = 0.9 A t g = 0 a3 = 0.7 A t 3 = -1 a, = 0.4 A t , = -2 a, = 0.3 A t 5 = -4

S , W/ ( m 2 * ~ ) V , W / (m2*K) C , m* o r d imens ion less

(At i s t h e t ime de lay of h e a t f l u x s i n e wave r e l a t i v e t o t h e ground s u r f a c e t empera tu re s i n e wave.)

SECTION A: SOIL THERMAL CONDUCTIVITY: k upper = 0.8 W/(m*K); k lower = 0.9 W/(m*K) (Systems 1 t o 13, 21 t o 26)

* Table 1 l i s t s numerical va lues of Cn, 6, and ATn f a c t o r s . The Sn and Vn f a c t o r s a r e given a s numbers and a s express ions i n t h e form of Equations 5 and 6. These l a t t e r express ions a r e v a l i d f o r 1(R<5 and f o r uniform i n s u l a t i o n cover over the i n s u l a t e d s e c t i o n of t h e basement

I n s u l a t i o n System

Insulation --p, Concrete (n .: _ . . . , . . .

1

F l o o r Segments

S n , V n and Cn F a c t o r s

1 m s t r i p a d j a c e n t t o w a l l

n= 4

0.42 0.24 2.6

Wall Segments

S=

. . .

C e n t r e n= 5

0.17 0.05 0.5

T o p s t r i p j u s t below

g r a d e n= 2

1.9 1.9 0

Bottom s t r i p

n= 3

0.74 0.6 5 1 .O

SECTION A ( c o n t ' d )

I n s u l a t i o n System I I Wall Segments I Floor Segments

Insulation

Concrete 0 ..

V 1 .

Sn* v n and Cn Factors

Top s t r i p j u s t below

grade n= 2

1 m s t r i p adjacent t o w a l l

n= 4

Bottom s t r i p

n= 3

Centre n= 5

SECTION A ( c o n t ' d )

I n s u l a t i o n System Wall Segments

Insulation T, , Sn, V n Top s t r i p

Concrete and Cn j u s t below Bottom $ ;: F a c t o r s g r a d e s t r i p

.I..... n= 2 n= 3

7 . . , . . S= (0.67+1.12~)'~ ( 1.30+1.47~)-I V= (0.67+1.14~)'1 (1.42+1.58~)-1 C= 0 0.6

._,..;:

6 . I . ' . S= (0.69+1.08~)'~ (1.28+1.23~)-1

V= (0.69+1.11~)'~ (1.41+1.36~)-~ , + 0 0.6 . . . .; . . .

7 S= (0.73+1.04~)^1 (1.42+1.03~)-1 V= (0.72+1.08~)'~ (1.53+1.2 1~)'~ C= 0 0.6

': ..:.::

Floor Segments

1 m s t r i p a d j a c e n t t o w a l l

n= 4

(1.82+0.055~)-1 (2.79+0.11~)'1

2.4

(3.48+0.64~)'1 (5.43+0.988)'1

2.4

(2.60+0.92~)-1 (4.21+0.58~)-I

2.4

C e n t r e n= 5

0.19 0.07 0.5

(4.44-0.13~)~~ (1 1.13-0.58~)'l

0.5

(4.93+0.71~)'~ (12.9 1+1.25~)'~

0.5

SECTION B: SOIL THERMAL CONDUCTIVITY: k upper = 1.2 W/(m*K); k lower = 1.35 w/(m*K) (Systems 14 to 20, 97 to 99)

Insulation System I Wall Segments Floor Segments

Insulation S,, V, Top strip 1 m strip .'... T, , and Cn just below Bottom adjacent Concrete

Centre # .- 0 "

Factors grade strip to wall n= 5 " .: . . n= 2 n= 3 n= 4

. . . .: .

3. 9 9 .... . . S= 2.12 0.98 0.59 0.26

V = 2.10 0.88 0.35 0.08 C= 0 1 .O 2.6 0.5

........ . ... 7 14 S= (0.48+1.37~)-1 (0.85-0.008~)-~ 0.59 0.27 V= (0.48+1.388)-1 (0.93-0.0094~)-~ 0.35 0.09 C= 0 1 .O 2.6 0.5

- _ ' , I . . . . .. 15

.'.'.,.. T,., S= (0.51+1.09~)'~ (0.97+1.38~)'1 (1.36-0.03~)'~ 0.29 V= (0.52+1.11~)'1 (1.06+1.49~)'~ (2.11-0.062R)'l 0.11 C= 0 0.6 2.4 0.5

. . ..', . : . : . . .

1 , 16 .'.': : S= (0.52+1.06~)'~ (0.96+1.2~)'~ (2.76+0.54~)'~ (2.93-0.07~)'~

V= (0.53+1.08~)-I (1. 15+1.33R)-l (4.39+0.88~)-1 (7.25-0.30~)'~ C= 0 0.6 2.4 0.5

. . . ,. .' + ' .' : .-

.. -:: , l7

s= (0.56+1.02~)-I (1.08+1.01~)-1 (1.90+0.89~)'~ (3.27+0.76~)'1 V= (0.55+1.06~)-I (1.15+1.18~)-I (3.14+1.58~)-1 (8.46+1.55~)'1 C= 0 0.6 0.5

.. . .:.:.:-:' I I

SECTION B ( c o n t ' d )

I n s u l a t i o n System I Wall Segments

Inw!ation T, , S n , V , T o p s t r i p

and Cn j u s t below Bottom .- Concrete o :. F a c t o r s g r a d e s t r i p ' " . . . , ,

n= 2 n= 3 . , . . dl-J0.5 m , 18

S= (1.19+0.47~)-I ( 1.37+0.05~)-1 V = (1.18+0.51~)-I (1.60+0.077~)-I C= 0 1 .O

1.1 m . . . - . . .. 1 , l 9 S= (1.29+0.29~)-I ( 1.12+0.0027~)-I V = (1.31+0.30~)-I (1.27+0.0033~)-1 C= 0 1 .O

. . . . . . . . .

. . .:. 3 , 2o S= (0.62+1.06~)-1 (1 .58+0.26~)-I V= (0.61+1.09~)-I (1 .79+0.35~)-I C= 0 0.6

. , _... . . I .

97 S= (0.62+1.05~)-I (1.55+0.23~)-I V = (0.62+1.08~)-I (1.77+0.32~)-I

- . C= 0 0.6 . I . ' . ..:. ..:

-

S= (0.65+1.02~)-I (1.55+0.13~)-1 V- (0.63+1.07~)'~ (1.79+0.24~)-~ Cm 0 0.6

F l o o r

1 m s t r i p a d j a c e n t t o w a l l

n= 4

0.59 0.35 2.6

0.55 0.30 2.6

0.59 0.35 2.6

0.60 0.36 2.4

(2.26+0.09~)-1 (3.72+0.13~)-1

2.4

Segments

Cen t re n= 5

0.26 0.08 0.5

0.26 0.08 0.5

0.27 0.09 0.5

(3 -45-0.04R)-l (10.03-0.228)~~

0.5

(3.57+1.02~)-1 (10.67+2.71~)-1

0.5

SECTION C: SOIL THERMAL CONDUCTIVITY: k upper = 1.8 W/(m*K); k lower = 2.0 W/(m*K) (Systems 67 t o 76)

I n s u l a t i o n System I I Wall Segments I F l o o r Segments

Insulation

- . .-. Concrete 0 :

S n , V n T o p s t r i p 1 m s t r i p and Cn j u s t below Bottom a d j a c e n t C e n t r e F a c t o r s g r a d e s t r i p t o w a l l n= 5

n= 2 n= 3 n= 4 . .. :;:

-j , 67 S= 2.36 1.28 0.82 0.39 V= 2.33 1.14 0.49 0 .13 C= 0 1 .O 2.6 0.5

. . . . , . . I

SECTION C ( c o n t ' d )

I n s u l a t i o n System 1 Wall Segments F loor Segments

.-:, -.. l nsulation T, , Sn, V n Top s t r i p 1 m s t r i p and Cn j u s t below Bottom a d j a c e n t - C e n t r e ._ .. Concrete F a c t o r s Ln" .;. g r a d e s t r i p t o w a l l n= 5

. n= 2 n= 3 n= 4 . .

d J I o - 5 m , " S= (1 .14+0.34R)-l (1.06+0.03~)'~ (1 .29+0.006~)-1 (2.60+0.004~)-I V = (1.15+0.39~)-1 (1.26+0*05~)-1 (2.33+0.02~)'~ (8.31+0.04~)'~

i ...'..'. C= 0 1 .O 2.6 0 5 1.1 m .....,,. . . .

I .. .. . 3 , 73 S= (1.16+0.20~)-1 (0.84+0.002~)-1 0.84 0.39 V= (1.19+0.21~)-1 (0.95+0.002~)-I 0.49 0.13 C= 0 1 .O 2.6 0.5 . .

. . , . . . . . . . . . . . - . I . : . . --j , 74

S= (0.53+1.04~)-I ( 1.34+0.22~)-~ (1.23+0.001~)-I (2.49-0.008~)-l V= (0.53+1.07~)-I (1.52+0.3 lR)-l (2.13-0.02~)'~ (7 -28-0.09R)-l

. . C= 0 0.6 2.4 0.5 I ..,.'' "

, . . . . .

.-:. S= (0.53+1.03~)-1 (1.32+0.20~)-1 (1.76+0.08~)-I (2.28-0.028)-1 V = (0.53+1.07~)-1 (1.51+0.28~)'~ (2.9 1+0.12~)'~ 3 i 7 5 c=

(6.35-0.1 lR)-l 0 0.6 2.4 0.5 . . . . . . ,..: .: ' .' . .

s= (0.56+1.0~)'~ (1.29+0.11~)'~ (1.60+0.07~)-I (2.39+0.98~)-I V = (0.55+1.05~)-1 (1.53+0.19~)-1 (2.77+0.13~)-~ (6.83+2.56~)-I C= 0 0*6

I 0.5 . . I I I

U m f m C U U U

; a a a CJ m m d

m a 0

8 d d d 4 rl 11 II 11 G

m z m m D d D

1 4 d d l I I

M A nn b M 0 * @A d

a rn m & u r n

? 9 ? 9 : ; 000 c II

000

a e I I a m

I I m U

N h

U G

? ? m * 9 4

rn N S u 4 w 4

V w bO a cn

4 4 -4 d 4 4

1 I I I nn

I I nn nn d d

m 4 4 a d d In r.

d d " m a, m 4 m 9 92 o ? m b u n . . . l4 . . . . . u m 000 000 000 040 c I1 I I I I

n PI + +

al c 0 u .-'a rn U m h r. a U . . . . ? 4 c m PI m ln m \o

I V w w w w w

w w CA

rl L, 4 0 3 4 4 d 4 4 4

0 I I nn

1 , 1 nn

I I .-I a n-

d o l4 U

d d 4 m d d

In 4 d d

03 r- (U m u .Y r.mIn o q m m m m 'J) u 11 . . . . . . .

C c 004 00-4 004 O d d ? 4 ?

E a I I + + + + L, u u m a a m

4 Cd -In m 4 m 4 "l . . . . . . w A A m n 4 m m w w V W w w

u 4 4 4 4 4 4

c I I nn

I I nn

I I

2 nn & d u a ai d d d

W E m 0 m u 03 9 w o a 4 o A rn V) u - d m . . . . 9 :

U & l 1 hl N O A 4 0 ,+-'a " C. d 4 o

4 o u c 4 m V ) + + + + + +

9 03 corn 9 In (d 2 4 4 4 In m 3 . .

0 0 00 W V w w

0 0 w w

- cn

c el4 > U Z II I! I1 n I1 I1 I1 I1 It I1 I1 II V) > U V) > U m > w m > u

-a u c c m

V) cab

u m \O PI m m n m

E w U

m 5

C . . . . . . . . . . . . .... ....... .... . . . . . . - . . . . - . I . . . .

SECTION C: SOIL THERMAL CONDUCTIVITY: k upper = 1.8 W/m*K); k lower = 2.0 W/(m*K) (Systems 77 t o 83)

I n s u l a t i o n System I Wall Segment Floor Segments

lnsulstion Sn* vn Bottom 1 m s t r i p

, . . , . Concrete #l- and F a c t o r s Cn S t r i p n=3 a d j a c e n t n=4 t o w a l l n= 5 Cent re

U) . . .. ., . ., .

4 , 7 7

S = 2.42 1.04 0.42 V= 2.33 0.75 0.17 C= 0 1 5 0.3

. . . ....... .... . . . 7 8

S= (0.42+1.16~)-1 (0.90-0.007~) '~ (2.24-0.006R)'l V= (0 .43+1.20~) '~ ( 1.25-0.01~) '~ (5 .15-0.03~) '~ -:.:. ill( .-. . , . . . . , . . . C= 0 1.5 0.3

, 79

S= (0.42+1.088)'1 (2.0 1 + 0 . 4 6 ~ ) ' ~ (1 -88-0.03~)-1 , . . V= (0 .44+1.13~) '~ (2 .78+0.70~) '~ (3.91-0.09R)-l

I C= 0 1.5 0.3 . . ... , . , . . . .

. . I .

4 * 8 0

S= (0.49+0.97~)-1 (1.2 1 + 0 . 9 0 ~ ) - ~ (2 .08+0.81~) '~

.... . V= (0 .49+1.05~) '~ (1 .70+1.43~) '~ (4 .47+1.59~) '~ C= 0 1.5 0.3

. . :...:.:.: .:

4 4

I I nn d d 03 In

?"i? o m 0 + + \D 0

"i: hl In w w

4 4

I I nn tx !ai a In 0 y L n . . 004 + + U Cr) U -I . . d hl W W

d 4

I I nn d d m * ? 7 300 + + I- 9

? ? 0 - w w

- V)

c c u > U 0 11 I! II It II II I1 II I1

U r n > U Vl tr U r n > ~ -a o c e m

m a C 4

4 CU m a0 co 03

e aJ U

rl T3

b- .... ...... . ,. . - .' : : . . I t . . . . _ . . . . . . . .

4 4

I I nn & d 4 In

? 9 ? 000

I I 03 u .-I 4 . . m ul w w

4 4

I I nn d c4 m m o y m . . 00-4 + + 9 m l r l hl . . d hl ./ w

d 4

I I nn cd d

m 4 4 . . 000 + + 03 9

? ? 0 - w w

V) U c 2 w a Vl

LI 0 0

rz4

4-l

e 2 w a

V)

4 4 0 5

a, I4 u rn c II a~ C U

F-4

d m 3 a

-,-I 0 $4 U U u V) u II

C C E aJ

V - m '7 Q R(

L u . r l m U b II o u c SVl

4 d

I I nn d d d 03 0 0

o q m d o d I I

I- m ? ? CV Ln w w

d

I d l

! ~ i n 03 d 0 m o q m . . O C - + + m m ? 2 d - w w

d 4

I I n n d d b - d m . . 000 + + 0 b

9 ? ..4 4

w w

S l a b on grade: Units :

U, = 0.6 ~ t , = -1 S, W/ (m2- K) R , ~ * * K / w a5 = 0.4 A t 5 = -2 V , w / ( m 2 * ~ ) a, d imens ion le s s

C , m2 o r d imensionless AT, month

(At is t h e t i m e d e l a y of h e a t f l u x s i n e wave r e l a t i v e t o t h e ground s u r f a c e tempera ture s i n e wave.)

SECTION A: SOIL THERMAL CONDUCTIVITY: k = 0.9 W/m*K) (Systems 41 t o 53)

I n s u l a t i o n System I lo or Segments Insulated Wall

Inrutation 'n* 'n 1 m s t r i p Cowme A!t% . . . . . . . . . ...... . - Soit

F a c t o r s and Cn a d j a c e n t n=4 t o w a l l I Cent re n-5

L 4 1 S= 1.11 0.23 V= 1.02 0.13 C= 0.6 0.2

.,.'...'. ..... . . . .

L 42 S= (1.94+0.598)-1 (3.45-0.058)'~ V= (2.12+0.698)-I (5.59-0.12~) '~ C= 0.6 0.2

'.'.;.',.. . . . . . . . . . .

L 43 S= (1.3 1+0.998)-l (3.74+0.848)'~ V= (1.41+2.208)'1 (6.20+1.318)'~ C= 0.6 0.2

_..- . . . . . . . - . - . . . . . .

44 S= (1.13+0.0388)'1 (3.94-0.0378)'~ V= (1 .22+0.0378)-1 (6.90-0.0958)'~ C= 0.6 0.2

. . . . . L . .. . . . . I . . - . .

L, 45 S= (1.10+0.047~)'1 (4.03+0.888)'~ V= ( 1.20+0.0478)'~ (7.14+1.49~) '~ C= 0.6 0.2

. . . . . . . . . . . . . . .

SECTION A (cont'd)

Floor Segments

(4.13+0.82~)-1 (7.46+1.36~)-1 .

(7.94+1.39~)-1

SECTION A (cont'd)

Insulation System

Insulation

Concrete L . . '

141 5 1

7 0.5 m I

-

5 2 S= (1.69+@. 17~)'~ (5.10+0.028~)-I V= ( 1.97+0.27~)-I (9.75+0.14~)'~ C= 0.6 0.2 "..'_ -I=+ . . ,T

5 3 S= (1.68+0.23~)-I (5.12+0.06~)'~ V= ( 1.9 5+0.37~)'~ (9 .99+0.22~)-1 C= 0.6 0.2

I Floor Segments

Sns 'n and Cn Factors

S= V= C=

1 rn strip adjacent to wall

n=4

(1.54+0.076~)'1 (1.79+0.11~)'~

0.6

Centre n= 5

(5.02+0.0041~)-1 (9 .41+0.051~)-1

0.2

SECTION B: SOIL THERMAL CONDUCTIVITY: k = 1.35 W/m-K) (Systems 54 t o 66)

I n s u l a t i o n System

Insulated Wall

Insulation Concrete -l!!LI . _. . ... .. .. .. ..

Soil

L 54 - ..-... . .:: .' - ..

L 5 5 S= ( 1 .80+0.50~)-1 (2.40-0.027~)~~ V= (2.02+0.61~)-1 (3.97-0.065~)-1 C= 0.6 0.2

. . . . : : : : '

L 5 6 S= (1.13+0.95~)-I ( 2.60+0.8 5R)-l V= (1.25+1.198)'1 (4.40+1.37~)'1- C= 0.6 0.2

..:.. _. . . . . .:.-.

L 5 7 S= (1 .06+0.038~)-1 (2.66-0.02~)~~ V= (1. 17+0.038R)-l (4.68-0.058)-1 C= 0.6 0.2

.-:: ::.. . &. .. . . . .

L 58 S= ( 1.03+0.053~)-1 (2.74+0.88~)-1 V= (1.15+0.0548)-1 (4.88+1.52~)-1 C= 0.6 0.2

--:-: :. . , . . . .... , ...

I F l o o r Segments

'n9 v, and F a c t o r s Cn

S= V= C=

1 m s t r i p a d j a c e n t n= 4 t o w a l l

n= 5 Centre

1.29 1.14 0.6

0.34 0.19 0.2

SECTION B (cont'd)

Insulation System I Floor Segments Inpllaleci Wall

Insulation Concrete , Soil' --,- 0.2 m and.. Factors a d j a c e n t t o w a l l Centre

SECTION B ( c o n t ' d )

I n s u l a t i o n System I Floor Segments

Sn, vn 1 m s t r i p Concrete Li . . soil

and F a c t o r s Cn a d j a c e n t n=4 t o w a l l n= 5 Cen t r e

6 4

-I4- S= (1.18+0.038~)-1 0.30 V= (1 .39+0.058~)-1 0.16 C= 0.6 0.2

. 7 0.5 m

6 5 S= (1.34+0.11~)-1 (3.42+0.023~)-1 V= (1.64+0.17~)-1 (6.59+0.077~)-I C= 0.6 0.2

-r 6 6

S= (1.35+0.15~)-1 (3.46+0.039~)-1 . v= ( 1.66+0.25~)-I ( 6.80+0.14~)-1

C= 0.6 0.2

- . - . 7

SECTION C: SOIL THERMAL CONDUCTIVITY: k = 2.0 W/m*K) (Systems 84 to 96)

Insulation System Inmlatd W8l!

Insuimtian

Soil ,

L 8 4

-:.I... :...:..:

L 8 5

. . . . . . . . . ..............

L 8 6 ..... 1. :.:.:.: 87

S= ( 0.99+0.04~)-1 (1 -84-0.01R)-l V= (1.12+0.04~)-1 (3.25-0.038)-1 C= 0.6 0.2

. - . 1 . . . .

8 8 S= (0.96+0.06~)-1 (1 .90+0.881)-~ V= (1.11+0.058)-1 (3.41+1.53~)'1, C= 0.6 0.2

..... L . . . . . . . . . :.;. .

I Floor Segments

Sn, vn and Cn Factors

S= V = C=

S= V= C=

S= V= C=

1 m strip adjacent to wall

n= 4

1.48 1.29 0.6

(1.65+0.41~)-I (1.91+0.538)-1

0.6

(0.96+0.92~)'~ (1.10+1.19~)'~

0.6

Centre n= 5

0.50 0.27 0.2

(1.70-0.02R)-l (2.86-0.04~)-1

0.2

(1.84+0.85~)-1- (3.17+1.42~)'~

0.2

SECTION C (cont'd)

Insulation System I Floor Segments Insulated Wall

Insulation Sn* vn I m strip Concrete &- and C,

adjacent to wall Centre Factors n= 4 1 n-5 ski';:.. 7 0.2 m

I= 8 9 S= 1.15 0.48 V= 0.94 0.25 C= 0.6 0.2

. . . _ .

9 0 S= (1.80+0.46~)-I (1.76-0.02~)~~ V= (2.33+0.58~)-1 (3.10-0.04R)-l C= 0.6 0.2

J ! 9 1

S= (1.07+0.94~)-1 (1.92+0.85~)-1 '

V= (1.27+1.31~)-1 (3.44+1.468)-1 C= 0.6 0.2

-. ... ..; :. .

Ale7 9 2 S= (1. 52+0.42~)-1 (1 -86-0.02~)-1 V= (1.81+0.58~)-1 (3.35-0.05R)-l C= 0.6 0.2

. . '... . , . ,. ' . ' I

9 3 S= (0.92+0.84~)-1 (1 .95+0.84~)-1 V= (1.08+1.14~)-I (3.58+1.48~)-1 C= 0.6 0.2

, . , , . , . . . .

SEC'IION C (cont'd)

i.-atiOn I Floor Segments

Insulation 'n, "n 1 m strip Concrete and Cn adjacent to wall Centre Factors n=4 1 n-5

Sail

9 4

L S = (0.90+0.02~)-1 0.43 V= ( 1.08+0.0 3~)-l 0.24 C= 0.6 0.2

.- , . -

9 5 S= (1.06+0.06~)--I (2.34+0.01~)-I V= ( 1.35+0.1~)-I ( 4.50+0.058)-1 C= 0.6 0.2

9 6 S= (1.1+0.09~)-I (2.38+0.02~)-I V= (1.41+0.16~)-I (4 .70+0.08~)-1 C= 0.6 0.2

TABLE 2 Ground S u r f a c e Temperatures*

Loca t ion

Annual Amplitude Amplitude Mean Ground of Annual of Semi Annual,

Temp. OG, Cycle Ov, Cycle 0,,2 O C O K O K

Goose Bay, Labr. S t . J o h n ' s West , Nfld. T r u r o , N.S. K e n t v i l l e , N.S. C h a r l o t t e t o w n , P.E.I. F r e d e r i c t o n , N.R. La Poca t iGre , P.Q. Normandin, P.Q. Ste.-Anne de B e l l e v u e , P.Q. S t . August in , P.Q. Val D'Or, P.Q. Toron to , a n t . Kapuskasing, Ont. Vineland, Ont. Ottawa, Ont. Atikokan, Ont. Winnipeg, Man. Saskatoon, Sask. Regina , Sask. S w i f t C u r r e n t , Sask. Lacombe, Al ta . Edson, Al ta . Peace R i v e r , A l t a . Ca lga ry , A 1 t a. V e g r e v i l l e , Al ta . Summerland, R.C. Vancouver, B.C.

Mean 8.5 11.5 1.9

* I n a l l c a s e s t h e minimum ground s u r f a c e t e m p e r a t u r e o c c u r s i n January . If January i s d e s i g n a t e d a s m = 1, t h e n t h e s u r f a c e . t e m p e r a t u r e f i r s t harmonic can be e x p r e s s e d a s 0, s i n (30 (m+8)) , where m i s i n months and s i n e a n g l e is i n d e g r e e s . It f o l l o w s t h a t f i r s t harmonic v a r i a t i o n of t h e s u r f a c e , n, h e a t f l u x can be e x p r e s s e d a s

s i n (30(m+8+Atn) ).

TABLE A-1 Monthly Average Basement Heat Loss by Segments, W

;.ion t h Wall F loor T o t a l

Above 0.6 rn below Bottom 1 m S t r i p Center Grade Grade S e c t i o n

Average 107 113 151 265 126 7 6 2***

Winter season loss** 3.0 3.0 3.6 5.2 2.2 17.0 (GJ)

*Maximum r a t e of h e a t l o s s from basement **Winter s e a s o n l o s s : m = 1 0 t o 4 i n c l u s i v e

***Measured basement a n n u a l a v e r a g e h e a t l o s s (power) = 740 W Measured basement a n n u a l h e a t l o s s (energy) = 23.3 G J C a l c u l a t e d basement a n n u a l h e a t l o s s (energy) = 24 G J

CENTRAL AREA OF FLOOR FOR END SECTION

L L

CENTRAL AREA OF END FLOOR FOR MIDDLE SECTION

SECT1 ON

Figure 4 . Floor plan o f rec tangu lar foundat ion

ANNUAL AVERAGE POWER = 0.74 kW (MEASURED)

26 = 0.71 kW (CALCULATED)

22 - 20 - " MEASURED POINTS 18 - CALCULATED POINTS

16 - 14 -

12 -

10 SE PTl79 T I M E , h 10 SEPTl81

Figure 5 . Basement hea t l o s s DBR/hfRC t e s t basement,

Reprinted from ASHRAE TRANSACTIONS by permission of the American Society of Heating, Refrigerating and Air-Conditioning Engineers, Inc.

T h i s paper is being d i s t r i b u t e d i n r e p r i n t form by t h e I n s t i t u t e f o r Research i n C o n s t r u c t i o n . h l i s t of b u i l d i n g p r a c t i c e and r e s e a r c h p u b l i c a t i o n s a v a i l a b l e from t h e I n s t i t u t e mag be o b t a i n e d by w r i t i n g t o t h e P u b l i c a t i o n s S e c t i o n , I n s t i t u t e f o r Research i n C o n s t r u c t i o n , Na t iona l Research C o u n c i l of C a n a d a , O t t a w a , O n t a r i o , KIA 0R6.

Ce document e r t d i s t r i b u e sous f orme de t i rQ-8-part p a r 1' I n s t i t u t de recherche e n c o n s t r u c t i o n . On peut o b t s n i r une l i s t e d e s p u b l i c a t i o n s de 1 ' I n s t i t u t p c r t a n t s u r les t e c h n i q u e s ou Les recherches e n matisre d e bs t iment e n d c r i v a n t a l a S e c t i o n d e s p u b l i c a t i o n s , I n s t i t u t de recherche en c o n s t r u c t i o n , C o n s e i l n a t i o n a l d e r e c h e r c h e s du Canada, Ottawa ( O n t a r i o ) , KIA OR6.