1997; Katzenbach et al,. 1999). Research on injection has emerged through empirical and practical expérience, and as a conséquence most existing studies on ...
B o u c h e l a g h e m , F. ( 2 0 0 2 ) . Géotechnique
52, N o . 9, 6 6 7 - 6 8 2
Two large-scale injection experiments, and assessment of the advectiondispersion-filtration model F.
BOUCHELAGHEM*
A n assessment is presented of the v a l i d i t y of a theoretical m o d e l for miscible grout i n j e c t i o n i n a deformable porous m é d i u m . T h e m a t h e m a t i c a l f o r m u l a t i o n couples a n a l y s i s of the fluid flow a n d the grout m a s s t r a n s p o r t w i t h a study of the solid skeleton's displacements a n d the porous m é d i u m stucture é v o l u t i o n . I n p a r t i c u l a r , h y d r o m e c h a n i c a l coupling, grout d i s p e r s i o n a n d flltration w e r e c o n s i d e r e d i n o r d e r to p r o d u c e a r e a l i s t i c m o d e l of i n j e c t i o n w i t h i n a s a t u r a t e d deformable soil. T h e results of the theoretical f o r m u l a t i o n w e r e c o m p a r e d w i t h those obt a i n e d f r o m two o r i g i n a l large-scale i n j e c t i o n tests perf o r m e d i n the l a b o r a t o r y . C o n t r o l l e d l a b o r a t o r y tests p e r m i t t e d study of the b a s i c c h a r a c t e r i s t i c s of fluid flow a n d grout p r o p a g a t i o n for a m i c r o - c e m e n t grout, a n d a n e x a m i n a t i o n of the p e r f o r m a n c e of the c o m p l è t e i n j e c t i o n m o d e l was m a d e possible. A n u m e r i c a l solution of the f o r m u l a t i o n w a s p e r f o r m e d using the imite é l é m e n t m e t h od, a n d good agreement w a s obtained between the exp é r i m e n t a l a n d n u m e r i c a l results. T h e m e a s u r e d pore fluid p r e s s u r e s , soil displacements, grout front positions, porosities a n d h a r d e n e d b u l b dimensions w e r e c o m p a r e d w i t h t h e i r n u m e r i c a l c o u n t e r p a r t s . W h i l e the first l a r g e scale i n j e c t i o n e x p e r i m e n t c o n f i r m e d the f u n d a m e n t a l assumptions m a d e d u r i n g w r i t i n g of the m o d e l , the second i n j e c t i o n test offered a c o m p l è t e p h e n o m e n o l o g i c a l v a l i d a t i o n p r o c é d u r e , thus i l l u s t r a t i n g the c a p a c i t y of the m o d e l to r e p r o d u c e the b e h a v i o u r of the porous m é d i u m d u r i n g the i n j e c t i o n , for a situation s i m i l a r to a r e a l injection o p é r a t i o n .
KEYWORDS:
l a b o r a t o r y tests; t h e o r e t i c a l
modelling and analysis;
analysis; n u m e r i c a l
grouting
INTRODUCTION O w i n g to the c o m p l e x i t y o f m e c h a n i c a l and p h y s i c o - c h e m i cal interactions, and the v a r i e t y o f g r o u t i n g m i x t u r e s a n d applications, v e r y f e w studies have been dedicated t o the development o f a model describing grout propagation w i t h i n an i n j e c t e d s o i l ( H o n m a , 1984; M o r i et al, 1989; A z z a r , 1997; K a t z e n b a c h et al, 1999). Research o n i n j e c t i o n has emerged t h r o u g h e m p i r i c a l a n d p r a c t i c a l e x p é r i e n c e , and as a c o n s é q u e n c e m o s t e x i s t i n g studies o n i n j e c t i o n suffer f r o m a l a c k o f g é n é r a l i s a t i o n : t h e y always address a p a r t i c u l a r k i n d o f g r o u t or m é d i u m , or a s p é c i f i e i n j e c t i o n technique, w i t h o u t any systematic analysis o f the fundamental interactions f r o m the p o i n t o f v i e w o f p h y s i c s or mechanics. T o l e a d to a better u n d e r s t a n d i n g o f the i n j e c t i o n process, and to the establishment o f r a t i o n a l c o n c e p t i o n c r i t e r i a , a macroscopic m o d e l o f propagation o f a miscible grout i n a deformable porous m é d i u m is necessary.
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Cergy-Pontoise,
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N o u s p r é s e n t o n s une é v a l u a t i o n de l a v a l i d i t é d ' u n m o d è l e t h é o r i q u e p o u r l ' i n j e c t i o n de m o r t i e r m i s c i b l e dans u n m a t é r i e l p o r e u x deformable. L a f o r m u l a t i o n m a t h é m a t i q u e associe les analyses de l ' é c o u l e m e n t fluide et d u t r a n s p o r t de masse de ciment à l ' é t u d e des d é p l a c e m e n t s d u squelette solide et de l ' é v o l u t i o n de l a s t r u c t u r e poreuse. N o t a m m e n t , nous avons p r i s en compte le couplage h y d r o m é c a n i q u e , l a d i s p e r s i o n d u m o r t i e r et l a flltration afin de p r o d u i r e u n m o d è l e d'injection r é a l i s t e dans u n m a t é r i e l deformable s a t u r é . N o u s avons c o m p a r é les r é s u l t a t s de l a f o r m u l a t i o n t h é o r i q u e à ceux obtenus à p a r t i r de deux essais d ' i n j e c t i o n o r i g i n a u x à g r a n d e é c h e l l e e f f e c t u é s en l a b o r a t o i r e . L e s essais c o n t r ô l é s en l a b o r a t o i r e ont p e r m i s d ' é t u d i e r les c a r a c t é r i s t i q u e s de base de l ' é c o u l e m e n t fluide et de l a p r o p a g a t i o n d u m o r t i e r , p o u r u n m o r t i e r à m i c r o - c i m e n t ; nous avons a i n s i p u é t u d i e r l a p e r f o r m a n c e de tout le m o d è l e d ' i n j e c t i o n . Nous avons p r o d u i t l a solution n u m é r i q u e de l a f o r m u l a t i o n en utilisant une m é t h o d e d ' é l é m e n t s finis ; nous avons obtenu u n b o n a c c o r d entre les r é s u l t a t s e x p é r i m e n t a u x et les r é s u l t a t s n u m é r i q u e s . Nous avons c o m p a r é à l e u r é q u i v a l e n t n u m é r i q u e les pressions de fluide interstitiel, les m i g r a t i o n s d u sol, les positions frontales d u c i m e n t , les p o r o s i t é s et les dimensions de bulbe d u r c i a i n s i m e s u r é e s . T a n d i s que l a p r e m i è r e e x p é r i e n c e d ' i n j e c t i o n à g r a n d e é c h e l l e a c o n f i r m é les h y p o t h è s e s fondamentales faites p e n d a n t l ' é l a b o r a t i o n d u m o d è l e , le second essai d ' i n j e c t i o n a offert une p r o c é d u r e de v a l i d a t i o n p h é n o m é n o l o g i q u e c o m p l è t e , i l l u s t r a n t a i n s i l a c a p a c i t é d u m o d è l e à r e p r o d u i r e le c o m p o r t e m e n t d u m a t é r i e l p o r e u x p e n d a n t l ' i n j e c t i o n , d a n s une situation s i m i l a i r e à u n cas d ' i n j e c t i o n r é e l .
E x i s t i n g m o d e l s o f the i n j e c t i o n a n d transport o f m i s c i b l e grouts are dedicated to fluid flow and g r o u t transport, assume that soils have a r i g i d m a t r i x ( H o n m a , 1984; A z z a r , 1997; Baca, 1997; K a t z e n b a c h et al, 1999), and do n o t consider any c o u p l i n g b e t w e e n the mass transport i n s o l u t i o n and the m o d i f i c a t i o n s o f the porous m a t r i x , r e s u l t i n g f r o m h y d r o m e c h a n i c a l or f l l t r a t i o n effects. I n e x i s t i n g f o r m u l a t i o n s for the i n j e c t i o n p r o b l e m h y d r o m e c h a n i c a l c o u p l i n g is n o t m e n t i o n e d ; m o d e l l i n g w o r k is restricted to f o r m u l a t i o n o f the g r o u t transport é q u a t i o n ( w i t h n o r e a c t i o n t e r m ) and the fluid flow é q u a t i o n , i g n o r i n g the m o m e n t u m e q u i l i b r i u m . For real i n j e c t i o n cases the stresses i n d u c e d b y the fluid pressures developed d u r i n g the i n j e c t i o n are significant, l e a d i n g g e n e r a l l y to p l a s t i f i c a t i o n o f the s o i l mass a r o u n d the injected zone and to surface upheaval ( N i c o l i n i & N o v a , 2 0 0 0 ) , affecting i n t u r n the p e r m e a b i l i t y and the f l u i d f l o w p a t t e m . For h i g h i n j e c t i o n pressure values, plastic d é f o r m a tions m a y even be possible, l e a d i n g to fracture o f the porous m é d i u m , as n o t i c e d f o r instance b y H o n m a ( 1 9 8 4 ) a r o u n d the i n j e c t i o n tube d u r i n g large-scale i n j e c t i o n experiments i n the laboratory. I n contrast to the concerns o f p r e v i o u s m i s c i b l e g r o u t injection models, N i c o l i n i & N o v a (2000) performed a comprehensive finite é l é m e n t analysis, f o l l o w i n g a c o m p l e x
668
BOUCHELAGHEM
p r o c é d u r e to m a t c h the displacements observed i n the f i e l d d u r i n g the i n j e c t i o n p r i o r to a t u n n e l excavation. D u r i n g t h e i r n u m e r i c a l s i m u l a t i o n s t h e y i m p o s e d a field o f inelastic strains, parameterised b y several coefficients d e p e n d i n g o n the i n j e c t i o n p a t t e r n a n d the measured displacements, i n order to o b t a i n the elastic and plastic strain i n c r é m e n t s i n the r é g i o n o f the i m p r o v e d arch. The size a n d shape o f the b u l b s were d e t e r m i n e d b y the o v e r a l l d i m e n s i o n s o f the treated r é g i o n , and such a m e t h o d p e r m i t t e d the p r o d u c t i o n o f possible s c é n a r i o s o f displacement patterns, b y assuming d i f f é r e n t p e r m e a t i o n or ' c l a q u a g e ' f o r m a t i o n s and backa n a l y s i n g the displacement field. A g r e e m e n t b e t w e e n the e x p é r i m e n t a l data and the calculated values was achieved a p o s t e r i o r i , once the actual t r e n d and values t a k e n b y the displacements were k n o w n . H o w e v e r , i n a t o m o g r a p h i c i n v e s t i g a t i o n i t appeared that the soil i m p r o v e m e n t was o n l y effective i n some zones, as attested b y the increase i n m e c h a n i c a l strength a n d the decrease i n p e r m e a b i l i t y . The arch o f i m p r o v e d s o i l was n o t at a i l c o n t i n u o u s , b u t the p r o b a b l e c o n n e c t i o n w i t h the g r o u t p r o p a g a t i o n a n d the s o i l heterogeneities c o u l d n o t be i n v e s t i gated w i t h the p r o p o s e d m o d e l , as f l o w a n d transport p r o b l e m s were disregarded. T h e w h o l e effect o f the i n j e c t i o n o n the m e c h a n i c a l b e h a v i o u r o f the i n j e c t e d sand was i n c l u d e d i n the i m p o s e d d é f o r m a t i o n . A s a resuit, o n l y the effect o f the i n j e c t i o n o f the c é m e n t m i x e s o n the s o l i d skeleton's d é f o r m a t i o n s was considered d u r i n g the s i m u l a t i o n s , b y i m p l i c i t l y a s s u m i n g that the cernent g r o u t filled the v o i d s o f the n a t u r a l s o i l a n d seeped i n t o the g r o u n d , f o r m i n g an e l l i p t i c a l b u l b a n d causing s w e l l i n g o f the s o i l i n the i m p r o v e d zone. O w i n g to the uncertainties g e n e r a l l y presented b y the i n j e c t i o n o p é r a t i o n s r e g a r d i n g the effectiveness o f the s o i l i m p r o v e m e n t and thus the h o m o g e n e i t y o f treatment ( V a n der Stoel, 1999; N i c o l i n i & N o v a , 2 0 0 0 ) , i t seems necessary to study further g r o u t p r o p a g a t i o n d u r i n g the i n j e c t i o n experiments, i n order to o b t a i n p r é c i s e i n f o r m a t i o n o n the d i s t r i b u t i o n o f i n j e c t e d g r o u t and the i n j e c t i o n l e n g t h or effectiveness. C o m p r é h e n s i o n o f the i n j e c t i o n m e c h a n i s m w i t h i n a s o i l requires d é t e r m i n a t i o n o f the real g r o u t c o n c e n t r a t i o n d i s t r i b u t i o n together w i t h the i n j e c t i o n pressure or the i n j e c t i o n rate. T h i s m a t t e r is discussed i n this paper. A n o t h e r aspect neglected i n e x i s t i n g m o d e l s is flltration, a l t h o u g h its influence is a c k n o w l e d g e d f o r cement-based grouts (Yoneda et al, 1996; A z z a r , 1997) and silicate-based grouts ( H o n m a , 1984; M o r i et al., 1989). G r o u t mass d é p o s i t i o n over the s o l i d skeleton's surface c r é â t e s a c o u p l i n g between a i l the relevant variables, as the flltration alters the structure o f the porous m é d i u m , the c o m p o s i t i o n o f the g r o u t and the b e h a v i o u r o f the fluid phase. B i b l i o g r a p h i c a l study displays the l a c k o f c o u p l e d m o d e l s a i m i n g at d e t e r m i n i n g the é v o l u t i o n s o f the soil's displacements and porous m é d i u m structure under the effect o f i n j e c t i o n . E x i s t i n g i n j e c t i o n m o d e l s address the exclusive b e h a v i o u r o f one phase, either s o l i d ( N i c o l i n i & N o v a , 2 0 0 0 ) or fluid ( H o n m a , 1984; A z z a r , 1997), b u t g r o u t transport and i n t e r s t i t i a l pressure é v o l u t i o n m u s t be i n v e s t i gated together w i t h the d é f o r m a t i o n s o f the s o l i d skeleton as a w h o l e . M o s t o f the features observed can be e x p l a i n e d b y a g ê n e r a i m o d e l that c o m b i n e s the f u n d a m e n t a l c o n s e r v a t i o n é q u a t i o n s and the appropriate c o n s t i t u t i v e laws for each constituent w i t h i n a c o n t i n u o u s f r a m e w o r k , g i v i n g the same i m p o r t a n c e to the p h e n o m e n a o c c u r i n g w i t h i n the s o l i d and the f l u i d phases a n d to t h e i r interactions. M o r e o v e r , a bilatéral hydromechanical coupling and flltration m u s t be considered i n order to p r o d u c e a realistic m o d e l o f i n j e c t i o n w i t h i n a saturated d e f o r m a b l e m é d i u m . F o l l o w i n g this l i n e o f approach, a m a t h e m a t i c a l m o d e l o f m i s c i b l e g r o u t p r o p a g a t i o n w i t h i n a saturated porous m é d -
i u m has b e e n established, b y r e l y i n g o n Bear's approach (Bear & B a c h m a t , 1991) a n d o n p a r t i c u l a r assumptions m o t i v a t e d b y the experiments. T h e m a i n process investigated is g r o u t mass transport, assuming that the m i c r o - c e m e n t g r o u t can be studied as a m i s c i b l e and homogeneous c o m p o nent o f the fluid phase i n i t i a l l y p r é s e n t w i t h i n the i n t e r s t i t i a l space. T h e m i s c i b i l i t y a s s u m p t i o n was m o t i v a t e d b y a s é r i e s o f experiments ( B o u c h e l a g h e m & A l m o s n i , 2 0 0 1 ) , a n d leads to the conceptual r e p r é s e n t a t i o n o f the porous m é d i u m as a b i n a r y m é d i u m , c o m p r i s i n g a s o l i d phase and a connected fluid phase, w i t h three d i f f é r e n t constituents: the s o l i d skelet o n , the i n t e r s t i t i a l water a n d the i n j e c t e d grout. A l t h o u g h c o n v e c t i v e transport d o m i n â t e s d u r i n g g r o u t p r o p a g a t i o n , h y d r o d y n a m i c dispersion, w h i c h was d i s p l a y e d and measured during one-dimensional experiments ( B o u c h e l a g h e m & A l m o s n i , 2 0 0 1 ) , is n o t neglected, as is u s u a l l y the case for m i s c i b l e g r o u t i n j e c t i o n m o d e l s ( H o n m a , 1984; M o r i et al, 1989; A z z a r , 1997; K a t z e n b a c h et al, 1999) . F i l t r a t i o n was observed d u r i n g i n j e c t i o n tests o n s m a l l c o l u m n s , and the filtration rate was estimated f r o m dedicated o n e - d i m e n s i o n a l i n j e c t i o n tests ( B o u c h e l a g h e m & V u l l i e t , 2 0 0 1 ) . The variables d i r e c t l y affected b y g r o u t filtration are the g r o u t c o n c e n t r a t i o n a n d the porous m é d i u m structure, w h i c h i n t u r n m o d i f y the fluid's r h e o l o g i c a l properties, d e p e n d i n g o n the g r o u t c o n c e n t r a t i o n , the characteristics o f the fluid flow a n d the s o l i d displacements. T h e filtration mechanisms are c o m p l e x and o r i g i n a t e f r o m v a r i o u s sources such as g e o m e t r i c a l i n t e r c e p t i o n , s é d i m e n t a t i o n , d i f f u s i o n and a d s o r p t i o n m e c h a n i s m s ( H e r z i g et al, 1970). I n the absence o f m i c r o s c o p i c i n f o r m a t i o n about the deposit m o r p h o l o g y and the m e c h a n i s m s l e a d i n g to d é p o s i t i o n , n o a s s u m p t i o n can be m a d e r e g a r d i n g the d o m i n a n c e o f a p a r t i c u l a r filtration m e c h a n i s m , and the filtration t e r m i n t e grated w i t h i n the m a c r o s c o p i c m o d e l expresses the w h o l e set o f d é p o s i t i o n mechanisms i n a g l o b a l manner. M o d e l l i n g w o r k m u s t be supplemented b y appropriate experiments i n order to assess the v a l i d i t y o f the m o d e l . A p a r t i a l v a l i d a t i o n o f the m o d e l was p r e v i o u s l y presented for the o n e - d i m e n s i o n a l case, b y successful c o m p a r i s o n b e t w e e n the n u m e r i c a l results and e x p é r i m e n t a l results f o r pressure and g r o u t c o n c e n t r a t i o n front ( B o u c h e l a g h e m & A l m o s n i , 2 0 0 1 ; B o u c h e l a g h e m & V u l l i e t , 2 0 0 1 ) . To c o n t i n u e the process, the m o d e l p r o p o s e d h a d to be v a l i d a t e d against i n situ or large-scale i n j e c t i o n data. N u m e r o u s e x p é r i m e n t a l research a c t i v i t i e s are r e p o r t e d i n the literature o n the p e r m e a t i o n o f a g r o u t i n j e c t e d i n a porous m é d i u m . There are f e w p u b l i s h e d w o r k s related to field i n j e c t i o n cases ( V a n der Stoel, 1999; N i c o l i n i & N o v a , 2 0 0 0 ) , b u t several authors have presented large-scale inject i o n studies ( B a l a t & K r i s c h , 1982; H o n m a , 1984; M o r i et al, 1989; Yoneda et al, 1996; V a n der Stoel, 1999). T h e l i m i t a t i o n s o f the e x i s t i n g m o d e l s are also encountered i n the e x p é r i m e n t a l research o n i n j e c t i o n . O n l y the i n j e c t i o n pressure, the i n j e c t i o n rate and the hardened sand v o l u m e are measured d u r i n g m o s t g r o u t i n j e c t i o n e x p e r i ments, i n order to investigate the r e l a t i o n b e t w e e n the o p e r a t i n g c o n d i t i o n s , the g r o u t i n g patterns such as permeat i o n or f r a c t u r i n g o f g r o u t i n g , a n d the d i s t r i b u t i o n o f g r o u t e d m a t e r i a l after i n j e c t i o n G o u v e n o t , 1998; M o r i et al, 1989; T a r u m i & Sekine, 1993; V a n der Stoel, 1999). O n the other hand, w h e n surface m o v e m e n t s a n d displacements w i t h i n the s o i l were r e c o r d e d b y N i c o l i n i & N o v a ( 2 0 0 0 ) d u r i n g the i n j e c t i o n phase, o n l y the s o l i d skeleton's displacements were o f interest, and n o i n f o r m a t i o n about the flow r é g i m e or the g r o u t d i s t r i b u t i o n is available. A s a resuit, son w i t h the the c o u p l i n g displacements
the available data cannot be used for c o m p a r i c o m p l è t e f o r m u l a t i o n proposed: i n particular, b e t w e e n the fluid pressures a n d the s o l i d cannot be studied f r o m the e x i s t i n g e x p e r i -
TWO
669
LARGE-SCALE INJECTION EXPERIMENTS
ments. O w i n g to the l a c k o f e x p é r i m e n t a l results appropriate to the m o d e l under i n v e s t i g a t i o n , c o n t r o l l e d l a b o r a t o r y inject i o n e x p e r i m e n t s were developed for the purpose o f v a l i d a tion. A large-scale l a b o r a t o r y e x p e r i m e n t was c a r r i e d out at the l e v e l o f an i n j e c t i o n u n i t ( o r tube à manchette), and was c o m p l e t e l y i n s t r u m e n t e d to measure the displacements, fluid pressures and g r o u t front p r o p a g a t i o n , w h i l e c o n t r o l l i n g the m e c h a n i c a l and h y d r a u l i c b o u n d a r y c o n d i t i o n s . T h e results o f t w o large-scale i n j e c t i o n experiments p e r f o r m e d i n the l a b o r a t o r y are presented i n t h i s paper, to offer an assessment o f the p e r f o r m a n c e o f the c o m p l è t e t h e o r e t i c a l f o r m u l a t i o n proposed, for c o n d i t i o n s close to real i n j e c t i o n cases.
where ( B o u c h e l a g h e m & V u l l i e t , 2 0 0 1 ) a n d therefore, for reasons o f conciseness, w i l l o n l y be g i v e n here i n their final form. T h e mass balance f o r the s o l i d skeleton p e r m i t s é v a l u a t i o n o f the p o r o s i t y change under the effect o f d é p o s i t i o n a n d the s o l i d skeleton d é f o r m a t i o n s :
f
defines the constant c o n c e n t r a t i o n coefficient for the fluid phase at constant pressure. B represents the v a r i a t i o n o f the fluid d e n s i t y w i t h g r o u t c o n c e n t r a t i o n at constant pressure, and is defined i n the same w a y as B , as the fluid density varies with the pressure and the concentration: p = p ( p , p ) . k is the i n t r i n s i c p e r m e a b i l i t y o f the porous m é d i u m , 7J is the fluid density, and g is the g r a v i t y vector. c
p
f
f
f
g f
f
T h e g r o u t transport é q u a t i o n gives the é v o l u t i o n o f the g r o u t c o n c e n t r a t i o n w i t h i n the i n t e r s t i t i a l fluid phase under d o m i n a n t c o n v e c t i v e effects, n o n - n e g l i g i b l e dispersion w i t h i n the i n t e r s t i t i a l fluid a n d variable filtration as the g r o u t progresses i n the m é d i u m :
s s
+ Vp
-Vf. I — V • « D , ' T p
g
i n CL|uaLiuii \j)
(1
») 4 p
s
(6)
d?
T h e h y d r o d y n a m i c dispersion tensor o f Bear is e m p l o y e d , w h i c h i m p l i e s that under i s o t r o p i c c o n d i t i o n s the dispersion d é p e n d s o n t w o parameters, the l o n g i t u d i n a l d i s p e r s i v i t y constant a n d the transverse d i s p e r s i v i t y constant aj, w h i l e the d i f f u s i o n results i n an a d d i t i o n a l spherical c o m p o n e n t (Bear & B a c h m a t , 1991): D"
(a
L
V
- or)
f
+ a |V |I + T
f
J
D*
g w
I
(7)
|Vf| where ® is the tensorial p r o d u c t o f t w o vectors, I is the i d e n t i t y m a t r i x , | V f | is the fluid v e l o c i t y m o d u l u s , a n d D * is the d i f f u s i o n coefficient. g w
Some a d d i t i o n a l quantities appear i n the f o r m u l a t i o n o f the flow a n d transport é q u a t i o n s c o m p a r e d w i t h the classical f o r m u l a t i o n o f the h y d r o d y n a m i c dispersion (Scheidegger, 1974; D u l l i e n , 1979; H o n m a , 1984; B e a r & B a c h m a t , 1 9 9 1 ; Baca, 1997): - p g V - V i n é q u a t i o n (6) and - V • V i n é q u a t i o n (3) express the h y d r o m e c h a n i c a l c o u p l i n g b e t w e e n the s o l i d skeleton d é f o r m a t i o n s and the fluid flow, V • V b e i n g the v o l u m e t r i c d é f o r m a t i o n rate o f the s o l i d skeleton. The h y d r o m e c h a n i c a l c o u p l i n g is systematically i n c o r p o r a t e d i n the f o r m u l a t i o n since the study concerns the h y d r o m e c h a nical c o u p l i n g produced by injection into a deformable porous m é d i u m . f
l a n i e yaii
ui uic inaicuai
uciivauvc
ui t
a
dt
s
s
fluid phase density that is due to v a r i a t i o n s i n the g r o c o n c e n t r a t i o n . T h e f o r m u l a t i o n i n c o r p o r â t e s an a d d i t i o n c o u p l i n g b e t w e e n the fluid flow a n d the g r o u t c o n v e r t i ' transport w i t h i n the fluid phase, related to the v a r i a t i o n the fluid phase's r h e o l o g i c a l properties (density, v i s c o s i t w i t h the g r o u t c o n c e n t r a t i o n , w h i c h is n e w w i t h respect the usual treatment o f species transport i n s o l u t i o n under tl a s s u m p t i o n o f an i d é a l tracer ( M a r i e , 1972; Baca, 1997). The g l o b a l m o m e n t u m balance, associated w i t h the princ p i e o f effective stress a n d w i t h a linear elastic stress-stra r e l a t i o n s h i p , gives the é v o l u t i o n o f the displacements u n d the effect o f the fluid pressure increase and the i m p o s i m e c h a n i c a l stresses. C o n c e r a i n g the c o n s t i t u t i v e aspects, the é v o l u t i o n s o f tl density a n d v i s c o s i t y o f the fluid phase were measured the laboratory, a n d their v a r i a t i o n s w i t h the g r o u t concentr t i o n were established ( B o u c h e l a g h e m , 2 0 0 1 ) . A s a fil a p p r o x i m a t i o n , the a s s u m p t i o n is made that the density the fluid phase, p = p (~p , p ) , a n d its viscosity, 7 i , va l i n e a r l y w i t h the g r o u t c o n c e n t r a t i o n , p : f
f
f
g f
f
g f
p
=
f
p
w
f
1 +
P
imp
p
g
P imp gf
s
The t e r m
where p
g f
71 =
n) d p s
p*
1
s S
1
Xpi
dt
8
i n é q u a t i o n (3) is o b t a i n e d f r o m the t e r m for diffusive mass transfer f r o m the
fluid
phase to the s o l i d phase across the
interface surface ( B o u c h e l a g h e m & V u l l i e t , 2 0 0 1 ) . A s i m i l a r t e r m is p r é s e n t i n the g r o u t transport é q u a t i o n ( 6 ) : n) d p
— f (1 -pg —.
s
s t
dt
The first c o m p o n e n t (1 -
n) d ^ s
s
d; originates f r o m the v a r i a t i o n s o f the s o l i d skeleton density, as the s o l i d skeleton comprises the i n c o m p r e s s i b l e grains o f the i n i t i a l s o l i d skeleton and the filtrated g r o u t . 2 p represents the mass o f g r o u t deposit over the surface o f the s o l i d skeleton, per u n i t v o l u m e o f the porous m é d i u m and per u n i t time. The filtration induces a c o u p l i n g b e t w e e n the field é q u a t i o n s , o w i n g to mass transfer b e t w e e n the fluid and s o l i d phases. T h e expression o f the filtration rate, X, o b t a i n e d b y the averaging process ( B o u c h e l a g h e m , 2 0 0 1 ) , g f
X=X(pS , f
p
s \, A ) f
f,î
s
dfps
~dT
1 +
Wf
w
f
is the water density
imp
w h e r e fi and , « d é n o t e the v i s c o s i t y o f the w a t e r ai g r o u t respectively. The influence o f the fluid v i s c o s i t y v a r i a t i o n w i t h tl g r o u t c o n c e n t r a t i o n , w h i c h can be e x p l a i n e d b y the mise b i l i t y b e t w e e n the i n j e c t e d g r o u t and the water displaci w i t h i n the i n t e r s t i t i a l space, is significant at the b e g i n n i n g the i n j e c t i o n experiments, as attested b y the pressure v a r i tions (see b e l o w ) , w h i l e the pressure increase can be attri u t e d m a i n l y to filtration. g f
D e t a i l e d d e s c r i p t i o n o f the d é t e r m i n a t i o n o f the m a t e r i parameters o f the m o d e l , i n c l u d i n g v i s c o s i t y tests, the dete m i n a t i o n o f the fluid density é v o l u t i o n w i t h the g r o c o n c e n t r a t i o n , a n d o n e - d i m e n s i o n a l i n j e c t i o n experiments f dispersion and filtration rate measurements, has b e e n givi previously (Bouchelaghem & A l m o s n i , 2 0 0 1 ; Bouchelaghe & V u l l i e t , 2 0 0 1 ) . Therefore a i l the parameters were k n o v before u n d e r t a k i n g the large-scale i n j e c t i o n e x p e r i m e m F u r t h e r m o r e , the f u l l range o f m a t e r i a l parameters appearii i n the f o r m u l a t i o n o f the p r o b l e m , a n d thus r e q u i r e d f o r tl n u m e r i c a l m o d e l l i n g w o r k , has b e e n established indepe d e n t l y o f the large-scale i n j e c t i o n experiment.
(8)
differs f r o m the expressions u s u a l l y f o u n d i n the literature o n filtration ( H e r z i g et al, 1970). A f is the h y d r a u l i c radius, A f = Uof/Sf where [ % is the v o l u m e o f the fluid phase a n d Sf is the surface o f the fluid-solid interface per u n i t v o l u m e o f porous m é d i u m . T h e filtration rate, X, o f the a d v e c t i o n - d i s p e r s i o n - f i l t r a t i o n m o d e l varies i n the g ê n e r a i case w i t h the porous m é d i u m structure é v o l u t i o n , the a m o u n t a n d the m o r p h o l o g y o f the deposit. The term s
is the value o f the g r o u t c o n c e n t r a t i o n pr
The r e s u l t i n g m o d e l consists o f a single System o f unifii é q u a t i o n s , a l l o w i n g f o r the convective transport and disps sion for g r o u t , g r o u t filtration over the s o l i d skeleton surfac and the c o u p l i n g b e t w e e n g r o u t transport, f l u i d flow ai s o l i d skeleton d é f o r m a t i o n s .
Xps
{y
m p
fi
f
wt
(1 -
i
scribed at the i n j e c t i o n p o i n t s , a n d p
INSTRUMENTATION
I n the f o l l o w i n g , the i n s t r u m e n t a t i o n m o u n t e d o n tl m o d e l , the soil c o n d i t i o n s , and the i n j e c t i o n test p r o g r a m n are described. T h e m o d e l to be analysed is a three-dime sional c y l i n d r i c a l i n j e c t i o n m o d e l , 1-5 m i n diameter ai 1-2 m l o n g , i n w h i c h the g r o u t is i n j e c t e d f r o m a fini l e n g t h o f strainer a l o n g the i n j e c t i o n p i p e , to simulate a l i i source f o r the g r o u t i n j e c t i o n ( F i g . 1). The i n j e c t i o n p i p e p o s i t i o n e d so that its axis coincides w i t h the axis o f r e v o l t i o n o f the c y l i n d e r . T h e g r o u t c o u l d be injected i n t o tl
Measurements
(e)f nterstitial pressure transducers . . . (b) h
/ / / / / 7 / / / / / / / / V / / / / / / / m Test 1 * Test 2
/
^
1
T h e test p r o c é d u r e a n d the i n s t r u m e n t a t i o n are the same d u r i n g the t w o large-scale experiments, except that the sensors are b r o u g h t closer to the i n j e c t i o n tube d u r i n g the second test, i n order to catch the abrupt pressure gradient that seemed to occur i n the v i c i n i t y o f the i n j e c t i o n tube d u r i n g the first test. The i n s t r u m e n t a t i o n is also m o r e extensive: the m o d i f i c a t i o n s b e t w e e n the first a n d the second test appear i n F i g . 1, w h i c h shows the g ê n e r a i appearance o f the m o d e l a n d the p o s i t i o n s o f the instruments.
Injection parameters T w o pressure transducers, l o c a t e d at the t o p and b o t t o m o f the i n j e c t i o n tube, were used to estimate the i n j e c t i o n pressure. A s the tests were c o n d u c t e d under saturated c o n d i t i o n s , the i n f l o w and o u t f l o w rates were o b t a i n e d f r o m c o n t i n u o u s a c q u i s i t i o n o f the fluid i n f l o w and o u t f l o w masses respect i v e l y b y means o f t w o a u t o m a t i c scales.
Boundary
conditions
T w o v e r t i c a l displacement transducers were attached to the top surface o f the m o d e l d u r i n g the i n j e c t i o n tests to measure possible heave d u r i n g the i n j e c t i o n , a n d a force transducer was adjusted to the h y d r a u l i c j a c k to c o n t r o l the value o f the constant m e c h a n i c a l effort i m p o s e d d u r i n g the injection. I n order to get close to i n - s i t u test c o n d i t i o n s , hydrostatic b o u n d a r y c o n d i t i o n s s h o u l d be v e r i f i e d at the m o d e l ' s l a t é r a l surface. W h i l e o n l y p a r t i a l l y v e r i f i e d d u r i n g the first i n j e c t i o n test, a hydrostatic pressure p r o f i l e was i m p o s e d o n the l a t é r a l b o u n d a r y d u r i n g the second i n j e c t i o n test b y p l a c i n g a drainage médium (geotextile) o f permeability k = 2-4 X 1 0 ~ m / s a r o u n d the c i r c u m f e r e n c e o f the m o d e l . A s a resuit, the l a t é r a l surface was an e q u i p o t e n t i a l surface f o r the pressure head, w h i l e the top and b o t t o m surface were streamlines f o r the r a d i a l flow. A f t e r r e a c h i n g the l a t é r a l surface, the fluid flowed t h r o u g h holes made at the t o p o f the m o d e l . 2
the
injection
(b)
T h e second section c o n t a i n e d f o u r (three d u r i n g the first test) displacement transducers ( L V D T ) fixed to the l a t é r a l b o u n d a r y f o r r a d i a l displacement measurement. T h e r é f é r e n c e displacement corresponded to the state o f the soil after m e c h a n i c a l l o a d i n g and c o n s o l i d a t i o n , and so the measured displacements discussed b e l o w refer to the corrected displacements under the effect o f i n j e c t i o n alone.
(c)
T h e t h i r d section c o n t a i n e d seven electric probes f o r t e n s i o n measurement related to the g r o u t c o n c e n t r a t i o n (see next subsection).
/ / / /
sand mass under constant p u m p i n g pressure or at constant p u m p i n g rate. D u r i n g the experiments a constant p u m p i n g rate was used.
during
T h e first section c o n t a i n e d f o u r (three d u r i n g the first test) d i f f e r e n t i a l pressure transducers for i n t e r s t i t i a l fluid overpressure measurement. T h e r é f é r e n c e was m a d e w i t h respect to the i n i t i a l hydrostatic state.
' 1500 A, B: fluid pressure (d) vertical displacement transducer transducers within the injection tube (e) outflow rate measurement
set-up.
the soil
(a)
—
F i g . 1. E x p é r i m e n t a l
within
To p r o d u c e a set o f c o m p a r a t i v e results f o r use as a n independent test o f the v a l i d i t y o f the c o m p l è t e f o r m u l a t i o n proposed, i n a d d i t i o n to m o n i t o r i n g the b o u n d a r y c o n d i t i o n s a n d i n j e c t i o n parameters the é v o l u t i o n o f the m a i n field variables h a d to be d e t e r m i n e d w i t h i n the s o i l mass. D u r i n g the t w o tests, the m o d e l c a r r i e d three i n s t r u m e n t e d sections, shown i n a two-dimensional view i n Fig. 1 :
T h e w h o l e set o f transducers and apparatus was connected to an a u t o m a t i c data a c q u i s i t i o n p r o g r a m ( L a b v i e w , 1997) r u n n i n g o n a computer. A f t e r the g r o u t i n g process was c o m p l e t e d , the s o l i d i f i e d b u l b was extracted f r o m the m o d e l and samples were t a k e n to measure the strength a n d p e r m e a b i l i t y characteristics o f the hardened sand. Several density a n d p o r o s i t y measurements were m a d e near the t o p o f the m o d e l before r e m o v i n g the s o l i d b u l b .
Grout
concentration
front
monitoring
C o n c e n t r a t i o n measurements m u s t be available d u r i n g the i n j e c t i o n tests f o r c o m p a r i s o n w i t h the n u m e r i c a l concent r a t i o n field. Research has been c o n d u c t e d i n the l a b o r a t o r y to d é t e r m i n e the g r o u t c o n c e n t r a t i o n d u r i n g its p r o p a g a t i o n w i t h i n a saturated s o i l c o l u m n ( B o u c h e l a g h e m , 2 0 0 1 ; B o u c h e l a g h e m & A l m o s n i , 2 0 0 1 ) . Besides the m o d e l v a l i d a t i o n , d é t e r m i n a t i o n o f the g r o u t c o n c e n t r a t i o n d i s t r i b u t i o n is c r u c i a l for i d e n t i f i c a t i o n o f the m o d e l parameters. I n p a r t i c u lar, l o c a l g r o u t c o n c e n t r a t i o n values are necessary to characterise precisely the w i d t h o f the t r a n s i t i o n zone related to h y d r o d y n a m i c dispersion, and to a l l o w a l o c a l study o f filtration. C o n c e r n i n g the g r o u t c o n c e n t r a t i o n measurement w i t h i n the s o i l mass d u r i n g i n j e c t i o n , n o direct g r o u t - f r o n t m o n i t o r i n g d u r i n g the i n j e c t i o n test was r e p o r t e d i n the r e v i e w e d w o r k s . T h e s o l i d g r o u t d i s t r i b u t i o n a n d e f f i c i e n c y o f treatm e n t were c o m m o n l y evaluated instead i n ternis o f increase i n m e c h a n i c a l strength, p e r m e a b i l i t y r é d u c t i o n and p o r o s i t y decrease (Yoneda et al, 1996; K a t z e n b a c h et al, 1999; V a n der Stoel, 1999). Q u a l i t a t i v e i n f o r m a t i o n about the g r o u t p r o p a g a t i o n w i t h t i m e and the g r o u t i n g p a t t e r n — p e r m e a t i o n or h y d r a u l i c f r a c t u r i n g — w a s also o b t a i n e d b y u s i n g d y e d c h e m i c a l g r o u t ( B a l a t & K r i s h , 1982; H o n m a , 1984; K r i z e k & P è r e s , 1985; T a r u m i & Sekine, 1993). E l e c t r i c a l r e s i s t i v i t y measurements were used b y V a n der Stoel ( 1 9 9 9 ) before and after i n j e c t i o n o f a cement-based g r o u t to observe the variable d r o p i n r e s i s t i v i t y related to the g r o u t i n t r u s i o n , a n d thus to o b t a i n q u a l i t a t i v e i n f o r m a t i o n about the s o l i d g r o u t d i s t r i b u t i o n w i t h i n the treated soil. The first attempt to f o l l o w the g r o u t p r o p a g a t i o n front d u r i n g the i n j e c t i o n r e l i e d o n e l e c t r i c a l r e s i s t i v i t y or c o n d u c t i v i t y (inverse o f resistivity) measurements ( B o u c h e l a g h e m , 2 0 0 1 ) . To the author's k n o w l e d g e , no
rijection o p é r a t i o n s . A s the i n i t i a l s o i l c o n d u c t i v i t y is m u c h ower t h a n that o f the cernent g r o u t , c o n d u c t i v i t y measurenents m a d e at the l e v e l o f é l e c t r o d e s inserted w i t h i n the s o i l riass seemed a possible means to f o l l o w g r o u t p r o p a g a t i o n , he front m o v e m e n t b e i n g associated w i t h a sudden increase n conductivity.
30 - •
A second s é r i e s o f measurements were made w i t h a lomogeneous m i x t u r e o f sand saturated w i t h g r o u t , b y ' a r y i n g the c / w r a t i o a n d the p o r o s i t y value. F i g . 2 c o m >ares the c o n d u c t i v i t y v a r i a t i o n s o b t a i n e d for the g r o u t alone md the m i x t u r e o f g r o u t and sand w i t h a p o r o s i t y n = 0-4. rhe sand c r é â t e s a screen effect: the c o n d u c t i v i t y is about hree t i m e s l o w e r t h a n w i t h the g r o u t alone. B u t this d r o p is ;eneralised, and the w h o l e set o f values o b t a i n e d w i t h the n i x t u r e v a r y i n the same p r o p o r t i o n s as for the g r o u t alone. the sand does n o t reduce the r e l a t i v e increase i n c o n l u c t i v i t y w i t h the c / w r a t i o , the cernent c o n c e n t r a t i o n can t i l l be o b t a i n e d f r o m the c o n d u c t i v i t y v a l u e . T h e last a n d m o s t i m p o r t a n t s é r i e s o f tests c o m p r i s e d e s i s t i v i t y measurements d u r i n g the i n j e c t i o n i n a onel i m e n s i o n a l soil c o l u m n , as s h o w n i n F i g . 3. I f the g r o u t iresence can be detected, even f o r l o w c / w ratios, there is 10 s i m p l e c o r r é l a t i o n b e t w e e n the g r o u t c o n c e n t r a t i o n a n d he c o n d u c t i v i t y measurements d u r i n g the c o l u m n i n j e c t i o n ests. T h e r e l a t i v e p r o p o r t i o n s o f g r o u t a n d i n t e r s t i t i a l w a t e r n i t i a l l y p r é s e n t cannot be deduced f r o m r e s i s t i v i t y measurenents. F u r t h e r m o r e , as soon as g r o u t is p r é s e n t , even i n i n f i n i t e i i m a l quantity, the é l e c t r o d e reacts: there is n o t h r e s h o l d Tfect, w h i c h i m p l i e s that i t is n o t the g r o u t front b u t the
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A s é r i e s o f measurements were made. C o n d u c t i v i t y measirements were m a d e w i t h pure g r o u t , b y v a r y i n g the cernent/ vater ( c / w ) r a t i o b e t w e e n 0 a n d 0-5, i n order to investigate he r e l a t i o n between the g r o u t c o n c e n t r a t i o n and the resistivty; the é v o l u t i o n o f r e s i s t i v i t y w i t h t i m e was also measured. T h e measured c o n d u c t i v i t y changed q u i c k l y w i t h the c / w atio, i n a r a t i o o f 10 t i m e s the water c o n d u c t i v i t y value f o r 'ery l o w values o f c / w to 30 t i m e s the w a t e r c o n d u c t i v i t y 'alue f o r c / w = 0-33, as i l l u s t r a t e d i n F i g . 2 i n the c u r v e o f o n d u c t i v i t y v a r i a t i o n f o r the g r o u t alone. T h e c o n d u c t i v i t y ;ould thus be c o r r e l a t e d w i t h the c / w r a t i o . I n the t i m e nterval related to the g r o u t p r o p a g a t i o n , the superplasticiser, v h i c h acted as a setting a n d h y d r a t i o n retarder, stabilised he t e m p o r a l é v o l u t i o n o f the r e s i s t i v i t y associated w i t h the :hemical reactions o f c é m e n t h y d r a t i o n , and as a resuit the e s i s t i v i t y values showed no é v o l u t i o n w i t h t i m e .
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a r r i v a i o f the t r a n s i t i o n zone located ahead o f the front t h is detected. T h i s observation is c o r r o b o r a t e d b y c o m p a r i i the successive g r o u t front p o s i t i o n s as detected b y r e s i s t i v i measurements w i t h the g r o u t front results g i v e n b y i m a j analysis. T h e i m a g e analysis technique p r o v e d m o r e reliab t h a n r e s i s t i v i t y results for s t u d y i n g the h y d r o m e c h a n i c dispersion o f the g r o u t , and was used to o b t a i n the I o n i t u d i n a l d i s p e r s i v i t y coefficient d u r i n g the i n j e c t i o n w i t h a one-dimensional plexiglas c o l u m n (Bouchelaghem A l m o s n i , 2 0 0 1 ) . A s s h o w n i n F i g . 3, the r e s i s t i v i t y measur m e n t s g i v e g r o u t front p o s i t i o n s s y s t e m a t i c a l l y ahead those o b t a i n e d b y i m a g e analysis, s h o w i n g that the electroi reacts s y s t e m a t i c a l l y to c o n c e n t r a t i o n values l o w e r t h a n tl g r o u t front c o n c e n t r a t i o n value.
Nevertheless, as the i m a g e analysis m e t h o d used d u r i i the o n e - d i m e n s i o n a l i n j e c t i o n tests c o u l d n o t be e m p l o y é é l e c t r o d e s were inserted i n the s o i l mass d u r i n g the injectic o f the c y l i n d r i c a l m o d e l i n order to o b t a i n some informatic about the g r o u t transport. Other techniques were also envisaged, b u t t h e y are eith i n a p p r o p r i a t e to the m i s c i b l e f l u i d transport p r o b l e m ( A z z ; 1997), or destructive and i m p r é c i s e ( H o n m a , 1984; Kriz< & P è r e s , 1985).
—en. T h e experiments note a contrast i n the r e l a t i v e presre increase f r o m 1 to 10 between the c o n s t r i c t i o n m o d e [d the o c c l u s i o n m o d e . I t is reasonable to consider that a finite n u m b e r o f sites, :pending o n the s p é c i f i e surface area o f the porous m e d m , are available for d é p o s i t i o n . W h e n those sites are a i l t u r a t e d w i t h the filtrated g r o u t , a m o r e c r i t i c a l d é p o s i t i o n ode m a y b e g i n w i t h a n e w é v o l u t i o n l a w f o r the deposit. s the porous skeleton consists m a i n l y o f i r r e g u l a r particles ith d i f f é r e n t sizes, r a n d o m l y d i s t r i b u t e d w i t h i n a t r i - d i m e n anal d o m a i n , the i n f l e x i o n p o i n t s c o u l d be e x p l a i n e d b y a p o s i t i o n process o c c u r r i n g i n several steps: regular deposi>n, t h e n o c c l u s i o n m o d e , p o s s i b l y c o m p l i c a t e d b y r e t r a i n g a n d r e d e p o s i t i o n o f particles. T h e c r i t i c a l d é p o s i t i o n ode leads to a significant pressure increase w h e n the n u m :r o f c l o g g e d pores is h i g h enough. F u r t h e r m o r e (as s h o w n M a r o u d a s & E i s e n k l a m , 1964), the disparities q u i c k l y crease as soon as the d é p o s i t i o n is p r é s e n t . A i l the Lannels b e i n g c o n n e c t é e ! , the v e l o c i t y i n the less c o n s t r i c t e d ires increases and é l i m i n â t e s any d é p o s i t i o n , w h i l e i n the istructed pores the v e l o c i t y decreases, l e a d i n g to a self:nerated c l o g g i n g effect a n d to heterogeneities i n the essure d i s t r i b u t i o n i n d u c e d b y the heterogeneous pereability distribution. G i v e n the l a c k o f filtration data i n the f o r m o f deposit tantity or l o c a l c o n c e n t r a t i o n , a s e m i - e m p i r i c a l l a w has :en e m p l o y e d to relate the p e r m e a b i l i t y f u n c t i o n to the irous m é d i u m structure i n a s i m p l e m a n n e r i n the n u m é r al s i m u l a t i o n s . A g é n é r a l i s a t i o n o f the K o z e n y - C a r m a n [uation was chosen f o r its s i m p l i c i t y a n d its w i d e range o f i p l i c a t i o n . T h e K o z e n y - C a r m a n é q u a t i o n , expressed as a n c t i o n o f the deposit quantity, i m p l i c i t l y assumes that the p o s i t i o n leads to a g r a d u a i decrease o f the pore diameter a c a p i l l a r y m o d e l , b y a u n i f o r m d é p o s i t i o n over the t e n t a i surface o f the c a p i l l a r y tube, a n d leads i n v a r i a b l y t o regular increase i n pressure, w h i l e the flow v e l o c i t y mains constant. T h e c r i t i c a l increase i n pressure observed i r i n g the experiments at the v i c i n i t y o f the i n j e c t i o n p o i n t s n n o t be expressed w i t h the filtration l a w a n d p e r m e a b i l i t y n c t i o n used; the r e s u l t i n g pressure increase is too s m a l l f o r
o c c l u s i o n . T h e K o z e n y m o d e l is appropriate o n l y for thi flow o f fine suspensions t h r o u g h m é d i u m s that s h o w reducei filtration ( H e r z i g et al, 1970). I n the absence o f m i c r o s c o p i cal i n f o r m a t i o n about the e x p é r i m e n t a l d é p o s i t i o n values, i was necessary to assume a regular d é p o s i t i o n m o d e to obtaii q u a n t i t a t i v e results, b u t a c o m p l è t e filtration m o d e l mus consider the m o r p h o l o g y o f the deposit. The d é p o s i t i o n i n o t o n l y t a k i n g place o n the surface sites o f the pores; then are other m o d e s o f filtration ( H e r z i g et al, 1970). A n y loca i r î h o m o g e n e i t y o f the filtration rate ( w h i c h p r o b a b l y v a r i e w i t h the c o n c e n t r a t i o n , as attested b y the g ê n e r a i expressioi g i v e n for the filtration rate i n é q u a t i o n ( 8 ) ) , or any e v o l u t i o i o f the deposit m o r p h o l o g y cannot' be r e p r o d u c e d b y thi n u m e r i c a l pressures because a constant a n d u n i f o r m deposi t i o n rate was considered d u r i n g the s i m u l a t i o n s . A s a resuit the n u m e r i c a l s i m u l a t i o n s do n o t reflect the possible hetero geneities i n the g r o u t d é p o s i t i o n m e c h a n i s m , w h i c h ma; e x p l a i n the d i f f é r e n c e s observed b e t w e e n the n u m e r i c a l an< the real pressure values.
To c o n c l u d e , the pressures e v o l v e d u r i n g i n j e c t i o n unde the c o m p l e m e n t a r y c o n t r i b u t i o n s o f fluid v i s c o s i t y v a r i a t i o n a n d filtration. T h e v i s c o s i t y effects, p r é s e n t d u r i n g the i n i t i a p r o p a g a t i o n phase, are w e l l r e p r o d u c e d b y the n u m e r i c a m o d e l . W h i l e the linear dependence o f the v i s c o s i t y o n thi g r o u t c o n c e n t r a t i o n leads to an excellent p r é d i c t i v e behav i o u r o f the m o d e l d u r i n g the first part o f the experiment o n l y an o v e r a l l q u a l i t a t i v e a n d q u a n t i t a t i v e agreement be t w e e n the e x p é r i m e n t a l and the n u m e r i c a l pressures i achieved d u r i n g the rest o f the experiments. T h e influence o filtration becomes p r é d o m i n a n t w i t h t i m e , and c o m p r i s e p r o b a b l y heterogeneous and r e t r a i n i n g effects, as attested b; the i r r e g u l a r increase i n the e x p é r i m e n t a l pressures. B ; contrast the n u m e r i c a l pressures d i s p l a y a regular increasi under the effect o f the constant filtration rate and the s i m p l i permeability function employed. The numerical simulation show that the filtration, i n h e r e n t l y transient, leads to ; c o u p l i n g between the c o n c e n t r a t i o n field, the porous m e d i u n structure and the pressure field.
Displacements
T h e c o m p a r i s o n b e t w e e n the displacements c o r r e s p o n d i s to the w a t e r and the g r o u t i n j e c t i o n experiments is illustrate< i n F i g . 8, w h i c h shows the displacement é v o l u t i o n a r = 0-2 m for m o d e l /. • / ( . m o d e l w , and the e x p é r i m e n t a results. T h e c o m p a r i s o n b e t w e e n the w a t e r a n d the g r o u i n j e c t i o n experiments u s e f u l l y display s the c o u p l i n g betweei the g r o u t p r o p a g a t i o n a n d the displacements i n d u c e d w i t h i i the s o i l mass b y the pore fluid pressure variations. T h i é v o l u t i o n o f the e x p é r i m e n t a l corrected displacements i; s i m i l a r to the pressure é v o l u t i o n : the increase o f the displa cernent c u r v e f o l l o w s , w i t h a s l i g h t retardation, the corre s p o n d i n g e x p é r i m e n t a l pressure curves g i v e n i n F i g . 5.
W h i l e a transient é v o l u t i o n appears d u r i n g the g r o u t injec t i o n , as expected, the r e s u l t i n g pressure increase is instanta neous and constant d u r i n g the water i n j e c t i o n s i m u l a t i o i ( m o d e l w i n F i g . 8 ) . T h e displacements are w e a k , and thi adequacy o f the linear a n d elastic l a w e m p l o y e d is d é m o n strated i n b o t h e x p e r i m e n t s b y the g o o d agreement obtaine< i n the o v e r a l l t r e n d b e t w e e n the measured and the calculatei displacements. I n the case o f water, w i t h the l i n e a r elastii l a w e m p l o y e d , w h e n the steady state is reached and thi pressures are stabilised, the c o u p l i n g disappears a n d thi displacements do n o t e v o l v e ( L e w i s & Schrefler, 1999) D u r i n g the m i s c i b l e g r o u t p r o p a g a t i o n p e r i o d , the displace m e n t v a r i a t i o n s o f the s o l i d skeleton are coupled, b y mean; o f the v a r i a t i o n s o f pressure, to the p r é d o m i n a n t v i s c o u effects at first, a n d n e x t the filtration is the d o m i n a n mechanism.
w i t h i n the i n t e r s t i t i a l space, the deposit density increase m t a i l s a p e r m e a b i l i t y r é d u c t i o n a c c o r d i n g t o the K o z e n y Carman é q u a t i o n , w h i c h i n t u r n is responsible f o r the pressure a n d thus the displacement increase. A retardation effect c a n be n o t i c e d o n the e x p é r i m e n t a l :urves w h e n c o m p a r e d w i t h the n u m e r i c a l curves. T h i s c a n De e x p l a i n e d b y n o n - l i n e a r i t y effects o r b y a n i n c o m p l è t e •eaction o f the displacement gauges t o the p e r m e a t i n g g r o u t solution. Later, w h e n the g r o u t has penetrated sufficiently n t o the s o i l mass, the displacement d i s t r i b u t i o n o b t a i n e d from the experiments a n d the n u m e r i c a l s o l u t i o n c o i n c i d e luite well. D u r i n g g r o u t i n j e c t i o n , a l t h o u g h the measured displacenents are w e a k , h y d r o m e c h a n i c a l c o u p l i n g is p r é s e n t , a n d is ; o n v e n i e n t l y r e p r o d u c e d b y the n u m e r i c a l m o d e l . T h e use o f :he classical f o r m u l a t i o n o f the m o m e n t u m é q u a t i o n w i t h ;he p r i n c i p l e o f effective stress is n o t discussed. T h e p r é sence o f a t h i r d constituent, the grout, w h i c h displaces the n t e r s t i t i a l water i n i t i a l l y p r é s e n t , does n o t seem t o affect the Tiechanical interactions b e t w e e n the fluid phase as a w h o l e m d the s o l i d skeleton.
Concentration The g r o u t was i n j e c t e d i n t o the saturated soil f o r 45 m i n . Fig. 9 i l l u s t r â t e s the p o s i t i o n s o f the é l e c t r o d e s r e p o r t e d i c c o r d i n g to t h e i r times o f reaction, together w i t h the corresponding g r o u t c o n c e n t r a t i o n profiles o b t a i n e d f r o m the t u m e r i c a l c o m p u t a t i o n s at the same t i m e s . T h e concentrai o n é v o l u t i o n takes place under c o n v e c t i o n , dispersion a n d î l t r a t i o n p r é s e n t f o r the w h o l e d u r a t i o n o f the test. E a c h c o n c e n t r a t i o n curve is characterised b y a t r a n s i t i o n îone o f decreasing c o n c e n t r a t i o n between p j a n d 0. A spreading o f the t r a n s i t i o n zone takes place as the permea;ion progresses, o w i n g t o the d i l u t i o n o f the g r o u t at the evel o f the c o n c e n t r a t i o n front. T h e i m p o r t a n c e o f h y i r o d y n a m i c d i s p e r s i o n w a s already n o t i c e d d u r i n g the jne-dimensional tests i n the l a b o r a t o r y ( B o u c h e l a g h e m & M m o s n i , 2 0 0 1 ) ; the w i d t h o f the t r a n s i t i o n zone increases v i t h i n j e c t i o n l e n g t h . T h e filtration enhances the i r r é v e r s i b l e spreading o f the c o n c e n t r a t i o n front, a n d a i l the p h e n o m e n a considered are transient d u r i n g the m i x i n g a n d g r o u t p r o p a gation processes ( B o u c h e l a g h e m et al, 2 0 0 1 ) . g f
m p
The r a d i a l decrease i n the displacement v e l o c i t y a n d the •etardation effect entailed b y filtration e x p l a i n the n o n - u n i o r m rate o f advance o f the g r o u t front w i t h t i m e , s h o w n i n ?ig. 9. T h e progress o f the g r o u t front, w h i c h is v e r y fast at fie early stage o f the i n j e c t i o n , reduces w i t h t i m e . A t t = 4 3 0 s the g r o u t front has reached m o r e t h a n h a l f the iistance reached d u r i n g the f o l l o w i n g 30 m i n . O n the other î a n d , the pressure é v o l u t i o n is d é p e n d e n t l a r g e l y o n the j r o u t c o n c e n t r a t i o n d i s t r i b u t i o n d u r i n g the p r o p a g a t i o n Dhase, w h i c h shows the b i l a t é r a l c o u p l i n g between concen;ration a n d pressure. D u r i n g the n u m e r i c a l s i m u l a t i o n s , b y comparing the pressure profiles w i t h the c o n c e n t r a t i o n p r o î l e s b e t w e e n t w o successive instants, i t appears that the pressure increase w i t h space is closely related t o the p r é sence o f grout. T h e pressure increase is relevant i n the sand î l l e d w i t h grout, whereas i n the sand filled w i t h water the Dressure p r o f i l e remains close to the i n i t i a l pressure p r o f i l e , rhe g r o u t is sufficiently d i l u t e d far f r o m the i n j e c t i o n zone, 3artly because the filtration takes place upwards, f o r the r a n s p o r t t o o c c u r w i t h r e d u c e d filtration a n d thus a reduced pressure increase. ?
T h e é l e c t r o d e s inserted at p r é c i s e l o c a t i o n s w i t h i n the s o i l riass react at g i v e n instants, a n d the c o r r e s p o n d i n g p o s i t i o n s riay be c o m p a r e d w i t h the n u m e r i c a l g r o u t front p o s i t i o n s at :he same t i m e s o f reaction. T h e c o n d u c t i v i t y measurements
c o n d u c t i v i t y values o b t a i n e d cannot be related t o a g i v e n c o n c e n t r a t i o n value. A l t h o u g h the c o n d u c t i v i t y measurements are n o t f u l l y r e l i a b l e d u r i n g the p r o p a g a t i o n phase, the m e t h o d gives i n f o r m a t i o n about the r é g i o n s w h e r e the g r o u t is p r é d o m i n a n t w i t h i n the v o i d space, a n d i n t h i s respect the c o n d u c t i v i t y results a g r é e w i t h the n u m e r i c a l c o n c e n t r a t i o n field. T h e first measurements show that the g r o u t front advance g i v e n fry the n u m e r i c a l s i m u l a t i o n s is ahead o f the c o n d u c t i v i t y measurements. T h i s m a y be due t o an i n c o m p l è t e r e a c t i o n o f the é l e c t r o d e to the v e r y r a p i d g r o u t front advance at the b e g i n n i n g o f the i n j e c t i o n . A t t = 130 s, at the b e g i n n i n g o f the i n j e c t i o n experiment, the n u m e r i c a l g r o u t front is at r = 0-18 m . T h e c o n d u c t i v i t y measurements a g r é e w i t h the g r o u t front p o s i t i o n s g i v e n b y the n u m e r i c a l c o m p u t a t i o n s i n the m i d d l e a n d at the e n d o f the e x p e r i ment, w h e n the g r o u t is a r o u n d r = 0-3-0-4 m , a n d at r = 0-5 m . B e t w e e n r = 0-4 m a n d r = 0-5 m the é l e c t r o d e s give g r o u t front p o s i t i o n s ahead o f the n u m e r i c a l g r o u t front positions. T h e n u m e r i c a l results f o r c o n c e n t r a t i o n a g r é e w i t h the findings o f several authors d u r i n g p e r m e a t i o n g r o u t i n g f o r s i m i l a r l a b o r a t o r y i n j e c t i o n c o n d i t i o n s ( M o r i et al, 1989; Yoneda et al, 1996). T o estimate the d i s t r i b u t i o n o f s o l i d g r o u t i n samples t a k e n f r o m the hardened sand, the relative fraction, a , o f s o l i d g r o u t p r é s e n t w i t h i n the v o i d space is measured b y e x t r a c t i n g a c o m p o n e n t ( c é m e n t , silicate) f r o m the s o l i d grout. T h e o b t a i n e d values o f a indicate that, w i t h i n the hardened sand, the c é m e n t tends t o concentrate i n the area near the i n j e c t i o n h o l e . Values o f a are even o b t a i n e d that are larger t h a n that near the i n j e c t i o n h o l e , whereas a decreases as the distance f r o m the i n j e c t i o n h o l e increases ( M o r i et al, 1989; Yoneda et al, 1996). T h e e x p é r i m e n t a l g r o u t d i s t r i b u t i o n does n o t decrease u n i f o r m l y w i t h distance f r o m the i n j e c t i o n h o l e , especially at the l e v e l o f the g r o u t front. There is n o s t r a i g h t f o r w a r d r e l a t i o n between a, w h i c h is a measure o f the s o l i d g r o u t fraction contained w i t h i n the v o i d space, a n d the fluid g r o u t c o n c e n t r a t i o n o b t a i n e d f r o m the s o l u t i o n o f the a d v e c t i o n - d i s p e r s i o n é q u a t i o n d u r i n g the p r o p a g a t i o n phase, because the setting a n d h y d r a t i o n phases m u s t be p r o p e r l y t a k e n i n t o account i n order t o o b t a i n a. H o w e v e r , the e x p é r i m e n t a l s o l i d g r o u t d i s t r i b u t i o n results o b t a i n e d b y M o r i et al. ( 1 9 8 9 ) show a significant spreading o f the g r o u t front, v e r y s i m i l a r t o the n u m e r i c a l g r o u t c o n c e n t r a t i o n results, w h i c h c a n be p a r t l y a t t r i b u t e d t o the effect o f h y d r o d y n a m i c dispersion, as s h o w n b y the n u m e r i c a l c o n c e n t r a t i o n results i n F i g . 9, w h i c h shows a large t r a n s i t i o n zone. O n the other hand, the a values that are larger t h a n 1 , a n d the i r r e g u l a r i t i e s i n the g r o u t d i s t r i b u t i o n , m a y be a t t r i b u t e d t o p a r t i c l e d é p o s i t i o n or to the p r é s e n c e o f dead-end pores that m a y be reached b y g r o u t b y d i f f u s i o n . Here p a r t i c l e d é p o s i t i o n a n d d i f f u s i o n are b o t h i n c l u d e d w i t h i n the g l o b a l filtration t e r m o f the m o d e l a n d resuit i n a decrease o f the c o n c e n t r a t i o n at the l e v e l o f the g r o u t front position. T h e i n j e c t i o n e f f i c i e n c y o r i n j e c t i o n l e n g t h is g i v e n b y the size a n d shape o f the s o l i d b u l b taken f r o m the sample after i n j e c t i o n . F i g . 10(b) gives the n u m e r i c a l c o n c e n t r a t i o n field d i s t r i b u t i o n at t i m e t = 2 2 0 0 s, c o r r e s p o n d i n g to the e n d o f the first g r o u t i n j e c t i o n e x p e r i m e n t , a n d the n u m e r i c a l g r o u t front p o s i t i o n is g i v e n b y R = 0-3 m F i g . l l ( b ) represents the n u m e r i c a l c o n c e n t r a t i o n field f o r an a r b i t r a r y half-section o f the m o d e l at the e n d o f the second g r o u t i n j e c t i o n e x p e r i m e n t at t i m e t = 2 5 0 0 s. T h e i n j e c t e d r é g i o n is o f spherical shape, i n accordance w i t h the a x i s y m m e t r y a n d m a t e r i a l i s o t r o p y c o n d i t i o n s considered d u r i n g the n u m e r i c a l s i m u l a t i o n s . T h e a p p r o x i m a t e final front p o s i t i o n is l o c a t e d
BOUCHELAGHEM
680
at R = 0-51 m at the end o f the second i n j e c t i o n test. T h e r é g i o n c o n t a i n e d b e t w e e n the i n j e c t i o n tube and radius r = 0-4 m is a l m o s t c o m p l e t e l y saturated w i t h grout, whereas the r é g i o n b e t w e e n r = 0-4 a n d r = 0-6 m attests the h y d r o m e c h a n i c a l dispersion o f g r o u t w i t h i n the inters t i t i a l water. T h e m o d e l d e v e l o p e d concerns the i n j e c t e d g r o u t b e h a v i n g as a N e w t o n i a n f l u i d before the setting a n d h y d r a t i o n proceed. Nevertheless, the final g r o u t concentrat i o n , p o r o s i t y and filtrated g r o u t density d i s t r i b u t i o n s g i v e n by the n u m e r i c a l m o d e l are c o m p a r e d i n a first a p p r o x i m a t i o n w i t h the b u l b d i m e n s i o n s and w i t h the p o r o s i t y values measured o n the samples taken f r o m the b u l b after i n j e c t i o n . I t is assumed that o n l y the d o m a i n c o r r e s p o n d i n g to pg /pg =î 0-5 w i l l g i v e a s o l i d b u l b after setting a n d h y d r a t i o n are c o m p l e t e d . A s s h o w n i n F i g . 10, the d i m e n sions o f the i n j e c t e d zone and those o f the b u l b c o i n c i d e quite w e l l f o r the first g r o u t i n j e c t i o n test. D u r i n g the second g r o u t i n j e c t i o n the e x p é r i m e n t a l g r o u t f r o n t has a m a x i m u m diameter s l i g h t l y i n advance w i t h respect to its n u m e r i c a l counterpart, as the e x p é r i m e n t a l g r o u t f r o n t is l o c a t e d at r = 0-525 m i n F i g . l l ( b ) , but an exact c o m p a r i s o n requires a c o n s i d é r a t i o n o f the h y d r o - t h e r m o - m e c h a n i c a l c o u p l i n g s i n d u c e d b y the h y d r a t i o n phase, as part o f the g r o u t w i l l be d i l u t e d w i t h the i n t e r s t i t i a l w a t e r and w i l l not harden. f
z:m,j
f i m p
T h e t o t a l v o l u m e o f injected g r o u t f o r the w h o l e d u r a t i o n o f the test coincides f u l l y w i t h the q u a n t i t y c o m p u t e d f r o m the n u m e r i c a l m o d e l f o r b o t h tests. T h e t o t a l a m o u n t o f injected g r o u t represents 1 3 0 1 d u r i n g the first i n j e c t i o n test, w h i l e the t o t a l q u a n t i t y o f g r o u t injected d u r i n g the second test is 2 4 9 1. T h e n u m e r i c a l g r o u t field and the filtrated g r o u t field m a k e i t possible to back-calculate the t o t a l q u a n t i t y o f g r o u t i n j e c t e d w i t h i n the n u m e r i c a l m o d e l and to v e r i f y the mass balance. The v o l u m e estimated f r o m the n u m e r i c a l s i m u l a t i o n s , w h i c h corresponds to the g r o u t p r é s e n t w i t h i n the i n t e r s t i t i a l fluid phase and the filtrated grout, adds u p to 125 1 d u r i n g the first i n j e c t i o n test, and represents 2 4 2 1 (219 1 o f g r o u t i n s o l u t i o n , and 23 1 o f filtrated g r o u t ) d u r i n g the second i n j e c t i o n test.
Porosity and filtrated grout density The decrease i n p o r o s i t y w i t h i n the s o i l mass, due to the g r o u t d é p o s i t i o n over the s o l i d skeleton surface, i l l u s t r â t e s the é v o l u t i o n o f a porous m é d i u m structure i n the m a c r o scopic m o d e l u n d e r a regular d é p o s i t i o n m o d e , and can be d i r e c t l y v i s u a l i s e d f r o m the n u m e r i c a l results. A l t h o u g h the influences o f the setting and h y d r a t i o n processes are d i f f i c u l t to assess, the o v e r a l l agreement b e t w e e n the e x p é r i m e n t a l porosities and the n u m e r i c a l p o r o s i t y values i n F i g . 13 encourages confidence i n the p r é d i c t i v e m o d e l . T h e filtrated g r o u t density field i l l u s t r a t e d i n F i g . 14 is closely related to the g r o u t c o n c e n t r a t i o n field, since the filtration takes place at a constant rate w h e r e the g r o u t is p r é s e n t . I n particular, the retardation effect o n g r o u t p r o p a g a t i o n , due to d é p o s i t i o n over the s o l i d skeleton's surface, is t a n g i b l e and can be used to estimate the e f f i c i e n c y o f inject i o n . H o w e v e r , i f the r e t a r d a t i o n effect decreases the i n j e c t i o n l e n g t h , some benefits are also g a i n e d from the d é p o s i t i o n itself, as i t decreases the p e r m e a b i l i t y a n d i n creases the m e c h a n i c a l strength o f the treated s o i l .
CONCLUSION The p r i m a r y objective o f the w o r k presented i n this paper was to assess the v a l i d i t y o f a theoretical f o r m u l a t i o n o f g r o u t p r o p a g a t i o n a n d flow d i s t r i b u t i o n i n a d e f o r m a b l e porous m é d i u m . T h i s was to be achieved b y c o m p a r i n g results f r o m a t h e o r e t i c a l f o r m u l a t i o n w i t h those o b t a i n e d f r o m c o n t r o l l e d l a b o r a t o r y i n j e c t i o n experiments w i t h a
0-1
0-3
0-5
0-75
F i g . 13. C o m p a r i s o n b e t w e e n n u m e r i c a l p o r o s i t y time t — 2500 s a n d e x p é r i m e n t a l porosity
distribution
values
z: m .
F i g . 14. F i l t r a t e d g r o u t d e n s i t y
d i s t r i b u t i o n at t i m e t = 2 5 0 0 s
m é d i u m sand a n d a m i c r o - c e m e n t grout. T h e p h y s i c a l pat meters o f the m o d e l were d e t e r m i n e d i n d e p e n d e n t l y fro the t h r e e - d i m e n s i o n a l i n j e c t i o n experiments. T h e numeric i m p l e m e n t a t i o n o f the f i e l d é q u a t i o n s , a n d t h e i r c o m p a r i s o w i t h the t h r e e - d i m e n s i o n a l l a b o r a t o r y experiments, co firmed the v a l i d i t y and accuracy o f the m o d e l f r o m p h e n o m e n o l o g i c a l standpoint.
B y means o f the p r i m a r y v a r i a b l e s — g r o u t concentratic pressure field, filtered g r o u t density, m a c r o s c o p i c p o r o s i a n d s o l i d skeleton d i s p l a c e m e n t — a n d the set o f c o n s t i t u t i laws chosen, m o s t o f the relevant features o f the effect the i n j e c t i o n process o n the m o d i f i c a t i o n o f the p o r o m é d i u m structure, the fluid flow pattern, the s o l i d skeleti d é f o r m a t i o n s a n d the g r o u t front p r o p a g a t i o n were e x a m i n for a s i t u a t i o n close to a real p e r m e a t i o n g r o u t i n g operatioi
The first c y l i n d r i c a l m o d e l i n j e c t i o n , w h i c h must be .se'
played b y the d i f f é r e n t p h e n o m e n a , a n d resulted i n a first c r i t i c a l é v a l u a t i o n o f the fundamental assumptions m a d e d u r i n g the m o d e l w r i t i n g . T h e e x p é r i e n c e o f the first largescale i n j e c t i o n test l e d to m o d i f i c a t i o n s d u r i n g the second i n j e c t i o n test, w h i c h gave definite conclusions.
m e n t as c o m p a r e d w i t h i n - s i t u c o n d i t i o n s . B y i n j e c t i n g a fluid o f h i g h e r viscosity, or b y increasing the i n j e c t i o n rate value, possible n o n - l i n e a r i t i e s c o u l d be emphasised w i t h h i g h e r displacement values, a n d l e a d to the d e v e l o p m e n t o f a n o n - l i n e a r elastic m o d e l .
T h e second large-scale i n j e c t i o n e x p e r i m e n t has p r o d u c e d the first set o f results f o r use as an independent test o f the v a l i d i t y o f the c o m p l è t e f o r m u l a t i o n proposed. A c c u r a t e p r é d i c t i o n s were o b t a i n e d f o r the pore fluid pressures and the s o l i d displacements w i t h i n the s o i l mass, a n d the elect r i c a l r e s i s t i v i t y measurements related to g r o u t p r o p a g a t i o n , the s o l i d b u l b d i m e n s i o n s , the p o r o s i t y measurements o n samples t a k e n f r o m the s o l i d b u l b , and the t o t a l i n j e c t e d v o l u m e were c o m p a r e d w i t h t h e i r n u m e r i c a l counterparts.
I n order to o b t a i n i n j e c t i o n c r i t e r i a , i n j e c t i o n s c é n a r i o s can be studied w i t h the d e v e l o p e d p r o g r a m b y k e e p i n g i n m i n d the assumptions o f the u n d e r l y i n g m o d e l , b u t r e l i a b l e full-scale or i n - s i t u data are also necessary. Therefore final conclusions can be d r a w n o n l y after o b t a i n i n g a n d s i m u l a t i n g w i t h success the results o f the tests f r o m the site.
T h e s i m u l a t i o n results e x p l a i n the e x p é r i m e n t a l results and c o m p l é m e n t t h e m w h e r e necessary b y g i v i n g p r é c i s e i n f o r m a t i o n about the real g r o u t p r o p a g a t i o n i n the l a c k o f c o m p l è t e c o n c e n t r a t i o n data, b y s h o w i n g the p a r t p l a y e d b y convective g r o u t transport, dispersion, a n d é v o l u t i o n o f the r h e o l o g i c a l properties o f the fluid phase, and the p r é d o m i nant r ô l e p l a y e d b y filtration. T h e fluid pressure, g r o u t concentration a n d s o l i d displacement are s t r o n g l y coupled, not o n l y d u r i n g the g r o u t p r o p a g a t i o n phase, b u t as l o n g as the i n j e c t i o n rate is m a i n t a i n e d . D u r i n g the o n e - d i m e n s i o n a l and large-scale l a b o r a t o r y tests, the filtration a n d the v a r i a tions o f the p h y s i c a l properties o f the fluid phase, w h i c h occur frequently d u r i n g m i s c i b l e injections o f c h e m i c a l or cernent grouts, have m o r e influence o n the fluid pressure and g r o u t c o n c e n t r a t i o n é v o l u t i o n t h a n the h y d r o m e c h a n i c a l c o u p l i n g does. Confidence i n the a b i l i t y o f the t h e o r e t i c a l f o r m u l a t i o n to describe the m a i n p h y s i c a l processes i n v o l v e d d u r i n g the experiments, at least i n first a p p r o x i m a t i o n , is thus enhanced. Nevertheless, further e x p é r i m e n t a l studies are necessary i n order to lead to a m o r e sophisticated m o d e l . T h e g ê n e r a i expression o f the filtration rate, X, defined d u r i n g the d e v e l o p m e n t o f the t h e o r e t i c a l m o d e l d é p e n d s o n the g r o u t c o n c e n t r a t i o n , the filtered g r o u t density, the porosity, the h y d r a u l i c radius and other parameters o f the m i c r o scopic c o n f i g u r a t i o n . A s n o m i c r o s c o p i c i n f o r m a t i o n was available about filtration, a constant filtration rate was e m p l o y e d i n the n u m e r i c a l s i m u l a t i o n s . T h e r e s u l t i n g first-order a p p r o x i m a t i o n w i t h respect to c o n c e n t r a t i o n f o r the d é p o s i t i o n t e r m p r o v e d to be convenient f o r r e p r o d u c i n g m o s t o f the features observed d u r i n g the l a b o r a t o r y i n j e c t i o n e x p e r i ments a n d the full-scale i n j e c t i o n , b u t other d é p o s i t i o n modes t h a n the regular d é p o s i t i o n m o d e i m p l i c i t l y c o n s i d ered seemed to be p r é s e n t , such as particles r e t r a i n i n g a n d p a r t i a l or c o m p l è t e o c c l u s i o n . A p a r t f r o m o b t a i n i n g l o c a l deposit density data, the establ i s h m e n t o f a c o m p l è t e filtration m o d e l for the p a r t i c u l a r m i c r o - c e m e n t g r o u t suspension studied requires d é t a i l s o f the m o r p h o l o g y o f the deposit and the m e c h a n i s m s l e a d i n g to d é p o s i t i o n , as w e l l as the i n t é g r a t i o n o f porous m é d i u m structure characteristics other t h a n porosity, such as the s p é c i f i e surface. I f p o r o s i t y alone is retained to express the filtration effects, no other filtration m o d e t h a n a regular and isotropic d é p o s i t i o n m o d e w i l l be o b t a i n e d . I n a d d i t i o n to the i d e n t i f i c a t i o n o f a filtration l a w based o n the g ê n e r a i expression o f the filtration t e r m obtained, an appropriate p e r m e a b i l i t y f u n c t i o n m u s t be substituted f o r the g é n é r a l isation o f the K o z e n y - C a r m a n é q u a t i o n , i n order to take f u l l advantage o f the p o s s i b i l i t i e s o f the m o d e l developed. T h e displacements are w e a k and can be a p p r o x i m a t e d b y a linear elastic m o d e l , w h i c h explains the excellent agreement b e t w e e n the n u m e r i c a l m o d e l a n d the e x p é r i m e n t a l results. T h e large-scale tests are n o n - c o n c l u s i v e w i t h respect to the h y d r o m e c h a n i c a l c o u p l i n g aspects, o w i n g to over-
L i m i t a t i o n s s t i l l exist i n t e r m s o f the p r é d i c t i v e c a p a b i l i t y o f the m o d e l . M o r e fundamentally, n e w research is l o o k i n g for a g ê n e r a i l a w o f m a t e r i a l b e h a v i o u r that covers the f u l l range o f s o i l behaviour, f r o m the n a t u r a l s o i l to the g r o u t e d s o i l , as a f u n c t i o n o f the g r o u t i n g parameters and g r o u t i n g m e t h o d . C o n s i d é r a t i o n o f the fluid phase flow and g r o u t transport constitutes a first step towards the b u i l d i n g o f a u n i f i e d f r a m e w o r k c o v e r i n g the g r o u t p r o p a g a t i o n phase u n t i l t h ë e n d o f the g r o u t s o l i d i f i c a t i o n phase, a n d can e x p l a i n m u c h o f the p o s t - i n j e c t i o n behaviour. B u t further c o n s t i t u t i v e developments are necessary i n order to develop advanced s t r e s s - s t r a i n relationships based o n the t h e o r y o f elastoplast i c i t y or fracture m e c h a n i c s , m o r e appropriate f o r real inject i o n cases. To c o m p l è t e the t h e o r e t i c a l m o d e l and to c o n t i n u e the process o f v a l i d a t i o n , cernent g r o u t h y d r a t i o n and s o l i d i f i c a t i o n processes s h o u l d be considered, i n t r o d u c i n g the p r i n c i pes o f i r r é v e r s i b l e t h e r m o d y n a m i c s .
ACKNOWLEDGEMENTS T h e author wishes to t h a n k Jean M o t t i e r a n d D o r i s L e r o y f r o m the S o i l & R o c k M e c h a n i c s L a b o r a t o r i e s f o r t h e i r c o n t r i b u t i o n d u r i n g the c o n c e p t i o n a n d the r é a l i s a t i o n o f the l a b o r a t o r y i n j e c t i o n tests, a n d the Swiss N a t i o n a l F u n d f o r Scientific Research, grant n u m b e r 2 1 - 5 0 7 6 9 - 9 7 , w h i c h made t h i s research possible. T h e author is also grateful t o the reviewers w h o c o n t r i b u t e d greatly to the i m p r o v e m e n t o f the manuscript.
NOTATION /3
C
fluid
c o m p r e s s i b i l i t y c o e f f i c i e n t o f the
Af
hydraulic radius
X 7i
f
fif w
filtration
phase
fluid
phase
rate
viscosity o f
fluid
phase
viscosity o f grout
f
p
concentration coefficient o f the
j8p
viscosity o f water
f
p
intrinsic density o f
f
fluid
phase
ps
f
grout concentration w i t h i n the
pg
s
g r o u t c o n c e n t r a t i o n w i t h i n the s o l i d phase
P imp g f
fluid
phase
g r o u t c o n c e n t r a t i o n p r e s c r i b e d at t h e i n j e c t i o n points
p p p
a
s s
intrinsic density o f solid skeleton density o f water
w f
= ( 1 — n)p
filtered
sS
grout density
a
l o n g i t u d i n a l dispersivity constant
cij
transverse dispersivity constant
L
D*«"
diffusion
D™
h y d r o d y n a m i c dispersion tensor
g
gravity vector
k
intrinsic permeability
n p V
coefficient
g
porosity pore
f
a
|Vf | V
fluid
pressure
v e l o c i t y o f the a phase, a = fluid
velocity modulus
divergence
operator
solid,
fluid
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