C O M P O N E N T S O F P O R E W A T E R P R E S S U R E

A N D T H E I R E N G I N E E R I N G S I G N I F I C A N C E
by
J. K. MITCHELL 1
Uni versi t y of California, Berkeley
AB S T R AC T
Pore fluid pressures t ha t develop wi t hi n soil masses as a resul t of bot h mechanica] and
physico-chemical effects influence t he magni t ude of t he i nt er gr anul ar or effective stresses.
The i nt er gr anul ar stresses control, in many cases, soil behavi or in shear and compression.
The physical significance of pore wat er pressure i n a cohesive soil is exami ned i n t er ms of
several component s which combine t o give t he t ot al pressure. An analysis of fluid pressures
at various poi nt s wi t hi n a soil mass based on a condi t i on of no flow at equi l i bri um shows
t ha t changes i n any one component of t he t ot al pressure from poi nt to poi nt are offset by
changes in ot her components.
The analysis shows t ha t a pore pressure measurement reflects i nt erpart i cl e repulsive
pressures and wat er adsorpt i ve forces as well as purel y hydrost at i c pressures ari si ng t r om
mechanical effects. The i ndi vi dual component s of t ot al pore pressure are not di rect l y measur-
able except in special systems. Dat a are present ed which i ndi cat e t ha t a significant port i on
of t he swell of a compact ed soil is at t r i but abl e t o wat er pressure deficiencies caused by
mechanical and capillary component s which act in addi t i on t o osmotic pressure components.
Component wat er pressures are rel at ed t o stresses bet ween particles. I t is shouaa t ha t
i nt ergranul ar pressures are dependent on osmotic and adsorpt i ve component s of t he t ot al
wat er pressure.
I N T R O D U C T I O N
T h e p r i n c i p l e of e f f e c t i v e s t r e s s i s o n e of t h e mo s t i mp o r t a n t c o n c e p t s of
mo d e r n s oi l me c h a n i c s . I t h a s b e e n f o u n d u s e f u l a s a b a s i s f o r t h e u n d e r -
s t a n d i n g of s t r e s s a n d s t r a i n c h a r a c t e r i s t i c s of s oi l s a n d h a s b e c o me i n-
c r e a s i n g l y i mp o r t a n t i n p r a c t i c a l e n g i n e e r i n g p r o b l e ms . T c r z h a g i ( 1925) a p -
p e a r s t o h a v e b e e n t h e f i r s t t o r e c o g n i z e t h e i mp o r t a n c e of e f f e c t i v e s t r e s s e s
wi t h i n s oi l ma s s e s . B i s h o p ( 1 9 6 0 b ) h a s s u mma r i z e d t h e h i s t o r i c a l d e v e l o p -
me n t of t h e c o n c e p t of e f f e c t i v e s t r e s s e s i n s oi l ma s s e s a n d h a s c o n s i d e r e d
t h e t h e o r e t i c a l a s p e c t s of t h e p r i n c i p l e i n d e t a i l .
Ac c o r d i n g t o t h e p r i n c i p l e of e f f e c t i v e s t r e s s t h e s t r e n g t h a n d c o mp r e s s i -
b i l i t y p r o p e r t i e s of a s oi l d e p e n d n o t o n t h e t o t a l s t r e s s a p p l i e d t o t h e s oi l
1 Assi st ant Professor of Civil Engi neeri ng and Assi st ant Research Engineer, I nst i t ut e of
Tr anspor t at i on and Traffic Engineering, Uni ver si t y of California, Berkeley.
162
COMPONENTS OF PORE WATER 163
mass, but rather on the difference between the total stress and the stress
carried by the pore fluid. This difference is termed the effective or inter-
granular 1 stress and is given, for a saturated soil, by
- : ~ - u ( 1 )
where a = the total normal stress,
and u = the hydrostatic pressure in the pore fluid.
Analysis of the forces acting within a soil mass across a surface which
approximates a plane, but passes through the pore space and points of
interparticle contact, indicates t hat the average intergranular force per
unit area of the horizontal projection of the plane is given by
a i = a - - (1 - - a c ) U , (2)
where a c is the contact area of the soil particles per unit area of the plane.
Bishop (1960b) has demonstrated, however, t hat a - u controls the volume
changes of a granular soil independently of the contact area. Bishop also
points out t hat whether shear strength depends on a - u alone and not
on a c is still a matter for conjecture. I n most soils, however, the contact
area is probably of very small magnitude; thus eqs. (1) and (2) could be
expected to yield very nearly the same result.
The validity of the effective stress principle in satura$ed cohesionless
soils has been demonstrated by Bishop and Eldin (1950). The principle has
been found extremely useful in saturated clays as well; however, as pointed
out by Lambe (1960), Lambe and Whi t man (1959), Seed, Mitchell and Chan
(1960), Rosenqvist (1959) and others, forces in addition to those arising
from applied loads and hydrostatic water pressures come into play owing
to the surface activity of the clay particles. In spite of these additional
forces, the effective stress principle and information obtained through pore
water pressure m~asurements c~rrelate well with observed behavior of
many fine-grained soils. At the same time, pore water pressure studies have
yielded valuable information relative to soil structure and other physico-
chemical aspects of soil behavior.
Recent studies have shown effective stress as stated by eq. (1) to be in-
adequate to account for the behavior of partially saturated soils. Modi-
fications of eq. (1) have been made by Bishop (1960a, 1960b, 1960c),
Jennings (1960), Aitchison (1960), and Croncy and Coleman (1953). The
expression suggested by Bishop is the most general in t hat it accounts for
pore air pressures different from 1 atm, a condition t hat may easily arise in
practice. His expression is:
= a - u , # + x ( u a i , . - U w a t e , . ) , (3)
x It should be noted that intergr~nular stress defined in this manner is not the actual
stress transmitted between grain contacts, but represents the force carried by the solid
structure per unit area of the mass.
164 NINTH NATIONAL CONFERE1NCE ON CLAYS AND CLAY MINERALS
where x is a par amet er r angi ng bet ween 0 in a dr y soil and 1 in a s at ur at ed
soil. Such modi fi cat i ons of eq. (1) are necessar y since, in par t i al l y s at ur at ed
soils t he wat er pressure act s over onl y a par t of t he area of any pl ane t hr ough
t he soil.
As i ndi cat ed by eqs. (1) and (3) t he val ue of t he pore pressure, u, usual l y
det er mi ned by di rect measur ement , pl ays an essent i al par t in t he eval uat i on
of effective stress. I n syst ems where forces of a physi co- chemi eal nat ur e
are act i ve, t he physi cal significance of pore wat er pressure ma y be s omewhat
di fferent t han in syst ems free f r om part i cl e surface forces. Wat er l ocat ed
wi t hi n t he cl ay part i cl e force fields ma y be expect ed t o behave in a ma nne r
di fferent f r om free wat er. I t woul d seem logical, t herefore, t ha t por e wat er
pressures shoul d reflect t he influence of t hese force fields as well as st resses
i nduced by mechani cal st r ai n of t he syst em. Expr essi ons have been devel oped
rel at i ng t he change in por e wat er pressure t o a change in appl i ed t ot al st ress
in t er ms of t he rel at i ve compressi bi l i t i es of t he soil st r uct ur e and wat er
(Bishop and El di n, 1950), and t o shear and vol umet r i c st rai ns (Marsal and
Resines, 1960). Fundament al l y, however, t he st r ess- st r ai n and compressi -
bi l i t y charact eri st i cs of a cl ay soil are f unct i ons of its composi t i on and i nt er-
part i cl e force syst ems.
I n t hi s paper t he physi cal significance of por e wat er pressure is exami ned
in t er ms of t he vari ous component s i nduced by mechani cal and physi co-
chemi cal phenomena. Conclusions are dr awn per t i nent t o st udi es of t he
engi neeri ng behavi or of soil. The anal ysi s relies heavi l y on t he s t udy of
t ot al and component pot ent i al s of moi st ur e in soil devel oped by Bol t and
Miller (1958).
ACKNOWL E DGME NT S
The aut hor is i ndebt ed t o his colleagues Professor H. B. Seed, Pr of essor
C. L. Moni smi t h and Mr. R. B. Kr one of t he Uni ver si t y of California for
t hei r val uabl e criticisms and suggestions.
The drawi ngs were pr epar ed by Mr. G. Di erki ng.
T OT AL AND COMP ONE NT P ORE WAT E R P RE S S URE S
Total Pressure
I t is conveni ent t o consi der t he t ot al pressure as t he sum of s e ve r a l
component s measur ed wi t h r espect t o a specified reference st at e, usual l y a
body of free pur e wat er wi t h a fl at surface exposed t o at mospher i c pressure
and at t he same t emper at ur e as t he wat er under i nvest i gat i on. I t is i m-
por t ant t o not e t ha t at equi l i bri um t he t ot al pressure is t he same at ever y
poi nt and flow can occur onl y bet ween poi nt s of di fferent t ot al pressure.
Posi t i ve pressures cause a flow f r om t he poi nt under i nvest i gat i on t o-
wards t he reference pool.
COMPONENTS O~ PORE WATER 165
Components o/ Tot al Pressure
A numbe r of i nvest i gat ors, e.g. Edl efson and Ander son (1943), Bayer
(1956), Bol t and Miller (1958), Low and Demi ng (1953), Low (1958), Mar-
shall (1959), have consi dered t he t ot al soil moi st ur e or pressure in t er ms of
several component s. Bot h mechani cal and t her modynami c anal yses have
been used. The resul t s are general l y si mi l ar in form, al t hough cert ai n dif-
ferences in defi ni t i on and det ai l have been poi nt ed out b y Bol t and Frissel
(1960) who revi ewed t he per t i nent l i t er at ur e on soil moi st ur e t her mo-
dynami cs and deri ved a general equat i on of soil moi st ur e equi l i bri um.
The anal ysi s of t ot al and component pot ent i al s pr esent ed by Bol t and
Mille r (1958) is easi l y adapt ed for t he pr esent consi derat i ons of pore wat er
pressure and is s ummar i zed ext ensi vel y in a l at er section. I n t he present
paper pressures r at her t ha n pot ent i al s are considered, since pressures have
wide appl i cat i on in engi neeri ng pract i ce.
The four component s of t he t ot al fluid pressure (or t ot al head) under
conditions of const ant t emper at ur e are assumed due t o gr avi t y force fields,
hydr ost at i c pressure effects, osmot i c or ionic concent r at i on difference effects;
and adsor pt i ve force fields. As poi nt ed out by Bol t and Frissel (1960), in
any br eakdown of t he t ot al pressures i nt o component s t here is t he danger
of count i ng cert ai n effects t wi ce as t hey ma y be hi dden in ot her t erms.
I t ma y be, for exampl e, t ha t a ri gorous di vi si on bet ween osmot i c pressures
arising f r om doubl e l ayer i nt er act i ons and adsor pt i ve effects cannot be
made, t hus i nval i dat i ng t he use of separ at e component s for t hese t wo effects.
Thi s poses no serious pr obl em in t he pr esent paper, however, since quali-
t at i ve rel at i ons and concept s r at her t ha n ri gorous mat hemat i cal rel at i on-
ships are desired.
(1) Positional or elevation head, i.e. gravity pressure, z, arises f r om t he
differences in el evat i on bet ween t wo poi nt s.
(2) Hydrostatic pressure, p, arises f r om such f act or s as i ncompl et e sat u-
r at i on whi ch leads t o cur ved ai r - wat er i nt erfaces and in react i on t o ex-
t er nal l y appl i ed stresses. The hydr ost at i c component is t he " p u s h i n g " or
" pul l i ng" component bet ween part i cl es. I t is t he pressure t ha t woul d be
reflected by a pressure gage i nsert ed at t he poi nt i n quest i on. As will be
shown, t he magni t ude of t he hydr ost at i c component is dependent on t he
magni t udes of t he ot her pressure component s as well as t he mechani cal
stresses.
(3) Osmotic pressure, ~, arises f r om differences in ionic concent r at i on f r om
poi nt t o poi nt . The concept of osmot i c pressure in soils has been descri bed
elsewhere, e.g. Bol t and Miller (1958), Low (1959), Ladd (1959).
I t is i mpor t a nt t o keep in mi nd t ha t when considering t wo poi nt s at dif-
ferent ionic concent rat i ons, if t he ions are not free t o move, wat er will t end
166 NINTH NATIONAL CONFERENCE ON CLAYS AN]) CLAY MINERALS
to flow from the point of lower concentration towards the point of higher
concentration.
The osmotic pressure between two points of different concentration is
approximated for dilute solutions by the Van' t Hoff equation,
zt = R T (2: c a -- 22 cl) , (4)
where R = universal gas constant,
T = absolute temperature,
Z%, Xc~ = sum of concentrations of all ionic constituents at points 1
and 2, respectively.
I t is assumed in the development of eq. (4) t hat ionic force fields do not
mutually influence each other.
(4) The adsorption pressure, a, arises from the attraction of water mole-
cules by clay surfaces. Bolt and Miller (1958) place attractive soil-water
forces in two categories:
(a) Short,range chemical forces, extending only a few molecular layers from the surface,
caused by local ionic interactions, hydrogen bonds and London van der Waals forces.
(b) Long-range forces, which may be effective beyond 100 ]~, caused by interaction of
a water dipole with the electrostatic field originating in a charged soil surface.
Bolt and Miller consider it reasonable to ignore the effects of short-range
forces in usual soil-water systems as particle spacings exceed the range of
influence of these forces. I n the view of the author the more usual condition
for soils encountered in engineering problems is one of essentially particle-to-
particle (or particle-thin film of water and cations-particle) contact and
therefore short-range forces should not be neglected. If the short-range
forces are neglected the adsorptive pressure at any point is given by
8- - ]
a - - d ( v ) ~ , ( 5 )
8 z
where e = dielectric constant,
~o _- electrical potential at the point.
The potential ~ may be approximated by means of the Gouy-Chapman
theory of the double layer. Adequate theories for expression of the short-
range forces have not yet been developed.
The total pressure P is given by
P = z +p +~ +a , (6)
where z and p may be either positive or negative and n and a are usually
negative in soils.
COMPONENTS OF PORE WATER 167
NEGATI VE POI ~E- WATEI ~ PRESSURES I N SOI LS
Before analyzing component and total pressures at various points within
a soil, a few comments and data relative to negative pore pressures will be
considered as t hey aid in an understanding of osmotic effects and the in-
fluence of capillary effects on hydrostatic pressure. I t is well known t hat
water pressures less t han atmospheric exist in soils. Whether or not pressures
less t han zero absolute ( i . e . a state of tension in the water) can exist has been
the subject of considerable dispute in the literature. Aitehison (1960) has
considered the relative points of view and concludes t hat there is no satis-
factory argument against the use of a capillary model and the development
of large water tensions for describing the behavior of pore water at pressures
less t han atmospheric.
The fundamental causes of negative pressures appear to be osmotic and
adsorptive effects and the surface tension of water. Mechanical factors such
as a tendency towards straightening of bent particles on load release or a
tendency towards dilation of the soil structure on shear may also cause
negative water pressures but, in the final analysis, these effects are all de-
pendent on the adsorptive forces between water and soil.
Negative pressures may exist in both saturated and partially saturated
soils. The principal causes of negative pressures in saturated soils are prob-
ably osmotic effects, hydrostatic stresses resulting from a dilating tendency
on shear, and hydrostatic effects resulting from the stresses carried by bent
particles and distorted particle groups.
In partially saturated systems the surface tension of water comes into
play in conjunction with the adsorptive forces at particle surfaces, leading
to curved air-water interfaces which, in turn, result in additional pressures
either positive or negative, depending on whether curvature is coneave or
convex across the interface. I t is most convenient to think of this pressure
as a capillary hydrostatic pressure given by 2 z / r where T is the surface
tension and r is the radius of curvature of the meniscus.
It may be readily demonstrated t hat in partially saturated systems of
nominal salt content (say 0.05-0.5 N) the osmotic component and the hydro-
static component due to eapillary effects are of the same order of magnitude
for menisci of about 0.5 # radius of curvature. Capillary stresses become
increasingly effective at smaller pore diameters and for radii of curvature
of 0.1 # or less t hey may exceed the osmotic pressures by ten times or more.
Data illustrating a condition where osmotic and hydrostatic tension due
to mechanical effects are of the same order of magnitude in a partially
saturated soil are presented in Fig. 1. Samples of an expansive sandy-cl ay
soil were prepared to a water content of 17.3 percent, a dry density of
111.3 lb per ft a and degree of saturation of 90.6 percent, with distilled water
as the pore fluid. Two methods of eompaetion were used: kneading, which
168 NINT~ NATIONAL CONFERENCE ON CLAYS AND CLAY 1V[INERALS
at this water content induces a dispersed structure, and static, which leads
to a more floceulent structure as demonstrated by Seed and Chan (1959).
Samples were then permitted to expand under a surcharge of 0.1 kg per cm 2
in solutions of calcium acetate of different concentration. The relation
between the amount of swell and solution concentration in Fig. 1 shows
A l l s a m p l e s c o m p a c t e d a t a water conlent
o f 17.3 ~ t o o dry den$ity o f lll.3_+ 0 . 3 Ib
5"Oq ~ ~ - S a m p l e s p r e p a r e d b y static compaction
~ / / ~ (Flocculent strucfure)
4. 0
S a m p l e s p r e p a r e d b y kneading Compaction
/ ~ ( D i s p e r s e d structure )
2 0
I.O
S u r c h a r g e pressure-- O , / k g p e r s q c m
o I
0 o 4 o 8 /.2 1.6 2 . 0
C o n c e n t r a t i o n o f C a l c i u m A c e t a t e S o l u t i o n ]/7
w h i c h S a m p l e s A l l o w e d to S w e l l - m o l e s p e r l/ter
Fm~RE 1.--Effect of structure and electrolyte concentration of absorbed solution
on swell of compacted sandy clay.
t hat as concentration increases, swell decreases. This is a result of the
decrease in the difference between the osmotic pressure in the double layers
between particles and the osmotic pressure of the calcium acetate solution
with increasing concentration of calcium acetate. Similar results have been
obtained by Ladd (1959) for another soil. Also evident in Fig. 1 is the
significant difference between the amount of swell of samples prepared by
different methods of compaction.
I t may be noted t hat the present percent swell approaches a constant
value at the high salt contents, suggesting t hat osmotic or ionic concen-
tration difference effects have ceased to be an i mport ant factor in influencing
the amount of swell. I t is doubtful t hat any significant swell would be
observed in samples immersed in solutions more concentrated t han 2 N
if osmotic effects were the soIe cause of expansion. Thus, as indicated by
COMPONENTS O F PORE WATER 169
t he shaded areas in Fig. 1, osmot i c effects pr obabl y can account for some
0 t o 289 per cent swell dependi ng on t he concent rat i on of t he swelling
solution.
The r emai nder of t he swel l - - about 1 per cent for t he samples prepared
by kneadi ng compact i on and 3 + percent for t he samples prepared by
static c ompa c t i on- i s pr obabl y at t r i but abl e t o i ni t i al hydr ost at i c pressure
deficiencies arising from a combi nat i on of capi l l ary and part i cl e deformat i on
effects and f r om wat er adsorpt i ve forces at t he clay part i cl e surfaces. Mea-
surements have consi st ent l y shown, e.g. Lambe (1961), t ha t as-compact ed
pore wat er t ensi ons are significantly gr eat er for st at i cal l y compact ed t han
for kneadi ng compact ed samples of t he same soil. The flocculated struc-
tures associated wi t h st at i c compact i on lead t o more pr onounced effects
from bent particles and capi l l ary stresses (which hol d bent particles in plane
until rel i eved by exposure t o wat er) as a resul t of t he edge-to-face particle
associations. I n t he more dispersed kneadi ng st r uct ur es t he large shear
strains duri ng compact i on enable particles t o slide i nt o a more parallel
association wi t h a r esul t ant condi t i on of less part i cl e di st ort i on. As a
result, t he release of capi l l ary stresses is not accompani ed by large vol ume
expansions.
Wat er adsorpt i ve forces at part i cl e surfaces ma y have cont r i but ed
somewhat t o t he swell of t hese samples since i t has been observed t ha t an
initially ai r-dri ed sample will freel y absorb wat er f r om a 98 :k per cent
rel at i ve humi di t y at mospher e t o a wat er cont ent of about 20 percent .
As previ ousl y not ed t he compact i on wat er cont ent was 17.3 percent for
these tests.
ANAL YS I S OF COMP ONE NT AND T OT AL WAT E R
P RE S S URE S AT VARI OUS P OI NT S I N T HE
S OI L - WAT E R S YS T E M
Following t he analysis of Bol t and Miller (1958), i t is conveni ent t o
consider first an " i de a l " cl ay- wat er - el ect r ol yt e syst em at equilibrium.
I n Fig. 2 is shown a schemat i c r epr esent at i on of a par t of a sat ur at ed
soil mass composed of equal l y spaced paral l el fiat plates of uni f or m thickness.
Hydr ost at i c pressures due t o ext er nal l y appl i ed stresses ma y be acting.
Consider a pi ezomet er i nsert ed i nt o t he mass as shown i n Fig. 2. The
pi czomet er cont ai ns fluid t ha t is in equi l i bri um wi t h, but out si de t he force
field of, t he wat er i n t he doubl e layers. The fluid level in t he pi ezomet er is
adj ust ed so t ha t a no-flow condi t i on exists.
I f all pressures are measur ed rel at i ve t o a dat um of pure wat er at t he
same el evat i on, t hen at poi nt 1, Fig. 2: z --- 0; a = 0, since t he poinr is out
of t he range of adsorpt i ve force fields; Pl = hYl, where y! is t he uni t weight
CC,~ 12
170 Nr~TH NATIONAL CONFERENCE ON CLAYS AND CLAY :ViINERALS
of t he fluid i n t he pi ezomet er ; and ~: = RTfi. Thus t he t ot al pressure at
poi nt 1 is
P1 = P: + z~l. (7)
Poi nt 2 lies mi dway bet ween t wo cl ay surfaces separ at ed by a di st ance
2d. Theor et i cal equat i ons (Bolt, 1955) have been devel oped enabl i ng t he
comput at i on of osmot i c pressures bet ween i nt er act i ng plates, and solu-
t i ons have been t abul at ed (Bol t and Miller, 1955; Bol t , 1956). Thus ~2
can, in t heor y at least, be eval uat ed.
(
0 " ~m m ~ ~
O-
m
1 2 d
t - ~ - - - - / - P o r o u s Tip
V
0"
FIOUZ~E 2. --Schematic diagram of idealized sat urat ed cl ay-wat er system.
Since V~ ~ must equal 0 ff shor~-range forces are negl ect ed because t he
doubl e l ayer is symmet r i cal about t he mi d-pl ane, t hen a2 = 0, accordi ng
t o eq. (5). At equilibrium, t he condi t i on P~ = P: must exist, and assumi ng
t ha t t he el evat i on of poi nt 2 is t he same as t ha t of poi nt 1 :
P2 = :r~ P2 = ~: + Pl . (8)
Equat i on (8) shows t ha t t he hydr ost at i c pressure component s p: and ~o 2
must differ by an amount equal t o t he difference i n osmot i c pressure.
Poi nt 3 represent s t he general case of a poi nt l ocat ed bet ween t wo paral l el
i nt eraat i ng pl at es but not at t he cent er line. For si mpl i ci t y l et
Z 3 ~ Z 1 ~ 0.
COMPONENTS OF PORE W A T E R 171
The adsorpt i ve component is gi ven by eq. (5), and ~v S and ~s are gi ven
t heoret i cal l y by t he doubl e l ayer equat i ons. Since Ps = Px,
as q- ~ s q- ~~ = ~z q- 39a 9 ( 9)
Equat i on (9) i ndi cat es t ha t since t he t ot al pressure remai ns t he same
at all poi nt s, t he i ndi vi dual component s at poi nt 3 assume values such t hat
t hei r sum equals Pz. I f t he osmot i c and adsorpt i ve component s are given
correct l y by t he t heor et i cal expressions, t hen t he hydr ost at i c component 10s
assumes a val ue appr opr i at e t o sat i sfy t he condi t i on Ps = Px.
t
FIGURE 3.--Schematic diagram of partly saturated soil containing coarse particles
and i mperf ect cl ay orientation.
An i deal cl ay- wat er syst em such as considered t o t hi s poi nt is rarel y, if
ever, encount er ed i n nat ur e. I n t he mor e general ease t he presence of
coarse part i cl es and t he influence of i ncompl et e sat ur at i on must be con-
sidered. I n Fig. 3, i ncompl et e sat ur at i on and t he presence of coarse par-
ticles are i ndi cat ed; a pi ezomet er wi t h wat er level adj ust ed f or equi l i bri um
is shown. As i n t he precedi ng analysis, l et i t be assumed t ha t all poi nt s are
at essentially t he same el evat i on so t ha t z component s ma y be neglected.
Poi nt 4 represent s a poi nt i n t he fluid in equi l i bri um wi t h t he sample
and, as f or an ideal cl ay wat er syst em,
P 4 = n 4 + P 4 , ( 1 0 )
bot h of whi ch are measurabl e.
12"
172 NINTH NATIONAL CONFERENCE ON CLAYS AND CLAY MINERALS
Point 5 is located just inside a curved air-water interface out of the
range of the double layers surrounding fine or coarse particles. Analysis of
static equilibrium across the interface shows, with v positive as shown, t hat
2~
P5 = P~ - - - , (11)
r5
where r 5 = radius of curvature of the meniscus at point 5,
= surface tension,
P a = air pressure in the void.
Since both points 4 and 5 are out of the range of double layer fields,
the ionic concentrations are equal (7~ 4 = ~5) and adsorptive forces are zero,
so t hat : 2
P 5 = P5 + ~5 = Pa -- - - + Y~5~- 7~4 -t- pc, (12)
because P5 =/ ) 4 at equilibrium.
I t follows from (12) t hat
~94 ~--- Pa - - - -
r 5
2~ (13)
r~
This expression has been developed by others, e . g . Hill (1956), and has
been uscdas a basis for the measurement of negative pore pressures of a
magnitude greater t han would cause cavitation in usual measuring devices.
By increasing the air pressure around the sample the point of reference is
translated into the positive pressure range.
In Fig. 3 a water film is shown extending around the periphery of the
coarse particles, as it is known t hat coarse particles do possess an adsorbed
water film even though this layer is not thick relative to the particle size as
is the case for clays. There are, therefore, points of negative as well as
positive curvature within the system. At point 6 just inside the surface the
curvature is positive and the point lies within t he double layer. I t follows
t hat
2v
P ~ = Pa - - - - + e + a e . (14)
re
Since Pe --/ )5 = Pa,
2v 2~ 2v
P a + :~e - - - + ae = pa + :~5 - - - =P a + ~ - - - ,
r e re r5
and
(15)
z e W a6 = ~ 4 _~ 2 T ( 1 rs1)" (16)
Equation (16) indicates t hat the sum of the osmotic and adsorptive pressure
components at a point within the double layer is equal to the osmotic pres-
sure at a point outside the double layer plus the difference in hydrostatic
components due to interface curvature changes between the point in the
COMPONENTS OF PoRE WATER 173
double l ayer and a poi nt in t he field-free regions. I t was assumed in t he
devel opment of eq. (16) t ha t t he ai r pressure in all voi ds is t he same. Thi s
may be expect ed in par t i al l y sat ur at ed granul ar soils where part i cl e surface
phenomena are negligible and i n par t i al l y sat ur at ed clays cont ai ni ng inter-
connect ed ai r voids. I f air voi ds are isolated, however, t he ai r pressures
need not be t he same f r om poi nt t o poi nt . Isol at ed air voids would be
expect ed above some rel at i vel y low degree of sat urat i on. Thus, t he pressure
conditions wi t hi n a par t i al l y sat ur at ed cl ay are undoubt edl y much more
compl i cat ed t han t he precedi ng analysis woul d i ndi cat e.
Similar rel at i ons ma y be devel oped for poi nt 7, whi ch has negat i ve
meniscus cur vat ur e, and poi nt 8, whi ch lies mi dway bet ween parallel clay
plates. The cur vat ur e and concent r at i on at any poi nt s are, of course, dic-
t at ed by a number of fact ors such as ar r angement of particles, size of pores,
degree of sat urat i on, magni t ude of t he el ect rol yt e concent rat i on in t he
syst em as a whole, and wat er st ruct ure. I t is logical t o assume t hat t he
act ual vari at i ons of radi i of curvat ure, osmot i c pressure, etc., are such
t hat t he ener gy of t he syst em is a mi ni mum at equilibrium.
L I MI T AT I ONS OF T HE ANAL YS I S
Bol t and Miller (1958) poi nt out t hat t he expandi ng l at t i ce clays, e.g.
mont mori l l onoi d minerals, are t he onl y ones t ha t approach t he propert i es
assumed for ideal cl ay- wat er systems. Ot her clay minerals, such as t he
illites and kaolinites, are much t hi cker, have a much lower specific surface,
may devi at e wi del y f r om t he assumpt i on of t hi n flat plates, and ma y exhi bi t
behavi or t ypi cal of bot h coarse and fine particles. I n addi t i on t er r aced
r at her t han pl anar surfaces ma y exist, compl i cat i ng t he det er mi nat i on of
interparti.cle spacing.
The Gouy- Chapman t heor y of t he doubl e l ayer is itself severel y l i mi t ed
in appl i cat i on because of t he rest ri ct i ng assumpt i ons requi red for t he
solution of t he differential equat i ons. Al t hough i t has been r at her conclu-
sively demonst r at ed t ha t cert ai n cl ay particles ma y be .positively charged at
t hei r edges, t he effect of this reversal of charge f r om surface t o edge is not
considered in t he t heor y. The fact s t hat most nat ur al softs are more or less
r andom mi xt ur es of several el ect rol yt es and minerals and t hat t he cl ay
plates are not l i kel y t o be ar r anged in a precisely uni f or m parallel ar r ay
are f ur t her compl i cat i ng factors. I n addi t i on, i nt erpart i cl e spacings are
general l y small, possibly i nt roduci ng pressures in t he wat er not account ed
for by existing theories.
The adsorpt i ve component s were f ound in most cases t o be zero. I n actu-
al i t y t hi s woul d pr obabl y not be t he case. I t is more l i kel y t ha t a component
of t he adsorpt i ve force fields woul d be act i ve at all poi nt s bet ween t wo
adj acent particles, even at poi nt s where t he electric field st r engt h is zero.
I t is qui t e possible t hat wat er is adsorbed by t he f or mat i on of hydr ogen
174 Nr ~ NA~ONAL CO~ER~,~CE ON Cr.~ys A~D Cr~Y MI~m~ALS
bonds wi t h part i cl e surfaces or by ot her mechani sms not r el at ed t o t he
electric field. Nowhere in t he analysis has t he effect of i nt erpart i cl e at t r act i ve
forces on wat er pressure been considered. Ther e is no reason t o believe t ha t
van tier Waal s and ot her at t r act i ve forces kriown t o exi st bet ween part i cl es
go ent i r el y unf el t by t he wat er phase.
Thus, while quant i t at i ve appl i cabi l i t y of t he rel at i onshi ps i ndi cat ed by
t he above analysis has been demonst r at ed f or cert ai n hi ghl y idealized
syst ems (Bolt, 1956), di rect appl i cat i on of t he resul t s t o softs of t he t ype
eneount er ed by t he engi neer has been unsuccessful (Mitchell, 1960). Ther e
are, however, several f undament al concept s t ha t emerge f r om such an
analysis t ha t ma y ai d i n t he under st andi ng of cl ay behavi or when consi dered
on a pur el y qual i t at i ve basis.
C O N C L U S I O N S F R O M T H E A N A L Y S I S
The analysis of component and t ot al wat er pressures leads t o t he follow.
i ng conclusions r el at i ve t o t he under st andi ng of t he significance of por e
pressure measurement s in fine-grained softs.
(1) The t ot al wat er pressure i n a sof t - wat er syst em at equi l i bri um is
ever ywher e t he same and ma y consi st of a ny one or a combi nat i on of
several component pressures. At a gi ven densi t y ext er nal forces must usual l y
be appl i ed t o t he soft mass or wat er phase in or der t o mai nt ai n a no-flow
equi l i bri um condi t i on when t he l i qui d phase is i n cont act wi t h ext er nal
water.
(2) The t ot al pressure is measurabl e and gi ven by eq. (7) for t he case
of no el evat i on head.
(3) Doubl e l ayer i nt er act i ons and t he consequent repul si on bet ween
opposing part i cl es are refl ect ed by t he osmot i c pressure.
(4) At equi l i bri um t he component wat er pressures va r y f r om poi nt t o
poi nt i n such a way t ha t t he t ot al wat er pressure remai ns const ant .
(5) Ai r - wat er i nt erfaces of bot h negat i ve and posi t i ve cur vat ur e ma y
exi st in t he same soft -wat er syst em. I nt er f ace cur vat ur e t ha t resul t s f r om
an equi l i bri um bet ween surface t ensi on, adsor pt i ve forces, amount of
avai l abl e wat er and syst em geomet r y is refl ect ed by a change in hydr ost at i c
pressure f r om t he val ue exi st i ng beneat h a fl at ai r - wat er i nt erface.
T H E P H Y S I C A L S I G N I F I C A N C E O F P O R E
P R E S S U R E S A S M E A S U R E D I N S O I L M E C H A N I C S
T E S T S
O n t he basis of t he pressure concept s devel oped in t;he precedi ng sect i on
i t is of i nt erest t o a t t e mpt an i nt er pr et at i on of t he physi cal significance of
pore wat er pressures as usual l y measur ed duri ng st r engt h and compression
COMPONENTS OF PoRE W A T E R 175
tests on clays. Sat ur at ed clays onl y will be considered. Por e pressures
commonl y are measur ed by a sensing el ement (usually ei t her a porous t i p
i nsert ed wi t hi n t he sampl e or a porous st one at t he base of t he sample)
which is connect ed t o a measuri ng device, as shown ~chematically in Fig. 4.
Connection is made f r om t he sample t hr ough t he porous st one t o a nul l
= / ~ O ' 0 -3
I ~ I L ~ o - = O e v ] o f o r S t r e s s
. B
Sample s e a le d w /th /n
r u b b e r m e m b ro n e
I ~ - I / - N u l l
I ~ . ~ A ~ point
~ T q p re ssu re co n tro /
- - ~ M e ~ u ~
FIaUR 4.--Schematic diagram of trlaxlal test arrangement with null-point pore
pressure measuring system.
bal ance poi nt , A. The wat er level is mai nt ai ned at poi nt A t hr oughout t he
t est ; t he posi t i ve or negat i ve hydr ost at i c pressure, ~ox, requi red t o mai nt ai n
t he l evel at A is t aken as t he por e wat er pressure wi t hi n t he sampl e; t hi s
val ue of pressure is subst i t ut ed for u i n eq. (1).
Let poi nt C be some r epr esent at i ve poi nt bet ween particles. I f t he
syst em is i n equilibrium, t hen t he t ot al pressure at all poi nt s is t he same
and PA = Pc . The component s of t ot al pressure at poi nt A are px gi ven
by t he appl i ed back pressure, and t he osmot i c pressure at A, ~ , whi ch
depends on t he composi t i on of t he fluid at poi nt A. The osmot i c pressure
at C is det er mi ned by t he doubl e l ayer condi t i ons which, in t ur n, are
dependent on t he electric field st r engt h f r om t he part i cl e surfaces and t he
176 I~INTH ~TATIONAL CONFERENCE ON CLAYS AND CLAY MINERALS
amount and t ype of el ect rol yt e in t he sampl e. The hydr os t at i c pressure Pc
mus t have a val ue appr opr i at e t o sat i sfy t he condi t i on PA = Pc; t hus
Pc + ~c T ac = PA + ~A, (17)
and if pure wat er is used in t he measur i ng syst em,
7~ j = 0 , and PA ~Pc +7cc +ac" (18)
I t woul d t hus appear t ha t measur ed por e wat er pressure includes t he
hydr ost at i c pressure, t he osmot i c pressure and t he adsor pt i ve pressure
bet ween particles. Dur i ng a shear or consol i dat i on t est , pore pressure
meas ur ement s shoul d reflect t he net effect of changes in t he var i ous com-
ponent s. I t shoul d be not ed also t ha t t he pressure component s ma y va r y
f r om poi nt t o poi nt wi t hi n t he sampl e. Thus t he hydr os t at i c component ,
which is t he one t ha t is "f el t " by t he part i cl es in t he sense of a t hr us t whi ch
influences t he st at i c equi l i bri um of t he st r uct ur e, is a var yi ng quant i t y
t hr oughout t he sampl e.
I n t he devel opment of eqs. (17) and (18) i t was assumed t ha t t he sampl e
was in equi l i bri um wi t h t he measur i ng syst em. Thi s i mpl i es not onl y a
condi t i on of no-flow but also compl et e osmot i c equi l i bri um. Such a con-
di t i on will exi st onl y if t he el ect rol yt e concent r at i on in t he por ous st one
and measur i ng s ys t em is t he same as t he free el ect rol yt e concent r at i on of
t he sampl e. I f pur e wat er is used in t he measur i ng s ys t em t hen equi l i bri um
will exi st i ni t i al l y if t he cl ay cont ai ns onl y sufficient el ect rol yt e t o j ust
sat i sfy doubl e l ayer r equi r ement s and no excess. Ot herwi se t he measur i ng
syst em shoul d cont ai n el ect rol yt e of t he same t ype and concent r at i on as t he
free sal t in t he cl ay for eqs. (17) and (18) t o be val i d.
If, as is usual , a cl ay cont ai ni ng free sal t is connect ed t o a measur i ng
syst em cont ai ni ng Salt-free wat er t hen equi l i bri um will not be r eached
wi t hi n any conveni ent t est peri od. Ther e will be an a br upt el ect r ol yt e
concent r at i on change in passi ng f r om t he sampl e t o t he porous st one. Since
t he st one cannot r est r i ct t he move me nt of t he free sal t ~ons t her e will be a
slow diffusion of ions t hr ough t he st one unt i l t he free sal t concent r at i on in
bot h t he sampl e and t he s ys t em is t he same. Thi s process is ext r emel y slow
and ma y t ake weeks or mont hs t o r each compl et i on. Several t est s were r un
wherei n 0.5 N NaC1 and pur e wat er were pl aced on opposi t e sides of a
s at ur at ed fine porous st one of about 0.4 in. t hi ckness. No sal t was det ect abl e
on t he wat er side of t he st one af t er a 24 hr peri od. Since t he por ous st one
was not i mper meabl e t o ions, however, t her e was no measur abl e osmot i c
pressure across t he st one.
I n vi ew of t hese consi derat i ons, t herefore, eqs. (17) and (18) will not
be correct in mos t cases. The osmot i c pressure t er m, ~c, ma y be vi sual i zed
as consisting of t wo component s, ~c due t o t he concent r at i on of free
salt, and ~lcr caused by t he addi t i onal ions needed at poi nt C in order t o
COMPOnEnTS OF PoRE WATER 177
sat i sfy doubl e l ayer r equi r ement s. The doubl e l ayer ions are not free t o
diffuse i nt o t he measur i ng syst em; t herefore, osmot i c pressure ~ ' will be
reflected by PA" The osmot i c pressure ~ due t o excess sal t will not influence
t he val ue of pA. Thus, eq. (18) woul d be
PA ~- Pc ~'c' + ac = P B , (19)
where ~ is an osmot i c pressure due t o a difference in sal t concent r at i on
f r om poi nt C and a poi nt out of t he part i cl e force fields, b u t c o n t a i n i n g
free salt, such as poi nt B in Fig. 4. Thus, if poi nt s A and B are at t he same
el evat i on t he por e pressure meas ur ement gives t he t ot al pressure at C
rel at i ve t o a fluid cont ai ni ng free sal t in equi l i bri um wi t h t he cl ay; i . e. t he
pressure at O rel at i ve t o B. Thi s is preci sel y t he pressure desired in pr act i ce
since t he hydr os t at i c pressures t ha t devel op rel at i ve t o t he i n s i t u pore fluid
when a cl ay is sheared or compressed are t he ones t ha t will influence t he
effective stresses.
The foregoi ng consi derat i ons shoul d hol d t r ue regardl ess of t he sal t con-
t ent of t he measur i ng s ys t em so l ong as an appreci abl e quant i t y of sal t
and wat er does not diffuse in or out of t he sampl e before or duri ng a t est .
I f a significant a mount of free sal t diffuses out of t he sampl es and i nt o t he
measur i ng syst em, for exampl e, t her e will be a change in t he doubl e l ayer
osmot i c pressure, go, since doubl e l ayer concent r at i ons are ext r emel y
sensi t i ve t o free sal t cont ent of t he clay. I t woul d appear desirable, t here-
fore, t o t est sampl es as soon as possible af t er pl aci ng t hem in cont act wi t h
t he measur i ng syst em, t o keep t he vol ume of wat er i n t he measur i ng s ys t em
to a mi ni mum, and t o pr event t he flow of fluid bet ween sampl e and mea-
suring syst em, in order t o mai nt ai n t he ori gi nal sal t concent rat i ons at all
poi nt s wi t hi n t he sampl e. For l ong t e r m t est i ng equal concent r at i ons of
free sal t in bot h t he measur i ng syst ems and sampl e woul d be desirable.
Test s are cur r ent l y in progress whi ch are desi gned t o est abl i sh t he va-
l i di t y of t hese conclusions. The l i mi t ed dat a obt ai ned t hus f ar woul d t end
t o suppor t t he conclusion t ha t t he measur ed pore pressures are i ndependent
of sal t concent r at i on in t he measur i ng syst em.
A P H Y S I C A L I N T E R P R E T A T I O N O F E F F E C T I V E
S T R E S S
I t was poi nt ed out at t he out set of t hi s paper t ha t forces ot her t han t hose
due solely t o appl i ed stresses and pur el y hydr os t at i c wat er pressures are
act i ve in fi ne-grai ned soils. The anal ysi s of component and t ot al wat er
pressures i ndi cat es t ha t some of t hese addi t i onal forces are refl ect ed t hr ough
t he pressures devel oped in t he fluid phase. The concept of effective st ress
ma y be exami ned in t he l i ght of t hese findings. Mechani st i c appr oaches
t o t he expressi on of effective st resses in t er ms of i nt er par t i cl e forces as well
178 NINTI~I NATIONAL CONFERENCE ON CLAYS AND CLAY MINERALS
as appl i ed forces have been pr esent ed by Lambe (1960), Lambe and Whi t -
man (1959) and Seed, Mitchell and Chan (1960), among ot hers, all l eadi ng
t o final expressions of t he same general form. An al t er nat i ve appr oach based
on t he analysis of wat er pressure is possible.
Clay part i cl es are assumed t o be essent i al l y in cont act wi t h t he t ypi cal
part i cl e association bei ng corner- or edge-to-face as shown i n Fig. 5. Whet her
t he cont act s are mi neral -t o-mi neral or t her e is some few Angst r6ms separa-
t i on wi t h t he i nt er veni ng space filled wi t h adsorbed wat er and cat i ons is
X ~ . . . . . . . . . . . . ~-
p / , " / , " o f l e n g t h ~
FIauI~E 5.-Idealized representation of forces between clay particles.
not known. I t does not seem unreasonabl e, however, t ha t some t ype of
solid or semisolid cont act exists. A compl et el y sat ur at ed syst em is assumed.
I t is recogni zed t ha t no shar p boundar y, such as shown by t he dot t ed line,
separat es free and bound wat er. Such a line is shown onl y t o ai d i n t he
definition of a surface of l engt h l t hr ough whi ch slip mus t occur if t he
i nt erpart i cl e bond is t o fail in shear.
I n exami ni ng t he st at i c equi l i bri um of t hi s condi t i on t he forces t o be
considered, Fig. 5, ar e:
a ~ t he appl i ed average ext er nal stress.
A ' = t he net physi co-chemi cal at t r act i ve force bet ween particles. I t is
assumed t ha t at t r act i ons pr edomi nat e i n t he cont act zone and are
responsible for t r ue cohesion i n clays. These forces ma y arise f r om
van der Waal s at t r act i on, cement at i on, cat i on linkages, hydr ogen
bonds and ot her mechani sms. Repul si ve forces ma y also be act i ve i n
t he i nt er par t i cal cont act zone; A' is t aken as t he excess of at t r act i on
over repulsion.
p = t he hydr ost at i c component of t he t ot al por e wat er pressure.
The hydr ost at i c pressure 1o at any poi nt bet ween cl ay part i cl es is r el at ed
t o t he hydr ost at i c pressure i n t he fluid at a poi nt out of t he part i cl e force
fields PB; accordi ng t o eq. (19),
PB = P + ~" + a, (20)
Co~o~v. ~TS Or PoRE WATER 179
where ~" is t he osmot i c pressure at t he poi nt bet ween part i cl es rel at i ve t o
t he osmot i c pressure at a poi nt out si de of t he part i cl e force fields, and a is
t he adsor pt i ve component of wat er pressure. Bot h ~" and a are negat i ve
component s; t ha t is, t he hi gher concent r at i on of ions bet ween cl ay par -
ticles resul t i ng f r om i nt er act i ng doubl e l ayers and t he adsor pt i ve pressure
t end t o dr aw free wat er in. The effect of t hese pressures t hen is t o keep
part i cl es apar t . They ma y be consi dered as one t e r m R, t he i nt er par t i cl e
repul si ve pressure due t o t he physi co-chemi cal effects i nt r oduced by t he
surface act i vi t y of t he cl ay part i cl es. Thus eq. (20) becomes:
p~ = p + R,
but since t he pressure Iv B = ~ox, t he measur ed pressure, and p x is con-
vent i onal l y t e r me d u we obt ai n
u =p
Fur t her , since R is a negat i ve component we ma y wri t e
u = 2 - - R. (21)
Exami nat i on of t he st at i c equi l i bri um of t he part i cl es, Fi g. 5, shows
aa' + A' = Ta' + C,
where a ' is t he effect i ve ar ea cover ed b y t he part i cl es and G is t he cont act
force bet ween part i cl es.
Conver t i ng forces t o st resses gi ves
a + A' / a' = p + C/a' .
I t ma y be not ed t h a t C]a' is now t he act ual st ress t r ans mi t t ed bet ween
part i cl es per uni t ar ea of t he mas s ; i.e. t he t r ue i nt er gr anul ar stress, ~.
f l
L e t t i n g A' / a ' =A a n d p = u + R, we o b t a i n a + A = u + R+ a , or
= q + A - - (u +R) . (22)
Thi s expressi on, devel oped f r om a consi derat i on of por e wat er pressure
component s, is of t he s ame general f or m as pr evi ousl y der i ved expressi ons
for i nt er gr anul ar st ress ( La mbe and Whi t ma n, 1959; La mb e 1960; Seed,
Mitchell, and Chan, 1960). Rel at i ons such as (22) unf or t unat el y are qui t e
l i mi t ed i n t hei r appl i cat i on; not onl y because of t he assumpt i ons and
appr oxi mat i ons used i n t hei r devel opment , but also because met hods are
not avai l abl e for t he quant i t at i ve det er mi nat i on of t he quant i t i es A, R
and a' .
Fi gur e 6 has been pr epar ed t o i l l ust rat e t he var i ous i nt errel at i onshi ps t ha t
exi st bet ween appl i ed, por e wat er , and i nt er gr anul ar pressures. Four possi bl e
soil condi t i ons are i ndi cat ed wi t h t hr ee cas es of measur ed fluid pressure
shown f or each condi t i on. The u = 0 case refers t o a measur ed por e wat er
180 NI~T~I ~ATIONAL CONFERENCE ON CLAYS AND CLAY MINERALS
Tit ~ ~ r ~
~ ~ ~ .~
,~ ~,~ ~
~ ~
COMPONENTS O F PORE WATER 181
pressure of O, the a = 0 case refers to an equilibrium maintained by stressing
the fluid t hat communicates with the sample, and the general case refers
to the usual condition of bot h an applied normal stress and a measured
pore pressure. Complete saturation and the same void ratio are assumed
for each case.
Fig. 6(~) represents an ideal cl ay-wat er system composed of parallel
particles, not in contact, with no attractive forces active. Three possibilities
exist for maintaining equilibrium. As indicated by the u = 0 case the total
pressure of the pore fluid can be increased to zero by the application of a
normal stress a to the sample, which must be carried entirely by the pore
fluid since particles do not contact. The applied pressure induces a positive
hydrostatic component in the pore water which balances the negative
repulsive component. A second possibility is to decrease the total pressure
of the free water to a value of -- R as indicated by the a = 0 case. The third
possibility consists of adjusting the total water pressures inside and outside
the sample to the same value by applying a combination of normal pressure,
aa, and stress to the free water, h' y. Of course, an infinite number of aa
and h' y combinations can be found so t hat equilibrium will be maintained,
and the u = 0 and a = 0 cases are actually special cases of the general case.
The values of the various pressure terms listed under the diagrams in
Fig. 6 can be deduced readily from a consideration of the pressures shown
on the diagram, the t ype of soil structure depicted, and an analysis of the
statics of equilibrium. I t may be seen t hat for the ideal system of Fig. 6 (a)
R is measurable.
Fig. 6(b) represents a coarse system with insignificant R components
and contact between particles. Contact areas between particles have been
assumed to be insignificant. Conditions (a) and (b) are combined in Fig. 6 (c)
where a mixed system with particles in contact and electrical repulsion
forces active, but no attractive forces, is shown. I t may be noted t hat a
portion of the applied normal stress a must be carried by the water in order
to bring the total water pressure to zero. Only the difference ~ -- R can be
effective in creating an intergranular pressure ~.
The most general case is shown in Fig. 6 (d). I t is evident from a con-
sideration of the relationship shown under the figure t hat the intergranular
stress is increased by the amount of the attractive pressure A. The general
equation for equilibrium for the general case, Fig. 6(d), is of t he same
form as eq. (22) where h' y corresponds to u.
There arises from the analysis a further point of considerable interest;
namely, what is the true meaning of effective stress in a clay? I t is obvious,
as shown by eq. (22), t hat in a soil with significant electrical repulsive
and attractive forces, the intergranular pressure is not simply the difference
between the total applied pressures and the measured pore water pressures.
Lambe and Whi t man (1959) have considered this point in considerable detail.
182 NINTII N A T I O N A L CO~FEI~ENCE Olq ~ K Y S A N D C L A Y MI~EI~ALS
The possibility exists t ha t effective stresses and i nt er gr anul ar stresses are
not synonymous in clays. Seed, Mitchell and Chan (1960) suggest t ha t
st r engt h should be a f unct i on of t r ue i nt er gr anul ar pressure, and Lambe
and Whi t man (1959) poi nt out t ha t t he observed behavi or of expansi ve clays
does not correl at e well wi t h effective stress as defined by t he difference bet ween
appl i ed pressures and measured pore wat er pressure. I t is by no means sure,
on t he ot her hand, t ha t t r ue i nt er gr anul ar stress compl et el y cont rol s be-
havi or in fine-grained soils. For exampl e, voi d r at i o- pr essur e rel at i onshi ps
for even hi ghl y plastic softs, where R and A forces ma y be of appreci abl e
magni t ude, have been f ound t o correl at e well wi t h an "effect i ve st ress"
defined as t he difference bet ween t ot al appl i ed stresses and observed por e
wat er pressures. Compl et e clarification of t he probl em of t he significance
of i nt ergramfl ar and effective stresses in fine-grained softs must awai t t he
resul t s of f ut ur e research.
S UMMARY AND CONCL US I ONS
I t has been t he obj ect i ve of t hi s paper t o exami ne t he physi cal signi-
ficance of pore wat er pressure in clays and t o poi nt out some i mpl i cat i ons
per t i nent t o soil engineering. Tot al pore wat er pressure ma y be conveni ent l y
considered t o consist of t he combi ned effect of f our component s; ele-
vat i on, hydr ost at i c pressure, a pressure due t o t he adsorpt i ve force fields
of cl ay particles, and an osmot i c pressure arising f r om t he presence of dis-
solved salts and i nt er par t i cl e doubl e l ayer effects. Dat a are pr esent ed whi ch
i ndi cat e a significant por t i on of t he swell of a compact ed soil on exposure
t o wat er is at t r i but abl e t o wat er pressure deficiencies caused by mechani cal
and capi l l ary effects whi ch act i n addi t i on t o t he pressure deficiencies
arising f r om doubl e l ayer i nt eract i ons.
An analysis of t he pressures at var i ous poi nt s i n a clay, based on t he
condi t i on t ha t at equi l i br i um (no flow) t he t ot al pressure is ever ywher e
t he same, shows t ha t changes i n a ny one component f r om one poi nt t o
anot her are offset by changes i n t he ot hers.
I t ma y be concl uded f r om t he analysis t ha t a pore wat er pressure meas-
ur ement i n a soil t est reflects i nt erpart i cl e repul si ve pressures (osmotic
pressures) and wat er adsorpt i ve forces as well as pur el y hydr ost at i c pres-
sures arising f r om mechani cal effects. The i ndi vi dual component s of t he
t ot al pressure are not measurabl e, however, except i n special syst ems, and
l i mi t at i ons in t heor y pr event t he di rect comput at i on of t hese component s.
A physi cal i nt er pr et at i on of effective stress is at t empt ed by rel at i ng
component wat er pressures t o stresses bet ween particles. I t is shown t ha t
t hi s appr oach leads t o a rel at i onshi p of t he same general f or m as expressions
for i nt er gr anul ar pressures previ ousl y devel oped using di fferent approaches.
Models are present ed i l l ust rat i ng t he i nt errel at i onshi p bet ween component
C O M P O N E N T S OF 190RE W A T E R 183
wa t e r pr e s s ur e s , t o t a l wa t e r p r e s s u r e , t o t a l a p p l i e d p r e s s u r e a n d i n t e r -
g r a n u l a r p r e s s u r e i n c l a ys .
I t i s t o b e e x p e c t e d t h a t c o n t i n u e d r e s e a r c h wi l l l e a d t o i mp r o v e d u n d e r -
s t a n d i n g of t h e f or c e s a c t i v e i n a c l a y - wa t e r s y s t e m a n d a i d i n t h e d e t e r -
mi n a t i o n of t h e t r u e i n t e r g r a n u l a r p r e s s u r e s i n a s oi l ma s s a n d t h e e v a l -
u a t i o n of t h e t r u e " e f f e c t i v e " s t r e s s ; i . e. t h e s t r e s s c o n t r o l l i n g s oi l b e h a v i o r .
R E F E R E N C E S
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18~ I~INTH NATIONAL CONFERENCE ON CLAYS AND CLAY MINERALS
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