'R6s€arcfie,; c6nra, son ana uate;als aes'earctr'J*'i""' 'n'*n "
*o'"u-u-o o'n'"o'l *o "t:
** *:t:::::::16' NDA eiait:
,,rt*r{irr*l*rxrii'#!}ilt'#{"ff:#Wi:#;ffir:m:;:"-'Fastest curw fitting procedures are propos6d for vBrlical and radial consolidarions [r rapid loading m€hods ln \srijcal consolidation the
aManaging Director, Delhi Metro R ail Corporation, Bara Kharrrba Road, Connaught Place,
New Delhi- 1 1 000 1, INDIA. email : mdmetro@hotmail-com
sprofessor and Dean Engineering, J. B. Knowledge Park, Naharpar, Faridabad-121001, INDIA'
B
9
1 0
1 1
7 2
1 3
t 4
1 5
L 6
1 1
1 B
1 9
2 0
2 l
2 2
2 3
2 4
2 5
2 6
2 1
2 B
2 9
3 0
3 1
3 2
3 3
3 9 &oo Ultimate prirnary sefilement
compressiorn of a consolidating layer in terms of dial gauge reading
lnitial compression before the load increment, usually taken as zero
Corrected initial compression
Diameter of influence in radial drainage
Diameter of drainage well in radial drainage
Void Ratio
Drainage patlh in vertical drainage - half of thickness in double drainage
41 LL Liquid limit
48 LC Least court of the dial gauge
49 LIR Load Increment Ratio
2
34 List of Symbols
3 5
36 cv
31 cr
38 C"
4 0 5
4 L a
42 60
43 d,
44 d*
4 5 e
4 6 H
5 0 rltr
51 rn2
52 mr
53 l t
5 4
55 t t
5 6
57 n:(d/d") Drain well ratio
58 PL
se sl,
60 Jso
6 1
coefficient of consolidation with vertioal dminage
coefficient of consolidation with radial drainage
Compressiom lndex
Slope of straight line portion of 6-(dt/d6) plot in vertical consolidation
Sl'ope of straight line portion of 6-(d6/dt) plot in vertical consolidation
Slope of straight line portion of d- (d6/dt) plot in radiat consolidation
Constant in vertical consolidation for detecting secondary consolidation
before 50%U (Tewatia et al. 2007)
Constant in vertical consolidation for detecting secondary consolidation
after 6Ao/oU (Newly inhoduced in this paper)
Plastic limit
Shrinkage limit
Slope of tangent at the point of inflection in &tog(d6/dt) plot in vqticat
consolidation (Tewatia I 998a)
6 4 T r : 4d""
62
6 3
6 5
6 6
6 1
Effective stress
Experimental time measured from the instant of load increment
Time factor for consolidation with radial drainage
Time factor for consolidation with vertical drainage
Degree of consolidation with vertical/radial drainage
Pore pressure
T : t"',
H '
(J or U, =
u
6 - 6 0
4* -do
6 8
6 9
1a Introduction
1 L
7 2 Sridharan et al. (1999) suggested a rapid loading procedure to evaluate consolidation test
7 3 results in vertical consolidation. In the proposed method, the next load increment is applied as
7 4 soon as the necessary time required to identifu the percent consolidation is reached and to
15 evaluate the coeflicient of consolidation by one of the popular curve-fitting procedures. The
16 rectangular hyperbola method has been used to identify the percent consolidation (usually 70-
71 B0% [/) reached after any load increment, ffid to determine the coefficient of consolidation,
1 B before making the next load increment. Where, [/ is the degree of consolidation, The next load
19 increment is given so that LIR (load increment ratio) is one or nearly one. It was presumed that
B 0 at 7A% consolidation by settlement analysis, 70% pore pressure is dissipated or at 80%
B 1 consolidation settlement , 80Yo pore pressure is disspated; thus equating the degree of settlement
82 with degree of pore pressure dissipation. It was experimentally shown by them that this
8 3 presumption gives insignificent variation in cv. Tewatia et al. (2012b) gave theoretical
B 4 justification for this presumption for vertical and radial consolidation.
15 Hawlader et al. (2003) recognized the importance of structural viscosity and yielding
B 6 in controlling many of the phenomena associated with the consolidation of clays. The results
B 7 show that the deformation of thick clays in the field are different from those predicted from a
BB thin laboratory specimen using the square of the drainage length or the uniqueness of the end
B 9 of primary consolidation concepts. Augustesen et al. (2004) investigated the time-dependent
9 0 behavior of soils extensively through one-dimensional and tri-axial test conditions. The
9 1
92
9 3
4
description is carried out separately for creep, stress relu<ation, rate dependency, andstructuration in laboratory experiments. All of the above-mentioned phenomena axe presentin both sand and clay. The time-dependent phenomena are more pronounced in glay than
94 sand.
95 Conte (2006) presented a method for the analysis of coupled consolidalion in96 unsatuated soils due to loading under conditions of plane strain as well as axial synmetry.97 The method is based on the transfomration of the governing difrerential equations by the98 Fourier transfonn, when the soil system is deformed under plane strain conditions, or Hankel99 tansfonn for problems axial symmetry. The effect of such taosformations is to
100 simpliS considerably the solution from a computational point of view. In additiou using101 these tansformations '\e
same differential equations can be used to analyze consolidation
]-02 underboth the above conditions.
1 0 3 For most mechanisms proposed to explain secondary effects, one would expect
104 a more noticeable secondary effect in the laboratory tlnn in the field. Laboratory values of cn
105 (and t) are likely to be too low because Etarding secondary effects are likely to be mgch more
10 6 important in the labordory tlnn in the field due to the higher shain rarc in the laboratory (Iaylor
107 l%2; Barden 1965; Lo et oL ln6; Po*it 1SA. The time required to complete the t€st using
108 the rapid consotdadon method (Sridharan 1999) could be as low as 4-5 ft conpared with I or 2
109 weeks in the case of the conventional consolidation test on highly olayey soils. Rectangula
110 hyperbola method requires data of abors 707o U for determining cn 6m elrc, Where, c" md d16
111 are coeffcient of vertical consolidation and ullimde primry settlement, rcspectively. However,
LL2 the cn values are lower than tu€ cn due the effects of secondary consoliddion as secondary
113 consolidation essentially starts at 60%U (Sridharan et al. 1995). Also, it is not knovm to what
Il.4 extent cu values are affected by secondary consolidation,
The tend/rate of settlerment of any load on clay can be measured at any time without
knowing the past history of load increment. It can be a source of some useful infomration like
quick evaluation of consolidation characteristics in the laboratory and field time-compression
dataof the presenL past and future, tlpe and stage of consolidation, drainage conditions, time of
load increment etc. (Iewatia 2012). Using the rate of settlement
Tewatia 1998b; Tewatia et al. 1998; Tewatia and Bose 2006; Tewatia
loading mettrcd is proposed to evaluate cv minimizing the effects of
gives some estimate also that to ufuat extent co is affected by secondary
number of rapid loading methods for vertical consolidation but
consolidation (Vinod et al. ZAfi1' Tewatia et al. 2012a). A rapid
1 1 5
1 1 6
T I l
1 1 8
1 1 9
1 2 0
L 2 !
1 2 2
123
124
**{{
5
t25 radial consolidation that is much faster than the methods available in litemturc with the above
L26 mentioned merits also. The proposed methods can be used even when the settlement or time of
!27 load increment is not known.
1-28
129 ConsolidationTests
1 3 0
131 Experimental data used has been obtained from numerous standard oedometer tests on a
L32 variety of soils from Central Soil and Materials Research Station, New Delhi and Indian
133 Institute of Science, Bangalore (Tewatia 2010). Two typical clays Sawan-Bhadon (SB) Dam
1 3 5 PL:36% , Load: 100-200 lqa) llave been chosen just for example. Consolidation tests were
136 carried out as per standard procedures on remolded saturated specimens. For this purpose
I31 soils passing through 2 mm sieve were used. The soil was packed into the ring taking density
138 equal to 98% of the standard Proctor's maximum dry density. The consolidometer used was
L 3 9 of fixed ring type with a diameter of 60 mm and a height of 20 zrzr. The inside surfaces of the
i-40 rings were applied with silicon grease to avoid ring friction. A load increment ratio of one
747 was adopted and each load was maintained for sufEcient time until the compression virtually
1-42 ceases. Compression was measured using <lial gauges with a le xt cotxi of 0.002 mm.
14 3 Soils were mixed thoroughly at water contents slightly less than their liquid limit values
L 4 4 and were allowed for moisture equilibrium for one week before remolding the same in test rings.
145 This practice ensured saturation and rmiform moisture disnibution throughout the soil samples
L46 prepmed. For vertical cortsolidation double drainage was allowed. For radial consolidatio&
!41 radiatly inward central drainage was provided by sand drains (Fig 1). Central holes in the soil
14 8 mass were made with the help of thin, stiff, lubricated plastic tubes of outside diameter of the
149 sand &ain (i.e. 12.5 mm,,,vlich mrresponds to n:4.8). Utnost care was taken to avoid the
15 0 disturbance of soil mass around the drain. Then olean washed fine river sand passing a 425-pm
151 sieve and retained ona75-pm sleve was placed irside the drain in a loose state to minimize the
152 smearing etrects (Berry and Wilkinson 1969). At higher stress levels, the compressibility's of
153 sand and clay will be very much differenl resulting in a change in ratio n. To take care of this,
154 fine sand was placed in loose fonn" which probably would deform in the same ftrnge as that of
155 clay, keeping the ratio z the same, Carefirl measurements at the end of test revealed that
156 diameter of drain rcmained alnost unchanged.
157 To stop vertical drainage (in radial consolidation) the porous base plates was avoided by
1 5 8
1 s 9
1 6 0
161-
t62
1 6 3
L64
1 6 5
r66
161
1 6 8
L69
1 7 0
777
1 1 2
7 1 3
t 1 4
1 7 5
L 7 6
L77
1 7 8
7 1 9
1 8 0
1 8 1
1 8 6
inserting water proof rubber membranes with centnal holes of diametm equal to that of the sanddrain at the center' at each end of the sample with their outer diameter more than that of ttreporous base plates to prevent possible vertical drainage at the outer periphery of the sample;ttrus, only radial drainage was ensured.
vertical or one-dimensional consolidation
When a zustained load is applied on saturated clay it gradually undergoes reduction involune due to squeezing out of water. This is called primary consolidation. If the safnple islaterally confined, the pore pressure equal to the applied load develops immediattily thatvaries with time f and vertical distance z (Fig 2). Following is the partial differential eguationfor one dimensional or vertical consolidation
Where z is pore presswe and c, (also denoted ss cr) is coefficient of oonsolidation in verticat orz dtrer,tron. Solution of Eq 1 was obtained by Terzaghi (1923) as
Ozuoz-
Au0t
= C , (1)
(r:t *n#r,,r--pc
, - c r tr - ---:
H'
(2N+r)'tr 'r) Q)
(4)
Where (/is average degree of consolidation andTis time factor. Degree of consolidatiofU LL isrelated to the experimental settlemen! 4 by the following relationship
U _ 6 - 6 0
4* -4 (3)
L B 2
18 3 Where, dp is corrected initial compression and d76 is the ultinrde primary consolidation iTaylor1B 4 1948). Time factor, Z, is related to experimental time, t,by the following relation
1 8 5
1
1 8 7
1BB Where, Ilis drainage path of the consolidating layer. In literature (Fox 1948), Eq 2 is
1B 9 into two parts: (1) Parabolic Eq 5 and (2) Exponential Eq 6
1 9 0
1 9 1
:-92
1 9 3
]-94
T : L u t4
g 2(J:1 +exp(- 4rlE 4
a :2 ",(6p+6rt' ,#, + do
divided
(s)
(6)
1 9 5 Eq 6 is another form of Eq 2, where N:0. Figs 34 show [/ versus dUldZ and, U vercuf dT/dU
196 plots on linear and serniJog scales. The dU/dT is obtained from Eq 2 (fewatia 19984). Fig 4
L9'l is a symmetrical ,S-shaped curve having point of inflection at 50%U. k is clear from f igs 3-4
198 that Terzaghis 842 can be approximated into 3 parts. Fox's (1948) approximatioq @q 5)
1-99 holds good in the initial portion approximately from 040ToU, Exponential Eq 6 hofds well
200 from 60-100%U. The middle third W g0-60% t/) can be approximated with fu 7 (fiewatia
2or 2010)
2 0 2
203
2 4 4
205 1. The d-(d/dd) Method of Vertical Consolidation
2 4 6
201 Differentiating Eq 5 with respect to I/ and substituting the values of U and 7 frdm Eq 3
208 and 4 respectively, it can be shown
2 4 9
274
2 I \
2L2 Eq I is the equation of snaight line in the form: y : nr x + c; vihere mr is slope fnd c is
213 int€rcqt on the y-cis. The il(dt/di) plot (Fig 5, initial portion of curve OiKl is a stra{ght line
2I4 having a slope, ml,where
2 l . 5
(7)
(8)
216 (e)2 L 1
2LB And tho int€rc€pt on the d uk, c : do. In Fig 3, abscissa of straight line OC is increased by2r9 l'217 times and line oD is drawn that cub the theoretical snve oJ at 7(p/o consolidation.220 Therefore,abscissaoflineocisincreasedbyl.2lTtimesinFig5,sothatpD:I.2I7pc.Tfus
22t cuts the criwe orK at d7p. The omount of primary compression, (Arr) = (,D7oo - 6o) is obtained as2 2 2
\:ry
(4*-4):W
- mrlrHz _T mrc : r- v 2(6r* - 6J, 2 (Nil H),
2 2 3
224 The cu can b obtained as
2 2 5
234
(l 0)
( l l )
2 2 6
227 Eq 8 shows that uni6 of c.,, and m, arc same and cn is directly goportional to rnl. Ther€forc, a228 snaight line (i.e. if rz1 is constarn) in the initial portion of ddldd plot iadicates that cn is conshnt
229 and soil follows theoretical behavior.
230 The comprrssion index (c") rcp'€sents the slope of the linear portion of the eJog o'231' cuwe. Where, e is voids rario and o' is increase in eftctive pressurc, The C" rcmains constsnt
232 wi{hin a fairly large range of p,ressure, Ttnrs,
233
/1 Lgt :-c
Alog,o 6, los,or$l
2 (zc,log,o (LIR+ l))'
Le
235
2 3 6
2 3 1
238
239
244
24r
2 4 2
When the soil is laterally confine4 the change in the volume is proportional to change in the
thickness lH and the initial volume is proportional to the initial thickness 2fl (Punmia et al.
2008). The load increment ratio, LIR, (by definition) is lo'/os'. From Wrz
(12)
(13)
(14)
Le:#:C"log,o QIR+|)
Substituting in Eq I I
mrryrH2: : --Y 2(6r*- 4) '
- ry
T
When (usually) ZIR=/ is Eq t4 reduces to
co:4.333#
just by plouing a few points gf the 6-(dt/d\) plot after initial compression is over.
evaluated by Eqs I 0- 1 1 , ttren C o cart be determined by Eq 1 6 and firttrer load i
stopped (if desired).
2. The d-Jddldt) Method of Verticat Consotidation
- t
243
2 4 4
245
2 4 6
2 4 1
248
2 4 9
250
25t
2 5 2
253
254
255
2 5 6
2 5 7
258
259
2 6 0
2 6 L
2 6 2
2 6 3
2 6 4
265
2 6 6
2 6 7
268
2 6 9
2 1 0
2 1 L
2 1 2
or
(15
(16)
(r7)
v
The C" is related to the index es of soil,IZ etc. For example, Skemptonegafl s\bwed
c,:0.007 (LL-10%o)
for remolded samples. For ordinpry clay of medium to low sensitivity, the value of C" is1.3 times colresponding to the field consolidation line (Punmia et al. 2003). Therefore, C" isknown by Eq 17 (ot by some otl4ter method) then cn canbe quicHy evaluated by Eq 14 Eq 15,
f c n i s
can be
Differentiating Eq 6 with respect to T and substituti4g the values of t/
and 4 respectively, it can be shgwn
.' 4 Ht .d6,o - - - ; - ( ; ) - 6qoo7T- Cv clt
Eq 18 is the equation of shaight line in the form: y : 4t
* * c, v,rhere m2
intercept on y-mis. The 6-(d6/dt) plot is a shaight line h{ving a slope, rn2 :
intercept on d uis, c: 5roo. Thus, ct) eanbe evaluated as
1 0
4 H t2 1 3
2 8 4
295
2 9 6
2 9 7
298
299
3 0 0
3 0 1
302
c r = (l e)
(20)
ot *,
2 1 4
27 5 In Fig 5, extrapolated straight line portion of curve idy'./cuts &ais at the point Z that gives d,ap.2'7 6 At point N the experimental curve ,l1lf,/ deviates from theoretical nature and creep starts. At211 any point the vertical difference along &cis between the exhapolated shaight line and tlre218 curve i0fis the amount of creep settlement at that point.
219 In Fig 3, abscissa of straight line Pi is increased W 1.224 times and line pS is drawn280 that cuts the theoretical curve PiK at 30olo consolidation Therefore, abscissa of line ZR is28L increased by 1.224 times in Fig 5, so that g,s : 1.224 eR. This cuts the curve MNJ at 6n. T]ne282 amount of primary compressioq (AIi) = (droo - 60) is obtained as
283
285
28 6 3. The d-be(ddl,&) Methqd of Verticrl Consolidation
287
288 T"hrs is 6Jog(d6/dt) plot, originally proposed by Tewatia (1998a). Theoreti cal tl verus dU/dT
289 plot is shown in Fig 4. Its theory and procedures are explained by Tewafia (1998a) and
290 Tewatia et al. (2007). However, its merits fiom the angle of rapid loading method and
29L reasons for those merits were not analysed that are explained here. This plot is Symmetrical
292 S-shaped oxve having a point of inflection at 50%oU. The tangent at point of inflection cuts
293 do line at U:16.19%.If s5e is the slope of the tangent over one log cycle then c" is evaluated
294 as
A o - 4 0(4oo-4):ff i
0.2566 (ff),u,n a'C v - (2r)
And
J:O
(4oo -4) : r5o (22)
Like earlier two methods proposed above, time of load increment is not required to plot the
curve and evaluate cr. Advantage of this is taken to calculate the time of load increment
(using Terzaghi's theory) and compare it with the known time of load increment. If soil
follows pure Terzaghian behavior upto 5A-6A% consolidation that means if no secondary
1 1
3 0 3 consolidation is there then the calculated value of time
3 0 4 value of tirne of load increment should be sirme. Based
3 0 5 primary consolidation p is defined as
3 0 6
of load increment and the known
upon this principle a constant of
.d5 _(
* ) r cs t rc .s3 0 7 p - : 0.0802 Q3)sso
3 0 8
309 Where, I,lr-lg is the known timp for 16.197o oonsolidation. The p is a dimensionless constant
310 applicable to all soils fo[owing Terzaghi's one dimensional consolidation theory. Maximum
311 value of p: 0.0802 in case of pure primary compression. However, if any other extra
312 compression is running concurrently with primary compression which we call secondary
313 compression then p is less than 0.08a2. Tltrs property is used to detect the presence of
3 1 4 secondary compression in the range of primary compression before J0% U
315 Therefore, it can be stated: In all soils following Terzaghi's one dimensional
316 cotxolidation theory the product of time and rate of seftlement at 16.19% consolidation
3I'7 divided by the slope of the tangent at the point of inflection in semi-log16 plot of settlement
318 yersus rate of settlement equals 0.0802.In that case, Eq 21 gives true co. Tlis constant p,
31 9 can be named as constant of primary consolidation. In a similar way the expression for p at
32O the point of inflection can be derived as:. p: (d6/dt)sots/sso:0.2449. Less is the value of p
321" (F4 23) as compared to 0.0802, more is the c" (by Eq 2l) affected by secondary
322 consolidation. Tests were conducted on wide varieties of soils using the above equations and
323 it was found that in most of the inorganic soils the values ofcu were very close to true cv
324 (Tewatia et a]. 2007).
325
326 Why 6-log(d6/dt) method is fastest of all the methods of vertical consolidation:
32'7
328 ln literature, for U:0-60% Eq 2 is approximated with Fq's and for remaining 60-100U it is
329 identified wilh Eq 6. By simple mathematics it can be seen that Eq 5 alone is capable of,
330 evaluating do btrt for decnnining cu and droo Eq 5 alone is not sufficient (if C, is oot known)
3 31 and some other part is required. The other part (Eq 6) starts after 60%U. Dw ts tJais reason no
332 researcher could deterrnine c, nd 6nn before 60%U. But the symmehical S-cwve i,e. U-
333 log(du/dD or UJog(dT/dU) plot (Fig 4) discovered one more part between pmabolic and
334 exponential ones and divided Eq 2 in three parts in 40:20:40 ratio (Tewatia 1998a). Parabolic
L Z
3 3 5 part is Eq 5, o4Io/ou.Transition part is 40-@%u (Eq 7) and Exponential part is 60-l0u/ou336 @q 6). Combination of parabolic part along with middle transition part makes the suggested3 3 7 method capable of determining cn and, 61s6 at the lowest perce,lrt consolidati on (50ot5U\ and3 3 8 makes it fastest method of vertical consolidation.
3 3 9
340 Characteristic feature of vertical consolidation
34L
3 42 Tt:e 6-@/di) plot is a straigbt line in the initial portion and the &(ddldr,) plot is a sraiglt line in
343 the lder portion- On elog(dildt) or 6-log(dt/d\) plob it gives symmetical ,S-crrrve, that is
344 conver( rpwads in the initial portion and convex downwards in the later portion The point of
345 inflection lies d 50/oU. The slope of the tangent at the point infletion over one lo916 cycle is
346 equal to the anount of primary compressioq (6m- 6d or /I1(tewatia 19984 Tewada A al.
34't 2007).
3 4 8
3 4 9 Reletionship between t1, m2 arnil s56
3 5 0
351 Fmm Eqs 14,19 ad,22, it can b€ shown that
352
? q ? Q4)
3 5 4
3 5 5 Where, p is a dimensionless constant like p. Therefore, if a soil follows theoretical behavior
356 in initial, middle and later portion thenp= -0.258. In case of Sn Dan Soil @ig 5); rn1 =
357 156.5, mz: -200 aad s5s: 233 (from Tewatia 1998a; Tewatia et al. 2007). This gives p = -
358 0.577 + -0.258. This shows that secondary consolidafion essentially . starts at 607oU
3 5 9 (Sridhamn et al. I 995 ; Tewatia I 998E Tewatia et aI. 2007). Even if a soil follows or seems to
3 6 0 follow theoretical behavior after 60%U (i.e. e@6/@ plot is a straight line) its c" diaa etc. are
361 changed by the presence of secoadary consolidation and these are not the tue values.
3 6 2
363 The 6-6/dtUlathod of Radial Comolidation
364
3 65 Following is the radial consolidation equation for equal vertical shain condition (Banon 1948)
3 6 6
t t - ry : -#_-o.2sgsso
1 3
36i ,,:r-..J#) rrrl368 Where
36e r,-- + e6)d""
3 7 0
371 r[a=j .q,y-V;]n- -r A- Q7)
J I Z
37 3 Where, c, is coefficied of radiat consolidation snd z is the drain spacing ratio, given by
3'1 4
375 n: Nd, (28)
3 1 6
3'11 where,4 is the diameter of inflfrence (i.e. twice the effective radiat drainage pdh), and d*is the
3 7 8 diameter of tbe drain
3'1 9 Average degree of con{olidation U, is related to fhe experim€rfal settlemelrt d, by the
380 followingrelationship
3 8 1
6 - 6382 Il , = -:----:-e- Q9)
4* -4
3 8 3
38 4'
3 8 5
3 8 6
3 8 7
3 8 B
3 8 9
3 9 0
3 9 1
392
3 9 3
394
Where, do is coffected initial
Differentiating U, @q,25) wi
it can be shown that
This is equation of straight line
line, the intercept (c) of which
then cr carrbe evaluated as
6:- ryr#r*6no
compression and 6rc0 is the ultimate primary consolidation.
respect to Trand substituting their values from Eq29 w:dE4-26,
(30)
the form ! : rrtrx+c. Therefore d versus d6/dt plot is a straight
d a<is gives 6roo. Suppose, m,is the slope of this straight line,
F(n)d"2C , :
8m,(3 1)
3 9 5
3 9 6
391
3 9 8
3 9 9
4 0 0
4 0 1
402
4 0 3
4 0 4
4 0 5
4 0 6
401
4 0 8
4 0 9
4 1 0
4 l r
412
413
4 l . 4
4r5
476
411
4 1 8
479
420
42L
4 2 2
423
4 2 4
425
4 2 6
4 2 7
I 4
As soon as effects of initialt aonrpression are over in the beginning, i.e. as soon as sfiaight line
starts showing its presence (Fig 6); &oo, c, etc. can be obtained (say at 1045%(r.No faster
(incremental loading) method of radial (as well as vertical) consolidation is possible than this.
As the method determines c, and 6 too at an early stage, they may be assumed to be free from the
effects of secondary consolation in most of the inorganic soils. Characteristic feature of radial
consolidation is that it is straight line from beginning to end in the absence of initial and
secondary consolidation effects.
Rate of settlement in primary and secondary consolidation and its other
applications
From the characteristic fea.tures of vertical and radial consolidations it is clear that they both
give sfiaight line on 6-@A/dt) plot in later portion. When they both occur together i.e. in -3D
consolidation in polm co-,ordinates the rates of settlement (abscissa) of vertical and radial
straight lines at any settlernent are added and the resultant is again a snaight line on 6-(d6/dt)
plot in later portion. Tewatia et al. (2007) and TewatiaQ}I\ showed that primary consolidation
under complicated drainage (whether vertical, radial, -3D in polar or Cartesian (X-Y-Z ) co-
ordinates or any complicated mixtwe of all these) and loading conditions essentially gives
straight line on 6-(d6/dt) plot in later portion while secondary consolidation or creep is a straight
line on 6-log(di/dt) plot. By observing the rate of sefflement of a sfructwe for some time, type
and stage of consolidation and its settlement-time data of past" present and future can be
obtained.
Thke, 'Eray, be sc'$le #'Bstuse$ thd " rue aheady futnd to bc settting dus ts,
esss li&tios aad tb timr€. ef, load increment is not leiptm or no definite time of lod
iao@eet eau be assigned &€ to non-u*if€rm or ircegutrar loading. The drainage conditisns
in the fow&tiw nlay be very col@d or nst known. The leaning tower of Pissa and
Fastest methods of vertical and radial consolidations are suggested that can be used as rapidloading methods. The methods give almost true values of coefficients of vertical and radialconsolidations. In case of vertical consolidation a quick check is provided to estimate theeffect of secondary consolidation on the coefficient of consolidation. In case of radial
consolidation this check is not required in most of the inorganic soils. To perforrn rapid
loading tests radial consolidation is suggested instead of vertical consolidation becaqse it is
much faster than that. However, if C" is known or is to be determined from single loadin
then vertical consolidation is preferred. Characteristic features of vertical, radial, 3D and
secondary consolidations are given in terms of rate of settlement. It is shown that secondary
consolidation essentially begins at 60% consolidation.
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