stress distribution in soils under static loading

SOIL MECIIANIC3

S T R E S S D I S T R I B U T I O N IN S O I L S UNDEI~

3 T A T t C LOADING

L . T, A b r a m o v , I . M. K r y z h a n o v s k / / , and A . G . P e t r o v a

UDC e24.131.52Z

Although the problem of s t r e s s distribution in ~cils has been subject to an extensive theoretical and exper imental study it cannot be considered solved as the r e s e t s obtained so far a re ra ther contradictory,

At the V. V. Kuibyshev Moscow "Order ot Banner o~ Lar-or - t~tvt| Engineering tnstttute, D. ~. Bara- r~ov, under direct ion of Prof . N. A. Tsttovich, made studies for s t r e s s measurement in s~ils and for the development of new strain gages, which allowed D. S. Baranov and L. M. Bobylev to devise a new strain gauge wlth hydraulic t r ans fo rmer . The s t ra in gauges of this ~'pe allow measuring s t r e s se s inso i l s with nn accuracy of 5 -7~ ,

At the Soyuzdornli the authors pe r fo rmed exper imen~l studies for s t ress measurements In soil. The coll. The soil trench where the tests were made was 4.5 m wide and 3 rn deep over a length of 24 m. "the f loor of the trench consisted era natural ly compacted sandy loam layer of more than 10 m thick and the walh, were built of concrete. T~.~ trench was filled with a sandy loam which had a grain size distribution as shown in T~ble I ,

The s t r e s s e s in soil were determined under absolutely rigid bearing plates measuring 250, 358, 506, 716, 873, 1009, 1128, and 13~2 mm in diameter. The experi~e_,~ts were conducted by gradu:~lly increasing the loads from 0.2 to 2-4 kg/cm ~ in increments of 0.2 kg/cm :. "l'be load on a p~te was applied by a hydrau- llc Jack placed at the center of the plate with its ram pressL~g o~ a bearing frame of special c~nstructlon.

The s t r e s s e s in soil were measuredalongthepla~e axis at depths of 0.05, 0.2, 0.4, 0.6, 0,9, 1.0, 1.2, and IA m f rom the bottom of the rigid plate. The st ra in g - ~ e s were p!aced hurizontally, checked with a spi r i t level and connected to an automatic r e c o r d e r AI-1; ~ e i r location in depth ~ s determined by levelling. Before the tes ts all s t ra in gauges were cal ibrated in a special calibrating tank and tn a p ress following a procedure suggested by D, S. Baranov. A curve ~as plotted for each strain gauge showing O,.e relationship between stress and At, where A/represented the difference bet'~*een the zero reading according to AI-I and

TABLE I

G,+t__.__~n .z__u , , m.,__.~m -,,__+ ,m+.__r ,+i,,,,,+.b,,.,,ti.__._.._~ t..3+" ~r+___e,! l

• ll,S-- It,2:,...- O.O* -- ee'2 I ,-+ l.-+.l.+ I... I.+:_°I_. _+.o,1 o:,I:,:+I

fABLE 2

+- : ,.,, 1.11 I .~ ." 1++:+

-. . ,,.

De

e,t o.4 t.e

I,I~ O.~O l .e l 1,01 O,~l 0,~41 I , ~ O.tll I t .el 1,0+'I O,Se~ O.t,l 1,3] 1.311 1.01 1,:14 1,31 I . ~ l+¢J I.PII l.l~ I.II I.~' II.M

e.J I .e t . t [ 1,4 [

O.el, O. ,~ - - m IIi. tso 0.41+ O.~ O.W + O.ml O.'It[ -- B.(4 0.7'qt; 0.41+ 0 O.~l, O, PS 0,+, 0,I? @,M - - 0,4~ O, l+ 41oi,) iO,+~l 0.4, 0, |9

I

i

I

Fig. 1. Diagram showing position d s t ra in gauges during calibration in the t rench.

w

T r ~ s ~ * . e d f r o m O s n o v a a i y a , F u n d 3 , m e n t y i M e k ~ a n i k a G r l m t o v , N o . 6 , p p . I-3, November-Dc~.mber,

389

a} b) S e* O ~ ~J ~'lPkg/cm t

Fig. 2. Stress distribution in sandy loam, a) in relation to specific p r e s su re on plate, b) on different depths for plate d iameters des ig- nated as follows: x for 250 ram; A) 358 ram; O) 500 ram; A) 716 rara~ II) 873 ram; O) 1009 ram; @) 1128 rata; O) 1382 ram;

@ • •

o ...... L J

L j _ i : N T ~ : I I , ; ; j

I_1

It

the reading of the s t ra in gauge taken af ter a specific loading cycle . A di - rec t reLntionship between the loading and the s train gauge membrane de- formation was established on the basis of these c~xves. ? J t e r each se r i e s of tests an intermediate calibration of s train gauges was made. Moreover , the s train gauges were calibrated direct ly in the trench before eve ry tes t in accordance ~ t h the following procedure . The gauges were placed oa soil surface (Fig. 1) and covered with a 5 cra thick layer of sandy loafs consolidated by a v ibra tor . The plates with diameter ranging f re t s 506 to 716 mrs were careful ly g.-'ound into the tamped and straightened soil s u r - face and were loaded in s~ges increasing the p res su re f rom 0.5 to 3 kg/cm z in increments of 0.5 kg/tcra ~. The average ~ d r a t l e deviation of ca~brat lon data fr~ra ~ e computed s t r e s se s at the depth of 0.05 ra is

ce~ -- * ~ - - * L01%.

It was shown by experiments that for fine dusty sands with density ranging within 0.95 to 1.05 of the s tandard*, the repeated compression of soils under the plate had no effect on ei ther magnitude or t~:pe of s t r e s s d!strib~tion.

Zero readings were t ~ e n before loading the plate and the ~ubsequent

Fig. 3. S t ress distribution In homogeneous sell l~Ifsp~ce.

readings were taken five minutes niter each loading cycle , At the end of experiment the plate was completely unloaded and the last readings were taken which were e i ther equal or near to zero .

Altogether, fifty tests were ; ,erformed to study the pat tern of s t r e s s distribution in a s ingle- layer s y | - tern tinder the rigid pla tes .

~'Standard density Is the maximum density determined by the standard consolidation apparatws at the opti- mum water content of soi l ,

~ t i m u m water content is such at which the maximum density of soil is obtained with the leas t effort fo r consolidation.

390

Fig. 4o Stress distribution In sandy Ioam un- der a layer of crushed limestone measuring 25-70 xnm (tests No. 261, 262, 265, 266, DtS 50 Cm)o 1) Theoretical curves according to Korsunskli; 2) measured stresse~.

!

I .X

[

US_= -=- %~

Fig. 5. Diagram showir~g equal v e ~ - cal s t resses ,

The tests were repeated from 3 to 16 times for each strain gauge depth, pressure , a~d plate diameter. The average s t ress values ¢ for dlffere~t depths were computed accordingly. T*ne values d a" for a bearing plate 1128 mm in diameter are given In Table 2,

The stress distribution curves in relati~)n to depth, specific pressure or dimes,stem d plate L,'ansmitt- Lug the pressure were pl~tted using the aterage values (Fig, 2).

To determLqe a general relationship of stress distr ibution in home~eneous halfsp~ce ~,e stresses ¢ , corresponding to certain relative depths h/R, were computed in percentage of specific pre~stn'e on plate

The th~.'~oretfcal curve for stress distrltmtion or, corresponding to h/R and plotted accord~r,~ to l~',e data of ~,L B. Korsunskll for a homogeneous haffspace* is shown on Fig. 3. Tl~e e x i ~ r i m e ~ l results (points) eharacterlz|ng the stress distribution at various depths which are close eno~_gh to Me ~retic~l eta're are also sho~'n on this d~agram. In this connection, it is possiblu to f.xmclude that, in gener-,~I, ~ e pattern of s t ress dlstributlon for varying depths in a homogeneous sandy loam coincides with ~ e s~re~s d ~ s t r ~ t l o s Ls aa el~stle homogeneous hal~spaeeo

To Investigate the pattern of stress distribution in a heterogeneous medium, layersolf crus~ed stone were placed over ~e sandy soil: selected granite crushed stone measuring from 5 to 15 mrn in layers elf 20, 30, 40,50, .~nd 60 era, crttshed limestone measuring up to 2,5 ram, and crushed Iimcstc~.e in grain s i~cs from 25 to 70 mm In a layer 1,5 cm thick, The strain g~ugcs were placed in the s:ndy soil a t depths of 0.05, 0,2, 0.4, 0,6, 0,8, 1,0, 1,2, and 1.4 m from the bottom of crushed stone la£ers ,

The stresses were measured under the 340, 358, `500 and 716 mm diameter pL~tt-ao TEe test results were processcd In the same way as those for single-layer systems.

The tests have shown that for the two--layer systems with the top layer consisting ¢& fine crushed s~ne , the stress distribution at various depths follows the same law as for a single-layer sys~era. A ce r - eals s tress conccntration was observed in the ccx',rse crushed stone measuring 25-70 mm ~ r the .~enter of the plate (Fig. 4).

In order to study the stress distribution beyond the limits of the plate in the b o m ~ ~ halfsp~Ceo • e plate, after the stresses were measured along the ~ l s , was moved to a new/x~si~o~ La s ~ h a way that Ra cen ter shifted 10 em from the verticaY where the strain gauges were placed° In this ca.~¢ ~ e stress* measurements were taken at 20, 30, 40 and 50 cm from the center of the plate. The maximum distance was assumed to be not less than the plate diameter,

• Computation of stresses and displacemenh~ at ~ho footing of the structure, cax~sing tm~orm vertit~a! pres- sure In soil ou circular area, Collection He. 55 Nil |om~datlons. Stroiizdat, Ie.GG4.

391

The eu~'es ~in!ng potnt~ with equal stresses were plotted for the homogeneous half apace on the basis of t~st re:,ults (Fig. 5).

The following conclusions were re~tched on the ba~Is of performed tests=

I , The vertical stress distribution pattern arrived at ~ a result of experimeuts in the homogeneotm sand)' soil coincides with the theoretlcel stress dtstrlbutioa for elastic homogeneous hail'space.

2, The crushed stone layers o; two-layer syetemsandeoi1[s have the same distributing ability.

~92