A D V I C E T O DESIGNERS
COMPUTING THE SETTLEMENT OF A FOUNDATION CONSTRUCTED IN A ~RENCH Z. G. Ter-Martir~syan, D. M. Akhpatelov, and E. A. Sorochan
UDC 69.059.22:624.15
The scheme used to compute foundation settlements by the method of layer-by-layer sum-mtlon contains a number of drawbacks [i], for example, softening of the soil during excavation of the trenches is disregarded. Methods of settlement computation are refined in [2-5]; for a number of reasons, however, they have not been used in practice. In the approved Construction Rules and Regulations [6], it is recommended that for a significant foundation-embedment depth, the settlement be computed with allowance for softening of the soil at a trench depth of 5 m and greater. A method of computing the settlement of a foundation built in an open trench, which corresponds more closely to the actual behavior of the bed, is presented below. Let us examine the stress-strain state of a foundation bed during the excavation of a trench, the subsequent installation of a foundation, and the erection of a structure, taking into account axial stresses in this case, i~e., holding true to one of the basic assumptions adopted in the Construction Norms and Regulations (SNIP). In this case, the pressure acting along the lower surface includes the active load, and also the weight of the foundation and the soil on its edges. As in all current norms, the backfill is disregarded. Curves of the initial pressure azg (Fig. I) (due to the weight of the soil itself) in the soil mass, the pressure ~ g after trench excavation, the pressures a'~gp after foundation installationand erection of the structure indicate that the bottom of the trench rises by the magnitude_ o zp,, = o zg -- a~~, which will hereafter be called the softening pressure, as a resuit of a reduction in Ozg. ~ It follows from the boundary conditions that the softening pressure against the bottom of the trench (z = 0) is equal to the initial pressure Ozg,o at this depth. Settlement of the foundation, which exerts a pressure p on the bed, will occur as a result of an increase in a~g by the magnitude Uzp = a~gp -- ~ g , which we will hereafter call the supplementary pressure. It is obvious that ~zp is summed from azp ,, = Ozg -- u~g and Oz. z = a~.. -- °z-, which we will call, respectively, secondary-consolidation and incomplete consolidation pressures. Let us examine the possibility of predicting the redistribution of the stressed state in a soil mass during trench excavation and subsequent erection of a structure. i.
The initial pressure ~zg = 7(z + D) for a homogeneous foundation bed and Ozg = t=-I
7ihi for a laminar bed, where 7 and 7i are the specific gravities of the soils of the homogeneous bed and i-th layer, respectively, D is the depth of the trench, which is equal to the depth d of foundation embedment, h i is the thickness of the i-th layer, n is its ordinal number, and z is the depth as measured from the bottom of the trench for which Ozg is computed h
(obviously.,
E ht----z -~D). /,ffi!
2. If the profile of the trench is described by a curvilinear boundary, the difference between the initial pressure and the pressure in the curvillnear semiinlflnite region having weight will be Ozp,, in conformity with the solution available in [7]. Consequently, the solutions of [7] make it possible to compute Ozp,, for the excavation of a trench in homogeneous linearly deformable sol1 masses. Consideration of the nonlinear deformability and laminar nature in determining UzD,, by engineering methods is not possible in this stage. Analysis of available solutions of various edge problems in the nonlinear statement indicates, however, that consideration of nonlinearity significantly affects the strain state of the soll ....... Moscow Civil-Engineerlng Institute. Scientific-Research Institute of Bases and Under- ...... ground Structures. Translated from Osnovaniya, Fundamenty i Mekhanika Gruntov, No. I, pp. 2022, January-February, 1985. 30
0038-0741/85/2201-0030509.50
© 1985 Plenum Publishing Corporation
C
~ /I
s
~,~., t,/
i
I
j.
. I~ ~., ~,~
|
/!1t, IZ
"
Z
Fig. i. Pressure curves, a) Initial; b) after trench excavation; c) after foundation installation and erection of structure. TABLE I Value o f a p w h e n
~q= LIB = !
E = z/D
[
¢p= B/D 0,5 O,O
0,5 1,0 2,0 4,0 8,0
1,000
0,478 0,262 0,113 O,025
0,001
I,OGO 0,540 0,340 O, 170 0,070 0,026
4
t,000
1,000 0,810
0,7C4 0,496 0,356 0,228
I,OQO
0.944 0,898 0,758
0,626 0,516
16
0,5
1,000
1,000 0,587 0,425
O,c~O 0,970 0,920 0,860 0,800
l,O00 0.660 0,500 0.360 0,240 0.160
0,276
0,190 O, 132
t,O00
0,725
0,590 0,426
0,293 O,180
1,000
0,780
0,660
0,500 0,340
0,212
t.000
1,000 0,900 0,820 0,710 0,520 0,370
0,970
0,94.6 0,886 0,768 0,630
l
16
1,000
0,984
0,974
0,968 0,920 0,854
¢~BID
I
1,000 t 0,960 1,000 0,890 0,800 0,916 0,652 0,820 0,436 0,610
0,276
1,C00 0,782 0,652 0,526 0,340 0,216
n=L/B>~ 12
12i4
0,5
lJ
$ = BiD 4
2
"q=LIB.-~6 ~-.~B/D
= zlD O,O 0,5 I,O 2,0 4,0 8,0
I
2 0,664 O,5CO 0,284 0,176 O,Ced
~=LIB=3
0,428
1,000
0,992 0,980
0,946 0,832 0,670
16
[
1,000 0,996 0,984 0,974 0,944 0,868
0,2
0,5
1,000 0,708
1,000 0,768 0,610 0,440 0,292 O, 170
0,536
0,374 0,250 O. 147
J
0,8 1,000
0,826 0,687 0,507 0,333 0,196
I
, 1,000 0,866 0,734 0,550 0,360 0,214
I s
I 21 1,000 0,956 0,864 0,696 0,462 0,280
1,000 0,990 0,956 0,840 0,634 0,432
1,000 0,996 0,990 0,964 0,848 0,676
t6
I,(~0 0,9~8 0,992
0,984 0,952 0,874
TABLE 2 Soil= a n d normalized values o f their Hquid
Values o f k = E 1,0/E2 f o r void ratio • e q u t l to
limit
e-.
0,75<1L < 1 1L < 0,25 0,25<1 L < 0,75 0,75
0,5
1,5 1.5 1.5 2.0 2.0 2.0 2.5
2,0 2.0
2,5
2,0
2,5
2,5 2,5
3,0 2,5
2,5 3,0
3,0 3,5
2,5
e>l,l
3,0 3,0 3,0 3,5 3,0 3,5 4,0
TABLE 3 Values o f k = E 1,0/E2 f o r • equal t o Soils Coar=e sand= Sands o f m e d i u m fmenem Fine sand= Silty sands
0,45
0.55
0.65
1,5 1,5
2,0 2,0
2,6 2,5
2,0 2,0
2,5 3,0
3,0 4,0
0,75 w
4,0 5.0
mass and has a minor effect on the stressed state. For engineering computations, it is therefore admissible to determine Ozp,x from solutions in the linear statement. Similar conclusions can also be drawn for laminar foundation beds. On the basis of analysis of the distribution of stresses computed in accordance with the solution in [7], Akhpatelov compiled Table i for determination of the coefficients ap, which take into account the variation of Ozp,x with depth, as a function of the relative depth ~ = z/D, the ratio of the sides of rectangular trenches n = L/B, and the ratio of trench width to depth ~ = B/D. The softening pressureat depth z is Ozp,t = apOzg,o. The coefficient of the lateral pressure of the soils 31
a
b
eI
\
\\\.,,\
c
Fig. 2. Deformation of soll when unloaded and loaded in void ratio e/stress ~ (a) and strain z/stress o (b) coordinates.
~8
.....
i//// ,/..///..////r////.////r/
~C
Fig. 3. Scheme for computation of foundation settlement. 1) Boundaries of i-th layer; DL) grade elevatlon; NL) natural ground llne; FL) elevatlon of lower surface of foundation; B, C) lower boundary of compressible stratum. in the natural state was assigned a value of 1 in Table i. As computations indicatep the scheme adopted by certain authors to determine the softening pressure as the application of negative loads in a half space, which is the basic computation of supplementary pressures, generates significant errors. F~r computations in accordance with this scheme, uzp,~ diminishes significantly more vigorously with depth. 3. Since the dimensions of foundations are usually smaller than the dimensions of the trench, the value of ~zp can be determined by analogy with Table 1 of Appendix 2 in Construction Norm and Regulatlon (SNIP) [6] using the coefficient u, which takes into account the variation In ~supplementary pressures with depth. In this case, azp at the depth d of foundation embedment, which can be assumed equal to the depth of the trench, is equal to the average actual pressure p beneath the lower surface of the foundation. Thus, Ozp = Up. Let us consider the process of soll deformation at an arbitrary depth z + D (Fig. 2). Deformations due to the initial pressure at the moment of trench excavation have already occurred. A pressure reduction at Ozp,~, which is caused by trench excavation~ results in softening of the soll at Cp, while subsequent application of the pressure Ozp = azp,~ + Ozp,~ due to the structure leads to secondary oonsolidation of the soil at ~by due to the pressure azp,z and to incomplete consolidation at cd due to the pressure azp,2 (Ep = Eby in Fig. 2).
32
TABLE 4 Trench
L,m
Foundation
B,m I D=d,m
l,m
20 I
Y,kN/m3 El, MPa
20 [
E~, MPa
E,MPa
10 10 10
10 10 10
8=. cm
!
10
>I0
b
2 I
0,5
20
I
120
Settlements
J
I
/~ m.[ p, MPa
|
120
Soil
10
>10 b
2
[
0,2
20
2O ,o
i
120
20 ]
5
>I0 b
2
0,5
20
60
20 l
3,3
2
2
0,3
20
2O
4,9 2,5 1,0
3,8 3,8
t Sd , ¢m I
]
8,7
6,3
3,8
4.8
2,0 4,0 8,0
0
2,0 4,0 8,0 ............
Sd , crfl
7,1 7,1 7,1
10 10 10
10 10 10
3,6 1,8 0,7
7,3 7,3 7,3
10,9 9,1 8,0
11,1 11,1 11,1
10 10
10 10
1,0 0,2
2,0
2,0
3,0
3,4 3,4
2,2
In the general case, the deformation process is nonlinear in nature and differs for unloading and loading. For engineering computations, it is expedient to approximate the nonlinear relationship between pressures and deformations by a piecewise-linear relationship. Inconformity with the law adopted, the soil is characterized by three compression moduli: Epz -- softening; E, z -- secondary consolidation; and E= z -- incomplete consolidation (Epz = E, z in Fig. 2), which can be determined from the results of laboratory tests under compression conditions (without lateral expansion). The soil is initially brought to the initial state by applying gzg- Stepwise unloading is then carried out at Czp,, , and later loading of the soil in steps at czp. Epz is found from the unloading branch, and E,z and E=z from the loading branch. To determine ~ z , it is possible to set ~ = i, assuming that Poisson's ratio ~ is close to zero during unloading. It should be noted that GOST 23908-79 calls for testing of the soil by its loading and repeated loading after unloading. It is also possible that the computed moduli can be determined by plate tests where their conduction and interpretation are improved. The compression moduli Epz = E,z of soils situated at a depth z are calculated from the equation
~g --kE=
E~=~z=E1,
o %D,r
~,
%p.1
(1)
where E,,o is the compression modulus of the soil, which corresponds to its complete unloading during plate or compression tests, and k is a coefficient equal to the ratio of the compression moduli for completeunloading and loading. Tables 2 and 3, which were compiled on the basis of plate tests, give values of k, respectively, for clayey and sandy soils. With their use, it is possible to compute E,z. A computational scheme to determine the ascent of the bottom of the trench and subsequent settlement of the founsation bed is proposed on the basis of what has been stated above (Fig. 3). It is recommended to determine the final (stabilized) settlement of the foundation by the method of layer summation in accordance with the equation s d = s, + s=, where s, and s= are the portions of the final foundation settlement due to secondary-consolidation and incomplete-consolidation pressures.
sl =
~i %p, l i hi ' EU
£1
(2)
£
(3)
8s --=
t=1
~t %#,2i h=E2i ",
n is the number of layers into which the compressible stratum of the foundation bed is divided over the depth, h i is the thickness of the i-th layer, Ozp zi and azp,= i are the average stresses of secondary consolidation and incomplete consolidatzon zn the ~-th layer, whlch is equal to half the sum of these stresses on its upper and lowerboundaries (when ~zp, z i, when ~z p > ~ z p , , - - z~p , = = ~ z p - - z~p , ~ " , and when ~z P ~-~ z p , 1 - - z p , = = ~zp-- ~z p,,i = ~z p,'" 0). Eli and Ezi are the compression moduli, which characterize the deformability of the i-th layer of soil within the limits of the average pressure of secondary and incomplete con33
solidatlon, and 81 is a coefficient dependent on the value of ~ for the i-th layer of soil. According to [6], the lower boundary of the comDresslble stratum (B.C) can be determlned from the point of intersection of the 0.2Ozg and Ozp curves. Since an increase in the thickness of the compressible stratum leads to a significantly smaller increase in foundation settlement in the proposed method than in the existing method [6], the role of B.C is diminished. The computational scheme that we are proposing also makes it possible to determine the ascent of the bottom of the trench from the equation
~
/=1
pj a=p,,i hi
(4)
EPl
where the designations are the same as those in (2) and (3). Refinement of the proposed computational scheme should consist in an improvement in the reliability of the reflection of the laws governing deformation within the limits of the secondary- and incomplete-consolidation pressures, for example, by consideration of the structural strength of the soils, which varies with depth. Settlements computed from the proposed sd and existing s' d computational schemes [6] are presented in Table 4. It follows from the table that discrepancies between the settlements may be significant, especially for deep foundations.
CONCLUSIONS I. The method presented in Construction Norm and Regulation (SNIP) 2.02.01-83 for the computation of foundation settlements does not take into account the effect of redistribution of the stress-strain state of the bed as a result of trench excavation, and does not therefore reflect the actual behavior of the bed beneath the structure. Thus, the settlement may be equal to zero, or even negative for a deep embedment. 2. The proposed computational scheme, which is based on expansion of the existing method by the supplementary construction of softening-pressure curves using attenuation factors obtained on the basis of theoretical solutions, makes it possible to compute settlements with allowance for bilinear deformability of bed soils, and the shapes and sizes of the trench and foundation. LITERATURE CITED i.
2. 3. 4~
5. 6. 7.
34
M . I . Gorbunov-Posadov and S. S. Davydov, "On the combined behavior of beds and strucures," General Papers Submitted at the Eighth International Congress on Soil Mechanics and Foundation Engineering [in Russian], Stroiizdat, Moscow (1973). V . A . Florln, Fundamentals of Soil Mechanics [in Russian], Vol. If, Gosstroiizdat, Leningrad-Moscow (1961). N . A . Tsytovlch, Soil Mechanics (A Brief Course) [in Russian], Vysshaya Shkola, Moscow (1983). B . I . Dalmatov, "Conditions for the development of swelling deformations in soils during trench e~eavation," in: Scientific Works of the Leningrad Civil-Engineerin~ Institute. Sol]Mechanics, Beds, and Foundations [in Russian],No.98 (1),Leningrad (1975). R . A . Tokar', "Allowance for active pressures in computing deep foundation beds," Gidrotekh. Stroit., No. 7, (1949). Construction Normand Regulation (SNIP) 2.02.01-83, Foundation Beds of Buildings and Structures [in Russian], Stroiizdat, Moscow (1984). Z.G. Ter-Martirosyan and D. M. Akhpatelov, Computation of the Stress--Strain State of Multiphase-soil Masses (An Educational Textbook) [in Russian], Mosk. Inzh. Stroit. Inst. im. V. V. Kuibyshev, Moscow (1982).
