4. Compression and Consolidation of Soils 101
4.2 Compressibility Characteristics
The settlement is mainly dependent on the compressibility of soils and the loading. The reasons that induce settlement are as follows:
(1) External influencing factors:
a. The loading from building b. The drop in ground water level
c. The influence of construction d. The influence of vibrations
e. The change of temperature (2) Internal influencing factors:
a. The compressibility of solid phase b. The compressibility of liquid phase
c. The compressibility of void
As regards external factors, loading from buildings is the domi- nant factor, which causes compression of voids of soil. The process of the increase of the compression of saturated soil with time is called consolidation.
Settlement mainly includes two aspects: one is the total set- tlement; the other is the relationship of settlement and time.
To determine the settlement, the compressibility index must be determined, which can be obtained from the compression test of the field in situ test.
4.2.2 Oedometer test
Figure 4.1 depicts a schematic diagram of how an oedometer test is conducted. Consolidation settlement is the vertical displacement of the surface corresponding to the volume change at any stage of the consolidation process. The characteristics of a soil during one- dimensional consolidation or swelling can be determined by means of the oedometer test. Figure 4.1 shows a cross-section diagram through an oedometer. The confining ring imposes a condition of zero lateral strain on the specimen.
Depending on the ΔH–p relationship, thee–pcurve is obtained, which indicates the change of void under varying pressure.
Figure 4.2(a) shows the e–p relationship. It can also be plotted in a logarithmic scale (see Fig. 4.2(b)). For the different soil types, the deformations are different. For sands, thee–pcurve is flat, which indicates that the void ratio decreases slowly as pressure increases.
Load
Porous stone
Water Confining ring Specimen
Porous stone
Fig. 4.1. Oedometer test.
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(a) (b)
Fig. 4.2. Relationship between void ratio and effective stress. (a) e–p and (b)e–lgp.
Fig. 4.3. Thee–pcurve for soil.
For clay, the curve is steep, which means the void ratio decreases significantly as the pressure increases. For clay, the curve is steep, which means that the void ratio decreases significantly as pressure increases. The results also indicate that the compressibility of clay is greater than that of sand.
Three compressibility indexes can be determined from the com- pression curve, i.e., compression coefficient a, compression index Cc, oedometric modulus Es.
(1) Compression coefficient, a
a=−de
dp, (4.1)
where negative sign indicates that e decreases with an increase inp. As the change in the range of pressure induced by external loading is small, e.g., fromp1top2(see Fig. 4.3), the curveM1M2
can be approximately regarded as linear. The slope of the line is give as follows:
a= Δe
Δp = e1−e2
p2−p1. (4.2)
The compression coefficient a represents the decreased value of void ratio under unit pressure. So the larger the value of a, the larger the compressibility of soils.
It should be noted that a is not a constant for a certain soil type. In order to facilitate the comparison and the application of different regions, Code for Design of Building Foundation (GB50007-2011), China, takes a1−2 corresponding to p1 = 100 kPa and top2= 200 kPa to evaluate the compressibility:
a1−2<0.1 MPa−1 low compressibility soil, 0.1 MPa−1 ≤a1−2<0.5 MPa−1 medium compressibility soil,
a1−2≥0.5 MPa−1 high compressibility soil.
(2) Compression index, Cc
The compression index (Cc) is the slope of the linear portion of the e–lgp plot (see Fig. 4.4) and is dimensionless. For any two points on the linear portion of the plot,Cc is given as follows:
Cc= e1−e2
lgp1−lgp2 = e1−e2 lg(pp2
1) . (4.3)
Fig. 4.4. Calculation ofCc ine–lgp.
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Similar to the compression coefficient, the value of Cc can also judge the compressibility. The larger the value of Cc, the larger the void ratio is and the larger compressibility is. Generally, if Cc < 0.2, the soil belongs to the low compressibility soil type;
ifCc = 0.2–0.4, the soil is the medium compressibility soil type;
and ifCc >0.4, soil is the high compressibility soil type.
(3) Oedometric modulus,Es
The ratio of the incremental vertical stress σz to stress λz is called oedometric modulusEs:
Es = σz
λz. (4.4)
In the above oedometer test, vertical pressure increases fromp1 to p2, and the height decreases fromh1 to h2, simultaneously.
Incremental stress: σz =p2−p1. Incremental strain: λz = h1−h2
h1 . (4.5)
Oedometric modulus: Es= p2−p1 h1−h2h1.
(4) Relationship of oedometric modulus and compression coefficient Both oedometric modulus and compression coefficient are com- monly used to express the compressibility of ground in civil engineering. They are determined by the oedometer test. So they are dependent on each other.
The compression of soil layers is schematically shown in Fig. 4.5. The area of soil sample is a unit area. At the start
(a) (b)
Fig. 4.5. Schematic diagram of compression of soil layers. (a) Initial state and (b) compression state.
of compression, the volume of solids is Vs, and the volume of voids is Vv0. Taking Vs = 1, the void ratio is e0 =Vv0 and the total volume is 1 +e0 (see Fig. 4.5). At the end of compression, the volume of the solid Vs remains constant and the volume of voids reduces toVv1. The void ratio ise2 =Vv2 (see Fig. 4.5). So
λz = Vv0−Vv1
Vv0 = h0−h1
h0 = e0−e1
1 +e0 , (4.6) Es= σz
λz
p2−p1
e0−e1(1 +e0) = 1 +e0
a . (4.7)
It can be found from Eq. (4.7) thatEsis inversely proportional to a. The largerEsis, the smaller ais, which means the compressibility is smaller. In practice, if Es < 4 MPa, the soil belongs to the high compressibility soil type, if 4 MPa≤Es≤20 MPa, the soil belongs to the medium compressibility soil type, and if Es > 20 MPa, the soil belongs to the low compressibility soil type.
The compression of soil specimen under pressure is measured by means of a dial gauge operating on the loading cap. The void ratio (e) at the end of each increment period can be calculated from the dial gauge readings (s). The phase diagram is also shown in Fig. 4.5, and the calculation is done as follows:
h0A=Vv0+Vs= (1 +e0)Vs, (4.8) (h0−s)A=Vv1+Vs= (1 +e1)Vs, (4.9)
Vs = h0A
1 +e0 = (h0−s)A
1 +e1 , (4.10)
e1 =e0− s
h0(1 +e0), (4.11) s=e0−e1
1 +e0 h0, (4.12)
εv =εz = s h0
=e10−e1
1 +e0 = Δe
1 +e0, (4.13)
whereh0 is the thickness of the specimen at the start of the test and e0 is the void ratio of the specimen at the start of the test, which
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can be determined as follows:
e0= ds(1 +w0)ρω
ρ0 −1, (4.14)
where h1 and e1 are the thickness and void ratio at the end of any increment period, respectively, A is the area of the specimen, and s is the compression of the specimen under pressure p.
The coefficient of volume compressibility mv is defined as the volume change per unit volume per unit increase in effective stress.
If for an increase in effective stress from σ0 to σ1, the void ratio decreases frome0 to e1, then
mv = εv
Δσ = Δe
(1 +e0)Δσ = 1 1 +e0
e0−e1 σ1 −σ0
. (4.15)
The unit of mv is the inverse of pressure (m2/MN).
If mv and Δσ are assumed constant with respect to depth, then the one-dimensional consolidation settlement (s) of the layer of thickness h0 is given by
s=mvΔσh0 (4.16)
or, in the case of a normally consolidated clay, s= Cclg(σ1/σ0)
1 +e0 h0. (4.17)