CE 353 Geotechnical Engineering Dr M. Touahmia Touahmia
11
Compressibility Compressibility of Soil
Lecture Outlines: 1.
Introduction
2.
Elastic Se Settlement
3.
Consolida idatio tion Sett Settle lem ment
4.
OneOne-Di Dime mens nsio iona nall Labo Labora rato tory ry Con Conso solid lidati ation on Test est
5.
Void Ratio – Pressure Pressure Plots
6.
Norm Normall ally y Cons Consol olid idate ated d and and Over Overco cons nsol olida idated ted Soils Soils
7.
Calcu Calcula latio tion n of of Settle Settleme ment nt fro from m 1-D Pri Prima mary ry Cons Consol olid idati ation on
8.
Secondary Co Consolid lidation ion
9.
Time ime Rate Rate of Con Consoli solida dati tio on
Textbook: Braja M. Das, "Principles of Geotechnical Chapter 11). Ge otechnical Engineering", 7 th E. ( Chapter
Introduction •
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Structures are built on soils. They transfer loads to the subsoil through the foundations. The effect of the loads is felt by the soil normally up to a depth of about four times the width of the foundation. The soil within this depth gets compressed due to the imposed stresses. The compression of the soil mass leads to the decrease in the volume of the mass which results in the settlement of the structure. The settlement is defined as the compression of a soil layer due to the loading applied at or near its top surface.
The total settlement of a soil layer consists of three parts: 1. Immediate or Elastic Settlement (Se): caused by the elastic deformation of dry soil and of moist and saturated soils without change in the moisture content. 2. Prima Primary ry Cons Consoli olida dati tion on Sett Settle leme ment nt (Sc): volume change in saturated cohesive soils as a result of expulsion of the water that occupies the void spaces. 3. Second Secondary ary Con Consoli solidat dation ion Set Settle tlemen mentt (Ss): volume change due to the plastic adjustment of soil fabrics under a constant effective stress (creep).
S S S S T
e
c
s
Elastic Settlement
Defined as settlement which occurred directly after the application of a load (weight of the foundation), without a change in the moisture content. This is why the elastic settlement is also called immediate settlement.
The magnitude of the contact settlement will depend on the flexibility of the foundation and the type of soil. 2 1 s For perfectly flexible foundation: S e B I s I f
E s
For rigid foundation: S e rigid 0.93S e flexible , center
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= net = net
applied pressure
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At center: = 4, B' = B/2 B/2
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I s = shape = shape factor (Steinbrenner, 1934) 1 2 F F 1 F 1 & F & F 2: given in Table 1 & Table 2 s
1
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At corner: = 1 , B' = B μs = Poisson’s ratio Poisson’s ratio of soil E s = average modulus of elasticity measured from z from z = = 0 to about z about z = = 4 B
E E z z s
si
i
2
s
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for center: m’ = L/B, n’ = H/(B/2) = H/(B/2) for corner: m’ = L/B, n’ = H/B = H/B
I f = depth factor (Fox, 19482), Table 3.
Elastic Settlement Table 1: Variation of F 1 with m’ and and n’
Elastic Settlement Table 1: Variation of F 2 with m’ and and n’
Elastic Settlement Table 3: 3 : Variation Variation of I f with L/B and D f /B
Table 4: Representative Values of Poisson’s Poisson’s Ratio of soil
Table 5: Representative Values of the Modulus of Elasticity of Soil
Consolidation Settlement •
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Consolidation settlement
is the vertical displacement of the surface corresponding to the volume change in saturated cohesive soils as a result of expulsion of the water that occupies the void spaces. Consolidation settlement will will result, for for example, example, if a structure structure is built over a layer of saturated clay or if the water table is lowered permanently in a stratum overlying a clay layer. layer.
When a saturated clay is loaded externally, externally, the pore water pressure in the clay will increase. Because the coefficients of permeability of clays are very low, it will take some time for the excess pore water pressure to dissipate and the stress increase to be transferred to the soil skeleton gradually. Consolidation
is the time-dependent settlement of soils resulting from the expulsion of water from the soil pores. The rate of escape of water depends on the permeability of the soil.
Consolidation Settlement Consolidation of sand •
Permeability of sand is high
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Drainage occurs almost instantaneously – instantaneously – The The settlement is IMMEDIATE. IMMEDIATE.
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Elastic and consolidation processes cannot be isolated.
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Primary Consolidation is incorporated in the elastic parameters.
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Coarse-grained soils DO NOT undergo consolidation settlement due to relatively high hydraulic conductivity compared to clayey soils. Instead, coarse-grained soils undergo IMMEDIATE settlement.
Consolidation Settlement Consolidation of clay •
Permeability of clay is low
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Drainage occurs slowly – slowly – therefore, therefore, the settlement is DELAYED. DELAYED.
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Settlement can be separated (elastic, primary and secondary consolidation).
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Clayey soils undergo consolidation settlement not only under the action of “external” loads (surcharge loads) but also under its own weight or weight of soils that exist above the clay (geostatic loads). Clayey soils also undergo settlement when dewatered (e.g., ground water pumping) – because the effective stress on the clay increases.
Consolidation Settlement •
The time-dependent deformation of saturated clayey soil best can be understood by considering a simple model that consists of a cylinder with a spring at its ce nter:
(Undrained clay in short term)
(drained sand in short term)
During consolidation, pore water or the water in the voids of saturated clayey soils gets squeezed out – reducing the volume of the soil – hence causing settlement called as consolidation settlement.
Consolidation Settlement •
Variation of total stress, pore water pressure, and effective stress in a clay layer lay er drained at top and bottom as the result of an added stress, :
(a)
+ + u
(c) At time 0 t •
(b) At At time = 0
(d) At time =
During consolidation , remains remains the same, u decreases (due to drainage) while ’ ’ increases, transferring the load from water to the soil.
One-Dimensional Laboratory Consolidation Test •
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The characteristics of a soil during one-dimensional consolidation or swelling can be determined by means of the oedometer test. The main purpose of consolidation tests is to obtain soil data which is used in predicting the rate and amount of settlement of structures structures founded on clay. clay. 1. Plac Placee samp sample le in ring ring 2. Apply lo load 3. Meas Measur uree hei heigh ghtt cha chang ngee 4. Repe Repeat at for for new new load load..
Before
After
One-Dimensional Laboratory Consolidation Test •
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Oedometer Oedomet er Test Test
The oedometer test is used to investigate the 1-D consolidation behaviour of finegrained soils. An undisturbed soil sample 20 mm in height and 75 mm in diameter is confined in a steel confining ring and immersed in a water bath. It is subjected to a compressive stress by applying a vertical load, which is assumed to act uniformly over the area of the soil sample. Several increments of vertical stress are applied usually by doubling the previous increment. Two-way drainage is permitted through porous disks at the top and bottom. The vertical compression of the soil sample is recorded using highly accurate dial gauges. For each increment, the final settlement of the soil sample as well as the time ti me taken to reach the final settlement is recorded.
One-Dimensional Laboratory Consolidation Test •
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The compression of soil is possible only when there is an increase in effective stress which in turn requires that the void ratio of the soil be reduced by the expulsion of pore water. water. After a few seconds, the pore water begins to flow out of the voids. This results in a decrease in pore water pressure and void ratio of the soil sample and an increase in effective stress. As a result, the soil sample settles sett les as shown in the figure:
+ u +
One-Dimensional Laboratory Consolidation Test •
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The main purpose of consolidation test is to obtain soil properties which are used in predicting the rate and amount of consolidation settlement of structures founded on clay. The most important soil properties determined by a consolidation test are: – The pre-consolidation stress ( c’ ), This is the maximum stress that the soil has been subjected in the past. – The compression index (C c), which indicates the compressibility of a normallyconsolidated soil. – The swelling index (C s), (recompression index, C r ), which indicates the compressibility of an over-consolidated soil. – The coefficient of consolidation (C ( C v), which indicates the rate of compression under a load increment.
One-Dimensional Laboratory Consolidation Test •
The general shape of the plot of deformation of the specimen against time for a given load increment is shown below. From the plot, we can observe three distinct stages:
Mostly caused by preloading
Excess pore water pressure is gradually transferred into effective stress by the expulsion of pore water
Occur after complete dissipation of the excess pore water pressure, this is caused by the plastic adjustment of soil fabric
Void Ratio – Pressure Pressure Plots •
The step-by-step procedure for getting the void ratio-pressure relationship is as follows:
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Step 1: Calculate the height of solids, H solids, H s from:
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Step 2: Calculate the initial height of voids as:
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Step 3: Calculate the initial void ratio, eo:
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Step 4: For the first incremental loading 1 calculate the change in the void ratio as: Step 5: Calculate the new void ratio after consolidation: For the next loading, 2, the void ratio at the end of consolidation: At this time, 2 = 2’ . Specimen area = A
Void
Solid
Void Ratio – Pressure Pressure Plots •
The effective stress ’ ’ and and the corresponding void ratios e at the end of consolidation are plotted on semi-logarithmic graph:
In the initial phase, relatively great change in pressure only results in less change in void ratio e. The reason is part of the pressure got to compensate the expansion when the soil specimen was sampled. In the following phase e changes at a great rate
Normally Consolidated and Overconsolidated Soils •
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Normally Consolidated Soil: Soil: A soil that has never experienced a vertical effective stress that was greater than its present vertical effective stress is called a normally consolidated (NC) soil. Overconsolidated Soil: A Soil: A soil that has experienced a vertical effective stress that was greater than its present vertical effective stress is called an overconsolidated (OC) soil. When the effective pressure on the specimen becomes greater than the maximum effective past pressure, the change in the void ratio is much larger, and the e – log log ’ relationship is practically linear with a steeper slope (b (b to c to c)) or ( f to g to g ). ). This relationship can be verified in the laboratory by loading the specimen to exceed the maximum effective overburden pressure, and then unloading and reloading again (c ( c – d – d – – f f – – g g ). ).
Normally Consolidated and Overconsolidated Soils •
Preconsolidation pressure: the maximum effective past pressure, which can be determined as follow (Casagrande , 1936): 1. Esta Establ blis ish h poi point nt a, a, at which which the the e – log log ’ ’ plot plot has a minimum radius of curvature. 2. Draw Draw a hor horizo izont ntal al line line ab. ab. 3. Draw Draw the the lin linee ac ac tan tange gent nt at a. 4. Draw Draw the line line ad, ad, which which is is the bise bisecto ctorr of the the angle angle bac. bac. 5. Proj Projec ectt the str straig aight ht-l -lin inee portio portion n gh of gh of the e – log log ’ plot back to intersect line ad at f at f . The abscissa of point f point f is is the preconsolidation pressure, c ’.
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The overconsolidation ratio : OCR
c
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The OCR for an OC soil is greater than 1.
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Most OC soils have fairly high shear strength.
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The OCR cannot have a value less than 1.
c’ = ’ =
preconsolidation pressure
effective vertical pressure
Normally Consolidated and Overconsolidated Soils
Consolidation characteristics of of normally consolidated clay of low to medium sensitivity
Consolidation characteristics of overconsolidated clay of low to medium sensitivity
Calculation of Settlement from One-Dimensional Primary Consolidation •
Because of an increase of effective pressure, s, let the primary settlement be Sc. Thus, the change in volume can be given by:
Soil
Void •
For normally consolidated clays, that exhibit a linear e – log log ’ ’ relationship:
Solid
Calculation of Settlement from One-Dimensional Primary Consolidation •
For normally consolidated clays:
Compression index C c = slope of the e – log log ’ ’ plot plot Skempton (1944) suggested: C c = 0.009( LL-10) LL-10) •
For overconsolidated consolidated clays: clays:
If c then: Swell index C s = slope of the rebound curve 1 1 C C to C 10 5 s
If c then:
c
c
Secondary Consolidation •
It is the settlement due to plastic compression arising out of readjustment of soil particles at constant effective stress. It occurs after primary consolidation consolidation settlement.
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the secondary compression index can be defined as: a s:
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The magnitude of the secondary consolidation can be calculated as:
Time Rate of Consolidation •
Terzaghi(1925) derived the time rate of consolidation based on the following assumptions: 1. homoge homogeneo neous us clay-w clay-wate aterr system; system; 2. 3. 4. 5. 6.
com complet pletee satu satura rati tion on;; zero zero compre compressi ssibili bility ty for wate water; r; zero zero compre compressi ssibili bility ty for solid solid grains grains;; Onene-D flo flow; w; Darcy’s law is valid
Time Rate of Consolidation •
Variation ariat ion of o f U z with T with T v and z and z / H H dr :
Time Rate of Consolidation •
Variation of average degree of consolidation U with with time factor, T v (uo constant with depth):
Time Rate of Consolidation •
Table 6: Variat Variation ion of o f T v with U :
Time Rate of Consolidation •
Coefficient of consolidation (C (C v) Log-of-Time Method (Cassagrande) 1. Extend Extend the the straigh straightt line line porti portion on of of prima primary ry and secondary consolidation curve to intersect at A. A is d 100, the deformation at the end of consolidation. 2. Select times t 1 and t 2 on the curve such that t 2 = 4t 4t 1. Let the difference is equal to x. 3. Draw Draw a hori horizon zonta tall line line (DE) (DE) such such that that the vertical distance BD is equal to x. The deformation of DE is equal to d 0. 4. The The ordi ordinat natee of point point F repre represen sents ts the the deformation at 50% primary consolidation, and it abscissa represents t 50. 5. For 50% 50% ave avera rage ge degr degree ee of of conso consolid lidati ation on,, T v = 0.197 (see Table 6), so:
T 50
C t
v 50
H
2
dr
or
C v
0.197 H
2
dr
t
Time Rate of Consolidation •
Coefficient of consolidation (C (C v) Square-Root-of-Time Square-Root-of-Time Method (T (Taylor) aylor) 1. Draw Draw a line line AB AB throug through h the earl early y porti portion on of the the curve. 2. Draw Draw a line line AC AC such such that that OC = 1.15 1.15 OB. OB. The The abscissa of D which is the. intersection of AC and the consolidation curve, gives the squareroot-of-time for 90% consolidation. 3. For For 90% 90% cons consol olid idat atio ion, n, T 90 = 0.848 (see Table 6), so:
T 0.848 90
C t
v 90
H
2
dr
or
C v
0.848 H
2
dr
t
90
