4. COMPRESSIBILITY OF SOILS 4.1 INTRODUCTION i. Immediate … · 2014. 3. 8. · Soil...

Soil Mechanics-I(CENG-2202) Chapter 4 : Compressibility of soils

- 47 -

Department of Civil Engineering, Faculty of Technology

Addis Ababa University

4. COMPRESSIBILITY OF SOILS 4.1 INTRODUCTION Foundations of structures usually rest on soil. Due to the additional stress introduced by a foundation or due to other loadings, a soil mass will compress. This compression is a sum of different and distinct processes:

a. Deformation of soil particles b. Relocation of soil particles, and c. Expulsion of water or air from the void spaces

In general, soil settlement caused by different loadings can be categorized into three categories: i. Immediate settlement (or elastic settlement) Such a settlement is caused by the elastic deformation of dry soil and of moist and saturated soils without any change in the moisture content. Immediate settlement calculations are generally based on equations derived from the theory of elasticity. ii. Primary consolidation settlement The volume of saturated soils under pressure will decrease due to the expulsion of water from the void spaces. The associated settlement is known as primary consolidation settlement. It is usually the predominant type of settlement in fine grained soils, especially in clays. iii. Secondary consolidation settlement This type of settlement is observed in saturated cohesive soils and is the result of the plastic adjustment of soil fabrics. If follows primary consolidation settlement when soil is under a constant effective stress. The total settlement of a foundation can then be given by

ST = Sc + Ss + Se where ST = total settlement Sc = primary consolidation settlement Ss = secondary consolidation settlement Se = immediate settlement The total settlement obtained in this fashion must be within acceptable limits for any structure. For most practical purposes, the magnitude of the elastic settlement can be ignored compared to the consolidation settlements. Discussion here shall hence be limited to consolidation settlement. But it must be noted that the volume change due to expulsion of air is treated in geotechnical engineering under the title compaction characteristics of soils. Prior to discussion of soil settlements, discussing the nature of stresses in soils must be presented. It is due to stresses that soils undergo settlements.


- 48 -



4.2 EFFECTIVE STRESS Stresses in a soil mass may be caused by the self weight of the soil, and also by the external loads which may be applied to the soil. The pattern of stresses caused by the external loads is usually a complicated one, and the same may be the case for stresses induced by self weight of soil. However, there is one common situation in which the self weight of the soil gives rise to a very simple pattern of stresses-that is when the ground surface is horizontal and the nature of soil does not vary significantly in the horizontal direction. The stress caused in such a situation at a point in a soil mass is called the geostatic stress. However, if external loading contributes to this stress, the stress will simply be called as the total stress. In the geostatic situation, there cannot occur any shear stresses upon the vertical and horizontal planes within the soil. Hence, the vertical geostatic stress, say σz, may be computed simply by considering the weight of soil and weight of water above that depth.

In the figure above a soil column is standing with no seepage allowed. The total stress at the elevation of point A can be obtained from

( ) satAw HHH γγσ −+= This total stress can be divided into two parts

1. Effective stress or intergranular stress, σ’ – the sum of the vertical components of the forces developed at the points of contact of the solid particles per unit cross-sectional area of the soil mass.

2. Pore water pressure or neutral stress, u – a portion carried by water in the continuous void spaces. This portion acts with equal intensity in all directions.

A


- 49 -



The total stress can thus be rewritten as u+= 'σσ

or u−= σσ '

Substituting the values for the total stress and the pore water pressure into this equation

Hence, it can be easily stated that the effective stress at a point in a soil mass will be equal to its submerged unit weight multiplied by the depth of soil mass up to the considered point. The effective stress principle is arguably the most important principle in geotechnical engineering. The compressibility and shearing resistance of a soil depend to a great extent on the effective stress. Thus the concept of effective stress is significant in solving geotechnical engineering problems, such as lateral earth pressure on retaining structures, the load bearing capacity and settlement of foundations, and the stability of earth slopes. 4.3 CONSOLIDATION SETTLEMENT When a clayey soil is subjected to loading, elastic settlement occurs immediately. If the loading continues, then its volume goes on compressing gradually due to removal of water from the pores. This major compression, which goes on for months and years, is the consolidation, and strictly called the primary consolidation. During this process, the transfer of load from the soil pores to the soil grains takes place. Due to this gradual transfer of the excess hydrostatic pressure from the water to the soil solids, a change in the initial structure of the soil mass (plastic adjustment of soil fabric) may occur, which may cause some compression, called secondary compression or secondary consolidation. The time-dependent deformation of saturated clayey soil can best be understood by considering a simple model that consists of cylinder with a spring at its center and filled with water. Three cases may be observed.

a. Place a load, P, on the spring and keep the valve closed. There will be no deformation of the spring in this case. The excess hydrostatic pressure at this time can be given as

APu =∆

b. If the valve is opened, the water will flow outward. This flow will be accompanied by a reduction of the excess hydrostatic pressure and an increase in the compression of the spring. If Ps and Pw denote portions of P carried by the spring and the water respectively, after valve opening

Ps > 0 and Pw < P, i.e. APu


- 50 -



c. Finally the excess hydrostatic pressure dissipates, and the system will reach a state of equilibrium, and thus Ps = P and Pw = 0 These equations mean that after the excess pore water pressure dissipates the additional stress P will be carried by the soil skeleton, i.e. 'σσ =∆


- 51 -



One-dimensional laboratory consolidation test The process of consolidation settlement is studied in the laboratory by the one-dimensional consolidation test. This test is performed in a consolidometer (sometimes referred to as an oedometer). The schematic diagram of a consolidometer is shown below.

The soil specimen is placed inside a metal ring with two porous stones, one at eh top of the specimen and another at the bottom. The specimens are usually 64mm in diameter and 25mm thick. The load on the specimen is applied through a lever arm, and compression is measured by a micrometer dial gauge. The specimen is kept under water during the test. Each load is usually kept for 24 hours. After that, the load is usually doubled, which doubles the pressure on the specimen, and the compression measurement is continued. At the end of the test, the dry weight of the specimen is determined. From load and deformation values, a plot of deformation versus time for a given load increment is prepared.


- 52 -



Form this plot; we can observe three distinct stages, which may be described as: Stage I Initial compression, which is caused mostly by preloading Stage II Primary consolidation Stage III Secondary consolidation After time-deformation plots for various loadings are obtained in the laboratory, it is necessary to study the change in the void ratio of the specimen with pressure. The procedure is described as follows:

1. Calculate the height of solids, Hs, in the specimen using the equation

Solid

Specimen area =A


- 53 -



2. Calculate the initial height of voids as

Hv = H – Hs 3. Calculate the initial void ratio, eo, of the specimen

4. For the first incremental loading, σ1, which causes a deformation ∆H1, calculate the change in

void ratio as

sHHe 11

∆=∆

5. Calculate the new void ratio after consolidation caused by the pressure increment as e1 = eo – ∆e1

For the next loading, σ2 (that equals the cumulative load per unit area of the specimen), which causes additional deformation ∆H2, the void ratio at the end of consolidation can be calculated as

sHHee 212

∆−=

At this time, total stress σ2 = effective stress, σ’2. Proceeding in a similar manner, one can obtain the void ratios at the end of the consolidation for all load increments. The effective stress and the corresponding void ratios (e) at the end of consolidation are plotted on semi logarithmic graph paper. The typical shape of such a plot is shown below.


- 54 -



This figure shows that the upper part of the e-log σ’ plot is somewhat curved with a gentle slope, followed by a linear relationship for the void ratio with log σ’ having a steeper slope. This is an important phenomenon that required further explanation. A soil in the field at some depth has been subjected to a certain maximum effective past pressure in its geologic history. This maximum effective past pressure may be equal to or less than the existing effective overburden pressure at the time of sampling. The reduction of effective pressure in the field may be caused by natural geologic processes or human activities. During sampling, the existing effective overburden pressure is also released, which results in some expansion. When this specimen is subjected to a consolidation test, a small amount of compression (i.e. a small change in void ratio) will occur when the effective pressure applied is less than the maximum effective overburden pressure in the field to which the soil has been subjected to in the past. When the effective pressure on the specimen becomes greater than the maximum effective past pressure, the change in void ratio is much larger, and the e-log σ’ relationship is practically linear with a steeper slope. This relationship can be verified in the lab by loading the specimen to exceed the maximum effective overburden pressure, and then unloading and reloading again. The e-log σ’ plot for such cases is shown below, in which cd represents the unloading and dfg represents the reloading process.

This discussion leads to two basic definitions of clay based on stress history:

1. Normally consolidated clays, whose present effective overburden pressure is the maximum pressure that the soil was subjected to in the past

2. Overconsolidated clays, whose present effective overburden pressure is less than that which the soil experienced in the past. The maximum effective past pressure is called the preconsolidation pressure.


- 55 -



The preconsolidation pressure can be obtained from the e-log σ’ plot following the procedure suggested by Casagrande.

i. By visual inspection, establish point a, at which the e-log σ’ plot has a minimum radius of curvature

ii. Draw horizontal line ab iii. Draw the line ac tangent to the curve at a iv. Draw the line ad, which is the bisector of the angle bac v. Project the straight-line portion gh of the plot back to intersect line ad at f. The abscissa of point f

is the preconsolidation pressure, σ’c

The overconsolidation ratio (OCR) for a soil can now be defined as

''

σσ cOCR =

where σ’c = preconsolidation pressure of a specimen σ’ = present effective vertical pressure Settlement calculation from one-dimensional primary consolidation


- 56 -



Let us consider a saturated soil layer of thickness H and cross sectional area A under an existing average effective overburden pressure σ’o. Because of an increase of effective pressure, ∆σ’, let the primary consolidation settlement be Sc. Thus the change in volume can be given by ∆V = Vo – V1 = HA – (H –Sc) A = ScA But the volume change is due to the change in the volume of voids, ∆Vv ∆Vv = ∆eVs But, the volume of solids

oo

os e

AHe

VV+

=+

=11

Thus

∆V = ScA = ∆eVs = eeAH

o

∆+1

or

Sc = oe

eH+∆

1

For normally consolidated clays that exhibit a linear e-log σ’ relationship ∆e = Cc [ log (σ’o + ∆σ’) - log σ’ ] Where Cc is the slope of the e-log σ’ plot and is defined as the compression index. Substitution of this value into the equation of Sc yields

Sc = ⎟⎟⎠

⎞⎜⎜⎝

⎛ ∆++ o

o

o

c

eHC

'''log

1 σσσ

In overconsolidated clays, for σ’o + ∆σ’ ≤ σ’c, the slope of the plot is defined as the swell index, Cs. Hence,

Solid

Soil


- 57 -



∆e = Cs [ log (σ’o + ∆σ’) - log σ’ ] The settlement would then be

Sc = ⎟⎟⎠

⎞⎜⎜⎝

⎛ ∆++ o

o

o

s

eHC

'''log

1 σσσ

If σ’o + ∆σ’ > σ’c, then

Sc = ⎟⎟⎠

⎞⎜⎜⎝

⎛ ∆++

+⎟⎟⎠

⎞⎜⎜⎝

⎛+ c

o

o

c

o

c

o

s

eHC

eHC

'''log

1''log

1 σσσ

σσ

However, if the e-log σ’ curve is available, one can simply pick ∆e off the plot for the appropriate range of pressures. This number may be substituted directly into the equation of Sc. Several empirical relations have also been suggested for Cc and Cs. The common formulae for clays are the following. Cc = 0.009 (LL-10)

Cs = sGLL

⎥⎦⎤

⎢⎣⎡

100(%)0463.0

SECONDARY CONSOLIDATION SETTLEMENT We have noted earlier that at the end of primary consolidation settlement some settlement is observed due to the plastic adjustment of soil fabrics. This stage of consolidation is called secondary consolidation. During this phase the plot of deformation against the log of time is practically linear. The variation of the void ratio, e, with the time t for a given load increment is shown below.

From this figure, the secondary compression index, Cα, can be defined as


- 58 -



⎟⎠⎞⎜

⎝⎛∆

=−∆

=

1

212 logloglog tte

tteCα

The magnitude of the secondary consolidation can be calculated as

⎟⎠⎞⎜

⎝⎛=

1

2log' ttHCSs α

where Pe

CC+

=1

' αα

eP = void ratio at the end of primary consolidation H = thickness of clay layer The values of C’α as observed in various natural deposits are as follows:

• Overconsolidated clays = 0.001 or less • Normally consolidated clays = 0.005 to 0.03 • Organic soil = 0.04 or more

Secondary consolidation settlement is more important than primary consolidation settlement in organic and highly compressible inorganic soils. In overconsolidated inorganic clays, the secondary compression index is very small and of less practical significance.

4. COMPRESSIBILITY OF SOILS 4.1 INTRODUCTION i. Immediate … · 2014. 3. 8. · Soil...

Documents

Transcript of 4. COMPRESSIBILITY OF SOILS 4.1 INTRODUCTION i. Immediate … · 2014. 3. 8. · Soil...