Third Year Civil Soil Mechanics

Cairo University Faculty of Engineering

lecture 3 Soil Compressibility

Soil Compressibility Outline 1. Definitions 2. Parameters 3. Compressibility of Cohesionless Soils (Sand and Gravel) 4. Compressibility of Cohesive Soil 5. The oedometer Test for Compression Measurements 6. Swelling of Clay 7. Collapsibility of Sand

2009

Dr. Omar Y. Ezzeldine

1/12

Third Year Civil Soil Mechanics

Cairo University Faculty of Engineering

lecture 3 Soil Compressibility

1. Definitions Compressibility is the property through which particles of soil are brought closer to each other due to escape of air and/or water from voids under the effect of an applied pressure. Normally Consolidated Clay is a clay layer where the effective pressure is equal to the overconsolidation pressure. This means the presently acting effective pressure is the highest pressure it has been subjected to during its geological history. This clay will be highly compressible. Preconsolidated Clay or Overconsolidated Clay is a clay layer where the effective pressure is less than the overconsolidation pressure. This means that this clay has been, in the past, subjected to a higher pressure than the one presently acting. This clay will be of low compressibility. Under consolidated Clay is a clay layer where the effective pressure is higher than the overconsolidation pressure. This means that this clay has not "felt" yet of the total effective pressure it is currently subjected to.   Preconsolidation Pressure or overconsolidation pressure of a certain clay layer, is the largest pressure that has been acting on this layer during its geological history. Swelling Pressure is the pressure capable to maintain constant volume (or to bring back to original volume) of clay when subjected to water innundation and can be determined by the oedometer Collapsible Soil is a cemented sandy soil in dry condition. When this type of soil is submerged, it undergoes severe decrease in volume due to loss of cementation.

2009

Dr. Omar Y. Ezzeldine

2/12

Third Year Civil Soil Mechanics

Cairo University Faculty of Engineering

lecture 3 Soil Compressibility

2. Parameters Coefficient of Compressibility Definition Coefficient of Compressibility is the rate of change of void ratio (e) with respect to the applied effective pressure (p) during compression. Symbol and Equation av =

e

Δe Δp

av changes according to  stress level (po) Δe

Dimension

Δp

2 -1

[L F ] 1/MPa, cm2/kg, m2/t

p

po

Coefficient of Volume Compressibility Definition Coefficient of Volume Compressibility is the volume decrease of a unit volume of soil per unit increase of effective pressure during compression.

ΔV Δ Vs ΔV=Δe V Vo

eVs

Water

eVs

Water

Vs

Solids

V1 Vs

Solids Before Dimension

Symbol and Equations ⎛ ΔV ⎞ ⎛⎜ Δe V s ⎜ ⎟ Vo ⎟ ⎜⎝ (1 + e o )V s ⎜ mv = = ⎜ Δp ⎟ Δp ⎜ ⎟ ⎝ ⎠

2009

After

⎞ ⎟⎟ ⎠

=

1 (1 + eo )

⎛ Δe ⎜⎜ ⎝ Δp

av ⎞ ⎟⎟ = ⎠ (1 + e o )

Dr. Omar Y. Ezzeldine

[L2F-1] 2 2 1/MPa, cm /kg, m /t

3/12

Third Year Civil Soil Mechanics

Cairo University Faculty of Engineering

lecture 3 Soil Compressibility

Modulus of Elasticity Definition Modulus of Elasticity is the relationship between pressure in a certain direction and the resultant strain in the same direction. Symbol and Equation E=

p

Δp Δε

Linear  Elastic

Dimension

Δp

-2

[FL ] MPa, kg/cm2, t/m2

Non linear  Non Elastic

Δε

ε

Compression Index Definition Compression Index For a normally consolidated clay, the coefficient of compressibility is the slope of the linear relationship between void ratio(e) and log (p) where (p) is the applied effective pressure pressure. Symbol and Equation cc =

Δe Δ log p

e Normally  Consolidated

Over Consolidated

Dimensions

Δe

[Dimensionless]

Δ log(p) pc

2009

Dr. Omar Y. Ezzeldine

log (p)

4/12

Third Year Civil Soil Mechanics

Cairo University Faculty of Engineering

lecture 3 Soil Compressibility

3. Compressibility of Cohesionless Soils (Sand and Gravel) Cohesionless soils (sand and gravel) have higher permeability than cohesive soils (clay and silt). Under normal loading conditions, compressibility is immediate. 

p

Compressibility of cohesionless soils is lower than that of cohesive soils. Stress‐Strain curves of sands are as shown in figure. The relationship between stress and strain of sands is not linear and strains are not recoverable. However, because sand compression is small and immediate as compared to cohesive soils, elastic model could be used to represent sand compressibility.

E1

Dense  Sand E2 Medium 

E3

Loose 

ε

Typical values of Modulus of Elasticity of Sand: E Sand 2 (kg/cm ) Loose 100‐250 Medium 250‐750 Dense 750‐1500 Very Dense 1500‐4000 How to determine Modulus of Elasticity of natural sands It is difficult to obtain sand samples that represent natural sand condition for laboratory testing. Therefore, the modulus of Elasticity of sand is determined based on field tests or based on experience based estimations

2009

Dr. Omar Y. Ezzeldine

5/12

Third Year Civil Soil Mechanics

Cairo University Faculty of Engineering

lecture 3 Soil Compressibility

4. Compressibility of Cohesive Soil Cohesive soils (clay and silt) have very low permeability . Under normal loading conditions, compressibility is dependent on pore water dissipation rate. Compressibility of cohesive soils is time dependent and large in magnitude. Compressibility of cohesive soils is determined in the laboratory using the oedometer Effect of Stress History on Clay Compressibility 1 When a clay layer is formed for the first time, its compressibility is high. The relationship between the rate of reduction of voids ratio (e) and the increase of overburden stress on the log scale is linear: the virgin curve. 2 If a clay layer is formed for the first time with a total height (H), it is under an effective stress (p c ).  It follows the path (1‐2). 3 In the case overburden pressure is reduced to pressure (p 1 ), due to erosion for example, the clay does not follow the same curve (it is not elastic) but follows a more mild compressibility slope (2‐3). 4 At Point (3) the clay is overconsolidated, the overconsolidation ratio is equal to (p c /p 1 ).If the clay is subjected to additional stress its compressibility very small as compared to the virgin curve as long as the additional pressure is less than (p c ). 5 The clay continue to act as overconsolidated clay as long as its effective stress is less than the overconsolidation pressure (p c ) (3‐4). 6 If the effective stress is increased further, the clay acts as normally consolidated clay (4‐5). Consider a clay sample taken from a certain depth (H), how can we determine if this sample is overconsolidated or normally consolidated? 1 Calculate the overburden pressure at this depth (p o ). 2 Determine the preconsolidation pressure pc from the oedometer test. 3 If p o = p c , the clay is normally consolidated. 4 If p o < p c , the clay is overconsolidated. 5 If p o > p c , the clay is under H consolidated.

po =

∑γ H + ∑γ

above GW T

2009

Dr. Omar Y. Ezzeldine

sub below GW T

H

6/12

Third Year Civil Soil Mechanics

Cairo University Faculty of Engineering

lecture 3 Soil Compressibility

e 1

Normally  Consolidated

Effective pressure = p2 Overconsolidation pressure = p2

Normally Consolidated Clay formed by sedimentation 3 2

1-2 Effective pressure = p3 Overconsolidation pressure = p2 p3
4 Over Consolidated 5

Erosion is responsible for overconsolidation. Overconsolidation ratio = p2/p3

pc

log (p)

2-3

Δp

Δp

Clay acts as Overconsolidated as long as the effective stress under load (Δp) is less than pc.

Clay acts as Normally Consolidated when the effective stress under load (Δp) is higher than pc.

3-4

2009

4-5

Dr. Omar Y. Ezzeldine

7/12

Third Year Civil Soil Mechanics

Cairo University Faculty of Engineering

lecture 3 Soil Compressibility

5. The oedometer Test for Compression Measurements Objectives: To study compressibility of clay specimen:  1 Establish relationship between volume changes with respect to changes in effective pressure. 2 Define effect of stress history on the tested specimen. 3 Verify relationships related to theory of consolidation: ‐ Pore water dissipation. ‐ Relationship between pore water dissipation and volume change Equipment: 1 The set‐up of the test include a compression cell where the saturated specimen is placed and a hanging weight (Po

Lo L1 Compression  P1 Cell

Table

2 Load acting on the compression cell is magnified by the Lever Arm Ratio (LAR). P1  LAR Po  

Po

Lo Po L1

Procedure 1 Measure initial condition: eo, wo, Gs. 2 Prepare the specimen by trimming into the metal ring. 3 Place the ring inside the compression cell between two porous plates. A Metal cover is place above the upper porous plate to receive the applied load. 4 Set‐up the dial gage to zero reading. Fill the compression cell with water up to the upper porous plate level. 5 Place the hanging load such that the pressure on the clay specimen is equal to the first loading step (0.25 kg/cm2 for example). 6 Take readings of dial gage (compression of the specimen) with time until compression stops or for 24 hours.

2009

Dr. Omar Y. Ezzeldine

8/12

Third Year Civil Soil Mechanics

Cairo University Faculty of Engineering

lecture 3 Soil Compressibility

7 Increase the pressure on the specimen according to a certain scale. Unloading and reloading cycles could be carried out. 2 For example: 0.25 , 0.50, 1.00, 2.00, 1.00, 1.50, 2.00, 4.00, 8.00, 16.00 kg/cm .

Results: - Results are presented in term of relationship between applied cell pressure and compression (ΔH) - Change of voids ratio is calculated ⎛ ΔH ⎞ ⎟(1 + eo ) Δe = ⎜⎜ ⎟ H ⎝ o⎠ - Plot e-p curve - Plot e-log(p) curve

1+eo

Output Parameters: 1 Coefficient of compressibility (a v).

e

Δe  e 1

ΔH 

Water Solids Volume

= Ho

Water H

Solids Sample

of volume 2 Coefficient compressibility (mv). preconsolidation pressure (p c). ) 3 4 Compression Index (cc). 5 Recompression Index (cr). 6 Overconsolidation Ratio (OCR). 1 Coefficient of compressibility (av). From e-p plot, calculate the slope of the curve at various stress levels.

p

e

of volume 2 Coefficient compressibility (mv). For all values of a v , calculate m v by dividing a v by (1+e o )

log p

2009

Dr. Omar Y. Ezzeldine

9/12

Third Year Civil Soil Mechanics 3 Preconsolidation

Cairo University Faculty of Engineering

lecture 3 Soil Compressibility

Pressure

A P

α/2

Void Ratio e

α/2

σ′vm

E

cc

cr

pc

Vertical Stress σ′ p (log scale) Consider e-log p plot. Determine the point of maximum curvature (A). From this Point (A), draw a horizontal line and a tangent line. Draw the line bisecting the angle ( α ) between the horizontal and the tangent. Determine the point at the start of the linear portion of the curve (E). Extend the linear portion of the curve from Point (E) until it meets the bisection line at Point (P). 7 Preconsolidation pressure pc is the x-coordinate of Point (P) on the log scale. 1 2 3 4 5 6

4 Compression Index (cc). Compression Index is the slope of the linear portion of the compression curve. cc =

e1 − e 2 e −e Δe = = 1 2 Δ log ( p ) log ( p 2 ) − log ( p1 ) ⎛p ⎞ log⎜⎜ 2 ⎟⎟ ⎝ p1 ⎠

5 Recompression Index (c r). Compression Index is the slope of the equivalent linear portion of the loading-unl Ratio 6 Overconsolidation Calculate the overburden pressure at the level where the specimen is taken from (p o ). p OCR = c po

2009

Dr. Omar Y. Ezzeldine

10/12

Third Year Civil Soil Mechanics

Cairo University Faculty of Engineering

lecture 3 Soil Compressibility

6. Swelling of Clay General Remarks Swelling clay is normally hard dry clay. A swelling clay increases in volume when it has an access to water and is naturally of low water content. Such clays are of special mineralogical and chemical composition: -

Montmorillonite Illite Kaolinite

Clay has a very high swelling potential Clay has a Slight swelling potential Clay has no swelling potential

Measurement of Swelling Pressure Use the Oedometer to measure swelling pressure. Two tests are applicable: No swell test and recompression test. A) No Swell Test 1 Prepare a dry sample in the oedometer ring 2 Add water to innundate the compression cell. 3 Watch the upward movement of the sample. Increase vertical pressure after every small upward movement to keep the dial gage reading to zero. 4 Keep increasing the pressure on the cell until no upward movement could be measured. 5 The final applied vertical pressure is the swelling pressure. B) Recompression Test 1 Prepare a dry sample in the oedometer ring 2 Apply vertical pressure on the sample on stages until reaching a pressure level compared to the overburden pressure (p o ). 3 Add water to innundate the compression cell. 4 Allow some time to for the specimen to undergo swelling until the vertical upward movement is stopped. 5 Increase the vertical pressure to overcome the upward movement of the specimen until the dial gage is back to zero. 6 The vertical pressure added after innundation is the swelling pressure. Treatment of swelling clay 1 Swelling clay layer is to be replaced by compacted sand. 2 Restrict water use and use effective water insulation prohibit water from reaching the swelling clay layer. 3 Use rigid foundation system to resist the detrimental effect of differential heave. 4 Use chemical stabilization to reduce swelling (lime for example).

2009

Dr. Omar Y. Ezzeldine

11/12

Third Year Civil Soil Mechanics

Cairo University Faculty of Engineering

lecture 3 Soil Compressibility

7. Collapsibility of Sand General Remarks A collapsible soil suffers a reduction in volume due to wetting and/or submergence and loading. Usually of fine sands and silts and sometimes low content of clay in a loose structure state and mostly in a dry or near dry condition. As in Loess (wind blown fine sands and silts, slightly cemented by silt or chemicals as calcium carbonates). The danger is associated normally with uneven wetting which causes differential settlement. h

Measurement of Collapsibility (Collapse Ratio) Use the Oedometer Collapse Ratio (% From To 0.0% 1.0% 1 0% 1.0% 5 0% 5.0% 5.0% 10.0% 10.0% 20.0% 20.0% >20.0%

Collapse Ratio =

Δhc ho

ho Δhc

Danger of Problem No Problem Moderate Problem Problem Dangerous Problem Very Dangerous Problem

p pc

h o is the initial specimen height p c is the expected stress from structure or as per code (200 kPa).

Treatment By submerging soil by water for sufficient time (24, 48, 72, …hours) followed by heavy vibratory compaction. Sometimes and for high collapsibility, soil replacement may be used.

2009

Dr. Omar Y. Ezzeldine

12/12

Third Year Civil Soil Mechanics

Cairo University Faculty of Engineering

lecture 3 Soil Compressibility

5. The oedometer Test for Compression Measurements Objectives: To study compressibility of clay specimen: 1 Establish relationship between volume changes with respect to changes in effective pressure. 2 Define effect of stress history on the tested specimen. 3 Verify relationships related to theory of consolidation: - Pore water dissipation. -

Relationship between pore water dissipation and volume change

Equipment: 1 The set-up of the test include a compression cell where the saturated specimen is placed and a hanging weight (Po) system 2 Load acting on the compression cell is magnified by the Lever Arm Ratio (LAR). P1 = LAR (Po ) =

Lo L1 Compression  Cell

P1

Table

Po

Lo Po L1

Procedure 1 Measure initial condition: eo, wo, Gs. 2 Prepare the specimen by trimming into the metal ring. 3 Place the ring inside the compression cell between two porous plates. A Metal cover is place above the upper porous plate to receive the applied load. 4 Set-up the dial gage to zero reading. Fill the compression cell with water up to the upper porous plate level. 5 Place the hanging load such that the pressure on the clay specimen is equal to the first loading step (0.25 kg/cm2 for example). 6 Take readings of dial gage (compression of the specimen) with time until compression stops or for 24 hours.

2009

Dr. Omar Y. Ezzeldine

8/12