Site pages

Current course

Participants

General

MODULE 1. Fundamentals of Soil Mechanics

MODULE 2. Stress and Strength

MODULE 3. Compaction, Seepage and Consolidation of...

MODULE 4. Earth pressure, Slope Stability and Soil...

Keywords

## LESSON 23. Consolidation Test

**23.1 Introduction **

In the laboratory, the consolidation of a saturated soil specimen is conducted in a device called oedometer as shown in Figure 23.1. The test is done for undisturbed soil sample collected from field. The test is done by applying incremental external loading as shown in Figure 23.2. After allowing full consolidation, the next increment of loading is applied [as shown in Figure 23.2 (a)]. The change in void ratio (Δ*e*_{1}) due to application of loading increment, Δ*q*_{1} can be determined as:

\[\Delta {e_1} = {{\Delta {H_1}} \over H}(1 + {e_0})\] (23.1)

where *H* is the initial thickness of the soil sample, Δ*H*_{1 }is the change in thickness or height (compression) of the sample due to the application of Δ*q*_{1}, *e*_{0} is the initial void ratio of the sample. After completing the loading test, unloading test is also conducted as shown in Figure 23.2(b). In case of loading, as the stress increases void ratio decreases and for unloading case, as the stress decreases void ratio increases. After determining the void ratio (*e*) due to application of incremental pressure (*p*), *e* – log σ* _{v}'* is plotted (as shown in Figure 23.3) for both loading and unloading conditions. The σ'

*is the effective vertical stress which is determined from the applied incremental loading. The slope of the straight portion of the loading curve is compression index (*

_{v}*C*) and slope of the unloading curve is swelling index. Thus, the Compression index can be determined as:

_{c}*C*

_{c }= (

*e*

_{1}–

*e*

_{2}) / (log σ'

_{2}– log σ'

_{1}). According to Skempton (1944):

*C*

_{c }= 0.009 (

*w*

*– 10), where*

_{L}*w*

*is the liquid limit.*

_{L}The coefficient of compressible (a_{v}) can be determined as:

\[{a_v}={{\Delta e} \over {\Delta {{\sigma '}_v}}}\] (23.2)

where Δ*e* is the change in void ratio due to the change in effective vertical stress Δσ'* _{v}*. Similarly, the coefficient of volume change or coefficient of volume compressibility (

*m*

_{v}) can be determined as:

\[{m_v}={{{a_v}} \over {1 + {e_0}}} = {{\Delta e} \over {\Delta {{\sigma '}_v}}}\left( {{1 \over {1 + {e_0}}}} \right)\] (23.3)

where *e*_{0 }is the initial void ratio of the soil sample.

**Fig. 23.1. Laboratory consolidation test.**

**Fig. 23.2. Loading arrangement (a) Loading (b) Unloading.**

**Fig. 23.3. ***e ***– log σ**_{v}'** plot.**

**23.2 Over Consolidation Ratio**

Casagrande (1936) proposed to determine the pre-consolidation stress from *e* – log σ* _{v}'* plot as shown in Figure 23.4. Locate the point O where there is smallest radius of curvature. Draw a line OA parallel to stress or x axis. Draw a tangent OB at point O. Draw the line OC such that it bisects the angle AOB. Extend the straight portion of the

*e*– log σ

*plot. The stress corresponding to the point of intersection of extended line and OC line is the pre-consolidation pressure the soil was subjected. If the present effective overburden pressure σ'*

_{v}'

_{v}_{0}is equal to the preconsolidated pressure σ

*(maximum past effective overburden pressure), the soil is normally consolidated soil. However, if σ'*

_{c}'

_{v}_{0}< σ

*, the soil is overconsolidated. Thus, overconsolidation ratio (OCR) is defined as: OCR = σ*

_{c}'*/σ'*

_{c}'

_{v}_{0}.

**Fig. 23.4. Determination of preconsolidation stress . **

**23.3 Settlement Calculation**

Figure 23.5 shows the *e* – log σ* _{v}'* plots for normally consolidated and overconsolidated clay for settlement calculation. For normally consolidated clay the settlement (

*S*) can be determined as:

\[S={{{C_c}} \over {1 + {e_0}}}H{\log _{10}}\left( {{{{{\sigma '}_{v0}} + \Delta {{\sigma '}_v}} \over {{{\sigma '}_{v0}}}}} \right)\] (23.4)

where *H* is total thickness of the soil layer.

For over-consolidated clay: Case 1: σ'_{v}_{0}+Δσ'* _{v}* < σ'

_{c}*\[S={{{C_s}} \over {1 + {e_0}}}H{\log _{10}}\left( {{{{{\sigma '}_{v0}} + \Delta {{\sigma '}_v}} \over {{{\sigma '}_{v0}}}}} \right)\] * (23.5)

Case 2: σ'_{v}_{0} < σ'* _{c}* < σ'

_{v}_{0}+Δσ'

_{v}

**\[S={{{C_s}} \over {1 + {e_0}}}H{\log _{10}}\left( {{{{{\sigma '}_c}} \over {{{\sigma '}_{v0}}}}} \right)\] + \[{{{C_c}} \over {1 + {e_0}}}H{\log _{10}}\left( {{{{{\sigma '}_{v0}} + \Delta {{\sigma '}_v}} \over {{{\sigma '}_c}}}} \right)\] **** ****(2****3.6)**

where *C*_{s }is the swelling index.

**Fig. 23.5. Settlement calculation (a) Normally consolidated clay **

** (b) Overconsolidated clay .**

** **

**References**

Ranjan, G. and Rao, A.S.R. (2000). Basic and Applied Soil Mechanics. New Age International Publisher, New Delhi, India.

PPT of Professor N. Sivakugan, JCU, Australia.

** **

**Suggested Readings **

Ranjan, G. and Rao, A.S.R. (2000) Basic and Applied Soil Mechanics. New Age International Publisher, New Delhi, India.

Arora, K.R. (2003) Soil Mechanics and Foundation Engineering. Standard Publishers Distributors, New Delhi, India.

Murthy V.N.S (1996) A Text Book of Soil Mechanics and Foundation Engineering, UBS Publishers’ Distributors Ltd. New Delhi, India.

PPT of Professor N. Sivakugan, JCU, Australia (www.geoengineer.org/files/consol-**Sivakugan**.pps).