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Soil Consolidation refers to the process in which the volume of a saturated (partially or fully) soil decreases due to an applied stress. The term was introduced by Karl von Terzaghi also known as the "father of soil mechanics and geotechnical engineering". Terzaghi established the one-dimensional consolidation theory and changed the definition of the term since it was previously associated (and still is, in geosciences) with the compaction of clay sediments that formed shales.
When a load is applied in a low permeability soil, it is initially carried by the water that exists in the porous of a saturated soil resulting in a rapid increase of pore water pressure. This excess pore water pressure is dissipated as water drains away from the soil’s voids and the pressure is transferred to the soil skeleton which is gradually compressed, resulting in settlements. The consolidation procedure lasts until the excess pore water pressure is dissipated.
The increment of applied stress that causes consolidation may be due to either natural loads (e.g. sedimentation processes), or human-made loads (e.g. the construction of a building or an embankment above a soil mass) or even the decrease of the ground water table.
The duration of the consolidation process is a critical issue and highly depends on the permeability of the soil subjected to the load and on the drainage paths. In general, consolidation in sandy soils is a quick process (occurring possibly immediately during construction) whereas the process may last for many years or even decades in clay soils.
The consolidation procedure is commonly separated into 3 stages:
The simplest case of consolidation examined is the one-dimensional consolidation. In this case, the lateral strain of the soil mass is neglected. The testing procedure to quantify the critical soil properties associated with soil consolidation is the Oedometer Test. The term “Oedometer” derives from the Ancient Greek language and means “to swell”. The test is one of the most commonly conducted, and important, laboratory tests in geotechnical engineering. The Oedometer Test aims at measuring the vertical displacement of a cylindrical, saturated soil sample subjected to a vertical load while it is radially constrained. In the subsequent test, the incremental loading consolidation test is described. Note that there is also a constant rate of strain (CRS) test, that nowadays is becoming more popular
A typical Oedometer test set-up, shown in Figure 1, is composed of: i) a consolidation cell, ii) a loading frame, and iii) a deformation measurement mechanism.
The consolidation cell consists of the following components:
Typical diameter (D) to height (H) ratios of the soil samples are D/H = 3 - 4. The cross-section area of the soil specimen may be 20, 35 or 50 cm^{2} (D = 5 - 8 cm) and its height is H = 2 - 2.5 cm.
The loading frame configuration is composed of a loading beam and dead weights. The configuration allows for a constant load to be maintained indefinitely. The application of the load causes deformation of the loading frame, the porous stones and the soil sample. Since the test is intended to measure only the deformation of the soil, the other movements (machine deflections) must be measured and later subtracted from the total deformation. This is achieved by measuring the deflection of the set up using an aluminum sample, which is characterized by linear elastic, and thus known, response.
The vertical deformation measurements of the soil specimen is performed using a dial gauge (most often) or an electronic instrument.
Figure 1: Typical Oedometer test set-up (photo from the National Technical University of Athens)
The typical testing procedure consists of the following steps:
The load is maintained for a period of 24 hours (in certain clays the required time is 48 hours) during which the soil consolidates with drainage from the porous stones. Afterwards, the applied load is increased incrementally by doubling the applied stress at each stage. The number of the load stages and the maximum stress applied depends on the stress range of interest. During the loading process, water is provided into the cell so that the specimen remains fully saturated. At each loading stage, readings of deformation are taken systematically to develop a time-settlement curve. That is, after the application of each load, the deformation is measured at 6, 15, 30 seconds, then at 1, 2, 4, 8, 16, 30 min and at 1, 2, 4, 8 and 24 hours, respectively. When the maximum load is reached, and possibly in a load increment in between, an unloading stage is introduced that may be conducted in one or multiple steps; typically, the load is reduced by a factor of 4 at each step. When the test is completed, the final height of the sample and its water content are measured.
The following soil properties are derived from the Oedometer Test:
Figure 2: Typical diagram of void ratio - effective stress correlation obtained by Oedometer Test. The Compression C_{C} and Recompression C_{r} indices are also presented.
Therefore, C_{C} is:
C_{C} = Δe / Δlog (σ')
C_{C }usually ranges from 0.1 to 10 and has no units. For normally consolidated clays the index commonly ranges between 0.20 to 0.50 and for silts between 0.16-0.24. For sands, the index ranges between 0.01 to 0.06, although this is not a particularly meaningful parameter for a sand.
Some empirical expressions that relate the Compression Index, C_{C}, with the Liquid limit (LL) and Plasticity Index (PI) of the soil, are the following:
Table 1: Typical values of the C_{v} coefficient
SOIL | C_{v }(cm^{2}/sec) x 10^{-4} |
Soft blue clay (CL-CH) (Wallace & Otto, 1964) | 1.6-26 |
Chicago Silty Clay (CL) (Terzaghi & Peck, 1967) | 8-11 |
Mexico City Clay (MH) (Leonards & Girault, 1961) | 0.9-1.5 |
Organic Silts and Clays (OH) (Sivakugan,1990) | 1-10 |
The coefficient of consolidation, C_{V} can readily be estimated from the time-settlement curve using graphical methods. There are two, most commonly used, methodologies:
Casagrande Logarithm of Time Fitting Method (Casagrande and Fadum, 1940):
The coefficient of consolidation, C_{V}, is determined by estimating the time at 50% consolidation (t_{50}), as shown in the short animation/presentation below. Then, C_{V} can be estimated as:
C_{V} = 0.917 * (H^{2}_{dr }/ t_{50})
where H_{dr} is the drainage path. Given the initial height of the specimen (H_{i}) and the compression of the soil sample at 50% consolidation (ΔΗ), the drainage path (for double drainage), H_{dr}, is computed as:
H_{dr} = (H_{i} - ΔΗ) / 2
Taylor Square Root of Time Fitting Method (Taylor, 1948):
In this method, the dial readings are plotted against the square root of time. The coefficient of consolidation, C_{V}, is determined by estimating the time at 90% consolidation (t_{90}), as shown in the short animation/presentation below. Then, C_{V} can be estimated as:
C = 0.848 * (H^{2}_{dr} / t_{90})
where H_{dr} is the average drainage path (typically, half the specimen height).
Leonards, G.A. and Girault, P. (1961). A Study of the One-Dimensional Consolidation Test, Proc. Fifth Int. Conf. on Soil Mechanics and Found. Eng., Paris, Vol. 1, 116-130.
Sivakugan, N., (1990). Development of Marshy Areas in Colombo, Sri Lanka, Proc. Tenth Southeast Asian Geot. Conf., Taipei, Vol. 1, 469-472.
Skempton, A. W. (1944). Notes on the Compressibility of Clays. Q. J. Geol. Soc. London, 100(1-4), 119-135.
Terzaghi, K. and Peck, R.B., (1967). Soil Mechanics in Engineering Practice, John Wiley & Sons, New York, 729 pp.
Wallace, G.B and Otto, W.C. (1964). Differential Settlement at Selfridge Air Force Base, Jnl. Soil Mechanics and Found. Div., ASCE, Vol. 90, No. SM5, 197-220.
Wroth, C. P. and Wood, D. M. (1978). The correlation of Index Properties with Some Basic Engineering Properties of Soils. Canadian Geotechnical Journal, 15, 137-145.
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