Consolidation test consists of applying the pressure on a thin soil specimen in increments and keeping each pressure increment for sufficient time until the consolidation of the soil specimen and measurement of the vertical deformation of the soil specimen due to expulsion of pore water. All consolidation parameters including av, mv, Cc, cv etc. can be determined from the consolidation test under each pressure increment.
Equipment used for Consolidation Test of Soil:
The consolidation properties, required for calculation of the consolidation settlement, are obtained by conducting a consolidation test on a soil specimen in a geotechnical engineering laboratory. The apparatus used for conducting a consolidation test is called consolidometer or odometer.
Figure 11.18 shows the sectional elevation of a fixed-ring consolidometer. It consists of a cylindrical consolidation ring of 6 cm internal diameter, made of gun metal or stainless steel. The consolidation ring is placed in a consolidation cell. A soil specimen is cut from the undisturbed soil sample to the size of the internal diameter of the consolidation ring and is placed into the consolidation ring. A porous disc of the same size, of the soil as specimen is placed above and below the soil specimen to represent the pervious (drainage) soil layer in the field.
The top porous disc is just a little less than that of soil specimen in diameter. The bottom porous disc is bigger in size. Filter papers cut into the same size as of the soil specimen are used between the soil specimen and the porous discs to permit flow of water from the specimen during consolidation and prevent penetration of fine soil particles into the voids of the porous disc. A pressure pad and steel ball are placed over the top porous disc in the cell.
Types of Consolidometers:
Following are the two types of consolidometers:
1. Fixed-Ring Consolidometer:
It is shown in Fig. 11.18. In this type, the specimen ring as well as the bottom porous stone are fixed in position. The soil specimen moves in downward direction relative to the specimen ring during consolidation. It is possible to monitor water from the base of the bottom porous stone in the fixed-ring consolidometer.
2. Floating-Ring Consolidometer:
It is shown in Fig. 11.19. In this type, the specimen ring is not fixed in position. The soil specimen moves both in upward and downward directions relative to the specimen ring during consolidation. The advantage of floating-ring consolidometer is that skin friction between soil specimen and inside surface of the specimen is less compared to that in the fixed-ring consolidometer.
Test Procedure for Consolidation:
The consolidation cell is mounted on the loading platform of the odometer and a loading yoke is used to facilitate application of the load on the soil specimen. Figure 11.20 shows the consolidation test set up.
A dial gauge, with a least count of 0.002 mm, is mounted on the top of the pressure pad to record the compression of the soil specimen. An initial load of 5 kN/m2, called the seating load, is applied on the soil specimen to adjust the unevenness of the surface of the soil specimen. The seating load is maintained for 24 h (1 day) and is then removed.
The load is applied on the soil specimen in increments using a load increment ratio of 2. The load is applied by placing standard weights on the loading arm of the odometer to cause the required final stress of 10, 20, 50, 100, 200, 400, and 800 kN/m2 on the specimen in successive load increments.
The settlement dial gauge readings are taken at regular time intervals from the instant the stress of 10 kN/m2 is applied. Dial gauge readings are taken at elapsed times of 0, 1, 4, 9, 16, 25, 36, 49, 60, 64, 81,100, and 120 min and thereafter at hourly time intervals. These elapsed times are used for convenience of plotting the time as √t in the square root of time fitting method of determining the coefficient of consolidation.
Each load increment is maintained and dial gauge readings are taken for 24 h or until the consolidation of the soil specimen is completed as indicated by the negligible difference in successive dial gauge readings, whichever is later. The final dial gauge reading is taken just before the next load increment is applied. After this, the next load increment is applied and the dial gauge readings are taken as in the previous load increment.
After the consolidation of the specimen is completed under the maximum stress of 800 kN/m2, the load is gradually removed maintaining a load decrement ratio of 1/4. Thus, loads are removed in such a way as the stress is 200, 50, and 10 kN/m2 and then the load is completely removed. Each stress increment during unloading is again maintained for 24 h, the soil specimen is allowed to swell, and the dial gauge readings are taken at the same elapsed times as above or at hourly intervals.
After the load is completely removed, the consolidation cell is dismantled and the soil specimen is taken out. The final thickness of the specimen, the wet weight, and the dry weight are determined and recorded.
Observations Obtained from Consolidation Test:
The observations are recorded as given in Table 11.4.
Observation for Consolidation Test:
Diameter of the soil specimen (d) =
Area of the soil specimen, A = π d2/4 =
Mass of the consolidation ring =
Mass of the specimen and the consolidation ring before test =
Thickness of the soil specimen after test (Hf) =
Mass of the wet soil specimen after test (M) =
Mass of the dry soil specimen after test (Md) =
Final water content of the specimen, ωf = (M – Md)/Md =
Precautions Taken for Conducting the Consolidation Test:
The following precautions are to be taken for conducting the consolidation test:
i. The soil specimen should be carefully transferred from the soil sampler to the consolidation ring without causing disturbance.
ii. The inside surface of the consolidation ring should be smeared with silicon grease or oil to reduce the side friction.
iii. Water should be added regularly to the consolidation cell to ensure full saturation condition of the soil specimen.
iv. The consolidation equipment should be located in an isolated position to avoid any disturbance to the equipment setup as the dial gauge is very sensitive.
The equilibrium void ratio at the end of consolidation under each load increment is determined from the initial and the final dial gauge readings under that stress increment by using any of the two methods available:
(a) Change in the void ratio method and
(b) Height of the solids method.
In this method, the change in the void ratio under the last stress decrement is computed and is subtracted from the final void ratio to determine the void ratio at the beginning of the last stress decrement. In this way, the void ratio
under each stress decrement or increment is determined by working backward from the final stress to initial stress. Final void ratio is obtained from the relation –
et = [(G x ωf)/S] = G x ωf
[soil specimen is fully saturated and degree of saturation (S) = 1] where ωf is the final water content of the soil specimen at the end of the consolidation test. We know that –
[Δe/(1+ et)] = ΔH/Hf
Hence, change in the void ratio is obtained from the relation –
Δe = [(1+ et)/ Hf] x ΔH …(11.43)
where Hf is the final thickness of the soil specimen at the end of the consolidation test.
The height of soil solids, which is constant for the given soil specimen, is computed from the relation –
Hs = Volume of soil solids/Cross-sectional area of the soil specimen = [(Wd/Gρw)/A] = Wd/GρwA
The change in the thickness of the soil specimen is determined from the relation –
ΔH = (R0 – Rf) x 0.002
where R0 is the initial dial gauge reading under the given stress increment, Rf is the final dial gauge reading under the given stress increment, and 0.002 is the least count of the dial gauge in millimeter; ΔH is in millimeter. The height of the specimen is obtained as –
H = H0 – ΔH Þ H = Hf + ΔH
We know that the void ratio is given as –
Hence, the void ratio can be computed from the relation –
H – Hs/Hs …(11.44)
The coefficient of consolidation under each stress increment may be determined from any of the following three methods:
1. Improved rectangular hyperbola method.
2. Square root of time fitting method.
3. Logarithm of time fitting method.
Each of these methods are explained below:
1. Improved Rectangular Hyperbola Method:
Improved rectangular hyperbola method is observed to be simple, consistent, and reliable for determination of the coefficient of consolidation.
The procedure to determine the coefficient of consolidation in this method is as follows:
i. A graph is plotted with time on the x-axis and time/displacement (t/d) on the y-axis (see Fig. 11.21).
ii. After an initial curved portion, the graph gives straight line portion in the range of U = 60% – 90%.
iii. The straight line portion in the range of U = 60% – 90% is extended backward on to the y-axis.
iv. The slope (m) and the intercept on the y-axis (c) of this extended straight line are determined.
v. The coefficient of consolidation is determined from the relation –
Cv = Bmd2/c …(11.45)
where Cv is the coefficient of consolidation in the units of cm2/s or mm2/s depending on t, d, and H; B a constant equal to 0.2972343; m is the slope of the extended straight line portion of t versus t/d plot; c is the y-intercept of the extended straight line portion of f versus t/d plot; and d is the length of the drainage pathnoted.
It was observed that the straight line portion required for this method is readily obtained for a wide range of soils. Hence, the method is found to be consistent and reliable for determination of the coefficient of consolidation in most of the situations. Also, the method makes it easy to program the calculation of consolidation results including the coefficient of consolidation without necessarily plotting a graph of t versus t/d plot.
2. Square Root of the Time Fitting Method:
This method is suggested by Taylor based on the observation that time factor corresponding to 90% consolidation (T90) is equal to 1.15 times the time factor for 60% consolidation (T60).
The procedure to determine the coefficient of consolidation by this method is described as follows:
i. Plot a graph between √t and dial gauge reading in the given stress increment as shown in Fig. 11.22.
ii. Extend the initial straight line portion of the curve backward to meet the y-axis. The point of intersection of this line with the y-axis gives the corrected zero dial gauge reading (Rc).
iii. From Rc, draw a straight line such that its abscissa at any point is 1.15 times that of the initial straight line portion of the consolidation curve.
iv. The intersection of this line with the consolidation curve gives a point (P) corresponding to 90% consolidation. The abscissa of the point P gives √t90.
v. Compute the coefficient of consolidation from the relation –
Cv = (T90 x d2)/t90] …(11.46)
where T90 is the time factor corresponding to 90% degree of consolidation = –0.9332 log10(1 – 0.9) – 0.0851 = 0.8481, d is the length of drainage path = H/2, and H is the average thickness of the soil specimen in the given stress increment.
The method is suitable for soils that give a consolidation curve with an initial straight line portion.
3. Logarithm of Time Fitting Method:
This method was suggested by Casagrande based on the observation that the intersection of the straight line portion of logT–U relation and the asymptote of the lower portion gives the point corresponding to 100% degree of consolidation.
The procedure to determine the coefficient of consolidation by this method is described below:
i. Plot the time-dial gauge readings for the given stress increment with time on the x-axis on log scale (base 10) and dial gauge reading on the y-axis as shown in Fig. 11.23.
ii. Measure the vertical distance (a) on the curve between points corresponding to times t = 1 min and t = 4 min.
iii. The corrected dial gauge reading Rc is obtained by drawing a horizontal line at a vertical distance a above the point corresponding to t = 1 min.
iv. The consolidation curve logT–R consists of two straight line portions at each end with a curve joining the straight line ends. Extend the two straight line portions to intersect at point P.
v. The abscissa (x-coordinate) of the point P gives the time corresponding to 100% consolidation (t100) on the log scale and the ordinate gives R100.
vi. The dial gauge reading corresponding to 50% consolidation (R50) is obtained from the relation –
Rc – R50 = ½(Rc – R100) …(11.47)
vii. The abscissa (x-coordinate) of the point corresponding to R50 on the consolidation curve gives the time corresponding to 50% consolidation (log t50).
viii. Compute the coefficient of consolidation from the relation –
Cv = T50 x d2/t50 …(11.48)
where T50 is the time factor corresponding to 50% degree of consolidation –
T50 = (π /4) x (50/100)2 = 0.1963
Here d is the length of the drainage path = H/2 and H is the average thickness of the soil specimen in the given stress increment.
The logarithm of time fitting method requires the time–dial gauge readings in the secondary consolidation range beyond 100% degree of consolidation.
The permeability of the soil specimen under any given stress increment can be calculated from the coefficient of consolidation (Cv) using the relation –
k = Cv x mv x γw …(11.49)