Consolidation Test

Kwan Kam Hung

University No.: 2004170968

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THE UNIVERSITY OF HONG KONG Department of Civil Engineering Soil Mechanics – CIVL2006 Laboratory Report

Consolidation Test

Name: Kwan Kam Hung University No.: 2004170968 Group No.: S4 Experiment Date: 7th November, 2005 Submission Date: 22nd November, 2005

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Objective To determine 1. the compressibility and 2. the rate of consolidation of a remoulded sample of soil.

Apparatus 1. Consolidation Cell It is also known as the oedometer. It consists of a metal ring in which a soil specimen in the form of a disc is enclosed. The specimen is placed between 2 porous stone discs, with the upper one having a diameter slightly smaller than that of the metal ring and the lower one slightly larger. A loading cap is placed on the top. The whole assembly is placed in an open cell of water to which the pore water in the specimen has free access during the test. 2. 0.002mm/div. Dial Gauge It is used to measure the change in thickness (or compression) of the soil sample. It is connected to a computer and readings are taken in regular time intervals. 3. Loading Frame It is the location where the sample is under loading. 4. Weights It is put on the loading frame to provide the necessary constant load. 5. Spatulas It is used to assist the placement of the soil into the metal ring of the oedometer. It is also used to level off the soil specimen. 6. Electronic Balance It is used to weigh the soil samples.

Theory 1 The electricsoil balance. Consolidation is the gradual reduction in volume of a Fig. fully saturated of low

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permeability due to the drainage of some of the pore water under the application of a constant vertical load, or the removal of ground water which causes the water table to lower. This often occurs in clayey layer as the pore water will gradually be squeezed out as time goes on, leading to an increase in the effective stress. The process of consolidation continues until the excess pore water pressure set up by an increase in total stress has completely dissipated. The simplest case is that of one-dimensional consolidation, in which zero lateral strain is assumed. Consolidation settlement is the vertical displacement of the surface corresponding to the volume change at any stage of the consolidation process. Consolidation settlement may be resulted, for example, if a structure is built over a layer of saturated clay or if the water table is lowered permanently in a stratum overlying a clay layer. In cases in which significant lateral strain takes place, there will be an immediate settlement due to deformation of the soil under undrained conditions, in addition to consolidation settlement. The prediction of both the magnitude and rate of consolidation settlement are of great interest and importance to geotechnical engineers so as to ensure that serviceability limit states of any structures being built are satisfied. Usually, the consolidation process for a soil layer can be divided into 3 main stages:

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Time Initial Settlement Primary Settlement Secondary Settlement Settlement

Fig. 2 The typical Variation of Settlement with Time 1. Initial Settlement This corresponds to the change in the thickness of the soil layer as some of the gas pockets entrapped in the soil are squeezed out immediately upon the addition of load until the soil becomes saturated. At this stage the pore water is not squeezed out. Hence, all the additional load is taken up by the pore water pressure. 2. Primary Settlement At this stage, the pore water pressure is gradually dissipated as water is squeezed out, resulting in the reduction in the thickness as well as void ratio of the soil specimen. The additional load will then be gradually borne by the soil particles. 3. Secondary Settlement This is the consequence of creep obeys a linear law in the logarithm of time. Fig. 3 below shows the relationship between void ratio and the corresponding logarithmic value of the effective stress applied on the soil. Void ratio, e

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Increasing applied pressure

Log10 (Load) Fig. 3 A graph of void ratio e against log10 (load). The virgin compression curve for the soil sample is practically a straight line which corresponds to the loading curve for a clayey soil layer. If the load is allowed to released, the curve won’t trace back to the original curve but will trace another curve with a gentler slope. This curve is known as the unloading curve and the soil sample is said to be overconsolidated. The effective stress at the intersection between the virgin and unloading curve is known as the pre-compression stress. If the same sample is loaded again, the curve will follow the unloading curve and go back to the virgin curve as the applied stress increases. The degree of consolidation for an overconsolidated soil is much less than that of an undisturbed soil; hence it is safer for us to build structures over the over-consolidated soil. To quantify the compressibility of a soil, two coefficients are introduced, namely the coefficient of volume change mv and the compression index Cc. The coefficient of volume change is defined as the rate of change of void ratio with respect to the change in effective stress while the compression index refers to the rate of change of void ratio with respect to the change in logarithmic value of the effective stress. Very often, the compression index is adopted as it has a constant value for all values of effective stress. The progress of consolidation in-situ can be monitored by installing piezometers to record the change in pore water pressure with time while the magnitude of settlement can be measured by recording the levels of suitable reference points on a structure. The compressibility characteristics of a soil relating both to the amount and the rate of settlement during one-dimensional consolidation can also be determined in the laboratory by the oedometer test. Fig. 4 below shows diagrammatically a cross-section through the oedometer:

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Fig. 4 The cross-section of the oedometer. A soil specimen in the form of a disc, enclosed in a metal confining ring which has a smooth polished surface to reduce side friction, is sandwiched between 2 porous stone discs. The lower porous stone has a diameter slightly larger than that of the metal ring, with the upper one slightly smaller and hence can move inside the ring with a small clearance. A metal loading cap is fixed on top of the upper porous stone. The whole assembly is placed in an open cell of water to which the pore water in the specimen has free access. A vertical static load is then applied through a lever system in the loading frame. Under the condition of zero lateral strain (imposed by the metal confining ring), the compression of the soil specimen under pressure is measured by means of a displacement dial gauge operating on the loading cap. The test procedure is standardized in BS 1377 (Part 5) [4]. The initial pressure applied will depend on the type of the soil. Then a sequence of pressures is applied to the specimen, each being double the previous value. It is noted that for testing soil samples obtained from sites, the number and value of the load increments will depend on the type of soil as well as on the range of stress anticipated on site. The pressure applied for the first stage should normally be equal to the in-situ vertical stress at the depth from which the sample was obtained. Usually, each pressure is maintained for a period of 24 hours, and in some exceptional cases a period of 48 hours may be required, so that the specimen is fully consolidated. Compression readings are observed at suitable intervals during the period. At the end of the increment period, when the excess pore water pressure has completely

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dissipated, the applied pressure will equal to the effective vertical stress in the specimen. After full consolidation is reached under the final load, the load is removed, either in one or in several stages, and the sample is allowed to swell. The expansion of the specimen due to the removal of the final pressure is measured. The single-stage swelling period simply enables the specimen to stabilize before the final water content is determined. Otherwise, swelling might occur as the specimen is being removed from the oedometer and thus lead to error. The results from the test can either be presented by plotting the thickness (or the percentage change in thickness) of the specimen or the void ratio at the end of each increment period against the corresponding effective stress in either a natural or logarithmic scale. The void ratio at the end of each increment period can be calculated from the dial gauge readings and either the water content or dry weight of the specimen at the end of the test as follows: ∆h

Water ho

h1

Soilds

hs

Fig. 5 Phase Diagram (1) Water content measured at end of test = wf Void ratio at end of test (assuming Sr = 100%) = ef = wfGs Thickness of specimen at start of test = h0 Change in thickness during test =∆ h Void ratio at start of test = ei = ef + ∆ e where h − hs ei = o hs ef = ∆ e = ei − e f =

h1 − hs hs

ho − hs h1 − hs ho − h1 ∆h − = = hs hs hs hs

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∆e 1 + ei = ∆h ho

In the same way, ∆ e can be calculated up to the end of any increment period. (2) Dry weight measured at end of test (i.e. weight of solid)

=W

Thickness at end of any increment period = h1 Area of specimen

=A

Equivalent thickness of solids

= hs =

W Aρ γw

Initial void ratio

= ei =

ho − hs hs

Final void ratio

=ef =

h1 − hs h1 = −1 hs hs

Graphs of void ratio e after consolidation against effective stress σ ’ for saturated clay can be plotted. The graphs show an initial compression followed by expansion and recompression. The shapes of the curves are related to the stress history of the clay. The e - log σ ’ relationship for a normally consolidated clay is linear and is called the virgin compression line. The recompression curve ultimately joins the virgin compression line: further compression then occurs along the virgin line. During compression, changes in soil structure continuously take place and the clay does not revert to the original structure during expansion. The compressibility of the clay can be represented by the compression index Cc, which is the slope of the linear portion of the e - log σ ’ plot and is dimensionless. For any two points on the linear portion of the plot, CC =

ei − e f log(σ 1' / σ 0' )

The expansion part of the e - log σ ’ plot can be approximated to a straight line, the slope of which is referred to as the expansion index Ce. The value of coefficient of consolidation, CV, for a particular pressure increment in the oedometer test can be determined by comparing the characteristics of the experimental and theoretical consolidation curves, the procedure being referred to as curve fitting. One

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method to determine the coefficient of consolidation is root time method due to Taylor. The dial gauge readings are plotted against the square root of time in minutes and the average degree of consolidation against the square root of time factor. The theoretical curve is linear up to about 60% consolidation and at 90% consolidation the abscissa is 1.15 times the abscissa of the production of the linear part of the curve. This characteristic is used to determine the point on the experimental curve corresponding to U = 90%. The experimental curve usually consists of a short curve representing initial compression, a linear part and a second curve. The point corresponding to U = 0 is obtained by producing back the linear part of the curve to the ordinate at zero time. A straight line is then drawn having abscissae 1.15 times the corresponding abscissae on the linear part of the experimental curve. The intersection of the line DE with the experimental curve locates the point corresponding to U = 90% and the corresponding value t 90 can be obtained. The value T90 corresponding to U = 90% is 0.848 and the coefficient of consolidation is given by Cv =

0.848 d 2 t90

where d = Length of drainage path t90 = Time for 90% consolidation for each load increment

Procedures 1. Measure the inner diameter and height of the ring and determine its weight. 2. Fill the ring with remoulded soil and re-weigh. 3. Place the ring and soil in the porous plates and bearing plate in position and fill the cell with water. 4. Place the cell in the loading frame, adjust the lever arm and set the dial gauge. 5. Apply the first load and note the dial gauge reading at the following times after applying the load: 1

1

1

1

1

0, 4 , 1, 2 4 , 4, 6 4 , 9, 12 4 , 16, 20 4 , 25, 36, 49, 64, 81 and 100mins. Note: Plot the gauge readings were against square root of time as test proceeds. 6. After the load has been on for at least 8 hours, take the final gauge reading, apply the second load increment and take readings as before. 7. Repeat steps 5 and 6 until the following loads have been applied to the sample: 25, 50, 100 and 200kPa. Note: 10lbs. on the hanger are equivalent to 100kPa on the sample.

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8. Release the load and take the sample and ring from the cell. Dry the surfaces of the sample with filter papers and re-weigh. 9. Place the sample in the oven for at least 24 hours, remove from and re-weigh.

Results and Calculations Inner Diameter of Ring (m) 0.0763 Height of Ring (m) 0.0188 2 Cross Sectional Area A (m ) 0.0045723 Table 1 The dimensions of the metal ring of the consolidation cell. 1. Calculations of the Final Void Ratio ef of the Soil Samples. Water Content w =

Ww × 100% Ws

=

mw × 100% ms

where w = water content Ww = weight of water Ws = weight of solid mw = mass of water ms = mass of solid Void Ratio e Assume the samples are fully saturated at the beginning of the test. Therefore, the degree of saturation, Sr is equal to 1. The volume of void is equal to the volume of water. Sr =

wGs e

e = wGs

when Sr = 1

where e = void ratio Sr = degree of saturation Gs = Specific gravity = 2.65 Sample Loading (kPa) Mass of disc (g) Mass of disc + wet soil + ring (g) Mass of disc + dry soil + ring (g) Mass of ring (g)

A 25 70.4 317.4 268.4 91.9

B 50 74 316.5 267.2 92.3

C 100 75.7 314.6 263.4 92.9

D 200 75.3 315.9 269.7 94.3

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Mass of water in the soil (g) Mass of dry soil (g) Water content w1 (%) Final void ratio ef

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49.0 106.1 46.183 1.2238

49.3 100.9 48.860 1.2948

51.2 94.8 54.008 1.4312

46.2 100.1 46.154 1.2231

Table 2 The data obtained from the test, the calculated final water content w and the calculated final void ratio of the soil sample. 2. Calculation of the Equivalent height hs of the Soil Solids Sample A B C Loading (kPa) 25 50 100 Mass of Dry Soil (kg) 0.1061 0.1009 0.0948 Dry Weight of Sample W (N) 1.0408 0.98983 0.92999 Cross Sectional Area A (m2) 0.0045723 Equivalent Height hs (mm) 8.7562 8.3274 7.8240

D 200 0.1001 0.98198 8.2614

Table 3 The calculated equivalent height hs of the soil solids.

Time t (min) 0 0.25 1 2.25 4 6.25 9 12.25 16 20.25 25 36 49 64 81

Sample Load (kPa) Square root of time 0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 6.0 7.0 8.0 9.0

1 25

t

(min1/2)

2 3 4 50 100 200 Actual displacement (mm) 0.006 0.002 0.000 0.000 -0.250 -0.371 -1.084 -1.130 -0.270 -0.436 -1.250 -1.360 -0.284 -0.481 -1.406 -1.564 -0.296 -0.523 -1.554 -1.742 -0.304 -0.555 -1.682 -1.872 -0.312 -0.577 -1.778 -1.952 -0.316 -0.597 -1.844 -1.998 -0.320 -0.611 -1.880 -2.018 -0.324 -0.621 -1.904 -2.032 -0.328 -0.630 -1.916 -2.040 -0.330 -0.639 -1.926 -2.048 -0.332 -0.647 -1.932 -2.054 -0.334 -0.653 -1.936 -2.060 -0.342 -0.655 -1.938 -1.928

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100 10.0 -0.342 -0.657 -1.940 -1.932 Final settlement at a day later -0.346 -0.669 -1.952 -1.938 After rebound 0.026 -0.272 -1.496 -1.292 Table 4 The actual displacement at the corresponding time during the test.

AG Graph 1 The graph of compression against square root of time for sample A

0.05 0

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A Gr Graph 2 The graph of compression against square root of time for sample B.

0.1

A Gr

0 0

Graph 3 The graph of compression against square root of time for sample C.

-0.1

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A Gr Graph 4 The graph of compression against square root of time for sample D. 3. Calculation of the Corrected Compression h0 for the Soil Samples. From the graphs of compression against square root of time, we can determine the corrected compression ho for each load increment, i.e. the difference between the intercept of the initial straight line portion of the curve with the y-axis and the final compression. Sample A B C D Loading (kPa) 25 50 100 200 y-Intercept of Initial Straight Line Portion (mm) -0.2486 -0.3591 -1.0012 -0.9823 Final Compression after Rebound (mm) 0.026 -0.272 -1.496 -1.292 Corrected Compression after Rebound h0 (mm) 0.2746 0.0871 -0.4948 -0.3097

0

0

Table 5 The calculated corrected compression after rebound h0 for the soil sample. 4. Calculation of the Change in Void Ratio δ e for Each Increment. The change in void ratioδ e can be obtained by the following expression: δh δe = o hs where δ ho = Change in thickness of the specimen hs = Height of the solid in the specimen Sample A Loading (kPa) 25

-0.5

B 50

C 100

D 200

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Corrected Compression after Rebound h0 (mm) 0.2746 0.0871 -0.4948 -0.3097 Equivalent Height hs (mm) 8.7562 8.3274 7.8240 8.2614 Change in Void Ratio δ e 0.031361 0.010459 -0.63254 -0.037488 Table 6 The calculated change in void ratio δ e for the soil sample. 5. Calculation of the Initial Void Ratio ei for Each Pressure and Determination of the Compression Index. Sample A B C D Loading (kPa) 25 50 100 200 Change in Void Ratio δ e 0.031361 0.010459 -0.063254 -0.037488 Final void ratio ef 1.2238 1.2948 1.4312 1.2231 Initial void ratio ei = Final void ratio + |δ e| 1.2552 1.3053 1.4945 1.2606 Log (Pressure) 1.3979 1.6990 2 2.3010 Table 7 The calculated initial void ratio ei for the soil sample.

1.55

Graph 5 The Graph of void ratio against Log (Pressure). Compression index = - (slope of the graph) = - (-0.0612) = 0.0612

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6. Determination of the Time t90 for Each Load Increment. Sample A B Load (kPa) 25 50 Square root of t90 (min1/2) 3.4 3.3 t90 (min) 11.56 10.89 Compression at t90 (mm) -0.31592 -0.58812 Table 8 The time t90 determined from Graphs 1 to 4.

C 100 3.3 10.89 -1.8185

D 200 2.8 7.84 -1.9119

7. Calculation of the Coefficient of Consolidation Cv for Each Load Increment. The coefficient of consolidation Cv can be calculated from the following expression: Cv =

0.848 d 2 t 90

where t90 = Time for 90% consolidation for each load increment d = Length of drainage path Length of drainage path (assuming double drained stratum) 1

= 2 (Original soil thickness - Deformation at U = 90%) Sample A B C Load (kPa) 25 50 100 Square root of t90 (min1/2) 3.4 3.3 3.3 t90 (min) 11.56 10.89 10.89 t90 (s) 693.6 653.4 653.4 Original Soil Thickness (mm) 18.8 Compression at t90 (mm) -0.31592 -0.58812 -1.8185 Drainage path d (mm) 9.5580 9.6941 10.309 Coefficient of consolidation Cv (cm2/s) 0.0011169 0.0012196 0.0013793 Table 9 The calculated coefficient of consolidation Cv for the soil sample.

D 200 2.8 7.84 470.4 -1.9119 10.356 0.0019334

Discussion 1. Interpretation of the Graphs of Compression against Square root of Time. Comparing the graphs of compression against square root of time with the typical experimental curve and the theoretical curve as shown below, it can be seen that the shapes of the graphs obtained from this experiment were very similar to the two curves.

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Fig. 6 A typical experimental curve (on the left) and the theoretical curve (on the right). The graphs can be divided into 2 regions: the initial settlement and the primary settlement. The sudden changes in thickness of the 4 samples at the beginning of the experiment correspond to the stage of initial settlement. As the loading was just applied, the air pockets entrapped in the soil sample were squeezed out, causing a sudden compaction of the soil and resulting in sudden settlements. Hence, the rapid and substantial compression at this stage was not truly consolidation. That is why when calculating the initial void ratio ei and the final void ratio, the final compression had to be corrected by subtracting from it the y-intercept of the initial straight line portion of the curve in order to obtain the actual amount of compression for calculation. After the stage of initial settlement, the curve became more or less a straight line. This linear portion of the curve right after the initial settlement corresponds to the stage of primary settlement. In this stage, pore water was gradually squeezed out of the soil specimen, leading to a reduction in the thickness as well as the void ratio e of the sample. As time progressed, the rate of change in the thickness of the soil specimen decreased and the settlement would finally become almost constant. The soil specimen was said to be fully consolidated at this stage and the excess pore pressure had all been dissipated. The applied pressure was equal to the effective vertical stress in the specimen, and there would be no further reduction in thickness for soil samples. Theoretically, there should be a third stage of secondary settlement as discussed in the

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theory session. However, as the time for the test was not long enough, the creep effect was not significant in the experiment. Thus, secondary settlement could not be observed in the four graphs.

2. Interpretation of the Values of the Calculated Void Ratios. It can be observed that the calculated values of final void ratios after rebound of the four soil specimens were different from their corresponding initial void ratios ei. This means that the volume of the soil specimens did not return to their original values upon unloading. This phenomenon can be explained by the fact that some voids in the specimens were driven off by stress as the specimens were compressed. Although unloading took place at the end of the experiment, those voids might not fully reform. Hence, the values of the final void ratios after rebound of the four samples were smaller than their corresponding initial void ratios ei.

3. Interpretation of the Graph of Void Ratio against Log (Pressure). With reference to Graph 5, the graph is of negative slope. This means the larger the applied pressure, the larger the reduction in void ratio. The compressive index of unloading is smaller than that of loading. The void ratio follows one curve when compression increases but follows another straight line during unloading. This phenomenon is acceptable since when the soil is compressed, some voids may be driven off by stress, meaning the disappearance of voids. Although there is an unloading after compression, those voids will not fully reform after the unloading. This may explain why voids ratio cannot reach original value during unloading. The void ratio for sample C (100kPa) is rejected, since it deviates from the trend line a lot, this may due to some experimental errors.

4. Interpretation of the Values of t90 and the Coefficient of Consolidation C v. It can be observed that the values of t90 for the four samples were in the range from 6 to 12 minutes. This shows that the consolidation processes did happen in a fairly fast rate, and the soil sample was indeed very permeable. In addition, it can be seen that the values of t90 generally decreases with increasing applied load. This means that the rate of consolidation increases with the magnitude of the applied load. Finally, it was found that the values of the coefficient of consolidation Cv generally increases with increasing applied load. Such trend satisfies with the theoretical result.

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5. Remarks According to BS 1377, the oedometer test should be carried out with only one soil sample which is to be loaded, unloaded and reloaded repeatedly. However, this procedure would require a long time to complete and quick results are not possible. Hence, for our experiment, 4 samples were used instead, each with a different applied load. As a result, even though the phenomenon of consolidation was studied in this experiment, the findings might not be accurate enough as the properties of the 4 samples might not be the same and thus leading to inconsistency errors.

6. Assumptions In this experiment, calculations and analysis were done based on the one-dimensional consolidation theory (put forward by Terzaghi). However, several assumptions were made in the theory: 1. The soil is homogeneous. 2. The soil is fully saturated. 3. The solid particles and water are incompressible. 4. Any compression and flow that takes place is one-dimensional. 5. Strains are small. 6. Darcy’s law is valid at all hydraulic gradients. 7. The coefficient of permeability and the coefficient of volume compressibility remain constant throughout the process. 8. There is a unique relationship, independent of time, between void ratio and effective stress.

7. Sources of Errors 1. The soil specimens might not be fully saturated. This would affect the calculated values of the final void ratios after rebound and the subsequent calculations of the initial void ratio. 2. The soil specimens were not homogeneous. 3. The assumption that water is incompressible might not be true, especially under a high loading of 200kPa. 4. The initial void ratios ei of the four samples were not the same. This affects the resulted value of the compression index Cc. 5. There might be an imperfect fit of the disc of soil in the metal confining ring so that lateral strains occurred until full contact was developed. This would lead to excessive compressibility of the soil samples at lower stress levels.

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6. Large air bubbles might be entrapped in the soil samples due to insufficient compaction. The consolidation process might then be affected as extra voids were introduced to the specimens. 7. The first few readings for the change in soil thickness were subjected to errors, as the pore water inside the soil samples would not take up the applied load instantaneously, but might require several minutes to complete the process.

Conclusion In the experiment, the consolidation of the remoulded soil sample under four different applied loadings was studied. It was found that the void ratios e of the soil samples decreased with time due to the drainage of pore water. The compressibility index was determined from the graph of void ratio e against logarithm of applied pressure and was found to be 0.0612. In addition, it was discovered that the rate of consolidation decreased with time but increased with the applied loading. The time for 90% consolidation t90 and coefficient of consolidation Cv were found using the root time method (Taylor’s method). The rates of consolidation under four different applied loadings are summarized in the table below: Sample A B C D Load (kPa) 25 50 100 200 Coefficient of consolidation Cv (cm2/s) 0.0011169 0.0012196 0.0013793 0.0019334 Table 10 Summary of the coefficients of consolidation Cv for the remoulded soil sample under 25, 50, 100 and 200kPa applied loadings.

Reference 1. R. F. Craig, Soil Mechanics, E & FN Spon Press, 6th Edition, 1997. 2. R. Whitlow, Basic Soil Mechanics, Addison Wesley Longman Limited, 3rd Edition, 1995.