ABSTRACT
The shear behavior of a cemented gravely sand that can be considered as the representative of Tehran alluvium has been studied using triaxial equipment. Artificially cemented samples were prepared using gypsum plaster as the cementing agent. The plaster was mixed with the base soil at the weight percentages between 1.5 and 6. The critical state concepts were used to illustrate the mechanical behavior of tested soil.
Keywords: soil; critical state concepts; gravely sand; mechanical behavior and triaxial test.
INTRODUCTION
Critical state concepts have been used as a framework to illustrate the mechanical behavior of the sandy soils for many decades. Casagrande (1936) was the pioneer of this approach. He introduced the critical void ratio using the results of direct shear tests as the void ratio in which no increase or reduction of soil volume occurs during drained shearing. Seed and Lee (1966) introduced the critical state line as the variation of the critical state void ratio with confining stress. The soil with initial state at the right side of this line contracts during shearing. This results to reduction of volume during drained shearing and positive pore pressure during undrained condition. However, a dilative behavior can be observed for the soil with an initial state in right side of the mentioned line. Using the results of stress controlled triaxial test, Polous (1981) defined the steady state condition as the state in which the soil deforms continuously in constant volume, constant effective normal stress, constant shear stress and constant rate of relative deformation. This criterion is consistent with that of Casagrande (1936).
There are quite a number of papers and case studies available in literature regarding the critical state concepts in sandy soil. However, it should be noted that the majority of these studies are associated to fine and uniform sands. There is a lack of data for the non uniform or gravely sands due to some intrinsic problems in testing this category of soils. Haeri and Hamidi (2005) investigated the steady state characteristics of a gravely sand with a maximum particle size of 9.525 mm. They performed triaxial tests on soil samples. Although the loading continued up to 20 percent strain level, a steady state zone was observed rather that a unique steady state point which usually forms in uniform sandy soils.
Hosseini et al. (2005) investigated the behavior of a gravely sand with a maximum grain size of 19 mm using critical state concepts. Their results suggest that variations in fabric and structure of gravely sand do affect its behavior. Samples at the same void ratio showed significantly different behavior. However, the critical state line defined in q-p' stress space did not show considerable scatter. Ironically, in n-p' space the test results did not show a unique critical state line. As a result upper and lower limits were defined in this space for the critical state.
In the case of cemented soils there are some papers available in literature. Coop and Atkinson (1993) developed a framework for using critical state concepts in cemented sands. They used a double logarithmic space i.e. Ln(q)-Ln(p') to define the critical state line. They showed that the critical state line for cemented sand is a little lower than that of uncemented one in this space that means a slightly lower friction angle in critical state for cemented soil in comparison to that of uncemented one. They used gypsum plaster as the cementing agent and a light silicon oil to saturate the samples to prevent degredation of cemented gypsum bonds. As they stated, the lower friction angle of cemented soil in critical state may result from cement adhering to the sand particles after yield. It should be noted that the friction angle of gravely sand cemented with gypsum increases with cement content (Hamidi et al., 2004 and Haeri et al., 2005).
Coop and Atkinson (1993) also indicated the critical state line in n:Ln(p') space for gypsum cemented sands. According to their results the critical state line of cemented sand is lower than that for uncemented one in this space.
Cuccovillo and Coop (1999) made a comparison between critical state lines of two intact and reconstituted cemented sandy soil. According to their results both lines were coincided in q:p' stress space. As a result they concluded that the structure does not affect the critical state characteristics of the sandy soil at this space. This is in some contrast with that of Coop and Atkinson (1993).
It should be noted that nearly all previous studies were done using fine and uniform sandy soil except Hosseini et al. (2005) who studied on steady state characteristics of well graded gravely soils.
In the present research, coarse grained sandy gravel with a maximum grain size of 12.5 mm is used to study critical state concepts of gypsum cemented gravely sand. In this regard, some new features of the behavior of cemented grvely sand in steady state condition are illustrated and clarified.
PHYSICAL PROPERTIES OF THE TESTED SOIL
The gradation curve of tested soil is an average of different gradation curves of soils gathered from different parts of Tehran alluvium. The tested soil contains 49 percent sand, 45 percent gravel and 6 percent fines in Unified System of Soil Classification and is named as well graded gravely sand. However, this soil is classified as well graded sandy gravel with fine in British system of soil classification. Figure 1 shows the gradation curve of all samples of Tehran alluvium and also the gradation of tested soil. The maximum particle size is limited to 12.5 mm. The physical properties of the soil are summarized in Table 1. All parameters were determined in the soil mechanics laboratory using standard methods. The ASTM D-854 was applied to determine the specific gravity. Also the ASTM D-4253 and ASTM D-4254 were applied to evaluate the maximum and minimum void ratios respectively. All parameters were evaluated with several tests and the average value was taken.
Figure 1. Gradation curve of tested soil
SAMPLE PREPARATION
Samples were prepared in a three part split mold with an internal diameter of 100 mm and a height of 200 mm. With the maximum particle size of 12.5 mm the ratio of sample diameter to the maximum particle size is about 8. Each sample was prepared in eight layers. For each layer the proper amount of the base soil was mixed with the desired weight of gypsum plaster and 8.5 percent of distilled water. The gypsum contents were 1.5, 3, 4.5 and 6 percent of weight. The mixed material was purred in the mold and compacted until the desired height was reached. The unit weight of soil samples was kept 18 kN/m3. This value corresponds to a relative density of about 65 percents. After sample was prepared, the mold was opened and the sample was cured in a 50°C oven to reach a constant weight. At this time the gypsum bonds reach their maximum strength and stiffness. The temperature was kept constant in curing time. The samples were kept in a time period of about one week to ensure quite dry condition.
TEST PROGRAM
The cured sample was set up on the base pedestal of a standard triaxial cell connected to a digital data logger and electronic sensors. First the outer side of the sample was covered with a thin film of a mixture of clay and fine sand to minimize membrane penetration effects. Two membranes were used with an average thickness of 0.6 mm to prevent membrane being punctured by sharp edges of coarse grains. The sample was saturated using light silicon oil instead of water to prevent the reduction in stiffness and strength of gypsum bonds. The used silicon oil has a very low viscosity of 3.2 mm2/s.
The saturation process was done in three stages. First the CO2 was flushed for an hour through the sample with the minimum available pressure to push out air bubbles trapped in pores. Then, the light silicon oil was flushed from the bottom of the sample with a low hydraulic head until the sample pores are filled and the oil exits from the top of the sample. In order to ensure the saturation of the sample, the cell pressure and back pressure were ramped simultaneously with a low difference of 10 kPa. The back pressure was increased up to 200 kPa. The process continued until Skempton's B coefficient of 0.95 was reached.
The sample consolidated to the desired confining pressure. The volume change was measured exactly at the end of consolidation. After that the axial load was applied with a low rate of 0.2 mm per minute. The cell pressure, back pressure, volume changes, pore pressure, displacement and axial load were recorded using a data logger system.
Table 1. Physical properties of tested soil
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Soil property | Value |
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Soil name | SW-SM |
Specific gravity | 2.58 |
Average particle size | 4 |
Effective diameter | 0.2 |
Fine content | 6 |
Sand content | 49 |
Gravel content | 45 |
Minimum unit weight | 16.00 |
Maximum unit weight | 18.74 |
Average particle size | 4 |
Effective diameter | 0.2 |
Fine content | 6 |
Sand content | 49 |
Gravel content | 45 |
Minimum unit weight | 16.00 |
Maximum unit weight | 18.74 |
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ANALYSIS OF TEST RESULTS
The results of triaxial tests are processed using several variables such as s1, s3, e, ev, e, Du, q, p' and n. The effective major and minor principal stresses are named as s1 and s1; e and ev are the axial and volumetric strains, e is the void ratio and Du is the excess pore pressure, q, p' and n are deviatoric stress, mean effective stress and the specific volume which are defined respectively as:
q = s1 - s3 | (1) |
p'= (s1 + s2 + s3)/3 | (2) |
n = 1 + e | (3) |
CRITICAL STATE SURFACE
The preliminary results of tests on cemented soils can be found in Hamidi et al. (2004) and Haeri et al. (2005). The results of triaxial tests on uncemented soils are extracted from Asghari et al. (2003). Figure 2) shows the stress paths for drained and undrained triaxial tests conducted on the uncemented and 3 percent cemented soil with gypsum. The peak and final states are nearly coincided for uncemented soil samples. As a result the failure envelope and the critical state line are nearly equal for uncemented soil. However, for the cemented soil the peak points of the stress paths are different from the final states shear stress. This results in two different lines for failure envelope and critical state. It seems that cementation increases the distance between failure envelope and the critical state line. Also the figure shows that the final state for drained tests is somewhat higher than that for undrained one. This may result in different critical state lines in drained and undrained conditions. Hamidi et al. (2004) showed that the failure envelopes of the cemented soil are different in drained and undrained conditions. However, ignoring this case, in the present study, a unique line is used to define the critical state of the soil.
Figure 2. The stress paths for uncemented and cemented soil
(a) Uncemented (b) 3% cemented
Figure 3 shows the variation of the specific volume with mean effective stress for uncemented and 3 percent gypsum cemented soil for different confining stresses. For the undrained condition, there are no changes in specific volume of the soil. The variation of the specific volume in uncemented soil in drained state confirms a contractive behavior with continuous reduction in volume at final state. For the cemented soil the specific volume decreases initially and then increases. This shows a dilative behavior in final strains for the soil. It seems that critical state can be determined in n:Ln(p') coordinates for the two groups.
Figure 3. Variation of the specific volume with confining stress
(a) Uncemented (b) 3% cemented
Using the results of the tests, the projection of the critical state surface on q:p' and n:Ln(p') planes were derived. The projection of the critical state surface on q-p' and n:Ln(p') planes can be shown with the following equations that results in two straight lines as follow:
q = M p' | (4) |
n = t - l Ln(p') | (5) |
t is a constant indicating the value of n at the mean effective stress of 1 kPa. This is dependent on the intrinsic characteristics of the soil. The triaxial tests continued until the membrane was punched with sharp edges of coarse grained aggregates. Although two membranes were used for each sample, it was punched due to the existence of subangular coarse gravel grains. However the majority of samples experienced the strain level of about 15 percent or more before membrane puncture. Haeri and Hamidi (2005) showed that the actual critical state in which the mechanical parameters of gravely sand remain constant occurs in strain level of 20 percent or more. As a result there is some approximation in determining the critical state parameters from these tests. However in the present study, the results of tests in which the final axial strain are about 15 percent or more are considered in critical state calculations. The critical state of cemented and uncemented soil in q-p' space is shown in Figure 4) for both drained and undrained tests. As indicated in this figure, a unique line can be assigned to the points associated with the uncemented soil with a very low scatter. While there is a larger scatter in data associated with the cemented soil. It might be reasonable to define lower and upper limits for the critical state condition for cemented soil. The limits are shown in Figure 4 in addition to the best fit for the critical state line. As these limits show, the critical state line of the cemented soil may be lower, upper or coincident with the uncemented soil one. In this regard, Coop and Atkinson (1993) showed that the critical state line of cemented soil is lower than that of uncemented soil. Also Cuccovillo and Coop (1999) indicated that the critical state lines for reconstituted and intact samples are almost coincided. The difference between these researches can be attributed to the different soil fabric, soil structure and cement type.
Figure 4. Critical state line and its limits in q:p' space
The projection of the critical state on n:Ln(p') space is shown in Figure 5). Only the tests with the final axial strains of about 15% or more are considered in this Figure. This figure shows more scatter in data for uncemented soil compared to that of q:p' space shown in Figure 4). This may be attributed to the effect of soil fabric and structure and also to the method of void ratio calculation after consolidation. The scatter in data is more profound for cemented soil as it was observed in q:p' space as well for that soil. However, all the data are located at the right side of the critical state line of uncemented soil. As shown in Figure 5 two sets of limits are defined for both uncemented and cemented specimens. If we use a linear regression for both uncemented and cemented soils, two parallel lines could be drawn. It can be concluded that the critical state lines of uncemented and cemented gravely sands are nearly parallel in n:Ln(p') coordinates, the cemented one being at higher specific volumes.
Figure 5. Critical state and its limits for cemented and uncemented soils in n:Ln(p') space
NORMALIZED CRITICAL STATE LINE
Atkinson and Bransby (1978) defined two parameters to normalize the critical state line as shown in Figure 6.p'e which is the effective mean principle stress associated with an equal specific volume on isotropic consolidation line and p'cs that is the effective mean principle stress associated with an equal specific volume on critical state line. Coop and Atkinson (1993) suggested using the latter parameter due to the large effects of cementation and soil structure on the isotropic consolidation line. Using the equation of the critical state line in n:Ln(p') coordinates, the equation of p'cs for uncemented and cemented soils will be as given in equations 6 and 7 respectively.
p'cs= exp [(1.72-n)/0.053] | (6) |
p'cs= exp [(1.81-n)/0.053] | (7) |
Figure 6. Definition of two parameters for normalizing the critical state line
The stress space for the test results is normalized using p'cs concept as shown in Figure 7). This figure shows that all stress paths move towards a zone that seems to be the critical state locus. Contrary to the uncemented soil, the stress paths move to some levels higher than critical state and then move downward over a surface similar to the Roscoe surface for cemented soil (Roscoe et al., 1958). In this figure a stress path of an uncemented sample under a confining stress of 500 kPa is only presented. The stress path is completely under critical state locus. Haeri et al. (2005) showed that the increase in confining stress reduces the effect of cementation on the shear response of cemented soil due to the break down of the cemented bonds under isotropic pressure during consolidation. As a result we may expect that the cemented soil under very high confining pressures may show a stress path similar to that shown in Figure 7) for uncemented soil. This hypothesis will complete the Roscoe surface for the cemented soil.
Figure 7. Stress paths and critical state locus in normalized stress space
Atkinson and Little (1988) suggested using the two logarithmic coordinates to find the Hvorslev surface for granular material. The projection of the Hvorslev surface on q:p' space is defined for the tested soil and is shown in Figure 8). Although a line can be attributed to each of the cemented and uncemented soils, the scatter in the data shows that defining a limit for each soil as the Hvorslev surface might be more representative. The data corresponding to the critical state are also shown in this figure and the critical state lines and the limits for each soil type are also shown in the figure. Figure 9) shows the projection of the Hvorslev and critical state surfaces on n:Ln(p') space. In this space the scatter in data are more and there are wider limits.
Figure 8. The projection of Hvorslev surface on the q:p' plane
Figure 9. The projection of Hvorslev surface on the n:Ln(p') plane
In order to reduce the scatter in data, both Hvorslev and critical state lines are drawn in normalized coordinates. Both axes are normalized to (p0:p'cs) in which p0 is the amount of initial confining stress. The result is shown in Figure 10). The Hvorslev and critical state lines intersect in the presented normalized space. As indicated in this figure, although the scale is magnified 100 times, the scatter in data for the Hvorslev surface is very low and a unique line can be drawn for it. However, the scatter in data for the critical state line is more obvious. The mentioned normalization process can help us towards the understanding of the behavior of the cemented soil.
Figure 10. The Hvorslev and critical state lines in normalized coordinates
SUMMARY AND CONCLUSION
The critical state concepts were used to investigate the mechanical behavior of a cemented gravely sand. The data associated with the critical state condition of cemented soil in q:p' space has some scatter. As a result it might be better to define a range for the critical state. The defined range shows that the critical state line of a particular cemented soil may be upper, lower or the same as that of uncemented soil. In n:Ln(p') space the data of uncemented soil has more scatter. As a result two sets of limits are defined in this space for uncemented and cemented soils. The Hvorslev surface was defined for the cemented soil as well. The projection of this surface on q:p' and n:Ln(p') spaces are also defined. Due to the effects of soil fabric and structure of tested gravely sand two sets of limits were considered for these two types of soils in n:Ln(p') spaces as there are some scatter in data for these soils. The data are plotted in a normalized space in order to overcome the scatter in data for critical state line and Hvorslev surface.
REFERENCES
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