Geotechnical Properties of Soft Soil and Their Determination
Geotechnical Properties of Soft Soil and Their Determination
Once the consolidation theories and methods of analysis are in place, the next step in the design process is to obtain soil parameters to feed into equations or computer software for analysis. This is not a simple task because the determination of soil parameters is still one of the most challenging tasks facing geotechnical engineers. On the one hand, we need to obtain a value for each soil parameter. On the other hand, few soil parameters are constant. For example, the coefficient of consolidation is assumed to be a constant in either Terzaghi's or Barron's consolidation theory (see Chap. 2). However, in practice, the coefficient of consolidation for soft soil is not a constant. Its value is affected by many factors, such as the overconsolidation ratio, the stress state, the fabric of soil, and even the method of determination (Holtz and Kovacs, 1981; Chu et al., 2002). Therefore, the so-called engineering judgement is sometimes required in deciding which value would be the most appropriate. Good engineering judgement comes from good understanding of soil behavior and the past experiences in dealing with the similar types of soil and geotechnical problems. The coefficient of permeability is another key parameter required for vertical drain design. However, the coefficient of permeability of soil remains one of the most difficult soil parameters to be determined. This is partially because permeability has the widest range of variation among all the soil parameters. Its value can vary from 10−11 m/s
for soft clay to 10−3 m/s for sand and gravel, a change of 108 times. Although the permeability of the soil which has to be treated with vertical drains is normally low, the error in permeability estimation can still easily range from 10 to 100 times. This is not surprising because the permeability of the same soil can change 100 times during the consolidation process. An error of one order of magnitude in permeability can result in an error of the same order of magnitude in the time taken to achieve a specific degree of consolidation based on Terzaghi's consolidation theory.1 Therefore, it makes a lot of economic sense to conduct some proper site investigation and determine the soil parameters as accurately as possible.
The specific soil parameters that are required for designing soil improvement work involving vertical drains in soft clay includes:
- The preconsolidation stress, , and the overconsolidation ratio (OCR).
- The coefficient of consolidation in both horizontal and vertical directions, ch and cv.
- The coefficient of permeability in both horizontal and vertical directions, kh and kv.
- During the installation of vertical drains, the soil surrounding the drain is disturbed by the mandrel which has to be inserted into the soil to install vertical drain. To take this so-called smear effect into consideration, extent of the smeared zone, ds, and the permeability of the smeared soil, ks, need also to be determined.
- The coefficient of compressibility, Cc, the coefficient of recompressibility, Cr, and sometimes the secondary compression index, Cα, are required for settlement estimation.
- The undrained shear strength, cu, and the undrained Young's modulus, Eu, may also be required for analyzing the stability of a dike or the stability of a drain installation rig on soft clay.
As mentioned before, the values of ch and cv, or kh and kv change with stress state or OCR. One has to accept the fact that neither the permeability nor the coefficient of consolidation of soil is a constant. As such, the selection of those parameters has to be based on its in-situ stress conditions and the anticipated stress changes. Therefore, it is also necessary to establish relationships between the coefficient of permeability and void ratio, and relationships between the coefficient of consolidation and the stress state. A proper site investigation should be planned not only to determine the soil parameters but also to understand how the soil parameters vary with stress and loading conditions.
In addition to the soil properties, the properties of vertical drains also need to be determined. This will be discussed in the next chapter as a separate topic.
Generally, the consolidation parameters of soil can be determined using laboratory tests, in-situ tests, and back calculation from field measurements. In laboratory tests, the stress states and drainage conditions can be defined precisely. The variation of soil parameter with stress and consolidation process can be evaluated. However, the results are usually affected by sample disturbance. It is also very time consuming to conduct laboratory consolidation tests. Normally, in-situ tests can be conducted relatively faster, and they are therefore more useful than laboratory tests in identifying the soil profile and characterizing the soil behavior over a large extent. However, in in-situ tests, the stress and drainage conditions are generally not well defined. The data interpretation from physical measurements to soil parameters is sometimes based on arbitrary assumptions or correlations established only for a specific soil. Therefore, when in-situ tests are adopted, laboratory tests are still required to verify the assumptions and the correlations. The back calculation from field measurements can provide a good check on the selection of design parameters. However, the back-calculated value is only a factored parameter. It reflects not only the soil property but also other factors, such as the disturbance to the soil during construction.
The types of laboratory and in-situ tests suitable for determining consolidation properties are summarized in Table 3.1. The settlement prediction methods for projects using vertical drains are
|Table 3.1 Types of test for measurement of consolidation properties.|
|Type of test||Name of test||Parameter determined||Remarks|
|Notes: (i) In this case, kv is calculated based on the value of cv.||ii) When secondary consolidation is measured.||(iii) kh is measured directly as part of the consolidation test.|
|Laboratory test||Oedometer test||cv, kv (indirect measurementi), Cc, Cr, , and||Need good quality ‘undisturbed’ samples|
|Rowe cell test||ch and kh (directiii or indirect measurement)|
|Other consolidometers||ch and kh (direct or indirect measurement)|
|In-situ test||Piezocone dissipation test (CPTU)||ch and kh (indirect measurement)||Based on pore water pressure dissipation|
|Pressuremeter or self-boring pressuremeter (SBPM) test||ch and kh (indirect measurement)||Based on lateral pressure change or pore water pressure dissipation|
|Flat dilatometer test (DMT)||ch and kh (indirect measurement)||Based on lateral stress change|
|Field permeability test (e.g., BAT permeameter)||kh (direct measurement)||Using a piezometer|
|Back-analysis||Based on pore water pressure measurements||ch (factored value)||Using piezometers|
|Based on settlement measurements||ch (factored value)||Using settlement gauges|
the same as for other projects without the use of vertical drains. As these methods are covered in many textbooks (e.g., Holtz and Kovacs, 1981), only the methods for determining the consolidation parameters of soil will be discussed in this chapter. The scope of the discussion will be confined to outlining the methods available
and assessing the merits and limitations of each method, rather than illustrating the details of each method that can be used to determine consolidation parameters.
For soil improvement projects requiring settlement and rate of settlement estimation, laboratory consolidation tests are essential, because the compressibility of the soil is still best estimated by laboratory consolidation tests. If relatively good quality samples can be taken, laboratory test results can be quite reliable (Chu et al., 2002). Laboratory tests are also the most direct means of evaluating the variation of the soil parameters with stress level and consolidation process. The procedure for obtaining consolidation parameters from each test is outlined below with working examples, so that the typical consolidation properties can be discussed with reference to specific tests.
3.2.1 Oedometer Test
Despite its simplicity, the oedometer test can provide reasonably reliable measurements for compressibility and consolidation properties of soft clay in the normally consolidated range (Smith and Jardine, 1991). However, it cannot be used to determine the coefficient of consolidation in the horizontal direction.
An oedometer test is normally conducted using step loadings with the subsequent load being double its previous one. The completion of each stage of consolidation is determined using either the end of primary consolidation (EOP) or the 24-hour loading (24 h) method. In the former, the next stage of load is applied when the primary consolidation is just completed. In the latter, each load is applied for 24 h.
For determining cv, two methods are normally used: (a) Taylor's method, that is the square-root time method and (b) Casagrande's method, that is, the log-time method. In Taylor's method, the dial reading recorded during consolidation is plotted versus the square-root time. An example is shown in Fig. 3.1. Using this curve, the time taken for 90% of consolidation to take place, t90,can be determined.
The cv can then be calculated as:
where T90 =0.848 is the time factor corresponding to 90% average degree of consolidation and Hdr is the drainage path. For double drainage, Hdr = H/2. If single drainage is used, Hdr = H. H is the original height of the oedometer specimen.
If Casagrande's method is used, the dial reading recorded is plotted versus logarithm time. The time taken for 50% of consolidation, t50, is determined. An example is shown in Fig. 3.2. The cv is calculated as:
where T50 =0.197 is the time factor for a 50% average degree of consolidation.
Once cv is determined, the permeability in the vertical direction, kv, can be determined indirectly using the following relationship:
where ρw = 1.0 Mg/m3 and γw = 9.81 kN/m3 is the density and unit weight of water, g = 9.81 kN/m2 is gravity, e0 = initial void ratio, av = the coefficient of compressibility, and mv = the coefficient of volume change. The definitions of av and mv are illustrated in Fig. 3.3.
Some comments on the oedometer test can be made as follows:
- As pointed out before, neither av nor cv is a constant. Consequently, kv is not a constant either. As kv is controlled by both av and cv, it may not increase or decrease monotonically with cv.
- The cv measured by Taylor's method is generally larger than that measured by Casagrande's method. A comparison made for
San Francisco Bay mud is shown in Fig. 3.4. The cv value is also affected by whether the test is conducted using the EOP or 24 h method. An example is shown in Fig. 3.5 for the Singapore marine clay.
- Oedometer test can be used to determine only cv. Although there are suggestions to use a vertically trimmed (i.e., the loading surface is parallel to the axis of the sampling tube) specimen to determine ch (Head, 1986), the value obtained in this way is not reliable (Chu et al., 1997). An example will be given at a later stage.
- The permeability kv can be determined only indirectly from cv using conventional oedometer tests. Direct permeability measurements can be made by modifying the oedometer cell to permit a steady flow in the specimen, for example, Tavenas et al. (1983). One method of using the NTU consolidometer is explained in Sec. 3.2.3.
- It is observed by Tavenas et al. (1983) that the change in void ratio and change in permeability follows the following relationship:
- where Ck = the permeability change index. Its value can be roughly estimated as Ck =0.5e0. The e versus log and e versus log k relationships obtained from direct permeability tests using a modified oedometer cell on Louiseville clay are shown in
Note to Fig. 3.6 The e versus log and e versus log k relationships obtained from direct permeability tests using a modified oedometer cell on Louiseville clay Fig. 3.6. The same relationships can be established for other clays, including the Singapore marine clay, as shown in Fig. 3.7. The relationship given in Eq. (3.4) can be used to determine kv in the normally consolidated (NC) range. In the overconsolidated (OC) range, the change in void ratio ∆e is small, but the change in kv is large. Therefore, Ck in the OC range can be different from that in the NC range.
Example 3.1 Oedometer test on Singapore marine clay
One set of oedometer test on undisturbed Singapore marine clay is shown in Fig. 3.7. The sample was taken from the lower marine clay2.
Note to Fig. 3.7 Oedometer test results on Singapore marine clay: (a) the e versus log and e versus log k relationships; (b) the mv, cv, and kv versus log relationships.
It had an initial void ratio of 2.246. The test was conducted using 24 h loading. The curve is shown in Fig. 3.7(a). From this curve, the preconsolidation stress can be determined as and the compression index and recompression index as Cc =1.33 and Cr =0.2, respectively. It is noted that the curve in the virgin compression range is not straight, that is, the value of Cc decreases with increasing . This is typical of soft clay, as can also be seen in Fig. 3.6 as well. The variations of the coefficient of volume change, mv, coefficient of consolidation, cv, and permeability, kv with are shown in Fig. 3.7(b). Generally, mv and kv reduce with , although the variation is small in the OC range. The cv reduces considerably when exceeds the , but it does not change much in the NC range, as shown in Fig. 3.7(b). This is a very important feature to note when we select the cv value for vertical drain design. The e – log kv relation is shown in Fig. 3.7(a). The Ck value is 1.12, which agrees with 0.5e0 =1.123 well.
3.2.2 Rowe Cell Test
As the oedometer test does not permit horizontal drainage, Rowe cell or other consolidometers which have provisions for horizontal drainage have to be used to determine ch and kh of soil. The Rowe cell was developed by Rowe and Barden (1966) to overcome the disadvantages of oedometer cell and to study the effect of soil fabric. Rowe cells with diameters of 75, 150 and 250 mm are commercially available. As the soil samples are normally within 100 mm in diameter, 75 mm diameter Rowe cell is commonly used. However, if samples with diameter larger than 150mm can be retrieved, it would be better to conduct some consolidation tests using the 150mm diameter Rowe cell, because the ch value is affected by the dimension of the specimen when the soil tested is nonhomogeneous.
184.108.40.206 Testing arrangement
A cross-section view of the Rowe cell is shown in Fig. 3.8. Unlike the oedometer test, the vertical load is applied by hydraulic pressure through a diaphragm. Both the equal stress and equal strain
boundary conditions can be simulated using either a rigid loading plate or a flexible porous plastic disk, as shown in Fig. 3.9(a) or Fig. 3.9(c). The specimen is sealed within the cell. As such, a back pressure can be applied, and the volume change and pore water pressure can be measured.
For the measurement of ch and kh, the drainage conditions can be arranged in one of the following ways: (a) to allow water flow to the periphery and (b) to allow water to flow to the center. In the former, a porous lining, usually porous plastic with the side facing soil smoothed, is used, as shown in Fig. 3.9(a) or (b). In the latter, a center drain, usually sand drain, can be installed, as shown in Fig. 3.9(c) or (d). The sand drain is installed by drilling a hole at the center of the specimen and then filling the hole with sand. The diameter of hole should be less than 10% and ideally 5% of the
sample diameter. The sand should be well graded. The fines and particle size larger than 0.3 mm in the sand should be removed. The sand should be de-aired by boiling it in distilled water. If direct permeability measurement is to be made, both the periphery porous lining and the center drain need to be installed to allow water to flow either from the periphery to the center or from the center to the periphery during permeability measurement.
220.127.116.11 ch Measurement
The procedure for conducting a Rowe cell test is similar to that for an oedometer test, except that the volume change and pore water pressure data are recorded in addition to the vertical displacement. The pore water pressure in the center of the specimen is normally measured. However, when center drain is used, pore water pressure at a point that is 0.55 the radius distance from the center can be measured. When the test is conducted using equal strain, the volume change and vertical displacement can be converted from one to another if both readings are recorded correctly. As the stress distribution is likely to be nonuniform, the pore water pressure measured does not represent the consolidation behavior of the whole specimen. When the test is conducted using equal stress, the specimen does not settle evenly. The vertical displacement measured in the center may not match the volume change any more. In this case, the volume change is more representative of the consolidation behavior of soil.
Taylor's or Casagrande's methods can still be used to determine ch based on vertical displacement or volume change or pore water pressure data. Both Eqs. (3.1) and (3.2) are still applicable, except that in the case of radial drainage, Hdr should be the diameter or the radius of the specimen. However, the time factor, T50 and T90,and the method to determine t50 or t90 will be different depending on the drainage arrangement and boundary conditions. For tests conducted using equal strain or equal stress, the values of T50 and T90 for both outward and inward radial drainage are given in Tables 3.2 and 3.3, respectively. The time factors for cases with vertical drainage are not given in the tables, because it would not be necessary to use Rowe cell to determine cv. This is because the Rowe cell test does
|Table 3.2 Time factors used in data interpretation for Rowe cell tests under equal strain loading (modi.ed from Head, 1986).|
|* Note: The slope factor was 1.15 when using Taylor's method for oedometer test.|
|Radial outward||0.288||Determined from ΔV or ΔH versus √t curve with a slope factor of 1.17*||0.0866||Determined from ΔV or ΔH versus log t curve|
|0.374||Determined from p.w.p. (at the center) versus √t curve with a slope factor of 1.17||0.173||Determined from p.w.p. (at center) versus log t curve|
|Radial inward||2.595||Determined from ΔV or ΔH versus √t curve with a slope factor of 1.17*||0.781||Determined from ΔV or ΔH versus log t curve|
|2.595||Determined from p.w.p. (at 0.55R) versus √t curve with a slope factor of 1.17||0.778||Determined from p.w.p. (at 0.55R) versus log t curve|
|Table 3.3 Time factors used in data interpretation for Rowe cell tests under equal stress loading (modified from Head, 1986).|
|Radial outward||0.335||Determined from ΔV versus t0.465 curve with a slope factor of 1.22.||0.0632||Determined from ΔV versus log t curve|
|0.479||Determined from p.w.p. (at the center) versus t0.465 curve with a slope factor of 1.12||0.20||Determined from p.w.p. (at center) versus log t curve|
|Radial Inward||2.631||Determined from ΔV versus √t curve with a slope factor of 1.17*||0.771||Determined from ΔV versus log t curve|
|2.625||Determined from p.w.p. (at 0.55R) versus √t curve with a slope factor of 1.17||0.765||Determined from p.w.p. (at 0.55R) versus log t curve|
not offer more advantages over the oedometer test as far as cv is concerned.
18.104.22.168 Direct permeability measurement
After ch is determined from consolidation test, kh can be calculated using Eq. (3.3). On the other hand, kh can also be determined directly from the permeability test at the end of each consolidation stage in the Rowe cell test. To achieve this, both a peripheral drain and a center drain need to be installed. During a consolidation test, the drainage is allowed to flow to either the center or the peripheral drain. After the specimen is consolidated under a given stress, a constant head can be applied across the peripheral and the center for permeability measurement. The pore water pressure distribution across the specimen during permeability measurement is illustrated schematically in Fig. 3.10 in which an inward flow is assumed. Using Dracy's law, the permeability can be calculated using the following equation3:
kh = permeability in horizontal direction (m/s),
q = rate of flow(m3/s),
3 Using Dracy's law:
, where z is the elevation head
r2 = radius of specimen (m),
r1 = radius of central well (m),
H = height of specimen (m),
γw = unit weight of water = 9.8kN/m3,
p1 = the pressure at peripheral (kPa) and,
p2 = the pressure at central drain (kPa)
If the permeability of soil is too low, the flow may be too small. As a result, the above illustrated constant head method may not work. One way to overcome the problem is to increase the hydraulic gradient, that is, the pressure difference, p1 − p2. However, the pressure difference has to be controlled within a certain limit to prevent excess stress nonuniformity from occuring inside the soil specimen.
The pressure inside the specimen should also be controlled in such a way that the effective vertical stress and the OCR of the soil will not be greatly affected. Alternatively, the falling head method can be used. A procedure for conducting the falling head permeability test using a modified oedometer cell is described in Tavenas et al. (1983).
It should be pointed out that the Rowe cell test is not easy to conduct because it is prone to testing errors. The reliability of the test data should be verified before the data can be used. Furthermore, the maximum stress which can be applied to a Rowe cell is sometimes limited by the air or water pressure available.
Example 3.2 Rowe cell tests
A Rowe cell test on Singapore marine clay was conducted using a 150mm diameter Rowe cell. The test was conducted with equal strain and radial outward drainage. A center sand drain of 5 mm diameter was installed. The radial drainage path was 73.5 mm. The load was applied in step in the same way as for the oedometer test. The data recorded during the load increment from 80to 160kPa is shown in Fig. 3.11. It can be seen that the pore water pressure and volume change curves are similar in shape, that is,
the pore water pressure dissipation took place simultaneously with volume change. As the test was conducted with equal strain, the volume change calculated based on the vertical settlement agrees well with the volume change measured. Using the volume change measurement, t50 = 210min can be determined. The ch can then be calculated as:
It should be pointed out that ch could not be calculated using pore water pressure measurement because the pore water pressure was measured at 0.55R (R is the radius) position.
Example 3.3 Comparison between tests conducted using Rowe cell and oedometer
A comparison of the oedometer test results and the Rowe cell test results for Singapore marine clay is shown in Fig. 3.12. The two oedometer tests were conducted on a horizontal-cut and a vertical-cut specimen (see Fig. 3.12(a)), respectively. The Rowe test was conducted with horizontal drainage to the boundary. The oedometer test on the vertical-cut specimen was meant to measure ch of soil. It can be seen from Fig. 3.12(b) that the cv (or ch)measured by the two oedometer tests are almost the same, but are smaller than that obtained from the Rowe cell test. Therefore, in terms of ch measured, the method of using the oedometer test on vertical-cut specimen is not reliable.
3.2.3 NTU Consolidometer
Despite its many advantages, the Rowe cell suffers from some disadvantages as mentioned before. A new consolidometer has been developed by Chu et al. (1997) to overcome some of the shortcomings of the Rowe cell and combine some of the advantages of the oedometer cell. A cross-section of the new consolidometer is shown
in Fig. 3.13. It adopts the oedometer setup, but allows flows in the horizontal direction and the measurement of volume change and pore water pressure. To test undisturbed soil specimens trimmed from a 100 mm diameter thin-walled tube sample, the new consolidometer is designed to accommodate an 80mm in diameter by 20mm in height specimen. The device has an enclosed chamber so that the back pressure can be applied, and volume and pore water pressure changes can be measured. The vertical loads on the specimen can be applied in stages through a rigid platen by an oedometer compression frame or by a triaxial compression machine to conduct constant rate of strain tests. The oedometer is also designed as a floating ring to reduce the friction between the specimen and the ring. During the test, all the readings can be taken by a data-logger. The consolidometer is shown in Fig. 3.14.
The vertical and horizontal drainage arrangements for the NTU consolidometer are shown in Fig. 3.15. For double vertical drainage, two porous disks are used at the top and bottom (Fig. 3.15(a)). When single drainage is used, the pore pressure at either the top or the bottom can be measured. For horizontal drainage, a porous plastic ring is used between the specimen and the side wall to permit horizontal flow to the side and then to the porous disk at the base (Figs. 3.15(b) and 3.15(c)). In this case, a latex rubber disk is used at the soil and base porous disk interface to prevent the vertical flow. A thinner stainless steel ring is used so that the dimension of the specimen will be the same as that used for tests with vertical drainage. The pore pressure in the center of the specimen can be measured from the top by a pore pressure transducer.
The new consolidometer also permits the permeability in the horizontal direction to be measured directly. In this case, a sand drain with a diameter of 3–5 mm needs to be installed in the center of the specimen (Fig. 3.15(c)). At the end of each consolidation stage, a pressure head can be applied between the center and the boundary,
and the permeability can be measured by the constant head method discussed in Sec. 3.2.2. A comparison of the coefficient of permeability of Singapore marine clay measured using the NTU consolidometer by tests with different drainage conditions is presented in Fig. 3.16. The permeability measured directly using the constant head method with horizontal flow to the center is also shown in Fig. 3.16. The permeability measured by the direct method is lower than that determined indirectly in this case, although a relatively good agreement was achieved in other tests on Singapore marine clay, as reported by Chu et al. (2002).
3.2.4 The Characteristics of the Consolidation and Permeability Parameters
On the basis of laboratory test data presented above, the following observations can be made:
- cv or ch are not constant, as commonly assumed.
- In general, kh >kv and ch >cv for soft clay deposits due to the
influence of soil fabric (Leroueil et al., 1990; Bo et al., 1998e; and Chu et al., 2002).
- cv or ch decreases drastically as consolidation stress approaches the preconsolidation stress, that is, when the OCR of the soil reduces, see Figs. 3.5, 3.7(b), 3.12(b), and 3.16.
- The change of cv or ch in the normally consolidated range is relatively small and may be approximated as constant, see Figs. 3.7(b), 3.12(b), and 3.16.
It should also be pointed out that cv, ch, kv or kh of remolded soil is lower than that of undisturbed soil tested at the same stress level. The difference is particularly larger in the overconsolidated range (Jamiokowski et al., 1985). Therefore, the ch or kh of the soil in the smear zone, the zone disturbed by the installation of vertical drains, will be smaller than that of the undisturbed soil. That is why the ch or kh of the soil in the smeared zone needs to be determined. The properties of the smeared soil will be discussed later.
3.3.1 Piezometric Cone (CPTU) Dissipation Tests
CPTU dissipation test is one of the most commonly used in-situ tests for soft clay. The test involves pushing in a cone at a constant rate of penetration to a prescribed position and then holding it there to allow the pore water pressure to dissipate. There are several types of cones. One of them is shown in Fig. 3.17. The diameter of the cone is 70 mm. The cone has a cone tip area of 1000 mm2 and a 60°tip angle. It has two porous elements, one on the shoulder of the sleeve and another on the cone tip, as indicated in Fig. 3.17. The cone most commonly used in Singapore is the type which looks the same as that shown in Fig. 3.17, but without the porous element on the cone tip. When the cone penetrates into soft clay, an excess pore water pressure is generated. The rate of dissipation of this pore water pressure can be used to calculate ch:
where t50 = time taken for 50% of consolidation to take place, that is, when ∆u(t)/∆u(0) = 0.5, T50 = Theoretical time factor and, Rr = Radius of the cone.
The dimensionless time factor T50 is affected by factors such as the tip geometry, the porous element location, and the rigidity index of soil, Ir. The rigidity index is defined as G/cu,where G is the shear modulus and cu is the undrained shear strength of the soil. The theoretical solutions given by Baligh and Levadoux (1986) and Teh and Houlsby (1991) are commonly adopted in determining the value of T50.
It should be pointed out that the value of T50 also depends on the methods of analysis adopted. The dissipation curves derived by Baligh and Levadoux (1986) and Teh and Houlsby (1991) for piezometric cone with a single porous element on the shoulder are given in Fig. 3.18. It can be seen that Baligh and Levadoux's (1986) method gives a larger T50 for the same pore pressure ratio. The major difference between the two solutions is that the rigidity index is taken into consideration in Teh and Houlsby's (1991) solution but not in Baligh and Levadoux's (1986). The curve shown in Fig. 3.18 for Teh and Houlsby's solution is given for Ir = 100. For Ir of other values, a modified time factor, T* can be used. T* is defined as (Teh and Houlsby, 1991):
The relationship between the degree of consolidation and the modified time factor T* are given in Table 3.4 for a piezometer element on the shoulder of the cone.
Generally, the ch (CPTU) obtained directly from Eq. (3.6) is normally much larger than the ch back calculated from field monitoring data or the ch value at NC state obtained from laboratory tests (Chu et al., 2002). Baligh and Levadoux (1986) explained that the ch (CPTU) obtained from Eq. (3.6) corresponds to the unloading and reloading, that is, the OC state. To obtain the ch value of soil at the NC state, a conversion has to be made. One suggestion made
|Table 3.4 Relationship between degree of consolidation and the modified time factor (data after Teh and Houlsby, 1991).|
|Degree of consolidation %||20||30||40||50||60||70||80|
by Baligh and Levadoux (1986) is:
Cr and Cc = recompression and compression indices from oedometer test and e0 = initial void ratio. Normally Cr/Cc =0.05to0.10.
Once ch is obtained, the permeability can be determined indirectly using the following relationship:
It is noted that only ch is obtained directly from CPTU tests. To estimate cv, the following relationship may be used:
Some typical kh/kv values are given in Table 3.5.
The pore water pressure dissipation versus time curve obtained from a CPTU holding test in Singapore marine clay is shown in Fig. 3.19. The data can be replotted in a normalized curve as shown in Fig. 3.20. From Fig. 3.20, t50 = 30 min can be obtained. The CPTU used has a diameter of 35 mm or a radius of Rr =17.5 mm.
(a) Using Baligh and Levadoux's (1986) solution: From Fig. 3.18, T50 =5.5
Take the typical value of RR/CR = 0.12 for Singapore marine clay:
|Table 3.5 Typical kh/kv values for soil.|
|Nature of Clay||kh/kv||References|
|Nearly homogeneous clay or massive marine clay||1~2||Olson and Daniel (1981), Leroueil et al. (1990), Bo et al. (1998e)|
|Some macrofabric, for example, marine clay with lenses, etc.||2~4||Chan and Kenney (1973)|
|Deposits containing embedded and more or less continuous permeable layers||3~15||Olson and Daniel (1981), Jamiokowski et al. (1985), Baligh and Levadoux (1986)|
(b) Using Teh and Houlsby's (1991) solution:
Assuming Ir = 100, then from Fig. 3.18 we have: T50 =2.5
The above calculation shows that the ch(NC) calculated using Teh and Houlsby's method is smaller than that using Baligh and Levadoux's method.
The ch versus depth profiles interpreted from CPTU tests in Singapore marine clay at four different locations at Changi East are presented in Fig. 3.21. The rigidity index for Singapore marine clay
was taken as 200, based on SBPT results. The ch values shown in Fig. 3.21 have been converted into those corresponding to the NC state. It can be seen that the ch generally increases with depth, and the data from the four different locations generally fall within a range of 2–4.5 m2/yr. It should be pointed out that the ch obtained using Baligh and Levadoux's (1986) method is typically 40% higher than that using Teh and Houlsby's (1991) method. This difference is mainly because the rigidity index Ir is considered in Teh and Houlsby (1991) but not in Baligh and Levadoux's method (1986). In general, the ch values obtained using Teh and Houlsby (1991) agree better with laboratory measurements. Similar conclusions have also been made by Danziger et al. (1997).
3.3.2 Flat Dilatometer (DMT) Dissipation Tests
The commonly used DMT was the Marchetti type, which has a steel blade of 96 mm in width, 230mm in length, and 14 mm in thickness with an approximate 16° cutting edge, as shown in Fig. 3.22. A 60mm diameter membrane with a sensing disc behind is attached to one side of the blade. A DMT test involves pushing or driving in a DMT blade into the soil and expanding a 60mm diameter thin metal membrane by means of gas pressure. In this test, only the
total lateral stress σh but not the pore water pressure is measured. According to Marchetti and Totani (1989), for test in soft clays, a significant proportion of the measured total lateral stress against the blade is the pore water pressure. The decay of σh corresponds largely to the decay of pore water pressure generated by penetration of the blade. An approximate relationship can be established between the rate of decay of σh and the ch of the soil. Three readings can be taken from the test:
A: lift-off pressure, P0
B: move the center of the membrane for 1.0mm, P1
C: return of the membrane to the lift-off position, P2.
The ch of the soil can then be estimated from a DMT dissipation test using either the A-reading (DMTA) or the C-reading (DMTC).
22.214.171.124 DMTC method
This method was proposed by Schmertmann (1988). The change in C value can be plotted versus √t from which t50 can be obtained.
where R2 =600 mm2 for standard Marchetti dilatometer. T50 = theoretical time factor which is affected by factors such as Eu/cu ratio (Eu and cu are the undrained Young's modulus and shear strength, respectively) and the pore water pressure parameter at failure, Af. Schmertmann (1988) recommended the use of Gupta's (1983) solution for T50. For Af =0.9, the percentage of pore water pressure ∆ui dissipation as a function of E/cu, as derived by Gupta (1983), is reproduced in Fig. 3.23. If Af =0.5, Fig. 3.23 can be used with a correction factor η =0.8, as suggested by Schmertmann (1988). The η value for other Af was not given by Schmertmann (1988). However, if a linear relationship between η and Af can be assumed, the η may be estimated as:
126.96.36.199 DMTA method
This method was proposed by Marchetti and Totani (1989). When the change in DMTA value versus log t is plotted, a point of inflexion, that is, the point of reverse curvature, can be identified. Using the time corresponding to this point, tflex, ch can be calculated as:
where C is a constant with values ranging from 5 to 10. For Singapore marine clay, C = 5 is normally used.
Similar to CPTU dissipation tests, the ch(DMTC) or ch(DMTA) determined from DMT tests corresponds to unloading/reloading range. To obtain the ch value in the normally consolidated range, ch(NC), a correction similar to CPTU test has to be made. Another correction method was suggested by Schmertmann (1988) to use an OCR-dependent deduction factor K:
The K value can be taken as 1–7 corresponding to OCR ranging from heavily OC to NC states, as shown in Table 3.6 (Schmertmann,
|Table 3.6 Relationship between correction factor and OCR.|
|OCR State||K value|
1988). However, whether this method or the method suggested by Baligh and Levadoux (1986) in Eq. (3.8) is more suitable varies from case to case. With the Singapore marine clay, a correction factor given in Eq. (3.8) appears to be more reasonable (Chu et al., 2002).
The DMTC versus √t curve of a DMT dissipation test in Singapore marine clay is shown in Fig. 3.24, from which t50 = 9 min can be determined. The other properties of the soil are: OCR = 2, Eu/cu =100, and Af =0.5.
Using Fig. 3.23, the time factor is 1.1. For Af =0.5, the correction factor η =0.8. Thus,
T50 = 1.1 × 0.8= 0.88
ch(DMTC) = 600T50/t50
= 600 × 0.88/9.0
= 58.7mm2/ min
= 31 m2/yr
Converting to the NC state:
ch(NC)= ch(DMT C)/5= 31/5=6 m2/yr
As in Example 3.5, the DMTA versus log t curve obtained from the same DMT dissipation test is shown in Fig. 3.25, from which tflex =9 min can be determined.
Using Eq. (3.14) and taking C =5, the ch value can be estimated as:
Converting to the NC state:
ch(NC)= ch(DMTA)/5= 30/5=6 m2/yr
The ch(DMTA) obtained agrees well with the ch(DMTC) obtained from Example 3.5. However, sometimes, the point of flexion is not obvious. Consequently, tflex cannot be determined precisely.
For Singapore marine clay at Changi East, the ch versus depth profiles as derived from DMTA dissipation tests at four different locations are presented in Fig. 3.26(a). The ch values presented have been converted to the values at the NC state. It can be seen from Fig. 3.26(a) that the ch values obtained for the four locations are mainly within the range of 1–5 m2/yr. The ch values obtained from DMTC dissipation tests are also plotted in Fig. 3.26(b) together with those from DMTA tests for comparison. Generally, it is observed that the ch values obtained from C-readings are higher, although a good agreement is seen for Location 1C.
3.3.3 Self-Boring Pressuremeter (SBPT) Holding Test
The self-boring pressuremeter was originally developed at Cambridge University. One of the versions is shown in Fig. 3.27. For more information on SBPT see Mair and Wood (1987). During a SBPT holding test, the dissipation of pore water pressure was measured by a pore water pressure cell. The ch values can be calculated using Eq. (3.7) by taking Rr as the radius of the SBPT probe and t50 as the time taken for the excess pore pressure to fall to half its maximum value. For SBPT tests, the time factor T50 depends on the pore water pressure generated at the wall of the probe, and its value can be estimated from the relationship given by Clarke et al. (1979), as shown in Fig. 3.28. In using Fig. 3.28, the undrained shear strength, cu, is required. The value of cu can also be determined from the SBPT. For details refer to Mair and Wood (1987).
Similar to the CPTU and the DMT, the ch values determined from SBPT tests correspond to the unloading/reloading range, and a correction based on Eq. (3) is required to obtain the ch value for the NC range.
The ch versus depth profiles obtained from SBPT tests for Singapore marine clay at four different locations at Changi East, Singapore, are shown in Fig. 3.29(a). These values have been converted to those corresponding to the NC state. It can be seen from Fig. 3.29(a) that the ch values obtained from the four test locations range from 2.5 to 20m2/yr. These values are calculated from the pore water pressure change measured by the pore pressure cell (PPC). Like the DMT, the ch values may also be obtained indirectly using the total stress change measured by the total pressure cell (TPC). A comparison of the two measurements is made in Fig. 3.29(b). The differences between the two measurements appear in general to be insignificant.
3.3.4 BAT Permeability Test
The BAT permeameter developed by Torstensson (1977) was used to determine directly the in-situkh values. The BAT filter was 30mm
in diameter and 40mm in thickness. The tests were carried out as an ‘inflow’ test. As water flowed into the probe, the air pressure in the chamber changed. The value of kh is determined from:
where P0 is the initial system pressure, V0 is the initial gas volume, F is the shape factor, U0 is the static pore water pressure, and Pt is the pressure at time t. All the pressures are absolute.
The kh values measured by BAT permeameter and obtained from other in-situ tests for Singapore marine clay are compared in Fig. 3.30. The comparison shows that the kh values measured by BAT permeameter are lower than the other measurements. The same observation was made at the other locations within the reclamation site, as reported by Bo et al. (1998e).
3.3.5 Comparisons of Different Methods
On the basis of the data obtained for the Singapore marine clay at one site, different methods for determining ch are compared in Fig. 3.31. In Fig. 3.31, the in-situ tests and the Rowe cell test measure the ch values, whereas the conventional oedometer test measures cv. The laboratory and in-situ tests presented in this paper were conducted for the intact soil, that is, before the installation of vertical drains. The ch back calculated based on settlements measured at different elevations are also presented in Fig. 3.31. In the back calculation, the ultimate settlement was estimated from Asaoka's method (Asaoka, 1978). As shown in Fig. 3.31, the back-calculated ch values were lower than the ch values determined by either laboratory or in-situ tests. Similar observations have been
made at other sites for Singapore marine clay (Chu et al., 2002) and by Balasubramaniam et al. (1995) and Chun et al. (1997) for Bangkok clay. Prefabricated vertical drains were used in those sites. It implies that when vertical drains are used in soft marine clay, the overall ch value of the soil can be lower than the ch value of the intact soil. This could be due to the disturbance to soil induced by the installation of vertical drains. The effect of disturbance can be very large, particularly when the drains are installed as a close spacing (Chu et al., 2002).
It has been generally observed from the comparisons made in Fig. 3.31 and from other cases that:
- The ch of Singapore marine clay determined by the Rowe cell test is generally 2–4 times larger than the cv determined by the conventional oedometer test, indicating the anisotropic nature of the soil.
- For Singapore marine clay, the ch value derived from the CPTU dissipation test agrees well with that from the Rowe cell tests, but is generally lower than that from other in-situ tests.
- The ch value obtained from the SBPT holding test exhibits a larger variation in comparison with that from other tests. In general, the ch value measured by SBPT is much larger than that obtained from other in-situ or laboratory tests.
- The ch deduced from the DMT dissipation test is usually larger than that from the CPTU dissipation test, but smaller than that from the SBPT holding test. However, there are other cases where the ch from the DMT is smaller than that from CPTU or larger than that from SBPM (Chu et al., 2002).
As mentioned in the introduction, when vertical drains are installed, an oversized mandrel has to be used to push the drains into the soil. The soil around the drain is disturbed after the installation of drains. As a result, the permeability of the soil in the disturbed zone, or the so-called smear zone, is reduced. A recent study on the consolidation behavior of the Singapore marine clay indicates that the back-calculated coefficient of consolidation for a clay layer installed with drains is smaller than that measured by laboratory on undisturbed soil and in-situ tests (Chu et al., 2002). One of the major reasons for this is the smear effect (Chu et al., 2002). Therefore, the smear effect can become quite significant. This is particularly so when vertical drains are installed at close spacing.
The smear effect has been studied by a number of researchers. Several methods have also been proposed to consider the smear effect in the design of vertical drains, as discussed in Chap. 2. In the method proposed by Hansbo (1981), the smear zone is assumed to be an annulus of smeared clay around the vertical drain. The average degree of consolidation reached can be estimated using Eqs. (2.24) and (2.25) given in Chap. 2. In Eq. (2.24) the diameter of smear zone ds and the permeability of the smeared soil ks have to be determined.
Several studies have been conducted to determine the radius of the smear zone and the effect of smear zone on the consolidation of soil. Hansbo (1981, 1993) estimated ds =(1.5 ~ 3.0)dw. This relation has been commonly used. On the basis of a laboratory study, Indraratna and Redna (1998) observed that the smear zone can be as large as ds =(4 ~ 5)dw. The study made by Holtz and Holm (1972) also suggest that ds be equal to two times the equivalent diameter of the mandrel. The parameter ds is difficult to quantify because it is affected by many factors, such as the type, the shape, and the size of the mandrel, as well as the type and the sensitivity of soil.
The parameter ks is normally estimated using a reduction ratio, ks/kh. Hansbo (1981, 1997) suggested that the ratio be put equal to the ratio of the permeability in the horizontal direction to that in the vertical direction. Indraratna and Redna (1998) reported that the ratio is in the range of 2–3. Some further studies have been carried out at Nanyang Technological University, Singapore. Some of the findings will be briefly introduced below.
3.4.1 Laboratory Model Tests
Some model tests usinga1m in diameter consolidation tank were conducted by Xiao (2002). The schematic diagram of the test setup is shown in Fig. 3.32. A single circular sand drain of 50mm diameter was installed in the center of a clay layer. Miniature pore water pressure transducers were used to measure pore water pressures developed at different radial distances from the drain. The water content distributions in the soil with radial distances are plotted in Fig. 3.33. It can be seen from Fig. 3.33 that the smear zone was about 100 mm in radius, which is about four times the radius of the drain. The excess pore water pressure distribution is also plotted in Fig. 3.34. In terms of pore water pressure change, the smear zone can be 300 mm in radius, which is six times larger than the radius of the drain. Based on this study, the diameter of the smear zone is 4–6 times of the drain diameter, that is, ds =(4 ~ 6)dw. The normalized void ratio versus the normalized radial distance, r/rw, obtained from
Xiao's (2002) model tests are plotted in Fig. 3.35. The normalized void ratio refers to the ratio of the void ratio in the smear zone to that in the intact zone. The normalized radial distance is the radial distance normalized by the radius of the equivalent drain, rw = dw/2. In Fig. 3.35, the test data obtained by Onoue et al. (1991) and Hird and Moseley (2000) from similar model tests are also presented for comparison. It can be seen from Fig. 3.35 that this ds =(4 ~ 6)dw generally holds at least for the three cases compared. However, it should be pointed out that those laboratory model tests were conducted on reconstituted clays in which soil structures did not play a major rule. The undisturbed clay could behave in a way quite different from the reconstituted clay. The smear effect could be larger. To verify this, some field measurements were also made.
3.4.2 Field Tests
188.8.131.52 Excess pore water pressures
Bo et al. (2000c) conducted field tests that included monitoring the pore water pressure changes in the soil during drain installation and measuring the change in permeability values before and after the installation of vertical drains. Before the installation of vertical drains,
piezometers were installed at various elevations and radial distances from the point where the vertical drains were to be installed. Thus, the pore water pressure changes during and after the installation of vertical drains could be monitored.
In one field test, four piezometers, PP-237, PP-239, PP-240, and PP-243 were installed in the soil before installation of vertical drains at elevations of –11.2, –16.2, –20.2, and –37.5 mCD respectively, as shown in Fig. 3.36. A vertical drain was installed at radial distances of 1.27 m from PP-237, PP-240, and PP-243, and 2.85 m from PP-239, as shown in Fig. 3.36. The pore water pressures measured by the four piezometers are presented in Fig. 3.37. It can be seen from Fig. 3.37 that the disturbance of vertical drain installation to soil at a radial distance of 1.27 m is obvious as the pore pressures shot up at three different elevations. However, the disturbance was very small to soil 2.85 m away from the drain, because very little pore water pressure change was monitored. The equivalent drain diameter was 66 mm. If the zone of disturbance was 1.27 m, then the disturbed zone was about 20times the equivalent of drain diameter. It may be argued that the disturbed zone; is not the same as the
smear zone, at least it indicates that the smear zone should be larger than 6dw, the diameter of the smear zone based on laboratory tests.
The excess pore water pressure distributions shown in Fig. 3.37 appear to indicate that the smear zone for the lower marine clay is larger than that for the upper marine clay, that is, the smear zone increases with depth. Generally, during penetration of a mandrel (or a cone), the deeper the soil is, the higher the excess pore water pressure. A higher pore water pressure change will induce a higher hydraulic gradient and a greater change in the stress state in the soil. Thus the soil within a larger domain will be affected. On the other hand, the size of the smear zone may also be related to the sensitivity of the soil. The sensitivity of the lower marine clay is greater than that of the upper marine clay.
184.108.40.206 Change in in-situ permeability
Since it is the reduction in the permeability of soil that affects the performance of vertical drains, BAT permeability tests (see Sec. 3.3.4) were conducted before and after drain installation to determine the change in in-situ permeability. The BAT permeability used was 30mm in diameter and 40mm in length.
The permeability of the undisturbed marine clay as measured before the installation of vertical drains ranged from 10−9 to 10−10 m/s. After the installation of vertical drain, BAT permeability tests were conducted at radial distances of 0.3, 0.5 and 1 m away from the drain at several elevations. The test results are shown in Table 3.7. The results generally indicate that the further away from the drain the smaller the reduction in permeability. The change in permeability became small when the soil was 0.5 m away from the drain in the upper marine clay and 1.0 m away in the lower marine clay. As shown in Table 3.7, the reduction in the permeability ranges from 3.4 to 11.0 times for the upper marine clay, and from 1.8 to 8.1 times for the lower marine clay at a distance of 0.3 m away from the drain. It may be deduced from these results that the radius of the smear zone is between 0.3 and 0.5 m, and the reduction in permeability ranges from 1.8–11.0. In other words, the diameter of the smear zone is: ds =(4.5 ~ 7.6)dw. As for the reduction in the
|Table 3.7 In-situ permeability values measured before and after PVD installation.|
|Elevation (mCD)||Type of marine clay||Prior to penetration (m/s)||After penetration (300 mm) (m/s)||Reduction Ratio||After penetration (500 mm) (m/s)||Reduction Ratio||After penetration (1000 mm)|
|-4.9||Upper||4.9 x 10-10||1.4 x 10-10||3.4||5.2 x 10-10||Nil||2.6 x 10-10|
|-8.0||Upper||7.4 x 10-10||0.7 x 10-10||11.1||6.0 x 10-10||Nil||-|
|-11.0||Upper||0.6 x 10-10||0.8 x 10-10||Nil||5.9 x 10-10||Nil||-|
|-16.4||Lower||14.4 x 10-10||1.8 x 10-10||8.1||9.9 x 10-10||1.5||-|
|-19.9||Lower||13.2 x 10-10||7.3 x 10-10||1.8||10.0 x 10-10||1.3||-|
permeability, the in-situ permeability measurements indicate a reduction in the range of 1.8–11.1 at a distance 300 mm away from the drain, that is, ds =4.5dw.
However, it needs to be pointed out that the BAT permeability test itself is affected by the smear effect. This is because the filter tip has to be pushed into the soil before permeability is measured. The filter tip is smeared in the same way as for vertical drain. Therefore, the permeability values given in Table 3.7 tend to be on the lower side. Nevertheless, the relative magnitudes should still hold.
220.127.116.11 Permeability of remolded soil
Laboratory tests were also conducted on both ‘undisturbed’ and re-molded samples to quantify further the amount of reduction in permeability due to smear effect. The remolded samples were prepared in such a way to maintain the moisture content of the soil at the same level. Some test results are given in Table 3.8.
The reduction ratios shown in Table 3.8 are lower than the ratios obtained from field tests (Table 3.7). This could be partially due to some unavoidable sample disturbance. The permeability of the soil can be considerably underestimated if the samples are disturbed. The tests on the remolded samples, on the other hand, should give a good indication of the permeability of the smeared soil. Therefore, the reduction ratios shown in Table 3.8 are perhaps underestimated. When we compare the permeability of the remolded soil (shown in Table 3.8) with that after PVD installation (shown in Table 3.7),
|Table 3.8 Permeability measured for undisturbed and remolded soil samples.|
|Elevation (mCD)||Type of marine clay||Undisturbed samples (m/s)||Remolded samples (m/s)||Reduction ratio|
|-10.0||Upper||4.2 x 10-10||2.3 x 10-10||1.8|
|-13.0||Upper||3.9 x 10-10||2.4 x 10-10||1.6|
|-18.4||Lower||4.1 x 10-10||2.1 x 10-10||2.0|
we may conclude that after PVD installation, the permeability of the soil within 300 mm from the point of installation is more or less the same as that of the remolded soil. The reduction ratio based on laboratory measurements was from 1.6 to 2.0. This is lower than the ratio obtained by field tests which range from 1.8–11.1. On the basis of this study, a reduction of factor of 2 is only the lower bound value, particularly for structured soil.
To summarize the research findings presented above, the diameter of the smear zone can be 4–7 times larger than the equivalent diameter of the drain, that is, ds =(4 ~ 7)dw. This agrees with the previous studies made by Indraratna and Redna (1998), Onoue et al. (1991) and Hird and Moseley (2000). The reduction factor in permeability can normally be taken as 2. However, a higher reduction factor of 2–10 may have to be considered if the soil is very sensitive or highly structured.
The consolidation properties of soft clay and the parameters required to analyze the consolidation process of soft clay with vertical drains are described in this chapter. Laboratory and in-situ methods that can be used to determine those parameters are discussed, as also the properties of the soil in the smeared zone and the range of the smear zone. To sum up, there are three key points to be noted. First, neither the coefficient of permeability nor the coefficient of consolidation is a constant. Both parameters vary with the stress states and stress history of soil. Knowledge of the in-situ stress history and loading conditions are required before suitable soil parameters can be determined. Second, some special laboratory or in-situ testing techniques are required in determining the permeability and coefficient of consolidation in the horizontal directions. Third, the smear effect can reduce considerably the permeability in the smeared zone. So, when vertical drains are installed at a close spacing, the smear effect has to be taken into consideration.
"Geotechnical Properties of Soft Soil and Their Determination." Soil Improvement: Prefabricated Vertical Drain Techniques. . Encyclopedia.com. 21 Sep. 2018 <http://www.encyclopedia.com>.
"Geotechnical Properties of Soft Soil and Their Determination." Soil Improvement: Prefabricated Vertical Drain Techniques. . Encyclopedia.com. (September 21, 2018). http://www.encyclopedia.com/construction/engineering-construction-and-transportation-magazines/geotechnical-properties-soft-soil-and-their-determination
"Geotechnical Properties of Soft Soil and Their Determination." Soil Improvement: Prefabricated Vertical Drain Techniques. . Retrieved September 21, 2018 from Encyclopedia.com: http://www.encyclopedia.com/construction/engineering-construction-and-transportation-magazines/geotechnical-properties-soft-soil-and-their-determination
Encyclopedia.com gives you the ability to cite reference entries and articles according to common styles from the Modern Language Association (MLA), The Chicago Manual of Style, and the American Psychological Association (APA).
Within the “Cite this article” tool, pick a style to see how all available information looks when formatted according to that style. Then, copy and paste the text into your bibliography or works cited list.
Because each style has its own formatting nuances that evolve over time and not all information is available for every reference entry or article, Encyclopedia.com cannot guarantee each citation it generates. Therefore, it’s best to use Encyclopedia.com citations as a starting point before checking the style against your school or publication’s requirements and the most-recent information available at these sites:
Modern Language Association
The Chicago Manual of Style
American Psychological Association
- Most online reference entries and articles do not have page numbers. Therefore, that information is unavailable for most Encyclopedia.com content. However, the date of retrieval is often important. Refer to each style’s convention regarding the best way to format page numbers and retrieval dates.
- In addition to the MLA, Chicago, and APA styles, your school, university, publication, or institution may have its own requirements for citations. Therefore, be sure to refer to those guidelines when editing your bibliography or works cited list.