Description:DESCRIPTION:
Field of the invention:
[0001] The present disclosure generally relates to the technical field of geotechnical engineering, related to a method for determination of radial coefficient (Cr) of consolidation in clays of high compressibility by obtaining the relation between the coefficients of consolidation in radial and vertical directions (Cr and Cv).
Background of the invention:
[0002] Saturated clays, commonly encountered near water bodies and coastal plains, pose challenges for construction due to their tendency to settle under load. The settlement of structures on these soils is influenced by the compression index (Cc), while the time required for consolidation completion depends on the coefficients of consolidation (Cv and Cr).

[0003] The coefficient of consolidation in the radial direction (Cr) describes the rate of pore pressure dissipation and volume change when stress is applied. Cr is crucial for designing efficient PVD systems used to accelerate consolidation in clay soils. However, there are limitations associated with determining Cr. Standard geotechnical tests primarily measure the coefficient of consolidation in the vertical direction (Cv). Particular laboratory tests for Cr exists, but they are less common and require specialized equipment. While some correlations attempt to estimate Cr based on Cv, their accuracy can be unreliable and time consuming.

[0004] Due to the focus on Cv and the lack of readily available Cr data for various clays, design engineers often resort to estimations or assumptions for Cr, potentially leading to inefficiencies in PVD system design. These limitations in obtaining reliable Cr data for particular clay types hinder the effectiveness of ground improvement projects for saturated clays.

[0005] The existing approaches present no particular relationship between Cv and Cr for different types of clays. The designers often assume the value of Cr based on the known value of Cv, to design the PVDs. Cr on the other hand, has the maximum impact on the draining parameters of soft soils is an important parameter in the design of PVD’s and other types of ground improvement systems, especially for soft clays. Hence, there is a need to establish a reliable relation between Cv and Cr for particular clay types, for better design and effective performance of PVDs.

[0006] By addressing all the above-mentioned problems, there is a need for a method for determining radial coefficient (Cr) of consolidation in a particular type of clay with high compressibility by obtaining the relation between the coefficients of consolidation in radial and vertical directions (Cr and Cv). There is also a need for a method that eliminates the need for complex Cr testing and empowers engineers to design more efficient prefabricated vertical drain (PVD) systems for clays by providing a user-friendly method for determining Cr based on Cv data. There is also a need for a method that facilitates the design of effective PVD systems, thereby providing improved ground stabilisation practices for construction projects involving saturated clays, mitigating settlement risks, and enhancing the long-term performance of structures built on the soils. Further, there is a need for a method that provides a straightforward and practical method for engineers to implement in real-world applications, improving the efficiency and effectiveness of ground improvement practices.
Objectives of the invention:
[0007] The primary objective of the present invention is to provide a method for determining radial coefficient (Cr) of consolidation in a particular type of clay with high compressibility by obtaining the relation between the coefficients of consolidation in radial and vertical directions (Cr and Cv).

[0008] Another objective of the present invention is to provide a method that eliminates the need for complex Cr testing methods.

[0009] Another objective of the present invention is to provide a method that empowers engineers to design more efficient prefabricated vertical drain (PVD) systems for clay foundations by providing a user-friendly method for determining Cr based on Cv data.

[0010] Another objective of the present invention is to provide a method that facilitates the design of effective PVD systems, thereby providing ground stabilization practices for construction projects involving saturated clays, mitigating settlement risks, and enhancing the long-term performance of structures built on the soils.

[0011] Another objective of the present invention is to provide a method that provides accurate Cr data, which allows optimal PVD spacing and configuration, thereby leading to faster consolidation and improved foundation stability.

[0012] The other objective of the present invention is to provide a method for engineers to implement in real-world applications, improving the efficiency and effectiveness of ground improvement practices.
Summary of the invention:
[0013] The present disclosure proposes a method for determination radial coefficient of consolidation (Cr) in clays of high compressibility. The following presents a simplified summary in order to provide a basic understanding of some aspects of the claimed subject matter. This summary is not an extensive overview. It is not intended to identify key/critical elements or to delineate the scope of the claimed subject matter. Its sole purpose is to present some concepts in a simplified form as a prelude to the more detailed description that is presented later.

[0014] In order to overcome the above deficiencies of the prior art, the present disclosure is to solve the technical problem to provide a method for determination radial coefficient of consolidation (Cr) in clays of high compressibility by obtaining the relation between the coefficients of consolidation in radial and vertical directions (Cr and Cv).

[0015] According to one aspect, the invention provides a method for determining the coefficient of consolidation in radial direction for saturated clays. The method eliminates the need for complex Cr testing methods and empowers engineers to design more efficient prefabricated vertical drain (PVD) systems for clay foundations by providing a user-friendly method for determining Cr based on data. The method facilitates the design of effective PVD systems, thereby providing improved ground stabilization practices for construction projects involving saturated clays, mitigating settlement risks, and enhancing long-term performance of structures built on the soils. The method provides accurate Cr data, which allows optimal PVD spacing and configuration, thereby leading to faster consolidation and improved foundation stability.

[0016] Two clay samples are collected from various depths in boreholes and subjected to laboratory tests to determine plurality of index properties and consolidation characteristics. The index properties include water content, atterberg limits, grain size distribution, specific gravity, and void ratio. In one embodiment herein, the consolidation characteristics include the coefficient of vertical consolidation (Cv), compression index (Cc), coefficient of volume compressibility, and the coefficient of radial consolidation (Cr). The collected clay samples are classified as high compressibility clays (CH) according to the Indian standard soil classification system.

[0017] At another step, one or more tests are conducted for the tested clay samples by an oedometer to determine the coefficient of consolidation in a vertical direction (Cv), thereby obtaining Cv data. In one embodiment herein, the oedometer is having a diameter of at least 60 mm and a height of at least 20 mm.

[0018] The tested clay samples are subjected to specialized radial consolidation tests and curve fitting techniques for determining the coefficient of consolidation in a radial direction (Cr), thereby obtaining Cr data. In one embodiment herein, the curve fitting techniques includes log t method, inflection point method, and one-point method.

[0019] At another step, the Cv and the Cr ratios are analyzed based on the determined Cv data and the Cr data, thereby obtaining a correlation between the Cr / Cv for determining the Cr for high compressible clays (CH).

[0020] Further, at other step, the variation of the analyzed Cv and Cr ratios is investigated by applying consolidation pressure to the two clay samples. The applied consolidation pressure varies between 0.25-2.4 kg/cm².

[0021] Further, objects and advantages of the present invention will be apparent from a study of the following portion of the specification, the claims, and the attached drawings.
Detailed description of drawings:
[0022] The accompanying drawings, which are incorporated in and constitute a part of the specification, illustrate an embodiment of the invention, and, together with the description, explain the principles of the invention.

[0023] FIG. 1 illustrates a flowchart of a method for determining coefficient of consolidation in radial direction for saturated clays, in accordance to an exemplary embodiment of the invention.

[0024] FIG. 2 illustrates a graph representing the variation of Cr/ Cv ratios obtained by different methods with consolidation pressure (p) of at least one clay sample, in accordance to an exemplary embodiment of the invention.

[0025] FIG. 3 illustrates a graph representing the variation of Cr/ Cv ratios obtained by different methods with consolidation pressure (p) of at least one clay sample, in accordance to an exemplary embodiment of the invention.

[0026] FIG. 4 illustrates a graph representing the variation of consolidation pressure (p) and the ratio of coefficient of consolidation in a radial and vertical direction, in accordance to an exemplary embodiment of the invention.
Detailed invention disclosure:
[0027] Various embodiments of the present invention will be described in reference to the accompanying drawings. Wherever possible, same or similar reference numerals are used in the drawings and the description to refer to the same or like parts or steps.

[0028] The present disclosure has been made with a view towards solving the problem with the prior art described above, and it is an object of the present invention to provide a method for determination of radial coefficient of consolidation (Cr) in clays of high compressibility by obtaining the relation between the coefficients of consolidation in radial and vertical directions (Cr and Cv).

[0029] According to one exemplary embodiment of the invention, FIG. 1 refers to a flowchart 100 of a method for determining coefficient of consolidation in radial direction for saturated clays. The method eliminates the need for complex Cr testing methods. The method empowers engineers to design more efficient prefabricated vertical drain (PVD) systems for clay foundations by providing a user-friendly method for determining Cr based on Cv data. The method facilitates the design of effective PVD systems, thereby providing improved ground stabilization practices for construction projects involving saturated clays, mitigating settlement risks, and enhancing long-term performance of structures built on the soils. The method provides accurate Cr data, which allows optimal PVD spacing and configuration, thereby leading to faster consolidation and improved foundation stability.

[0030] At step 102, two clay samples are collected from various depths in boreholes and subjected to laboratory tests to determine index properties and consolidation characteristics. In one embodiment herein, the index properties includes water content, atterberg limits, grain size distribution, specific gravity, and void ratio. In one embodiment herein, the consolidation characteristics include the coefficient of vertical consolidation (Cv), compression index (Cc), coefficient of volume compressibility (Mv), and the coefficient of radial consolidation (Cr).

[0031] In one embodiment herein, one clay sample with a high percentage of fines (87%), a liquid limit of 88%, a plastic limit of 26%, and a differential free swell of 73%. In one embodiment herein, another clay sample has the high percentage of fines (92%), the liquid limit of 96.5%, the plastic limit of 27%, and the differential free swell of 82%. The two clay samples are classified as high compressible clays (CH) according to the Indian standard soil classification system. The properties of the clay samples are shown in Table 1.

[0032] Table 1: Properties of the Clay Samples

S.No
Property Value
Clay Sample 1 Clay Sample 2
1 Grain size distribution
(a) Gravel (%)
(b) Sand (%)
(c) Fines (%)
0
13
87
0
8
92
2 Specific gravity 2.74 2.75
3 Plasticity Characteristics
a) Liquid Limit (%)
b) Plastic Limit (%)
c) Plasticity index (%)
d) Shrinkage limit
88
26
62
7.53
96.5
27
69.5
8.53
4 IS Classification CH CH
5 Differential Free Swell (%) 73 82
6 Compression index (Cc) 0.69 0.88

[0033] In one embodiment herein, the coefficient of consolidation in the vertical direction (Cv) is a standard parameter measured in laboratory oedometer test. It describes the rate at which water gets drained out vertically from the soil pores when vertical stress is applied. A higher Cv indicates faster consolidation in this direction.

[0034] In one embodiment herein, the coefficient of consolidation in the radial direction (Cr) describes the rate at which water gets drained out sideways from the soil pores when stress is applied. It's particularly important for PVD systems, as these drains collect water flowing radially within the clay layer. A higher Cr indicates faster radial drainage, making PVDs more effective.

[0035] At step 104, tests are conducted on clay samples in an oedometer to determine the coefficient of consolidation in a vertical direction (Cv), thereby obtaining Cv data. In one embodiment herein, the oedometer is having a diameter of at least 60 mm and a height of at least 20 mm.

[0036] The oedometer is also known as fixed ring type consolidometer, a laboratory device used in geotechnical engineering to measure the consolidation characteristics of soil samples, particularly how much they compress due to expulsion of pore water under increasing vertical loads. This information is crucial for understanding the behavior of foundations under structures and designing stable foundations for buildings, roads, and other infrastructure projects.

[0037] Initially, a saturated soil sample is placed in the oedometer. Vertical loads are applied in stages, and for each load increment, the settlement of the sample is monitored over time until the rate of settlement becomes negligible. The time for this process may vary from minutes to days. The data on load, settlement, and time is used to determine the soil compressibility (compression index, Cc) and coefficient of consolidation in the vertical direction (Cv). The Cv reflects the rate at which water is drained out of the soil pores under pressure.

[0038] The data obtained from oedometer tests are used for various geotechnical engineering applications such as settlement prediction, design of foundations, evaluation of soil improvement techniques, and understanding of soil behavior. The data obtained from the oedometer is used for estimating the amount of settlement under the weight of a structure. The data obtained is used for selecting the appropriate foundation type and depth based on the soil bearing capacity and settlement characteristics.

[0039] The data obtained from the oedometer is used for assessing the effectiveness of ground improvement methods like soil replacement or grouting by comparing the consolidation behavior of treated and untreated soil samples. The data obtained from the oedometer is used for investigating the compressibility and seepage properties of different soil types.

[0040] At step 106, the tested clay samples are subjected to specialized radial consolidation tests and curve fitting techniques for determining the coefficient of consolidation in a radial direction (Cr), thereby obtaining Cr data. The curve fitting techniques includes log t method, inflection point method, and one-point method.

[0041] In one embodiment herein, the specialized radial consolidation laboratory tests involve a cylindrical clay sample placed in a cell with a central drainage path or compartments allowing for radial water flow. By applying constant stress and monitoring the pore pressure dissipation or volume change with time, Cr can be calculated.

[0042] The log t method involves plotting the logarithm of time (log t) versus the degree of consolidation (U) obtained from the oedometer test. The slope of a specific portion of the curve is related to Cv, and further calculations could be used to estimate Cr. The inflection point method identifies the inflection point on the U vs t curve from the oedometer test. The time at this point is used along with the sample dimensions and other soil properties to estimate Cr.

[0043] In one embodiment herein, the one-point method is a simplified method using a single data point from the U vs t curve. The time corresponding to a specific degree of consolidation (e.g., 50%) is used with empirical correlations to estimate Cr.

[0044] At step 108, the Cv and the Cr ratios are analyzed based on the determined Cv data and the Cr data, thereby obtaining a correlation between the Cr/Cv for estimating the Cr for high compressible clays (CH).

[0045] Further, at step 110, the variation of the analyzed Cv and Cr ratios is investigated by applying consolidation pressure to the two clay samples. The applied consolidation pressure varies between 0.25-2.4 kg/cm².

[0046] According to another exemplary embodiment of the invention, FIG. 2 refers to a graph 200 representing the variation of the Cr and the Cv ratios obtained by different methods with consolidation pressure (p) of one clay sample. In one embodiment herein, the vertical consolidation tests are conducted for the clay samples using an oedometer of 60mm diameter and 20mm height. Using the data of consolidation tests performed on clay samples, the coefficient of consolidation in the vertical direction (Cv) is determined using Taylor's method, Casagrande’s method, log (H2/t) vs. U curves method, one-point and vt60 Feng and Lee’s method under different consolidation pressures (0.1kg/cm2, 0.2 kg/cm2, 0.4 kg/cm2, 0.8 kg/cm2, 1.6 kg/cm2 and 3.2 kg/cm2).

[0047] The radial consolidation test for the clays was done using an oedometer of 60mm diameter and 20 mm height. A central sand drain of diameter 10mm (i.e., n=6) is made with clean sand passing through 425 µ sieve and retained on 75 µ sieve, poured in loose state to reduce the smear effect. The compression readings are measured using a dial gauge of least count 0.002. The Cr is determined using steepest tangent, log t, Inflection-point, One-point and log (de2/t) vs. Ur methods, at different normal pressures (0.1kg/cm2, 0.2 kg/cm2, 0.4 kg/cm2, 0.8 kg/cm2, 1.6 kg/cm2 and 3.2 kg/cm2).

[0048] In one embodiment herein, the horizontal axis represents the consolidation pressure (p) applied to the clay samples, measured in kilograms per square centimeter (kg/cm²). The vertical axis represents the ratio between the coefficient of consolidation in the radial direction (Cr) and the coefficient of consolidation in the vertical direction (Cv).

[0049] In one embodiment herein, the graph 200 shows two lines, representing the Cr/Cv ratios for the two different clay samples. The Cr/Cv ratio appears to change with consolidation pressure (p) for both clay samples. The plots show Cr/Cv ratios against applied normal pressures (from 0.2-3.2 kg/cm2) for both the samples in various methods such as the Log t, Inflection point, one-point, and log (de2/t) vs Ur curve methods.

[0050] Table 2: Cr/Cv ratios obtained from different methods for clay sample 1
Normal
Pressure p (kg/cm2) Log t method Inflection point method Log(de2/t) vs U method One-point method
0.1 1.31 1.66 0.69 0.59
0.2 0.78 2.97 0.71 0.53
0.4 1.69 3.51 1.43 1.01
0.8 2.55 4.0 2.61 1.68
1.6 3.4 5.17 3.70 2.12
3.2 4.26 6.72 4.8 2.92

[0051] Table 3: Cr/Cv ratios obtained from different methods for clay sample 2
Normal Pressure p (kg/cm2) Log t method Inflection point method Log(de2/t) vs U method One-point method
0.1 1.83 2.93 3.47 0.94
0.2 0.72 2.43 1.24 0.28
0.4 1.46 2.98 1.95 0.81
0.8 3.53 4.13 3.21 1.97
1.6 5.15 7.16 4.83 2.98
3.2 7.5 10.6 6.50 3.87

[0052] The average Cv values determined using Taylor’s method are found to be 2.6 and 3.3 times the Cv values evaluated from Casagrande’s method for the two samples.

[0053] According to another exemplary embodiment of the invention, FIG. 3 refers to a graph 300 representing the variation of Cr/ Cv ratios obtained by different methods with consolidation pressure (p) of one clay sample. The ratio of coefficients of consolidation in radial and vertical directions (Cr/Cv) for sample 1 and sample 2 under load increments of 0.2-3.2 kg/cm2 is given in Table 4 and Table 5 respectively.

[0054] Table 4: Cr/Cv ratios of clay sample 1 for different pressure ranges
Range of Normal Pressure p (kg/cm2) Log t method Inflection point method Log(de2/t) vs. U method One-point method
>0.1 = 0.4 1.26 2.72 0.9 0.71
>0.4 = 0.8 2.56 3.7 3.53 1.94
>0.8 = 1.6 3.4 4.12 5.21 2.53
>1.6 = 3.2 4.26 5.5 4.11 2.12

[0055] Table 5: Cr/Cv ratios of clay sample 2 for different pressure ranges
Range of Normal Pressure p (kg/cm2) Log t method Inflection point method Log(de2/t) vs U method One-point method
>0.1 = 0.4 1.35 1.9 2.22 0.68
>0.4 = 0.8 2.53 4.43 2.6 1.4
>0.8 = 1.6 5.15 5.87 3.7 2.48
>1.6 = 3.2 7.46 9.15 5.9 3.7

[0056] According to another exemplary embodiment of the invention, FIG. 4 refers to a graph 400 representing the variation of consolidation pressure (p) and the ratio of coefficient of consolidation in a radial and vertical direction. The relation generated after performing the experimental work is Cr/Cv = 1.688 ln (p) + 3.766 and the regression coefficient obtained is 0.999. The average values of Cr/Cv for different ranges of pressures are presented in Table 6.

[0057] Table 6: Average values of Cr/Cv for different pressure ranges
Normal Pressure p (kg/cm2) Log t method Inflection point method Log(de2/t) vs U method One-point method
0.1 – 0.4 1.31 2.3 1.6 0.7
0.4 – 0.8 2.55 4.07 3.07 1.67
0.8 – 1.6 4.3 5.0 4.5 2.5
1.6 – 3.2 5.86 7.3 5.0 2.9

[0058] The relationship between the coefficients of consolidation in the vertical and radial directions is given in Table 7 and the variation is plotted in the graph 300 of the FIG. 3.

[0059] Table 7: Average values of Cr/Cv for different pressures
Average Normal Pressure p (kg/cm2) Cr/Cv
0.25 1.47
0.6 2.84
1.2 4.06
2.4 5.28

[0060] Numerous advantages of the present disclosure may be apparent from the discussion above. In accordance with the present disclosure a method for determining radial coefficient (Cr) of consolidation, is disclosed. The proposed invention provides a method for determining radial coefficient (Cr) of consolidation in a particular type of clay with high compressibility by obtaining the relation between the coefficients of consolidation in radial and vertical directions (Cr and Cv).

[0061] The method eliminates the need for complex Cr testing methods. The method empowers engineers to design more efficient prefabricated vertical drain (PVD) systems for clay foundations by providing a user-friendly method for determining Cr based on Cv data. It facilitates the design of effective PVD systems, thereby providing improved ground stabilization practices for construction projects involving saturated clays, mitigating settlement risks, and enhancing long-term performance of structures built on the soils. The method provides accurate Cr data, which allows optimal PVD spacing and configuration, thereby leading to faster consolidation and improved foundation stability. The method provides a straightforward and practical method for engineers to implement in real-world applications, improving the efficiency and effectiveness of ground improvement practices.

[0062] It will readily be apparent that numerous modifications and alterations can be made to the processes described in the foregoing examples without departing from the principles underlying the invention, and all such modifications and alterations are intended to be embraced by this application.
, Claims:CLAIMS:
I/We Claim:
1. A method for determination of radial coefficient of consolidation in clays of high compressibility, comprising:
collecting two clay samples from various depths in boreholes and subjecting the two collected clay samples to laboratory tests for determining plurality of index properties and consolidation characteristics;
conducting one or more tests for the clay samples in an oedometer to determine the coefficient of consolidation in a vertical direction (Cv), thereby obtaining Cv data;
conducting specialized radial consolidation tests and plurality of curve fitting techniques to the tested clay samples for determining the coefficient of consolidation in a radial direction (Cr), thereby obtaining Cr data; and
analyzing ratios of the Cv and the Cr based on the determined Cv data and the Cr data, thereby obtaining a correlation between the Cr/Cv for estimating the Cr for high compressible clays (CH);
2. The method as claimed in claim 1, wherein the method comprises:
applying consolidation pressure to the two clay samples and investigating the variation of the analyzed Cv and Cr ratios.
3. The method as claimed in claim 2, wherein the applied consolidation pressure varies between 0.25-2.4 kg/cm².
4. The method as claimed in claim 1, wherein the plurality of index properties includes water content, atterberg limits, grain size distribution, specific gravity, and void ratio.
5. The method as claimed in claim 1, wherein the consolidation characteristics include the coefficient of vertical consolidation (Cv), compression index (Cc), coefficient of volume compressibility (Mv), and the coefficient of radial consolidation (Cr).
6. The method as claimed in claim 1, wherein the plurality of curve fitting techniques includes log t method, inflection point method, and one-point method.
7. The method as claimed in claim 1, wherein the two collected clay samples are classified as high compressible clays (CH) according to the Indian standard soil classification system.
8. The method as claimed in claim 1, wherein the oedometer having a diameter of at least 60 mm and a height of 20 mm.