Effect of Compaction Energy on the Behavior of Coefficient of Consolidation for the Compacted Fine-Grained Soils

Abstract

Construction exploits marginal areas and landfills due to a lack of suitable worksites. Several researchers are interested in the engineering behavior of compacted fine-grained soils. Clay mineral composition suggests compacted fine-grained soils behave physicochemically. Six natural soils and one artificial soil with varying clay mineralogical compositions (kaolinite, montmorillonite, and K-M) and liquid limits (46, 55, and 68%) were selected and they were categorized into three different groups [G-1 (46%) {K & M-soils}, G-2 (55%) {K & M-soils}, and G-3 (68%) {K, M, & K-M soils}. Consolidation tests were conducted in one dimension under various placement conditions (95% of optimal on dry and wet sides and at optimum), energy levels (Light (LC) and Heavy Compaction (HC)), and seated pressures (σ) from 6.25 to 1600 kPa (@ load increment ratio of 1). The effect of energy level concept was studied by defining the energy ratio of Cv (CvER) = {Cv @ HC/Cv @ LC}) and average ratio (CvAR = Average of CvER) using Proctor compaction energy ratio or standard energy ratio (SER). The values of Cv for heavy compaction can be estimated directly from light compaction energy level values using correlations (R² = 0.86 to 0.99).

1. Introduction

There are three primary criteria of structures found on soils: strength, stiffness, and stability, for which the subsoil is expected to be in a compacted state. These properties provide the scope for numerous studies on compacted soils. The study of compacted soils becomes all the more critical in the present-day scenario wherein the lack of good bearing capacity in constructional sites is forcing the people to use the sites that have been considered for ages as unsuitable for constructional activities. Compressibility is one of the essential factors to be considered, and it is because the number of good construction sites available for construction is becoming a significant challenge for the construction industry. It is imperative that the construction be done on soils with low bearing capacity, susceptible to large settlements. Given the ever-growing demand for construction sites, it is inevitable to reclaim the marginal lands after subjecting them to various ground improvement techniques. In the consolidation behavior of the soil, the main factor controlling the soil behavior like settlement and time of consolidation is the Coefficient of Consolidation (Cv). The Cv depends upon the soil’s compression and void ratio and the load or pressure acting on it. The compression of soil depends upon the clay mineralogical composition of the soil. In this present experimental study, the variation of Cv is compared for the soils compacted at standard Proctor energy and modified Proctor energy (independent of placement conditions and typical methods of determining the Cv) and the magnitude of Cv values were compared with the effect of energy ratio of Cv (Cv_ER) with reference to the standard energy ratio (SER).

2. Literature review on consolidation studies

McRae [1] developed an index for compaction effort, which is used for the amount of effort required for the compaction of different types of soils. Several researchers like Hilf [2], Jumikis [3], Ring et al. [4], and Wang and Huang [5] have described methods to estimate the optimum water content and maximum dry unit weight of fine-grained soils for standard Proctor compaction test. Benson and Trust [6] conducted the hydraulic conductivity test on thirteen compacted clays compacted to different compaction efforts. Blotz et al. [7] described an empirical method for estimating maximum dry unit weight (γ_d max) and optimum moisture content (OMC) of clayey soils for different compaction energies.

The coefficient of consolidation (Cv) is a vital consolidation characteristic of a soil required during the time rate of consolidation analysis. Terzaghi’s one-dimensional consolidation theory [8], Biot’s theory of three-dimensional consolidation [9], and large strain consolidation theory (Mikasa [10], Gibson et al., [11], Monte and Krizek [12]) are some of the theories developed to model the complex process of consolidation. However, for minimal strain conditions Terzaghi’s one-dimensional consolidation theory can be used for the time rate of consolidation analysis. The study of clay mineralogy on Coefficient of Consolidation by Robinson and Allam [13] showed that for different clay mineralogy of soils, the coefficient of consolidation varies for different pressure ranges and is analyzed through original compression behavior. The increase in Cv values with a variation of pressure for different clay minerals like kaolinite and illite powdered quartz is observed, and the mechanical properties characterize their compressibility behavior. Montmorillonite clay mineral with water as pore fluid within which the compressibility behavior characterized physico-chemical properties of soil, and the variation of Cv with consolidation pressure depends upon compressibility behavior in terms governed by the mechanical or physico-chemical properties of soil. Shiva Prashanth Kumar et al. [14] studied the Coefficient of Consolidation (Cv) in CH soils where Cv for applied pressure was compared with three different methods of determining Cv. The methods involved are Casagrande logarithm of time fitting [15], Taylor’s square root of time fitting [16], and inflection point [17]. For all the selected soils, the Cv with applied pressure was correlated by a power law and had the same trend of variation for the pressure range of 50 to 1600 kPa. Madhav and Kurma Rao [18] studied the consolidation characteristics of Kaolinitic clay and concluded that the recovery ratio of a dispersed system is higher than that of a flocculated system irrespective of the pressure increment. Limited experimental data are available in the geotechnical engineering literature illustrating the variation of Cv with consolidation stress. Terzaghi and Peck [19] observed relatively constant Cv values over a wide range of consolidation stress. Leonards and Ramiah [20] observed an upward trend of Cv values for remolded residual clay up to a particular value of consolidation stress and decreased with the consolidation stress exceeding that value. They also noted that the values of Cv for the remolded glacial silty clay continued to increase with consolidation stress.

Table 1 exhibits trends in the variation of coefficient of consolidation with pressure for different clay minerals.

Soil type	Dominant clay mineral	Liquid limit: %	Plasticity index: %	Variation of Cv with σ’	Reference
Bentonite	Montmorillonite	118.0	72.0	Decrease	Samarasinghe et al., [21]
Kaolinite	Kaolinite	—	—	Increase
Kaolinite	Kaolinite	49.0	11.8	Increase	Sridharan et al. [22]
Coarse kaolinite	Kaolinite	48.0	12.4	Increase	Sridharan and Prakash [23]
Fine kaolinite	Kaolinite	46.8	17.4	Increase
Black cotton soil-2	Montmorillonite	100.8	48.9	Decrease
Bentonite	Montmorillonite	393.4	343.3	Decrease
Kaolinite	Kaolinite	53.0	21.0	Increase	Robinson and Allam [13]
Montmorillonite	Montmorillonite	321.0	263.0	Decrease

Table 1.

Variation of cv with σ’ and clay mineral type.

The data suggest that the Cv value decreases for montmorillonite soils and increases for kaolinitic soils with increase in consolidation stress. Robinson and Allam [13] showed that the variation of coefficient of consolidation with the increase in consolidation stress on soils undergoing virgin compression is characterized by mechanical or physico-chemical properties depending upon the dominant clay mineral composing the soil. The literature review on the coefficient of consolidation of soils indicates that limited study has been reported on the coefficient of consolidation of compacted fine-grained soils having different clay mineralogical compositions having different energies imparted.

3. Experiments conducted

Nearly twenty-five soil samples were selected for the experimental program from different locations in Karnataka state, India. These soils were subjected to preliminary laboratory investigation for index properties soils involving Atterberg limits, specific gravity [24], free swell index [25], and grain size analysis [26]. The Atterberg limits were determined using the Casagrande percussion method [27], shrinkage limit [28], and the nature of their clay mineralogical composition was judged by the free swell ratio technique (Prakash and Sridharan [29]). Six field soils were finalized out of 25 soils based on the liquid limit and clay mineralogy, and one commercially available clay mineral was chosen i.e. China clay for the requirement of pure kaolinite clay mineral. The selected soils were classified into 3 different groups (G-1, G-2, and G-3) based on the ascending order of liquid limit.

Soils of liquid limit 46% (G-1) (W_L < 50%)

1. Field soil from Bogadi (passing 425 μm sieve), Mysuru District, which contains kaolinite as the predominant clay mineral.

2. Field soil from Nanjangud (passing 425 μm sieve), Mysuru District, which is a montmorillonitic soil.

   • Soils of liquid limit 55% (G-2) (50% < W_L < 60%)

3. Field soil from Kollegala, (passing 425 μm sieve), Chamarajanagar district, which contains kaolinite as the predominant clay mineral.

4. Field soil from Kuderu, (passing 425 μm sieve), Chamarajanagar district, which is a montmorillonitic soil.

   • Soils of liquid limit 68% (G-3) (60% < W_L < 70%)

5. Field soil from Bannur, (passing 75 μm sieve), Mysuru District, in which both kaolinite and montmorillonite clay minerals are dominant.

6. Field soil from CFTRI lay out, (passing 75 μm sieve), Mysuru District, which contains montmorillonite as the predominant clay mineral.

7. Commercially available clay mineral China clay (representing the kaolinitic soil passing 75 μm sieve) obtained from Seema Chemicals, Bangalore.

Table 2 shows the physical and index properties of the soil types discussed above.

S. No.	Soil	Specific Gravity	Liqui d limit (wL): (%)	Plastic limit (wP): (%)	Plasticity index (Ip): (%)	Shrinkage limit (wS): (%)	Grain Size Distribution			IS classification	Clay Mineralogy
							Clay size (%)	Silt size (%)	Sand size (%)
1	G-1	2.61	46	22	24	13.7	13.0	16	71	CI	Kaolinitic (K- soil)
2		2.70	46	23	23	18.7	7.5	19.5	73	CI	Montmorillonitic (M-soil)
3	G-2	2.74	55	26	29	15.9	37.0	34.5	28.5	CH	Kaolinitic (K- soil)
4		2.85	55	26	28	11.5	39.0	21.0	40.0	CH	Montmorillonitic (M-soil)
5	G-3	2.69	68	30	38	16.1	45.0	55.0	—	CH	Kaolinitic- Montmorillonitic (K-M soil)
6		2.72	68	33	35	13.9	51.0	49.0	—	MH	Montmorillonitic (M-soil)
7		2.67	68	30	38	24.8	63.0	37.0	—	CH	Kaolinitic (K- soil)

Table 2.

Physical and index properties of soils studied.

3.1 Compaction tests

Standard and modified compaction tests were conducted for the soils under study (Standard or Light Compaction [30]), and (Modified or Heavy Compaction [31]). For the compaction tests, around 6 to 9 samples of 2.5 kg were taken and mixed with different percentages of moisture contents kept for a gestation period of 5 to 7 days. After placing the soil samples for saturation period, the Proctor compaction tests were conducted on the soil samples to achieve maximum dry density and optimum moisture content.

3.2 Consolidation tests on compacted soils

3.2.1 Sample preparation for consolidation testing

The consolidation ring has a 6 cm diameter (internal) and 2 cm depth or height, and inside the ring, the silicon grease was applied before it is going to compact with soil, which reduces the friction between the soil and ring when the pressure is applied. The consolidation tests were done at three levels of initial molding water contents—corresponding to γ_d max (i.e., OMC), 0.95 γ_d max on the dry side of optimum and 0.95 γd max on the wet side of optimum. The soil sample in the consolidation ring is compacted with the required moisture content and maximum dry density in the consolidation ring and then assembled with a consolidation cell to be positioned with consolidation equipment. The consolidation ring with compacted soil sample with required molding water content and dry density was assembled in its position on the consolidation cell. The cell used for the laboratory experimentation is a permanent or fixed ring type with drainage paths on two sides of the cell, and it has the facility to conduct the falling head permeability test on the soil sample. The consolidation ring has a 6 cm diameter (internal) and 2 cm depth or height, and inside the ring, the silicon grease was applied before it is going to compact with soil, which reduces the friction between the soil and ring when the pressure is applied.

3.2.2 Load: deformation - time measurements for compacted soils

Consolidation tests were conducted according to [32]. The soil samples are kept in desiccator saturation until they reach the optimum moisture content. M-soil sample exhibited swelling on the addition of water into the consolidation cell. In such cases, time-swelling readings were recorded till the equilibrium was reached. The loads applied on soil samples vary from 0.0625 kg/cm² (6.25 kPa) (after the permeability measurements were taken) to 16 kg/cm² (1600 kPa) with an increment ratio of 1. Time-compression readings were recorded under each consolidation stress increment until the near-equilibrium state was reached. The samples were unloaded upon arriving at the ultimate loading i.e., 1600 kPa in stages (1/4^th). Then the samples were dismantled and weighed and their final heights were measured.

The following five typical methods were chosen for computing coefficient of consolidation (Cv) because of their in-built merits:

1. Casagrande Method [15]

2. Taylor’s Method [16]

3. Log-log Method [23]

4. Rectangular Hyperbola Method [33]

5. One-point Method [34]

3.2.3 Casagrande method

Time of settlement at 50% degree of consolidation [T₅₀ = 0.197] is considered for the proposed method. The test was carried out up to the end of primary consolidation. The variation of time-compression data with typical S-curve shapes is more useful than the other variations. The t₅₀ corresponding to the 50% degree of consolidation was calculated using ${\mathrm{\Delta }}_{50}$ & ${\mathrm{\Delta }}_i$ (Initial compression), and it is estimated using the equation below

$${\mathrm{\Delta }}_{50}=\left[\frac{{\mathrm{\Delta }}_{100}-{\mathrm{\Delta }}_i}{2}+{\mathrm{\Delta }}_i\right]$$E1

$$\mathrm{Cv}=0.197\frac{H^2}{{\mathrm{t}}_{50}}$$E2

3.2.4 Taylor’s method

Time of settlement: at 50% degree of consolidation [T₉₀ = 0.848] compression can be found at 0 and 100% primary consolidation. Ninety percent consolidation time varies with different specimens and with different thickness of specimens, but the compression dial is read frequently for a period of up to 1 hr. after initiation of loading. For no initial compression and negative compression this method is not useful. Here 100% primary consolidation is 1/4th of more than the difference in dial gauges compression readings corresponding to 0 and 90% consolidation. For rapid consolidation soils, it is not accurate. The cv value by Taylor’s method yields more than the Casagrande method because it is considering T₅₀. Values of Casagrande to Taylor are varying from 0.2 to 1. Leonard [20] reported that the effect of secondary compression may strongly influence the value at t₉₀ obtained from √t, so Δ₁₀₀ obtained from Casagrande is more reliable.

$$\mathrm{Cv}=0.848\frac{H^2}{{\mathrm{t}}_{50}}$$E3

For initial settlement => Taylor’s method is reliable.

For Primary consolidation (Δ₁₀₀) => Casagrande is reliable.

3.2.5 Log-Log method

During some particular stages of the consolidation process, different soils may respond in a way that is consistent with Terzaghi’s theory (percentage of consolidation). This might be one of the reasons for the complications that the existing curve-fitting techniques experience when trying to calculate the coefficient of consolidation, Cv. When compared to other techniques, it has been demonstrated that the slope of the early linear component of the theoretical log U-log T curve is constant throughout a greater range of degrees of consolidation, U. In the proposed method, the initial portion of the graphical construction log U-log T i.e. straight line portion is well defined and the plot arrived at log U = 100% degree of consolidation at T = π/4, which is corresponding to U = 88.3%.

$$\mathrm{Cv}=\frac{\pi }{4}\frac{H^2}{{\mathrm{t}}_{88.3}}$$E4

The method is more flexible; it is evident when identifying the characteristic straight lines and more accurate when these lines were intersecting each other. It does not rely on initial compression to calculate C_V.

3.2.6 Rectangular hyperbola method

The variation of t/Δ vs. time was plotted (Measuring values of Slope (m) and intercept (C)) to determine the Cv at 60% degree of consolidation.

$$\mathrm{Cv}=0.24\frac{{\mathit{mH}}^2}{\mathrm{c}}$$E5

From R-H Method Δ₁₀₀ can also be obtained for 100% primary consolidation.

$${\mathrm{\Delta }}_{100}=H_0\left[0.862\frac{1}{m{H}_0}-3.677\ast {10}^{-4}\right]$$E6

Soils with secondary compression show two straight lines and the initial compression cannot be estimated from this method directly.

3.2.7 One point method

In response to the finding that the experimental behavior of soil without consideration of initial and secondary compression effects fits closely to the theory in the range of 40% < U < 60%. The value of the final compression ${\mathrm{\Delta }}_{100}$ is taken into account at the end of the loading period in order to calculate Cv. Each loading increment is often taken to be 24 hours long. To obtain the value of final compression, one must therefore wait 24 hours or longer and the compression equal to 50% consolidation $\left({\mathrm{\Delta }}_{50}\right)$, or 0.5 ${\mathrm{\Delta }}_{100}$, and the associated time t₅₀, is calculated. According to the mentioned time t₅₀, Cv is calculated.

$${\mathrm{\Delta }}_{50}=\frac{{\mathrm{\Delta }}_{100}}{2}$$E7

$$\mathrm{Cv}=0.197\frac{H^2}{{\mathrm{t}}_{50}}$$E8

4. Results and discussions

4.1 Coefficient of consolidation (Cv) of compacted fine-grained soils with variation of pressure based on liquid limit

The Coefficient of Consolidation (Cv) is a parameter that is being generally considered in estimating the Settlement characteristics. The Coefficient of consolidation (Cv) is determined from typical methods chosen for the present experimental study have been categorized into three different clay mineralogical soil groups of kaolinite, montmorillonite and kaolinite-montmorillonite having different liquid limit range (46, 55, and 68%) with the pressure varying from 6.25 to 1600 kPa.

Table 3 shows that the range of Cv values for the kaolinite, montmorillonite, and kaolinite-montmorillonite soils under study having the liquid limit range of 46, 55, and 68% and for the pressure ranging from 6.25 to 1600 kPa.

Coefficient of consolidation (Cv) (cm^2/s)
K-soils	M-soils	K-M soils
1.28 × 10^−7 to 8.21 × 10^−1	1.86 × 10^−7 to 9.76 × 10^−1	1.32 × 10^−7 to 8.7 × 10^−1

Table 3.

Coefficient of consolidation values of K-soils, M-soils, and K-M soils.

4.2 Variation of coefficient of consolidation (Cv) with respect to energy levels

The role of compaction energy on the engineering behavior of fine-grained soils is well documented in geotechnical literature. However, no attempt has been made to correlate the consolidation characteristics like Cv to compaction energy levels of different clay mineralogical fine-grained soils. In the documented literature, detailed discussions were made concerning desired changes in the engineering properties of soil due to the effect of compaction energy imparted on the soil. Further, the heavy compaction energy level to light compaction energy level is 4.54 (Standard Energy ratio (SER)). The variation of Cv (Light compaction) with Cv (Heavy compaction) has not been made in the past, as seen from the documented literature with particular reference to the clay mineralogy, placement condition, and pressure concerned.

Amid the consolidation characteristics illustrated in the documented geotechnical literature, the Cv is an extremely variable parameter and the number of methods (27) are highlighting the same. The computation of Cv values for the soil samples for different energy levels and clay mineralogy consumes lot of time and associated cost. The present experimental approach has been proposed to estimate the Cv values for heavy compaction energy level through light compaction energy level is of paramount importance from an economic perspective, which is illustrated in Figures 1–10.

Figure 1.

Correlation between cv (light compaction) and cv (heavy compaction) of K-soil (W_L = 46%) (50 kPa).

Figure 2.

Correlation between cv (light compaction) and cv (heavy compaction) of K-soil (W_L = 46%).

Figure 3.

Correlation between cv (light compaction) and cv (heavy compaction) of M-soil (W_L = 46%).

Figure 4.

Correlation between cv (light compaction) and cv (heavy compaction) of M-soil (W_L = 55%) (100 kPa).

Figure 5.

Correlation between cv (light compaction) and cv (heavy compaction) of K-soil (W_L = 55%).

Figure 6.

Correlation between cv (light compaction) and cv (heavy compaction) of M-soil (W_L = 55%).

Figure 7.

Correlation between cv (light compaction) and cv (heavy compaction) of K-M soil (W_L = 68%) (200 kPa).

Figure 8.

Correlation between cv (light compaction) and cv (heavy compaction) of K-soil (W_L = 68%).

Figure 9.

Correlation between cv (light compaction) and cv (heavy compaction) of M soil (W_L = 68%).

Figure 10.

Correlation between cv (light compaction) and cv (heavy compaction) of K-M soil (W_L = 68%).

Figures 1–10: The values have been taken into consideration in the logarithmic (base 10) scale to provide a clear depiction of the cv values on the ordinate and abscissa. In view of the enormous amount of experimental work and data, three reference pressures—50, 100, and 200 kPa were selected for soils with liquid limits of 46, 55, and 68%, respectively. This is because most sub-structures, especially those for shallow foundations, are required to have a minimum safe bearing capacity of 100 kPa, which is typically determined by shear and settlement criteria, with allowable settlements of ≤25 and ≤ 40 mm, respectively. From this, a comprehensive understanding of the variation of Cv with pressure with respect to the light compaction and heavy compaction energy levels has been achieved.

Figure 1 shows the variation of Cv (Light compaction) with Cv (Heavy compaction) for the soil having liquid limit of 46% (kaolinitic soil) from the chosen methods of determining Cv (@ 50 kPa pressure).

Figures 2 and 3 demonstrate the correlation between Cv (Light compaction) and Cv (Heavy compaction) values of combined typical methods of determining Cv chosen for the study and placement conditions of soils having a liquid limit of 46% (kaolinite and montmorillonite soil). The values of Cv have been compared with the line of equality to observe the deviation of values from the correlation equation.

Eq. (9) & Eq. (10) represents that, the relationship between values of Cv for heavy compaction to the light compaction energy level for the soils having different clay mineralogy and the liquid limit of 46%.

$$\mathit{Cv}\left(\mathit{\text{Heavy}}\right)=0.8371\mathit{Cv}\left(\mathit{\text{Light}}\right)+0.1825{\mathrm{R}}^2=0.90\text{For}\mathrm{K}-\text{Soil}$$E9

$$\mathit{Cv}\left(\mathit{\text{Heavy}}\right)=0.5755\mathit{Cv}\left(\mathit{\text{Light}}\right)-0.2672{\mathrm{R}}^2=0.91\text{For}\mathrm{M}-\text{soil}$$E10

Figure 4 shows the variation of Cv (Light compaction) with Cv (Heavy compaction) for the soil having liquid limit of 55% (montmorillonitic soil) from the chosen methods of determining Cv (@ 100 kPa pressure).

Figures 5 and 6 demonstrate the correlation between Cv (Light compaction) and Cv (Heavy compaction) values of combined typical methods of determining Cv chosen for the study and placement conditions of soils having a liquid limit of 55% (Kaolinite and Montmorillonite soil). The values of Cv have been compared with the line of equality to observe the deviation of values from the correlation equation.

Eq. (11) & Eq. (12) represents that the relationship between values of Cv for heavy compaction to the light compaction energy level for the soils having different clay mineralogy of same liquid limit (55%).

$$\mathit{Cv}\left(\mathit{\text{Heavy}}\right)=1.1138\mathit{Cv}\left(\mathit{\text{Light}}\right)+0.3846{\mathrm{R}}^2=0.86\text{For}\mathrm{K}-\text{Soil}$$E11

$$\mathit{Cv}\left(\mathit{\text{Heavy}}\right)=0.8337\mathit{Cv}\left(\mathit{\text{Light}}\right)-0.3101{\mathrm{R}}^2=0.93\text{For}\mathrm{M}-\text{Soil}$$E12

Figure 7 shows the variation of Cv (Light compaction) with Cv (Heavy compaction) for the soil having liquid limit of 68% (kaolinitic-montmorillonitic soil) from the chosen methods of determining Cv (@ 200 kPa pressure).

Figures 8–10 demonstrate the correlation between Cv (Light compaction) and Cv (Heavy compaction) values of combined typical methods of determining Cv chosen for the study and placement conditions of soils having a liquid limit of 68% (kaolinite, montmorillonite, kaolinite-montmorillonite soil). The values of Cv have been compared with the line of equality to observe the deviation of values from the correlation equation.

Eq. (13), Eq. (14), and Eq. (15) show the relationship between values of Cv for heavy compaction to the light compaction energy level for the soils having different clay mineralogy and the liquid limit of 68%.

$$\mathit{Cv}\left(\mathit{\text{Heavy}}\right)=1.0783\mathit{Cv}\left(\mathit{\text{Light}}\right)+0.5126{\mathrm{R}}^2=0.93\text{For}\mathrm{K}-\text{Soil}$$E13

$$\mathit{Cv}\left(\mathit{\text{Heavy}}\right)=1.051\mathit{Cv}\left(\mathit{\text{Light}}\right)+0.0864{\mathrm{R}}^2=0.91\text{For}\mathrm{M}-\text{Soil}$$E14

$$\mathit{Cv}\left(\mathit{\text{Heavy}}\right)=0.8077\mathit{Cv}\left(\mathit{\text{Light}}\right)+0.288{\mathrm{R}}^2=0.92\text{For}\mathrm{K}-\mathrm{M}\text{Soil}$$E15

From Figures 1–10 and Eq. (1) through Eq. (7), it can be observed that the values of Cv (heavy compaction) can be estimated by substituting the values of Cv (light compaction) for combined placement conditions of soils having different clay mineralogy with a fair degree of accuracy of regression values ranging from 0.86 to 0.99, irrespective of the method of determining Cv and placement condition. Furthermore, the values of Cv from the equation are closer to the line of equality in all of the soils that were investigated, with a lesser degree of deviation.

Based on the correlation equations derived from the present experimental study, the values of Cv can be directly estimated for the Reduced Standard Proctor (RSP) and Reduced Modified Proctor (RMP) energy level also, by considering the amount of energy to 60 percent of actual energy in the Modified and Standard Proctor effort, respectively (RSP = 60% of Standard Proctor Energy & RMP = 60% of Modified Proctor Energy).

4.3 Variation of energy ratio with coefficient of consolidation

The standard energy ratio (SER) derived from Proctor lubrication theory [35] i.e., the value of compaction energy determined from the heavy compaction energy to the value of compaction energy determined from the light compaction energy. Here the energy has been considered directly to determine the energy ratio. The defined SER equation represented in Eq. (16)

$$\text{Standard energy ratio}\left(\mathrm{SER}\right)=\frac{\text{Heavy compaction energy}\left[\text{IS}:2720-\text{Part}8\left(1983\right)\right]\left[2703\mathrm{KJ}/m^3\right]}{\text{Light compaction energy}\left[\text{IS}:2720-\text{Part}7\left(1980\right)\right]\left[596\mathrm{KJ}/m^3\right]}$$E16

From the reference of the SER, the new equation has been defined to compare in terms of coefficient of consolidation (Cv) point of view i.e., Energy ratio of Cv (CvER).

The Cv_ER represents the variation of Cv values with respect to the effect of energy ratio and pressure. Here, the values of Cv considered for the estimation of the energy ratio of Cv (Cv_ER) are the combined values of typical methods of determining Cv mentioned in the methodology and the placement conditions of dry side of optimum, optimum, and wet of optimum, for the individual pressures, respectively.

The energy ratio of Cv and average ratio are defined below in Eq. (17) & Eq. (18)

$$\text{Energy ratio of}\mathrm{Cv}\left(\text{CvER}\right)=\frac{\mathrm{Cv}\text{Value of Heavy compaction energy level}}{\mathrm{Cv}\text{value of Light compaction energy level}}$$E17

$$\text{Average ratio}\left({\mathrm{Cv}}_{\mathrm{AR}}\right)=\text{The average of values of}{\mathrm{Cv}}_{\mathrm{ER}}$$E18

The Cv_ER represents the variation of Cv values with respect to the effect of energy ratio and pressure as shown below in Table 4 for M-Soil having W_L = 46% (100 kPa).

Cv (Light Compaction)	Cv (Heavy Compaction)	CvER	*CvAR
1.07E-04	0.000661	6.16595	8.22
1.15E-04	0.001318	11.48154
4.37E-04	0.00195	4.466836
9.55E-04	0.002951	3.090295
0.000295	0.005495	18.62087
0.001	0.005495	5.495409

Table 4.

Estimation of the average ratio of cv values for the M-soil at 100 kPa pressure (WL = 46%).

Similar observations were made for the soils having different pressure range, clay mineralogy, and liquid limit.

Figures 11–13 show the relation between the average ratio of Cv values with respect to the pressures ranging from 50 to 1600 kPa for the soils having different clay mineralogy of liquid limits 46, 55, and 68%, respectively and have been compared with standard energy ratio (SER) i.e. 4.54.

Figure 11.

Variation of Cv_AR with pressure (W_L = 46%).

Figure 12.

Variation of Cv_AR with pressure (W_L = 55%).

Figure 13.

Variation of Cv_AR with pressure (W_L = 68%).

Tables 5 and 6 show the relation between the average ratio of Cv values with respect to the pressures ranging from 50 to 1600 kPa for the soils having different clay mineralogy of liquid limits 46, 55, and 68%, respectively.

Pressure (kPa)	CvAR
	WL = 46%		WL = 55%		WL = 68%
	K-soil	M-soil	K-soil	M-soil	K-soil	M-soil	K-M soil	SER
50	3.12	7.14	0.35	3.05	1.13	1.17	2.51	4.54
100	6.88	8.22	0.28	3.58	2.8	1.69	2.28	4.54
200	5.72	10.8	0.56	3.06	1.84	1.49	12.71	4.54
400	5.08	7.8	2.6	1.57	3.42	9.16	20.05	4.54
800	3.05	3.9	6.4	1.23	11.1	14.7	17.89	4.54
1600	1.4	1.6	5.01	1.27	17.66	8.03	17.16	4.54

Table 5.

Values of average ratio Cv_AR.

Pressure	Percentage amount of energy achieved @ Gradual consolidation loading
	G-1 (WL = 46%)		G-2 (WL = 55%)		G-3 (WL = 68%)
	K-soil	M-soil	K-soil	M-soil	K-soil	M-soil	K-M soil
50	68.72	157.27	7.71	67.18	24.88	25.77	55.28
100	151.54	181.05	6.17	78.85	61.67	37.22	50.22
200	125.99	237.88	12.33	67.40	40.52	32.82	279.96
400	111.89	171.80	57.27	34.58	75.33	201.76	441.63
800	67.18	85.90	140.97	27.09	244.49	323.78	394.05
1600	30.84	35.24	110.35	27.97	388.98	176.87	377.97

Table 6.

Variation of the percentage of energy achieved with reference to SER for the gradual consolidation loading or stress.

Table 5 shows the variation of Cv_AR with the consolidation stress.

Table 6 shows the variation of the percentage amount of energy achieved (defined from SER) at gradual consolidation loading ranging from 50 to 1600 kPa, for the soils under study. (Eq. (19))

$$\text{Percentage of energy achieved}\left(\%\right)=\frac{{\mathrm{Cv}}_{\mathrm{AR}}}{\mathrm{SER}}\ast 100$$E19

From Tables 5 and 6, it can be observed that as the liquid limit of soils increases the average ratio of Cv values increases for high liquid limit soils (W_L = 68%) (K, M, & K-M soils) having higher average ratio values (1.13 to 17.66, 1.17 to 14.7, and 2.28 to 20.05) and percentage amount of energy achieved (24.89 to 388.98, 25.77 to 176.8 and 55.28 to 377.97), respectively, than other soils pertaining to liquid limits 46 and 55% respectively for the same pressure range. Here the maximum value of Cv_AR is referred to as the maximum percentage of the amount of energy achieved at the gradual consolidation loading and it is considered as the percentage amount of energy achieved in terms of standard energy ratio (the soils compacted at dynamic loading for different energy levels) for the individual consolidation stress.

For the soil having W_L = 46%, the values of Cv_AR lies above the SER line for the pressure ranging from 100 kPa to 400 kPa (K-soil) and it is ranging from 50 kPa to 400 kPa for the M-soil, respectively (Figure 11). For the soil having W_L = 55%, the values of Cv_AR lies above the SER line for the pressure ranging from 800 kPa to 1600 kPa (K-soil) and it lies below the SER line, irrespective of the pressure range for the M-soil, respectively (Figure 12). For the soil having W_L = 68%, the values of Cv_AR are lying above the SER line for the pressure ranging from 200 to 1600 kPa (K-M Soil), 400 to 1600 kPa (M-soil), and 800 to 1600 kPa (K-soil), respectively (Figure 13).

From Figures 11–13 and Tables 5 and 6, it can be observed that the Cv_AR is having a decrease in tendency beyond 200 kPa (M-soil) and 400 kPa (K-soil), respectively, and reaches its minimal value at 1600 kPa for the W_L = 46%, the Cv_AR is having a decrease in tendency beyond 100 kPa (M-soil) and 800 kPa (K-soil) for the W_L = 55% and the W_L = 68%, it is beyond 800 kPa for M-soil and 400 kPa for K-soil i.e., the decrease in the trend of variation of Cv_AR is changing with the change in the liquid limit, and the percentage amount of energy achieved with respect to the pressure is also increasing with the increase in the liquid limit. The behavior of Cv_AR for K-soils is in decreasing trend for the 46% liquid limit, whereas for the 55 and 68% liquid limits, the increase in trend was observed. The occurrence is ascribed to the increase in the amount of percentage of fines when the liquid limit of the soil increases. For the soil having liquid limit of 68%, the void ratio increases with an increase in the percentage of fines i.e., for the soils having liquid limit 46% and 55% are having less percentage of fines having less void ratio compared to the 68% liquid limit soil irrespective of the clay mineralogy and the coefficient of consolidation achieved with the increase in pressure at the heavy compaction energy level is higher due to the higher compression of voids affects the increase in the values of Cv at heavy compaction energy level which in turn leading to the Cv_AR.

From Figures 11–13 and Tables 5 and 6, it can be also observed that, for W_L = 46%, the maximum value of Cv_AR for M-soil is having greater magnitude than the Cv_AR for K-soil. The maximum value of Cv_AR for M-soil is observed at a pressure of 200 kPa whereas for K-soil it is 100 kPa. For W_L = 55%, the maximum value of Cv_AR for M-soil is having greater magnitude than the Cv_AR for K-soil. The maximum value of Cv_AR for M-soil is observed at a pressure of 100 kPa whereas for K-soil it is 800 kPa. For W_L = 68%, The maximum value of Cv_AR for K-M soil is having greater magnitude than the Cv_AR for K and M-soil. The maximum values of Cv_AR were observed at 1600, 800, and 400 kPa, for K, M, and K-M soils respectively.

The mechanism of the energy ratio concept can be attributed to the fact that, according to Proctor’s capillarity and lubrication theory [35], water has a dual effect of capillarity (or suction) and lubrication. It is observed that due to high capillarity, the dry density is lower for dry soil and as water is added, the capillarity is reduced, and water also lubricates the particle interaction, giving rise to increased dry density up to the maximum dry density. It is depending upon the amount of energy imparted on the soil (Heavy and Light compaction) and also the pressure creates additional effort on the consolidation specimen with respect to a decrease in void ratio due to an increase in the rate of expulsion of water from soil voids. This behavior leads to an increase in the rate of compression and it is defined in the form of a coefficient of consolidation with the effect of energy ratio.

5. Conclusions

Based on a detailed experimental study of compacted fine-grained soils having different clay mineralogy, placement conditions, and energy levels, the following conclusions can be made:

• The magnitudes of Cv values computed by different user-friendly methods for K, M, and K-M soils vary from 1.28 × 10⁻⁷ to 9.76 × 10⁻¹ cm²/s, and M-soils exhibit a higher magnitude of Cv in relative comparison to K-soils and K-M soils by virtue of clay mineralogy.

• The Cv values of heavy compaction energy level can be estimated directly by knowing the Cv values of light compaction energy level only through correlation equations irrespective of the method of determining Cv and placement conditions (it is independent of the method of determining Cv of five user-friendly methods used in the experimental study).

• The Cv_AR values increase with an increase in pressure up to 400 kPa for W_L = 68% (K, M & K-M soils).

• The Cv_AR has a decreasing tendency beyond the pressure range of 400 kPa for K-soils and 200 kPa for M-soils (W_L = 46%), 800 and 100 kPa for K and M soils (W_L = 55%) and it is 400 and 800 kPa for K-M and M-soil, respectively.

• The maximum value of (Cv_AR) M-SOIL > Maximum value of (Cv_AR) K-SOIL (W_L = 46 & 55%), Maximum value of (Cv_AR) K-M SOIL > Maximum value of (Cv_AR) M-SOIL > Maximum value of (Cv_AR) K- SOIL (W_L = 68%).

Conflict of interest

The authors declare no conflict of interest.