Background

Geotechnical site characterization plays vital role in selection of pavement layers such as surface course, base course, subbase and subgrade. For most of the highway projects, cone penetration test (CPT) and dynamic cone penetrometers (DCP) are extensively used worldwide. These tests provide continuous and uninterrupted stratigraphic data with the improved resolution along the depth of penetration. The data obtained from these tests are less disruptive as compared to the data obtained from drilling operations. The CPT and DCP data has got a strong theoretical acceptance [19]. Soil samples cannot be retrieved during the operation of these tests. Visual inspection to promote the soil classification of subgrade is the only drawback in these tests. However, these tests are expedient, repeatable, and economical [30].

Most valid and acceptable information can be obtained about the subgrade or stratigraphy of a particular location, if combination of testing approaches are employed during the geotechnical site investigations [32]. The transformation error from measured to evaluated value of soil property can be significantly reduced with the use of two to three test methods at the site [6, 8, 22]. In the recent past, CPT has been considered as one of the combination tests in soil investigation in Ethiopia mainly to have a data that can cross verify the data obtained from other test so as to develop confirmed design. The CPT can thereby maximize geotechnical characterization of a subgrade at an affordable price. It can be distinguished that the DCP has gained popularity in road projects mainly due to its economy and simplicity to operate and also its superiority to provide repeatable results to assess soil property rapidly. A perfectly performing soil testing method is only an impossible fantasy as there is always adjustment between one parameter to another. It is a fact that, both CPT and DCP are well recognized approaches with a rich performance history in the different parts of the globe. The theoretical acceptance and recognition of CPT and DCP test data by the scientific community, gave a light further to develop correlation between CPT and DCP in this study. In addition, there are also number of correlations between standard penetration test (SPT), light dynamic probing test (DPL), and CPT [15, 17, 21, 31, 35]. However, there are no many such correlations available in the literature in the case of DCP relating to CPT.

There are many factors that influence correlations developed at different conditions: such as geology prevailing at the site, normalization and general treatment of data, degree of control of soil variability effects, the range of soil strength/stiffness and methods of determining correlations. Most of the correlations developed between the geotechnical parameters by the investigators may not meet all those criteria and preferred to develop simplified expressions or correlations as close to the accuracy by considering possible environmental factors [34].

Now a days, classification of soil types using CPT are interconnected directly to soil classification charts [7, 9, 12, 15, 20, 24, 27–29, 34]. Many number of probabilistic soil classification approaches are available in the literature [5, 16, 18, 36]. Among  the available soil classification charts, Robertson's soil classification chart has gained popularity because it accounts past observations and also engineering experience and judgment by the experienced professionals. The soil is based on two parameters such as: the normalized friction ratio, \(F_{R} = \left[ {\frac{{100f_{s} }}{{(q_{t} - \sigma_{vo} )}}} \right]\), and the normalized tip resistance, \(Q_{t} = [{{(q_{t} - \sigma_{vo} )} \mathord{\left/ {\vphantom {{(q_{t} - \sigma_{vo} )} {\sigma_{vo}^{\prime } }}} \right. \kern-0pt} {\sigma_{vo}^{\prime } }}]\), obtained from penetration test data, where f s , q t , \(\sigma_{vo}\), and \(\sigma_{{_{vo} }}^{\prime }\) are the sleeve friction, corrected tip resistance, vertical total stress, and vertical effective stress, respectively. The chart is divided into nine zones corresponding to nine different soil types, as presented in Table 1. For the known ratios of FR and Qt, the soil zone would be identified.

Table 1 Description of zones in Robertson’s soil classification chart (after [29])
Full size table

This paper integrates the soil domains collected along the highway path selected (Modjo to Hawassa in the area of southern Ethiopia) and developing the correlation between CPT and DCP. Two penetrometer test data was collected within the interval of 1 m to avoid the subgrade inconsistency and classification of soil domains using Robertson’s soil profiling is also discussed.

Site description and geology

The highway considered in this study links between Modjo and Hawassa in the area of southern Ethiopia. Most part of the highway selected is passing through Oromia region in Ethiopia and is a part of the major Mombasa—Nairobi—Addis Ababa highway. This highway has significant economic importance due to the connectivity with neighboring countries. In contemporary, it has a two lane, two—way carriage way stretching around total length of 209 km. The data was collected upto 25 km of the highway which was being rehabilitated into dual carriage way. The selected highway route has a flat terrain topography with no undulations. The geographical co-ordinates are 8° 39′ N, 39° 5′ E for Modjo, and 7° 3′ N, 38° 28′ E for Hawassa.

Methods

Penetrometers and testing

Numerous penetrometers are in practice worldwide for investigation and characterization of subgrade. There are many developments in geotechnical instrumentation which are noticed in both the penetrometers, but more have been made on the dutch cone penetrometer (DCPT). CPT has also got many improvements, which increases its capability to handle diverse ground conditions [4], accurately identifying soil types [3, 23, 29], and gives better estimates of relevant geotechnical soil parameters. The CPT equipment used in this study has the following accessories: anvil and driving rod, a 10 kg rammer, height of fall of 50 cm, 11 sounding rods, lifting device for sounding rods, and couplings all in a box casing weighing approximately 71 kg. The cone tip angle of the penetrometer used in this study is 60° and rods are 20 mm in diameter. Both qualitative and quantitative interpretation of the CPT readings in this study followed the guidelines of DIN: 4094—Part 2 [10].

The DCP used in this study has the following accessories: a steel rod with a cone at one end with a base diameter of 20 mm and apex angle of 60°. It is driven into the subgrade by a sliding hammer weighing 8 kg from a height of 575 mm. Two people are usually required to penetrate the equipment into soil. However, the manpower can be reduced to one person by using an electronic device to record the data. According to ASTM D 6951 method, apex angle 60° is better than 30° and became more popular in the recent past due to its durability in high-strength materials.

Statistical tool

In common practice, statistical tools can be used for analysis, interpretation, presentation, and organization of data sets. Among the available tools, descriptive statistics summarizes the data from mean or standard deviation, and inferential statistics, which draws conclusions from data that are subject to random variation (e.g., observational errors, sampling variation). In this study, ordinary least squares and the simple arithmetic mean methods are used to obtain the scatter plots of data pairs and different trends fitted to the data.

The best fit agreement between chosen alternatives was determined using Eq. 1 [11]. For a linear regression, the coefficient of correlation (r) can be determined using Eq. 2, and is checked for significance by comparing the critical values as recommended in the Pearson product—moment correlation table. The standard error of estimate (\(S\epsilon\)) was determined using Eq. 3.

$$R^{2} = \frac{{\sum (\hat{Y_{i}} - \bar{Y} )^{2} }}{\sum({Y_{i}}-\bar{Y})^2}$$
(1)
$$R^{2} = r^{2}$$
(2)
$$S_{ \in } = \sqrt {\frac{{\sum (Y_{i} - \hat{Y}_{i} )^{2} }}{z - 1}}$$
(3)

where, R2 is coefficient of determination, r is coefficient of correlation, Yi is the ith value of a data set, \(\bar{Y}\) is mean of the data set and \(\hat{Y}_{i}\) is the ith fitted value, z is the number of data points, and \(S_{ \in }\) is the standard error of estimate. The degree of uncertainty persuaded, while measuring a parameter can be transformed to a desired property [1, 26] using regression analysis. The magnitude of transformation uncertainty can be expressed by an indicator z. The coefficient of variation (COV) of the transformation uncertainty from parameter X to Y can be determined by the ratio between \(S_{ \in }\) and the mean as indicated by Eq. 4.

$$COV_{X \to Y} = \frac{{S_{ \in } }}{{\bar{Y}}}$$
(4)

where X → Y transform from parameter X to Y and \(\bar{Y}\) is the mean of parameter Y.

Results and discussion

Field observations

In this study, around 40 test points were chosen along the highway. Typical geotechnical characteristics of existing subgrade obtained from testing are presented in Table 2. In situ soil profile at chainage 8 + 450 RHS is shown in Fig. 1. Designation of the trend of gradation analysis, around six selected test points are presented in Fig. 2. From this figure, it can be seen that the percentage passing through sieve No. 200 is about 20 % at chainage 13 + 900 LHS and 79 % at the chainage 4 + 00 LHS and it can be seen that most of the soil is in the form of fine grained textures.

Fig. 1
figure 1

In situ soil profile at chainage 8 + 450 RHS

Full size image
Fig. 2
figure 2

Gradation analysis of test samples along the selected highway

Full size image

Atterberg limits such as liquid limit and plastic limits are also presented in Table 2. From this table, it can be noticed that, liquid limit values ranged from 22 to 56 %, while plastic limit values are ranging in between 16 and 43 %. Plasticity index values are varying from minimum 1 % to maximum of 29 %, indicating low to medium swell potential (Fig. 3). The soil domains in Fig. 3 are modified according to the Casagrande’s plasticity chart considering A—line classification system. Laboratory analyses of consistency limits with gradation analysis places the soil, in a quite wide range of soil types. Based on the American Association of State Highways and Transportation Officials (AASHTO) soil classification systems, soil along the proposed alignment includes A–2–4, A–4, A–2–5, A–2–7, A–1(a), A–1(b), A–7–6 and A–6. According to Unified Soil Classification System (USCS), the dominant soils along the highway stretch considered are positioned into inorganic silts or organic clays (MH or OH), inorganic clays (CL), inorganic silts or organic silts (ML & OL), and combinations of the two (CL–ML).

Fig. 3
figure 3

Classification of soil domains along the highway considered in the study

Full size image
Table 2 Geotechnical characteristics of subgrade along the highway route alignment
Full size table

The estimated natural moisture content (NMC) of existing subgrade is ranging from 11.2 to 16.9 %, while liquidity index is ranging from −1.5 to −0.3. In general, the range of liquidity index can be from −1.0 to +1.0 [25]. From the compaction test results, it can be seen that the value of maximum dry density (MDD) for soil is ranging from 1.07 gm/cc (10.7 kN/m3) at Ch.9 + 600 LHS to 2.10 gm/cc (21.0 kN/m3) at Ch. 3 + 300 RHS; and the optimum moisture content (OMC) is ranging between 7.8 and 25 % at Ch. 13 + 500 LHS and Ch.6 + 000 RHS, respectively.

Correlation agreements between CPT and DCP

It is necessitated to develop the relationship between CPT and DCP, with various combinations of sleeve frictions encompassing the selected highway route. This need has arisen from the necessity that to achieve reliable and consistent geotechnical analysis, CPT and/or DCP are essential. In this exploration, around 40 data pairs were gathered and plots are developed using various combinations and are presented in Figs. 4, 5, 6 and 7.

Fig. 4
figure 4

Statistical correlation between CPT (qc) and DCP (qc)

Full size image
Fig. 5
figure 5

Statistical correlation between CPT (qc + fs) and DCP (qc + fs)

Full size image
Fig. 6
figure 6

Statistical correlation between CPT (qc) and DCP (qc + fs)

Full size image
Fig. 7
figure 7

Statistical correlation between CPT (qc + fs) and DCP (qc)

Full size image

Method of least squares tool was used to obtain the best fit relationship between CPT (qc) and DCP (qc) and the best fit line is showed in Fig. 4. It can be seen from the figure that by considering all the data points the following expression is obtained.

$$DCP\,(q_{c} ) = 1.1209\,CPT\,(q_{c} )\, + \,0.2296$$
(5)

Equation 5 has high correlation of r = 1.305 and \(S_{ \in } = 0.9026\). The transformation uncertainty between CPT (qc) and DCP (qc) \(\left( {COV_{{trans\,CPT\,(q_{c} ) \to DCP\,(q_{c} )}} } \right)\) is therefore determined to be 30.73 %. Subsequently, filtering the data set, the new expression is obtained (Eq. 6) with r = 1.331 and \(S_{ \in } = 1.011\), which sorts \(\left( {COV_{{trans\,CPT\,(q_{c} ) \to DCP\,(q_{c} )}} } \right)\) descent to 25.15 %.

$$DCP\,(q_{c} ) = 1.2894\,CPT\,(q_{c} ) - 0.1977$$
(6)

In most of the circumstances, the magnitudes of sleeve friction are significant and could not be simply overlooked. Because in summing up the values, sleeve friction values improve correlation between the normalized parameters. A statistical correlation between CPT (qc + fs) and DCP (qc + fs) is presented in Fig. 5. From Fig. 5, the following expression (Eq. 7) can be obtained with a moderate correlation of r = 1.3585 and \(S_{ \in } = 0.9956\) as compared to CPT (qc) and DCP (qc) with transformation uncertainty of 28.64 %.

$$DCP\,(q_{c} + f_{s} ) = 1.1667\,CPT\,(q_{c} + f_{s} ) - 0.1119$$
(7)

Subsequently, sorting out the data set, a new correlation is obtained (Eq. 8) with r = 1.3239 and \(S_{ \in } = 1.039\), which forms \(\left( {COV_{{trans\,CPT\,(q_{c} + f_{s} ) \to DCP\,(q_{c} + f_{s} )}} } \right)\) descent to 26.55 %.

$$DCP\,(q_{c} + f_{s} ) = 1.2346\,CPT\,(q_{c} + f_{s} ) - 0.107$$
(8)

In addition, the relationships between CPT (qc) vs DCP (qc + fs) and CPT (qc + fs) vs DCP (qc) are furnished in Figs. 6 and 7. A statistical correlation between CPT (qc) and DCP (qc + fs) is presented in Fig. 6. From this figure, the following best fit (Eq. 9) is obtained with a high correlation of r = 1.4295 and \(S_{ \in } = 1.1297\). The transformation uncertainty between CPT (qc) and DCP (qc + fs) \(\left( {COV_{{trans CPT \left( {q_{c} } \right) \to DCP \left( {q_{c} + f_{s} } \right)}} } \right)\) is therefore determined to be 30.12 %.

$$DCP \left( {q_{c} + f_{s} } \right) = 1.1817 CPT \left( {q_{c} } \right) + 0.2173$$
(9)

Afterwards, filtering the data set, a new expression (Eq. 10) was obtained with \(r = 1.3377\) and S ɛ  = 1.1257, which makes \(\left( {COV_{{trans CPT \left( {q_{c} } \right) \to DCP \left( {q_{c} + f_{s} } \right)}} } \right)\) descent to 29.93 %.

$$DCP \left( {q_{c} + f_{s} } \right) = 1.1847 CPT \left( {q_{c} } \right) + 0.1776$$
(10)

Likewise, a statistical correlation (Eq. 11) between CPT (qc + fs) and DCP (qc) is developed from the data presented in Fig. 7. The correlation presented in Eq. 11 has a high correlation of r = 1.2411 and S ɛ  = 0.794.

$$DCP \left( {q_{c} } \right) = 1.1057 CPT \left( {q_{c} + f_{s} } \right) + 0.139$$
(11)

The transformation uncertainty between CPT (qc + fs) and DCP (qc) \(\left( {COV_{{trans CPT \left( {q_{c} + f_{s} } \right) \to DCP \left( {q_{c} } \right)}} } \right)\) is therefore determined as 22.18 %. After filtering the data set, the new expression (Eq. 12) is obtained with \(r = 1.2048\) and S ɛ  = 0.773, which makes \(\left( {COV_{{trans CPT \left( {q_{c} + f_{s} } \right) \to DCP \left( {q_{c} } \right)}} } \right)\) descent up to 21.78 %.

$$DCP \left( {q_{c} } \right) = 1.1029 CPT \left( {q_{c} + f_{s} } \right) + 0.1187$$
(12)

Robertson’s soil profiling

Soil profiling charts have been amended and improved from a large data base obtained from various geotechnical site characterization studies carried out by the good number of investigators [23, 33]. Previous researches have also illustrated the importance of cone design and the effect of water pressures on the measured penetration resistance and sleeve friction, because of uneven surface at the end [2, 4]. Consequently, cones of slightly different designs, but conforming to the international standard [14] and reference test procedures [13], will give slightly different values of qc and fs, especially in soft clays and silts.

The variation of the logarithm of normalized friction ratio ln (FR) and tip resistance ln (Qt) using CPT and DCP data points along the selected highway route, based on Robertson’s chart is presented in Fig. 8. As it can be observed from the figure that, the soil profile principally encompasses zone 4 (i.e., silt mixtures: clayey silt to silty clay), zone 5 (sand mixtures: silty sand to sandy silt), zone 6 (sands: clean sand to silty sand), and zone 8 (very stiff sand to clayey sand), with some scattered data points located in zone 9 (very stiff, fine-grained).

Fig. 8
figure 8

Distribution of the CPT and DCP data obtained along the highway route based on Robertson's soil classification chart

Full size image

Summary and conclusion

This paper integrated the geotechnical characterization of a selected highway route. The soils are characterized by organic and inorganic silts, organic and inorganic clays within the depth of subgrade. In contrast, relationships shaped in this study indicates that, CPT (qc + fs) and DCP (qc) correlations are very much improved compared to other combinations studied in terms of higher coefficient of correlation and least transformation uncertainty. Deliberation of sleeve friction measurements resulted in minor improvement in of correlations and these may be considered insignificant. According to Roberson’s chart, the distribution of the CPT and DCP data obtained along the highway route encompasses four zones. Zone 4 (i.e., silt mixtures: clayey silt to silty clay), zone 5 (sand mixtures: silty sand to sandy silt), zone 6 (sands: clean sand to silty sand), and zone 8 (very stiff sand to clayey sand), with some scattered data points are located in the zone 9 (very stiff, fine-grained). Overall, it is seen that the statistical correlations developed from the vast data points can help the site and design engineers to have a clear idea about the stratigraphy of a particular location for taking appropriate planning and design steps of an intended infrastructure project to meet the requirements of sustainability.