The California bearing ratio (CBR) test is the most widely spread method of determining the bearing strength of the pavement material and is fundamental to pavement design practice in most countries. This test is expensive, laborious and time consuming, and to overcome this, Quasi static cone penetrometer machine was fabricated and used to measure the consistency limits (liquid limit-LL, Plastic limit-PL and Plasticity index-PI), which were used to develop an empirical equation to determine CBR. Soil samples were collected and unsoaked CBR, PL, LL and PI were determined according to BS 1377 part 9 and BS 1377-2; 1990. Quasi static penetration forces at 20 mm depth of penetration were also determined at consistency limits. It was found that the force of 1020 gf and 60 gf was achieved at a depth of 20 mm at PI and LL respectively. The correlation and regression analysis between consistency limits, and the experimental CBR obtained showed coefficient of determination, R2 = 0.907 between CBR and all the parameters using multiple linear regression analysis (MLRA). The regression equation developed was used together with the relationship developed between the Quasi static Penetration force at consistency limits and the tested consistency limits to come up with the General Empirical Equation. Verification of the formula showed that the correlation can be used accurately to determine the un soaked CBR.
Transportation Infrastructure is a key component for any long term development program of any nation. The development of road network is regarded as an index of economic, social and commercial progress of a particular country [
Soil bearing capacity plays a very important role for the design of highway structure. It determines the design thickness of the pavement. The bearing capacity of the sub grade is mostly influenced by the type of soil, water content and its density [
In Uganda, it is a common practice to determine the subgrade soil bearing capacity for highway pavement design using CBR test measurement. To determine the CBR representative soil samples are compacted at predetermined optimum moisture content and maximum dry density for a given compaction energy of the soil material. Thereafter the CBR value is obtained only after immersion in water for 4 days and a plunger is used to penetrate the soil [
Research on correlation between DCP and CBR value has been performed on clay sand and sand soils. The study aimed at relating the result of DCP to CBR value, which takes into account the soil density [
However, [
Other methods are available to determine sub grade bearing capacity such as Plate Bearing test, and Hand Cone Penetrometer (HCP) test, also known as Proving Ring Penetrometer [
The quasi-static cone test procedures are essentially the same as for the fall-cone tests and are also described by [
Therefore to resolve this, it is necessary to determine CBR values using other parameters determined by Quasi static cone tests which can be easily determined by use of statistical analysis.
The study concentrated on soils in Masaka, Kalungu, Rakai, and Lwengo District in Uganda as shown in
[
CBR = ( DCP ) [ Log ( PI × C ) 26.51 + 8.89 ] [ F i − 0.0269 ( PI × C ) 2 + 0.541 PI × C − 5.72 ] .
Equation (1)
where: Fi: is the initial state factor, DCP is the dynamic cone penetration (mm/blow), PI: is the plasticity index, C: is the clay content.
However, [
[
Field CBRprediction= C0+C1γ + 0.025HCP. Equation (2)
where C0 and C1 are coefficients depending on the type of soil. HCP is the value of Hand Cone Penetrometer test.
For peat soils, the value of C0, C1, and C2 significantly influenced by fiber peat. The value of C0, C1, C2 is −1.250, 0.085, and 0.005 respectively.
But all this study needs to be carried out in other types of soils like peat soil.
[
log 10 SCBR = 0.397 + 0.917 log 10 UCBR R = 0.847 Strongrelationship Equation (3)
where;
SCBR = California bearing ratio for soaked soil samples;
UCBR = California bearing ratio for unsoaked soil samples.
The above relationship were carried out on fine grained soils and can used to determine the soaked CBR incase Unsoaked CBR or DCPI are tested. And [
CBR s = 0.2807 ( CBR u ) + 5.0352 ; R = 0.718 Equation (4)
CBR u = 293.4964 + 25.4466 ( LL ) − 59.5422 ( PI ) Equation (5)
where CBRs = California bearing ratio for soaked soil samples;
CBRu = California bearing ratio for unsoaked soil samples;
LL = Liquid limit;
PI = Plastic limit.
It was observed that CBR values decrease with increase in plasticity index and increase with increase in liquid limit. Also unsoaked CBR was largely dependent on Liquid limit and plastic limit. However, their research was carried out on soils with unsoaked CBR ranging 65 - 85. There is a need to consider also the soils with unsoaked CBR below 65. Although Equation (i) can be used to determine soaked CBR ranging from 65 - 85.
The liquid limit (LL) and plastic limit (PL) tests are among the most commonly specified tests in the geotechnical engineering industry and originate from the original research of Atterberg [
The study concentrated on determining the atterberg limits, quasi static cone penetrations forces at atterberg limits and California bearing ratio of soil samples and finding their empirical relationship. 50 samples of soils were tests and compared to find the relationship between these tests.
Materials tested were soils of different plasticity where the particles in the soil can bond to one another. The samples collected were kept in the polythene bags to avoid loss of the moisture content in the soil. The samples were taken to laboratory to be tested. Particles larger than 0.425 mm diameter were sieved out then the soils were mixed with distilled water and molded using palette knives. Particular care was taken to break down aggregated particles by hand powdering.
In order to have sufficient and reliable data, laboratory tests were conducted on soil samples obtained from Masaka, Kalungu, Lwengo ,and Rakai District in Uganda. A total of 50 distributed samples were collected. The representative samples selected on the basis of visual identification of the soils with different properties. Soil samples were 12 samples from Masaka, 9 samples from Kalungu 10 samples from Rakai and 19 samples from Lwengo district.
Tests carried out were thread rolling plastic limit as per clause 5 of BS 1377-2: 1990, liquid limit test using Fall-cone Tests as per section 2.3.2 to BS 1377-2: 1990, determination of unsoaked CBR at optimum moisture content and determination of quasi static force at 20 mm depth of penetration for soils at consistency limits. These tests were carried out to all 50 samples of soil collected as shown in
The results of the experimental testing program reported in from
For the development of alternative plasticity index parameters based on quasi-static cone penetration tests which provide upper and lower strength indices similar to the conventional BS 1377 liquid limit (LL) and plastic limit (PL), to develop the empirical relationship between conventionally derived consistency limits and CBR and to develop the empirical relationship between Quasi static cone Penetrations and California bearing ratio
The results in
The laboratory CBR tests were conducted for 50 samples comprised of soil collected in different areas in Uganda. The tests were conducted for unsoaked CBR. at optimum moisture content.
Fall-cone tests were conducted for 50 test soils of different plasticity obtained from different areas of Uganda. All fall-cone tests were conducted in accordance with the BS 1377-2: 1990 procedure. The derived LL values varied between 28 and 50.3 are presented in
Also Thread rolling plastic limit tests were conducted for 50 test soils comprising of soils from different areas of Uganda following the procedure set out in part 2 of BS 1377. For all the tested soils the PL ranged between 11 and 36, and is presented in
This section presents the results of quasi-static cone tests from which quasi-static Liquid and plastic limits were derived. Also presented are results of preliminary investigations on quasi-static cone penetration load versus depth relationships.
Quasi-Static Cone Tests for Fine SoilsThis was done using the fabricated mechanically driven cone devices. The quasi static cone penetrometer was consist of the 20 mm diameter bar cone shaped at the penetration tip similar to that fall cone penetrometer attached to the frame similar to tri axial frame as shown in
Quasi-static cone tests were conducted for various soils of different plastic ranges. The results are presented in
Before coming up with results in
From
Therefore a new plot of penetration force versus depth square was made. This is shown in
From
τ f = K Q / h 2 .
where τf is the undrained shear strength is the cone factor, Q is the weight of the cone and h is the depth of penetration.
Therefore the 50 tests for penetration were all made plotted by Penetration Force versus depth squared.
However, for some of the soils it is observed that some of the loads versus depth squared relationships are not entirely linear. This may be, among others factors, attributed to the load recording mechanism (load-cell) of the quasi-static cone devices. However, even with the curvature in the load versus depth squared relationships, linear regression curves indicated correlation factors (R) generally above 0.92.
From the graph of Force Versus penetration squared, the Force corresponding to penetration of 10 mm, 20 mm and 30 mm were determined for all the 50 samples. The aim was to determine which penetration depth matches the drop cone at plastic Limit and Liquid Limit.
From
Similarly
Therefore the 20 mm values are to be used for determination of quasi static force for both plastic and liquid limit.
Denoted LLqc, the quasi-static cone load associated with LL is obtained from the load versus penetration depth squared at liquid limit as shown in
shows the sample of a graph drawn for each soil sample tested at Liquid limit. For 50 test soils, LLqc ranged from 40.5 gf to 64.21 gf: overall averaging about 59.58 gf. Values of LLqc are summarized in
The above quasi static force of 59.58 gf is approximately 60 gf similar to Swedish fall cone of 60 gf. Therefore the LLqc at 60 gf and can be denoted by QL60.
Therefore, QL60 (Quasi static liquid limit) can be defined as the moisture content in the soil sample at which the quasi static force of 60gf can penetrate a soil sample up to a depth of 20 mm.
Denoted PLqc, the quasi-static cone load associated with PL is obtained from the load versus penetration depth squared at Plastic limit.
Therefore the PLqc is 1020 gf and can be denoted by QP1020.
Therefore, QP1020 (Quasi static Plastic limit) can be defined as the moisture content in the soil sample at which the quasi static force of 1020 gf can penetrate a soil sample up to a depth of 20 mm.
Thereafter the results were analyzed using single and multiple regression analysis. Accordingly, the 50 laboratory test of the independent and dependent variables were used in regression analysis and the Pearson correlation coefficient between CBR and soil index properties i.e. PL, LL, and PI were as follows.
The regression analysis after correlating CBR with LL is expressed by Equation (6):
CBR = 1.244 LL − 4.003 with, R2 = 0.187. Equation (6)
Therefore, LL can be used to explain 18.7% of the variation in CBR. The statistical output’s specifics show that the association between liquid limit and CBR that has been developed is not statistically significant (α > 0.05). This suggests that for all soil samples, there is a modest correlation between LL and CBR. According to the calculated Pearson’s correlation coefficient (R), liquid limit is a very poor predictor of unsoaked CBR. The above relationship indicates that as the liquid limit increases there is a slight increase in CBR.
The regression analysis after correlating CBR with PL is expressed by Equation 7
CBR = 2.285 PL − 6.797 with R2 = 0.669. Equation (7)
Therefore, PL can explain 66.9% of the variation in CBR. The statistical output data show that there is a statistically significant association between the plastic limit and CBR (α > 0.05). This implies there is a relationship between plastic limit and CBR. According to the calculated Pearson’s correlation coefficient (R), the plastic limit is a predictor for unsoaked CBR. The above relationship shows that as soils with high plastic limit had high unsoaked CBR.
The regression analysis after correlating CBR with plasticity index is expressed by Equation (8);
CBR = − 3.636 PL − 108.30 with R2 = 0.491 Equation (8)
Consequently, the dependent variable is predicted by the PI. The statistical output details show that there is a considerable correlation between the plasticity index and CBR (α < 0.05). This suggests a connection between PI and CBR. The plasticity index is a predictor for unsoaked CBR, according to the Pearson’s correlation coefficient (R) that was obtained.
The above relationship indicates that as the PI increase the CBR reduces which is in agreement [
A multiple linear regression analysis was carried out on fifty samples (n = 50) and after trying a set of alternative combination of predictors the following result were obtained.
1) Model 4: Correlation between CBR and Plastic index and Plastic Limit was carried out. The regression model obtained is a single linear expression with its corresponding coefficients as given by Equation (9) below;
CBR = − 2.601 PI + 1.868 PL + 47.340 R2 = 0.897. Equation (9)
As a result, the independent variables can explain 89.7% of the variance in CBR. According to the specifics of the statistical output, there is a statistically significant association between the plasticity index, plastic limit, and CBR (α < 0.05). The above relationship indicates that as the plastic limit increases the CBR increase this is because as the plastic limit increases the plasticity index reduces hence the CBR increase.
2) Model 5: Correlation between CBR and Plastic index and Liquid limit was carried out. The regression model obtained is a single linear expression with its corresponding coefficients as given by Equation (10) below;
CBR = 1.960 PI − 4.55 PL + 44.216 , R2 = 0.812. Equation (10)
As a result, the independent variable can explain 81.2% of the variance in CBR. The statistical results show that the relationship between the plasticity index, the liquid limit, and the CBR is statistically significant (α < 0.05). The above relationship indicate that as the Liquid limit increases the CBR reduces this is because as the liquid limit increases the plasticity index increase hence the CBR reduces as seen in 6.3.3. The relationship is also similar to that of [
3) Model 6: Correlation between CBR and Plastic Limit and Liquid limit was carried out. The regression model obtained is a multiple linear expression with its corresponding coefficients as given by Equation (11) below;
CBR = 4.566 PI − 2.650 PL + 46.705 , R2 = 0.841 Equation (11)
As a result, the independent variables can explain 84.1% of the variance in CBR. The statistical results show that there is a statistically significant association between the plastic limit, liquid limit, and CBR (α < 0.05). The above relationship indicate that as the Liquid limit decreases the CBR increase this is because as the liquid limit decreases the plasticity index decrease hence the CBR increases as seen in 4.6.3.
4) Model 8: Correlation between CBR and Plasticity Index, Plastic Limit and Liquid limit was carried out. The regression model obtained is a single linear expression with its corresponding coefficients as given by Equation below.
CBR = 1.645 PI + 6.040 PL − 4.250 LL + 49.534 , R2 = 0.907. Equation (12)
As a result, the independent variables can explain 90.7% of the variance in CBR. According to the specifics of the statistical output, there is a significant correlation between the plasticity index, plastic limit, liquid limit, and CBR (α > 0.05).
The above relationship indicate that the plastic limit and liquid limit are the major determinant of CBR which actually true because plasticity index which is another determinant depends on liquid and plastic limits.
Basing on the correlation between CBR and consistency limits, an empirical relation relationships was developed basing on replacing quasi static consistency limits with conventionally derived consistency limits. Since Equations (6)-(8) indicates a weak relationship, only Equations (10), (11) and (12) were considered in developing empirical relationships as fallows;
From Equation (9); CBR = − 2.601 PI + 1.868 PL + 47.340 the empirical relationship between the CBR, QP1020 and QPI was developed as shown in Equation (13) below
CBR = − 2.601 QPI + 1.868 QP 1020 + 47.340 Equation (13)
From Equation (10); CBR = 1.960 LL − 4.55 PI + 44.216 , the empirical relationship between the CBR, QP1020 and QPI was developed as shown in Equation (15) below
CBR = 1.960 QL 60 − 4.557 QPI + 44.216 Equation (14)
where: CBR = California Bearing ration;
QL60 = Quasi static Liquid limit (Moisture content in the soil sample a which the quasi static force of 60 gf penetrate the soil sample up to 20 mm);
QPI = Quasi static plasticity index (QPI = QL60 − QP1020).
From Equation (11): CBR = 4.566 PL − 2.650 QPI + 46.705 , the regression model obtained is a single linear expression with its corresponding coefficients as given by Equation (16) below.
CBR = 4.566 QP 1020 − 2.650 QL 60 + 46.705 . Equation (15).
From the Equation (12); CBR = 1.645 PI + 6.040 PL − 4.250 LL + 49.534 the empirical relationship between the CBR, QP1020 and QL60 was developed as shown in Equation (17) below
CBR = 1.645 QPI + 6.040 QP 1020 − 4.250 QL 60 + 49.534 Equation (16)
Therefore there is strong relationship between CBR and the three consistencies limits i.e. Plastic limit, Liquid limit and plasticity index.
where: CBR = California Bearing ration
QP1020 = Quasi static plastic limit (Moisture content in soil sample at which the quasi static force of 1020 gf penetrate the soil sample up to 20 mm)
QL60 = Quasi static Liquid limit (Moisture content in the soil sample a which the quasi static force of 60 gf penetrate the soil sample up to 20 mm)
QPI = Quasi static plasticity index (QPI = QL60 − QP1020)
Empirical Equation (16) happens to be the most accurate being that it was developed from regression Equation (12) and this equation makes use of the consistency limits with the coefficient of determination R2 = 0.907. Therefore, 90.7% of the variance in CBR can be predicted using the independent variables and finally due to the ease with which these tests are carried out. Empirical Equations (13)-(15) can be possible alternatives when it comes to cost effectiveness but they show fair coefficient of determination hence less predictability.
Using the actual CBR from tests and the predicted CBR from Equation (16), a control graph was plotted between actual experimental CBR and predicted CBR and is shown in
PercentageVariation = ( PredictedCBR − ActualCBR Actual ) × 100 Equation (17)
The average percentage variation obtained from the model is 10.9%, which is a good value proving that the predicted values of CBR are not far from the experimental values.
This research set out to address limitations of the current approaches used to evaluate the California bearing ratio and consistency limits through testing. These limitations are summarized below:
a) penetration rate effects in fall-cone tests,
b) Reliability associated with the thread rolling plastic limit test,
c) Health and safety issues in handling contaminated material,
d) Limitation in interpreting index tests for California bearing ratio, particularly at the conventional thread rolling, plastic limit and liquid limit.
In order to address the above issues, this research focused on developing alternative methods of determining California Bearing ratio and consistency limit testing using quasi-static cone penetration tests.
Therefore, the following conclusions were based on the findings of the research and limited to the sample sizes and soils tested within this research as follows:
1) An alternative quasi-static cone plastic limit (PLqc) and quasi-static cone liquid limit (LLqc) were proposed and were defined in Section 5.5 and 5.6 respectively.
2) Semi-empirical expressions were proposed for derivation of California bearing ratio and consistency limits in Equations (8)-(12) were based on correlations of California bearing ratio with liquid limits, Plastic limit and Plasticity index respectively.
3) Semi-empirical expressions were proposed for derivation of California bearing ratio and Quasi static consistency limits in Equations (13)-(17) were based on relationship between quasi static: liquid limits, Plastic limit, Plasticity index and California bearing ratio.
4) Using the derived relationship between Unsoaked CBR and Soaked CBR for other researchers for example [
Based on findings of this research, the following proposals are made for further development of the quasi-static cone approaches and consistency limits testing, for cohesive fine and mixed soils.
1) Undertaking extensive experimental programmes for soils of varied geology and plasticity, which may provide improvements of the alternative quasi-static cone approaches developed in this research.
2) Laboratory Unsoaked CBR were employed, and although the effect of soaked CBR testing as a reference may be otherwise evaluated, it is essential to evaluate consistency limits based on soaked CBR testing for consistency evaluations.
3) Further development should be undertaken on this fabricated Quasi static cone penetrometer to find out whether it can test the CBR directly without using consistency limit approach.
The authors declare no conflicts of interest regarding the publication of this paper.
Kaweesi, R. and Kyakula, M. (2023) California Bearing Ratio for Cohesive Soils from Quasi Static Cone Tests. Open Journal of Civil Engineering, 13, 367-387. https://doi.org/10.4236/ojce.2023.132028
| sample Number | SAMPLE | force 20 mm (FPL) gf | force 20 mm (FLL) gf | Plasticity Index (PI) % | Plastic limit (PL) % | Liquid limit (LL) % | California Bearing Ration (CBR) % | |
|---|---|---|---|---|---|---|---|---|
| 1 | s2 | 1081.89 | 63.75 | 12.5 | 15.5 | 28 | 48.4 | |
| 2 | W7 | 1009.26 | 55.77 | 12.5 | 25 | 37.5 | 55.6 | |
| 3 | W4 | 991.7 | 57.4 | 12.5 | 27.3 | 39.8 | 63.4 | |
| 4 | w1 | 1159.8 | 64.21 | 12.5 | 30.9 | 43.4 | 75.3 | |
| 5 | s12 | 1155.6 | 60.6 | 12.5 | 31.5 | 44 | 77.5 | |
| 6 | W10 | 994.9 | 57.4 | 12.5 | 27.3 | 39.8 | 64.8 | |
| 7 | W13 | 1006.42 | 58.22 | 12.8 | 15.8 | 28.6 | 45.6 | |
| 8 | W15 | 990.52 | 59.72 | 12.9 | 15.9 | 28.8 | 44.3 | |
| 9 | s6 | 902.51 | 54.05 | 13.2 | 18.5 | 31.7 | 48.7 | |
| 10 | W17 | 902.51 | 59.36 | 13.6 | 20.3 | 33.9 | 46.3 | |
| 11 | W19 | 1002.934 | 58.9 | 13.7 | 18.1 | 31.8 | 50.7 | |
| 12 | W21 | 976.59 | 59.87 | 13.7 | 26.4 | 40.2 | 44.8 | |
| 13 | m5 | 999.67 | 59.94 | 13.8 | 20.6 | 34.4 | 50.7 | |
| 14 | W22 | 1054.643 | 63.11 | 13.9 | 23.9 | 37.8 | 56.3 | |
| 15 | W2 | 997.35 | 63.11 | 13.9 | 24.9 | 38.8 | 57.8 | |
| 16 | W5 | 981.07 | 59.87 | 14.3 | 25.3 | 39.6 | 57.4 | |
| 17 | s1 | 1176.2 | 52.45 | 14.4 | 29.2 | 43.5 | 83.4 | |
| 18 | W8 | 1068.3 | 61.8 | 14.7 | 31 | 45.7 | 69.8 | |
| 19 | W11 | 984.65 | 59.98 | 14.8 | 35 | 49.8 | 70.3 | |
| 20 | W14 | 1013.42 | 60.17 | 16.3 | 35.5 | 51.8 | 60.8 | |
| 21 | m7 | 1078.5 | 40.546 | 16.6 | 28.6 | 44.85 | 73.4 | |
| 22 | W18 | 959.9 | 59.18 | 16.7 | 25.6 | 42.3 | 55.7 | |
| 23 | w16 | 1003.5 | 60.14 | 16.7 | 33 | 49.7 | 62.3 | |
| 24 | M1 | 1126.5 | 63.17 | 16.8 | 22.4 | 39.2 | 50.4 | |
| 25 | W20 | 1012.9 | 59.34 | 16.8 | 28.6 | 45.4 | 55.4 | |
| 26 | W3 | 995.96 | 62.2 | 16.9 | 33.4 | 50.3 | 61.4 | |
| 27 | W6 | 967.1 | 59.58 | 17.3 | 28.1 | 45.4 | 62.5 | |
| 28 | W9 | 995 | 60.11 | 16.9 | 33.4 | 50.3 | 60.4 | |
| 29 | W12 | 1055.19 | 61.68 | 17.6 | 22.9 | 40.5 | 48.9 | |
| 30 | s11 | 983.3 | 61.69 | 18 | 25 | 43 | 44.3 | |
| 31 | S10 | 1010.33 | 59.31 | 18 | 26.7 | 44.7 | 43.8 | |
| 32 | Y4 | 997 | 62.94 | 18 | 16.8 | 34.8 | 33.5 | |
| 33 | M2 | 978.3 | 61.21 | 18.2 | 15.3 | 33.5 | 25.15 | |
| 35 | s5 | 1023.2 | 57.74 | 18.4 | 14.4 | 35.8 | 17.45 | |
| 36 | Y7 | 990.6 | 54.99 | 19 | 11.5 | 31.5 | 16.36 | |
| 37 | Y2 | 1002.2 | 53.16 | 19.1 | 10.9 | 30 | 15.32 | |
| 38 | m10 | 1038.1 | 56.09 | 19.1 | 12.8 | 31.9 | 22.67 | |
| 39 | S7 | 1064.46 | 60.77 | 19.3 | 22.5 | 41.8 | 40.5 | |
| 40 | Y5 | 1026.5 | 59.338 | 19.4 | 30.9 | 50.3 | 46.67 | |
| 42 | s9 | 1144.4 | 59.88 | 20 | 25.6 | 45.6 | 48.07 | |
| 42 | Y11 | 1009.03 | 50.068 | 20 | 25.6 | 45.6 | 48.37 | |
| 43 | m6 | 1138.5 | 64.42 | 22.1 | 24.2 | 46.3 | 40.8 | |
| 44 | Y9 | 997.12 | 61.69 | 22.2 | 11 | 33.2 | 9.3 | |
| 45 | S4 | 982.79 | 63.07 | 22.6 | 13.8 | 36.4 | 14.4 | |
| 46 | Y3 | 1009.73 | 62.25 | 22.8 | 22 | 44.8 | 25.8 | |
| 47 | S3 | 1015.26 | 64.06 | 23.1 | 19.8 | 42.9 | 24.51 | |
| 48 | Y8 | 999.77 | 60.192 | 23.2 | 20 | 43.2 | 27.21 | |
| 49 | S8 | 995.77 | 63.27 | 24.5 | 21.5 | 46 | 26.3 | |
| 50 | Y1 | 1010.36 | 60.71 | 25.8 | 18.5 | 44.3 | 15.8 |