Because of the strong structural and sensitive behavior, the properties of marine soft soil change greatly when subjected to external disturbances, which leads to great difficulty in reflecting its real mechanical properties in the laboratory soil tests. The piezocone penetration test (CPTU) is one of the main technologies for in situ testing of geotechnical engineering. CPTU has the advantages of being fast and convenient, no sampling, low disturbance to soil, large amount of data, and reliable testing. The determination of the overconsolidation ratio (OCR) based on the CPTU results can solve the problems of soil disturbance and stress release, which occur during the consolidation test in the laboratory. However, there are still some problems such as lack of strict theoretical analysis of penetration mechanism and incomplete interpretation theory of in situ test parameters of CPTU. In this paper, the CPTU cone head is assumed to be hemispherical considering the penetration mechanism of CPTU. Moreover, the compaction modes of the CPTU probe penetrating into soil are adopted as spherical and cylindrical cavity expansion modes, respectively. The ultimate expansion pressures of the probe penetrating into soil under the spherical and cylindrical cavity expansion modes are first obtained by virtue of the theory of cavity expansion. Then, two prediction methods for OCR considering the roughness and penetration rate of the cone are proposed by combining the ultimate expansion pressures of the probe penetrating the approximate closed solution of cavity expansion in the modified Cambridge model, which is suitable for predicting the OCR of marine soft clay. Finally, to verify the reliability of the two proposed prediction methods, comparisons with the in situ CPTU tests of marine soft clay in two coastal areas and two existing prediction methods are made. The comparison results show that predictions of OCR of marine soft clay in this paper are close to Wayne’s method and more accurate than Chanmee’s method since the factors such as cone roughness and penetration rate are considered in the new proposed prediction methods. In order to improve the applicability in different cases of the OCR predictions, the average values of the two proposed methods are recommended as the reference value for the OCR of marine soft soil.
Overconsolidation ratio (OCR) of soils is one of the factors that affect the strength, stress-strain, and compressibility of soils. It is also an important parameter for foundation settlement calculation and slope stability analysis. In the previous studies on the overconsolidation ratio, most of the research results are based on heavily overconsolidated soil. There are few studies on normal consolidation and lightly overconsolidated marine soft clay, and there is still no unified understanding of the overconsolidation ratio (OCR) of coastal soft clay. The overconsolidation ratio is usually obtained by the laboratory consolidation test with field soil samples. Because it is difficult to overcome the problems of stress release and soil disturbance during the sampling process, the test results can hardly reflect the real situation of foundation soil. However, because of the structural and sensitive behavior of marine soft soil, its engineering properties are poor. When disturbed by external disturbances, its properties change greatly. Therefore, it is difficult to accurately calculate the overconsolidation ratio of marine soft soil by conventional methods.
The piezocone penetration test (CPTU), with the advantages of being fast and convenient, no sampling, low disturbance to soil, large amount of data, and reliable testing, is one of the main technologies for in situ testing of geotechnical engineering, which is applied to determine the parameters of geotechnical engineering [
At present, there are nearly 20 methods for determining the preconsolidation pressure or overconsolidation ratio (OCR) based on the CPTU test results [
(a) CPTU probe entity and (b) schematic diagram.
In recent years, some scholars have proposed some modified methods for predicting OCR. Zhang et al. [
As mentioned above, empirical prediction formulas for predicting OCR are fitted by regression from a large number of in situ test results; however, they have strong geographical limitations and are suitable for the special cases. The classical theoretical prediction formula is relatively simple and breaks through the limitation of clay types, but fewer factors are considered. Some important parameters such as penetration rate, friction between cone and soil, and large deformation are not considered in classical theoretical prediction formulas.
In this paper, the CPTU cone head is assumed to be hemispherical considering the penetration mechanism of CPTU. And the compaction modes of the CPTU probe penetrating into soil are adopted as spherical and cylindrical cavity expansion modes, respectively. Two prediction methods for OCR considering the roughness and penetration rate of cone are proposed by combining the ultimate expansion pressures of probe penetrating with the approximate closed solution of cavity expansion in the modified Cambridge model, which is suitable for predicting the OCR of marine soft clay. Finally, to verify the reliability of the two proposed prediction methods, comparisons with the in situ CPTU tests of marine soft clay in two coastal areas and two existing prediction methods are carried out.
The expanding process of the CPTU probe penetrating into the soil can be considered as the one-dimensional boundary value problem of the small cavity expansion in the geomechanics. The ultimate expanding pressure is derived by the cavity expansion theory, and then, the expression of the cone tip resistance is determined. Figure
Schematic diagram of cavity expansion. (a) Cavity before expansion. (b) Cavity in expansion.
Based on the above assumptions, cylindrical cavity expansion corresponds to the axisymmetric problem, while spherical cavity expansion corresponds to the spherical symmetry problem. For the plastic zone and the elastic zone, the soil element at the centre point of the cavity is
The solutions for the spherical and cylindrical cases can be developed together by assigning
The increment of radial and circumferential strains (Δ
Since the soil was initially acted upon by
Using Hooke’s law, the increments of radial strain and circumferential strain around a cavity can be related to the stresses as follows:
Moreover, the relevant boundary conditions of radial stress at
Therefore, the solutions of stress and displacement in elastic region can be obtained by virtue of equations (
Assuming that the radius of elastic-plastic boundary is
Subtracting equations (
According to the equation (
Then,
Substituting equation (
Similarly, the stresses
Using the conservation of volume, the boundary condition at the elastic-plastic boundary is
Substituting equation (
The soil in the plastic zone is analyzed by large strain theory and logarithmic strains are adopted. The strain coordination relationship is expressed as
The volumetric strain can be expressed as
For the undrained condition, the volumetric strain,
The boundary condition is obtained by conservation of volume:
The yield function based on the modified Cambridge model can be expressed as [
Substituting equation (
In the plastic zone, the total volumetric strain is the sum of the elastic volumetric strain and the plastic volumetric strain. In the undrained loading process, the total volumetric strain is zero; that is,
After integrating equation (
In the critical state
In the plastic zone, the difference between the deviator stress and the ultimate deviator stress is small. For the convenience of calculation,
Figure
Relationship between normalized radial stress and radius.
It can be seen from Figure
In the CPTU test, the radius of the bottom of the probe is
Assumed analysis model for piezocone penetration.
According to the similarity of the process of the probe penetrating into soil and the cavity expansion, in order to combine the cavity expansion pressure with the normal stress of the probe in the cavity expansion theory, the probe is simplified to a hemispherical cone with a radius of
The diagram of cone force analysis.
After integrating the normal stress and the shear stress on the 1/4 arc, the equilibrium condition is as follows:
When the cavity expanding radius reaches the CPTU probe radius
The penetration process of the probe is actually a penetration mode between the expansion of the spherical and cylindrical cavity. In order to analyse the excess pore water pressure generated by the penetration process of the probe, the two modes are separately considered. The process of penetrating saturated soft soil at standard rate (2 cm/s) can be considered as an undrained loading process. When the cavity is expanded under undrained condition, the excess pore water pressure of the surrounding soil at the tip shoulder can be expressed as [
By combining equations ( When When
Because of the characteristics of high moisture content, low shear strength, low permeability, and strong structure of marine soft clay, once disturbed, the strength of the soil will be weakened and the softening behavior will occur, and the strength change largely depends on the corresponding strain rate. The standard penetration rate of the CPTU test is 20 mm/s, and the strain rate of soil failure around the cone is much larger than the strain rate in the triaxial compression test conducted in the laboratory. As the shear rate increases, the undrained shear strength increases, so the effect of the strain rate difference on the undrained shear strength should be taken into consideration. Kulhawy and Mayne [
According to Yu [
For the soil element at the cavity wall
The penetration rate can be approximately considered as
Probe types | Cavity expansion mode |
|
|
---|---|---|---|
10 cm2 | Spherical | 1.59 | 1.64 |
Cylindrical | 1.56 | 1.61 | |
|
|||
15 cm2 | Spherical | 1.58 | 1.63 |
Cylindrical | 1.55 | 1.60 |
After considering the effect of strain rate, the undrained shear strength in equation (
After considering the influence of the difference in strain rate of the soil between probe penetration process and triaxial compression test on undrained shear strength, the OCR prediction method considering the influence of cone roughness and cone penetration rate can be obtained. When When
To validate the methods proposed in this paper, the predictions of equations (
Information summary of test input parameters.
Locations | References | Input parameters | |||||
---|---|---|---|---|---|---|---|
|
Λ | Cone tip angle | Cone bottom area |
|
Internal friction angle of soil | ||
Busan, South Korea | Singh and Chung [ |
0.6 | 1.0 | 60° | 15 cm2 | 11.0 | 29° |
St. Marcel, Canada | Lefebvre and Langlois [ |
0.6 | 1.0 | 60° | 10 cm2 | 11.25 | 26° |
Singh and Chung [
The predicted values of OCR by four methods for Busan site in Korea based on CPTU.
St. Marcel is located along the St. Lawrence River in Montana, southern Canada. Lefebvre and Langlois [
The predicted values of OCR by four methods for St. Marcel site in Canada based on CPTU.
From Figures
In order to compare the prediction accuracy between the two proposed prediction methods, Wayne’s method and Chanmee’s method, which are based on the CPTU test, more intuitively, the prediction values of OCR of the two test sites are compared with the measured datum in the graph with the measured values of OCR as the horizontal axis and the predicted values of OCR as the vertical axis as shown in Figures
Comparison of the measured values and predicted values of the OCR using Wayne’s method.
Comparison of the measured values and predicted values of the OCR using Chanmee’s method.
Comparison of the measured values and predicted values of the OCR using Method 1.
Comparison of the measured values and predicted values of the OCR using Method 2.
The data distribution of four methods in the zone of 80% accuracy and the relative error can be obtained by Figures
Analysis and comparison results of four methods.
Methods | Items | ||
---|---|---|---|
Within the zone of 80% accuracy (%) | Relative error | ||
CPTU | Wayne’s method | 69 | 0.187 |
Chanmee’s method | 46 | 0.256 | |
Method 1 | 73 | 0.162 | |
Method 2 | 85 | 0.129 |
According to reference [
The predicted values of OCR based on CPTU, DMT, and FVT for D2 test site in Busan, South Korea.
In this paper, the CPTU cone head is assumed to be a hemispherical cone head considering the penetration mechanism of CPTU. Moreover, the compaction modes of CPTU probe penetrating into soil are adopted as spherical and cylindrical cavity expansion modes, respectively. The ultimate expansion pressures of probe penetrating into soil under the spherical and cylindrical cavity expansion modes are firstly obtained by virtue of the theory of cavity expansion. Then, two prediction methods for OCR considering the roughness and penetration rate of cone are proposed by combining the ultimate expansion pressures of probe penetrating with the approximate closed solution of cavity expansion in the modified Cambridge model, which is suitable for predicting the OCR of marine soft clay. Finally, to verify the reliability of the two proposed prediction methods, comparisons with the in situ CPTU tests of marine soft clay in two coastal areas and two existing prediction methods are performed. The main conclusions are as follows: From the penetration mechanism of CPTU, it can be seen that the process of penetration of the CPTU probe into soil can be regarded as the process of cavity expansion from zero radius, and the radial stress increases with the increase of consolidation degree of soil. Under the same conditions, the radial stress of spherical cavity expansion mode is about 1.7 times compared with cylindrical cavity expansion mode. Two new methods proposed in this paper have better accuracy in predicting the OCR value of marine soft clay in general, with higher assurance rate within 80% of the prediction accuracy, which can better describe the trend of the OCR value of marine soft clay along with the depth. The comparative results show that predictions of OCR of marine soft clay in this paper are close to Wayne’s method and more accurate than Chanmee’s method since the factors such as cone roughness and penetration rate are considered in the new proposed prediction methods. In order to improve the applicability in different cases of the OCR predictions, the average values of two proposed methods are recommended as a reference value for the OCR of marine soft soil.
An executable file to calculate the two prediction methods for OCR is available from the corresponding author upon request.
The authors declare that they have no conflicts of interest.
This work was supported by the National Natural Science Foundation of China (grant no. 51678363), Shenzhen Science and Technology Project (no. JCYJ20150525092941052), and Underground Engineering (Tongji University) (no. KLE-TJGE-B0905).