In recent years it has been popular to incorporate the knowledge of the signal theory into the analysis of CPTu sounding. This paper provides one of the possible ways to perform the ground stratification based on the CPTu sounding using high-pass spatial filters, which are successfully used in the image analysis to detect sudden changes in the intensity of values on the image, that is, the edges.
The study consists of the three main sections. In the beginning, a definition of the edge, basic information on CPTu static sounding and high-pass spatial filters are presented. Further, the author's algorithm is introduced and an example of stratification performed with its use is presented. Finally, the analysis of its operation based on the test data set provided by the Organizers of TC304 Student Contest on Spatial Data Analysis (September 22, 2019, Hannover, Germany) is discussed. The conclusions are presented and the further direction of the algorithm development is outlined.
One of the main in situ testing method used in geotechnics to designate the properties of the soil is Cone Penetration Test (CPTu). The popularity of this method is ensured by the simplicity and rapidity of the testing.[7] The measurements recorded during the penetration tests is commonly used to recognize the underground stratification.
The Cone Penetration Test involves pushing a penetration rod finished with a special measurement cone into the ground. The penetration velocity is controlled and should be constant at 20 mm/s. The information from the test cone are sent to the computer at fixed time intervals. Currently, it is possible to probe even 2 times per second, which corresponds to registration in profile every 10 mm. Such frequent sampling may be considered as quasi-constant. During the test, the resistance under the cone tip
A highly significant parameter necessary in various interpretations is the friction ratio
During the whole process of ground investigation using a CPTu, sounding a crucial element is the properly performed interpretation of the measurement values obtained from the test. Even the best results may be lost significantly if the interpretation is incorrect. One of the basic applications of the CPTu test is the soil behaviour type classification based on normalized measurement parameters. There are a series of nomograms that allow to identify the soil in the profile. One of the most basic and widely used in the world is the 1986 Robertson classification.[7]
It is based on the relationship between the corrected resistance under the cone tip
Numbers of subdivisions and corresponding Soil Behaviour Types[7]
1 | Sensitive fine grained |
2 | Organic material |
3 | Clay |
4 | Silty clay to clay |
5 | Clayey silt to silty clay |
6 | Sandy silt to clayey silt |
7 | Silty sand to sandy silt |
8 | Sand to silty sand |
9 | Sand |
10 | Gravelly sand to sand |
11 | Very stiff fine grained |
12 | Sand to clayey sand |
Another very popular classification is the 1990 Robertson classification[11] is presented in Figure 2. It is a further development and improvement of the 1986 method. This classification is based on the normalized cone resistance
Numbers of subdivisions and corresponding Soil Behaviour Types[11]
1 | Sensitive, fine grained |
2 | Organic soils: peats |
3 | Clays: silty clay to clay |
4 | Silt mixtures: clayey silt to silty clay |
5 | Sand mixtures: silty sand to sandy silt |
6 | Sand: clean sand to silty sand |
7 | Gravelly sand to dense sand |
8 | Very stiff sand to clayey sand |
9 | Very stiff, fine grained |
It is possible to classify soil layers using the soil behaviour type index
SBT index classification proposed by Robertson and Wride[8]
SBT2 | Organic soils: peats | |
SBT3 | Clays: silty clay to clay | 2.95 ≤ |
SBT4 | Silt mixtures: clayey silt to silty clay | 2.60 ≤ |
SBT5 | Sand mixtures: silty sand to sandy silt | 2.05 ≤ |
SBT6 | Sand: clean sand to silty sand | 1.31 ≤ |
SBT7 | Gravelly sand to dense sand |
Cone Penetration Test provides a wide range of information for estimating soil properties in the profile. However, it should be noticed that the registration at a single point at a given depth is influenced by the spatial arrangement of layers located above and below the cone.[2]
This can be explained by analogy with the pile in the limit state when the failure mechanism pass through the layers above and below the position of the pile base (cone tip).[6][13] Therefore, the measurement characteristics
Figure 5 presents the schema of the effect of thin layer and transition zone. On the left side of the picture, five profiles with different capability are shown. On the right side, the cone resistance to depth relation is presented. For the week layer (Profile 1), the resistance under the cone tip is significantly lower than for the strong layer (Profile 2). Lines 3°, 4° and 5° presents the transition between various layers. When the cone is beginning to reach the strong layer, the resistance under the cone tip is smoothly increasing, and respectively, when it is leaving the strong layer, the resistance is smoothly decreasing.
The cone resistance is marked as
The effects related to the soil layering and correct stratification were studied very intensively over the years. In the work by Boulanger R.W. and DeJong J.T.,[2] there is an overview and summary of the achievements to this field. The book[7] contains a solution based on a simplified elastic solution developed by Vreugdenhil.[14] In order to reduce the influence of spatial distribution of layers around the cone on the CPTu sounding records of a certain depth, a correction coefficient of the cone's resistance is applied depending on the thickness and relative stiffness of the layers. The relative stiffness is expressed as the ratio of average resistance of a cone in the layer to registration in the surrounding soil.
A different approach to the stratification problem in CPT measurements is suggested in Boulanger and DeJong.[2] The authors postulate that the cone penetrometer behaves as a low-pass spatial filter and in order to get rid of the influence of adjacent layers, it is necessary to go through the inverse filtration procedure. Low-pass spatial filters are widely used in image and signal processing. A low-pass spatial filter is also called a fuzzy or smoothing filter. It averages rapid changes in intensity. The simplest low-pass spatial filter calculates the average from a particular pixel using its nearest vicinity. The result obtained from this operation replaces the pixel value. With this procedure, it is possible to smooth the image and blur the contours. Reverse filtering can help restore the value of the image before filtering, if it is possible to develop a function that has blurred the record. In the study stated above, a filter that allows to go through the reverse filtering procedure for CPT probing was developed.
Due to the above mentioned phenomena, that is, the occurrence of the thin layer effect and transition zone, precise detection of the location of layer boundaries is difficult, which often results in errors in recognition of the ground, determination of the layout and thickness of layers in the geological profile, which can further contribute to geotechnical design errors and affect the stability and safety of structures.[12]
The issue related to the separation of layers and the precise determination of their boundaries was dealt with by many researchers. Focciorusso and Uzzielli proposed a procedure of stratification based on cluster analysis and fuzzy algorithm.[4] On the other hand, the Bayesian approach presented by Wang, Huang and Cao[16] is used to separate layers but also allows to determine the probability with which a given soil will qualify for a specific SBT. This approach allows to determine the number of probable layers too. In recent years, the focus has been on the possibility of using machine learning to interpret CPTu sounding. The paper[15] presents a Bayesian unsupervised learning approach allowing to separate layers based on the analysis of parameter variability in two dimensions (
The authors’ paper presents the simple procedure of stratification using high-pass spatial filters, which gives a reasonable result with significantly computational cost in comparison to the mentioned above methods.
High-pass spatial filters are a widely used tool in digital signal and image processing.[3] These filters allow obtaining a sharper image or exposing certain image elements. Mathematically, the filtering effect can be presented as a convolution operation of a certain signal
In order to determine the spatial distribution of layers and assess the type of soil, an original idea of stratification based on a spatial high-pass filter was developed. The calculation procedure is presented below. The basic assumption are:
Robertson's SBT classification chart and normalisation of the parameters is performed according to, the Prewitt's operator is applied, stratification is based on the normalised cone resistance Wolfram Mathematica software is used.
In the first step, on the basis of the original measurement CPTu sounding values, the standardized parameters should be calculated.
Prewitt's operator described above is used in 2D objects, therefore, it is necessary to extend the dimension of the analysed parameter (
The following step is to apply a high-pass spatial filter to the image from the Step II. The algorithm uses the Prewitt operator.[3][5] Due to the lack of variability of parameters in the horizontal direction in the signal matrix resulting from the extension of the 1D to 2D image by copying their values, a horizontal task dimension greater than 3 does not affect the solution because the directional derivative in the horizontal direction is always zero. As a result of applying a filter, a matrix where value 1 correspond to the occurrence of an edge and 0 to its absence is obtained.
In case of a classification based directly on the classification index
After determining the strata boundary in the geological profile from the registration images, it is possible to return to the original standardized registrations. The process of evaluating the representative parameters within the separated layers is based on calculating the average value of each standardized parameter, taking into account the fact that transition zones exist near the layer boundaries.[2] The fact of the occurrence of disturbances at the strata’ borders is taken into account by rejecting the values located within 7 cm (approximately two diameters of the cone) from the boundary of the layer from the set taken into account for counting the average. The value of 7 cm was taken as the minimum thickness of the impact zone, for which the measurement results are most disturbed.[2]
In further operation, the classification should be made on the assumption of representative parameters; firstly based on
The final stage of the stratification procedure is to compare the results obtained for different classifications. If a point is classified into the same group of SBTs according to different classifications, it is more likely that the classification of the strata into a given group is correct.
The algorithm presented previously was implemented to solve a competition task in accordance with TC304 Student Contest on Spatial Data Analysis. The organizers of this contest provided the CPTu soundings results in the form of one training dataset and three tests datasets. The training dataset varied from the others in the fact that it was accompanied by a rational stratification carried out by professionals in order to compare it with the results obtained using the algorithm.
The results of the analysis are shown in Figure 7 to Figure 10. The subheadings are presented consecutively: a) image of registration
The algorithm presented in section 3, despite its high level of automation, requires control of the obtained results. It detects the strata boundary of high-contrast layers, which is clearly visible in Figure 8. Soils with parameters changing in a smooth way, with a clear trend but without value jumps may become problematic. Such soils are, for example, dumpling soils,[1] which are in the scope of the authors’ research and future development plans to examine the possibility of using this algorithm for their analysis. The use of different classifications may result in the detection of layer boundaries at different locations. The authors used the Robertson classification[11] as a reference classification. It is possible that an edge detected by analysing the variability of the sounding chart will not divide a particular layer into two due to the fact that the SBT classification is in the same order.
After analysing the results obtained from the stratification carried out using high-pass spatial filters, it can be concluded that it produces rational solutions. By separating the strata boundaries and then averaging the values inside the strata, the measurement becomes significantly insensitive to noise, which in case of separation of the strata in the ground profile is identified with a large number of very thin layers. In addition, in Figure 7 to Figure 10, it is possible to observe that the averaged parameters correspond closely to the actual soundings. The Organizers of the competition TC304 Student Contest on Spatial Data Analysis (September 22, 2019, Hannover, Germany) provided the test data set in the form of CPTu sounding and stratification carried out using proven methods and experts’ knowledge. The proposed algorithm was supposed to provide the best possible entry into the proposed stratification.
Figure 11 depicts a comparison of the results provided by the organisers of the competition with the results obtained using the algorithm. As it may be noticed, the stratification carried out through the algorithm seems to be reasonable and leads to a stratification that is similar to expert analysis. Separated strata boundaries occur at highly similar depths. Additionally, in most cases, the classification according to Organizers and authors is consistent. On this basis, it is possible to deduce that the algorithm works in a proper way.
The quality assessment of the degree-of-belief of stratification is a task that required the knowledge about exact strata boundaries locations in the ground. The qualitative analysis of the proposed algorithm in comparison to the different boreholes’ tests remains the subject of a future research work of the paper authors.
The novelty of the stratification method comes from the application of tools not previously used in this area, in the form of high-pass spatial filters, which were primarily used in digital image processing. The results of the analysis confirm the observation that CPTu registrations may be considered as a signal and there is nothing to prevent the possibility of employing similar tools for their processing.
A possible area to implement the algorithm described above may be the analysis of the spatial variability of dumping grounds, where additionally, there is a need to create a completely new classification, so this tool may be used for preliminary selection of layers with similar characteristics.