Analysis of underground stratification based on CPTu profiles using high-pass spatial filter

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 q_c and local skin friction on the sleeve f_s are registered. Additionally to classical CPT, the CPTu cone is equipped with the pore pressure measurement, which offer the possibility for measuring it at three different locations along the shaft: u₁, u₂, u₃.^[7] Because of the geometrical features of the cone (e.g., grooves in the places where filters occur) the registration is disturbed by atmospheric pressure and pore pressure. In order to get rid of them on the values of q_c and f_s recorded during the measurement, it is necessary to switch to standard values by introducing appropriate corrections taking into account additional geometrical parameters.^[7] The standardized resistance under the cone is marked as Q_tn and the friction on the sleeve as F_r – calculated according to formulas (1) to (6). (1)Qtn=qt−σν0Pa.CN{Q_{tn}} = {{{q_t} - {\sigma _{\nu 0}}} \over {{P_a}}}.{C_N}(2)Fr(%)=100⋅fsqt−σν0{F_r}(\%) = 100 \cdot {{{f_s}} \over {{q_t} - {\sigma _{\nu 0}}}}(3)qt=qc+u2⋅(1−a){q_t} = {q_c} + {u_2} \cdot (1 - a)(4)CN=(Paσν0')n{C_N}={\left({{{{P_a}} \over {\sigma _{\nu 0}^\prime}}} \right)^n}(5)n=0.381⋅Ic+0.05⋅Paσν0'n = 0.381 \cdot {I_c} + 0.05 \cdot {{{P_a}} \over {\sigma _{\nu 0}^\prime}}(6)Ic=(3.47−logQtn)2+(logFr+1.22)2{I_c} = \sqrt {{{\left({3.47 - \log {Q_{tn}}} \right)}^2} + {{\left({\log {F_r} + 1.22} \right)}^2}} where P_a – atmospheric pressure, σ^′_v0 and σ_v0, respectively – the effective and total overburden stress values, C_N – the correction factor for the effective overburden stress, n – stress exponent determined by the Soil Behaviour Type (SBTn) index I_c, q_t – corrected tip resistance, a – net ratio of the tip.^[10] All parameters are calculated in an iterative way.

A highly significant parameter necessary in various interpretations is the friction ratio R_f,⁽⁷⁾ which determines the ratio of sleeve friction to resistance under the cone tip and the standardized pore pressure parameter B_q,⁽⁸⁾ which is expressed as the ratio of the increase in ground water pore pressure to the difference in resistance under the cone tip, taking into account the effect of ground water pore pressure and primary stress. (7)Rf(%)=fsqt⋅100{R_f}(\%) = {{{f_s}} \over {{q_t}}} \cdot 100(8)Bq=u2−u0qt−qν0{B_q} = {{{u_2} - {u_0}} \over {{q_t} - {q_{\nu 0}}}}

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 q_t and the friction ratio R_f. The chart area has been divided into 12 Soil Behaviour Types (SBT) areas (Figure 1). Depending on the subdivision in which the measurement point will be located, it is qualified to a given SBT group. The Soil Behaviour Types are defined in Table 1.

Figure 1

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 Q_tn and the normalized sleeve friction F_r. The number of soil behaviour types has been reduced to 9, as depicted in Table 2. In 2009, Robertson updated the standardized cone resistance and linked it to the SBT diagram.^[10]

Figure 2

It is possible to classify soil layers using the soil behaviour type index I_c.^[8] By calculating the value of the I_c index, it is possible to determine the soil behaviour type.^[9] This method is based on Robertson's classification from 1990^[11] but it does not include types from areas 1, 8 and 9. The value of I_c is calculated from formula (6) based on Q_t and F_r. The SBT index I_c depends on numerous parameters, however, it is indicated that there is some correlation between the soil grain-size and the value of the I_c index, that is, the higher the index value, the smaller the grain-size.^[8] The I_c thresholds are showed on Roberson's soil behaviour type classification chart in Figure 3 and presented in Table 3.

Figure 3

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 q_c and f_s depend on the order and properties of all soils within the impact zone of the pushed-in cone (Figure 4).

Figure 4

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.

Figure 5

The cone resistance is marked as q^t if the registration would be free from the influence of weaker soil under and above it.^[2] Transition zones are defined as interval of depth near the layer boundary where the registration value increases or decreases even though changes rapidly only where the layer boundary occurs. A thin layer effect occurs when the peak q_c is smaller than the corresponding q^t. In the cases analyzed in the graphs, the thinner the layer, the difference between the two parameters becomes greater.

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 (Q_t, F_r).

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.

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 (q_c, f_s, Q_tn, F_r) from 1D to 2D by copying the data vector at least twice. Z × 1 → Z × 3, where Z – number of records in the probe. This procedure is executed for each normalized parameter individually. Each generated array is then normalised by dividing by a maximum value. In this way, the values in the array are in the range of 0 to 1. The last step is to assign a colour value such that the maximum value is white, the minimum value is black, and the intermediate values have grayscale shades. As the values of the parameters in the rows have the same values, they are represented by horizontal monochromatic stripes consisting only of grayscale shades.

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 I_c,^[9] the detected edges in the image may be immediately taken as the boundary of layers in the geological profile because this classification is based only on one parameter. In a classification based on Robertson's nomogram,^[10] the situation is complicated because it is based on two standardised values (Q_tn and F_r). In the images of registration after using Prewitt's operator, the edges are not always detected at the same depth for both parameters. In addition, due to the geometric structure of the cone, the resistance records on the friction sleeve is a few cm above the resistance measurement level under the cone tip, the maximum offset of the detected edges can be up to 10 cm. The algorithm first searches for the edge at Q_tn image and then verifies if the edge is also detected at F_r in the vicinity depth. If an edge occurs in this area, the edge in the image is identified with the border of layers in the geological profile; if not, the detected edges are not identical with the borders of layers in the geological profile.

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 Q_tn and F_r for the 1990 Robertson classification^[10] and next based on I_c for the classification based on the classification coefficient.^[9]

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.