Comparison of the Cone Penetration Resistance Obtained in Static CPTu, and Dynamic DPL and PANDA In Situ Tests

Abstract

The technique of static or dynamic probing is the most commonly used research method for characterizing soil media under in situ conditions. It allows engineers and geotechnical specialists to gain crucial insights into the soil properties, which are essential for designing foundations and other structural elements. One of the newest devices, the Panda variable energy dynamic penetrometer, has gained popularity due to its versatility and ease of use. It is widely used in Western European countries, especially in France, but remains practically unknown in Poland, where traditional methods as static and dynamic probe tests still dominate. The article presents a comprehensive analysis of field test results, including static cone penetrometer CPTu, lightweight dynamic penetrometer DPL, and the PANDA dynamic penetrometer. The aim of these tests was to evaluate the effectiveness of the Panda cone penetrometer by comparing the obtained results with those from the CPTu and the DPL. Correlational relationships obtained between the static (q_c) and dynamic (q_d) penetration resistance of the CPTu, DPL and Panda probes are presented.

1. Introduction

The technique of soil probing is a key method in geotechnics. It is a quick, efficient, and relatively low-cost method to investigate the properties of soil layers. Various techniques and tools are used, but all involve introducing a rod, typically with a conical tip, into the ground. This can be done either statically or dynamically. The results of these tests are mainly used to assess the deformability, mechanical, and physical properties of soils on-site. Determining the resistance on the cone allows for the derivation of geotechnical parameters f.eg. undrained shear strength c_u, friction angle φ or elastic modulus E based on correlational relationships. The measurement results can also be used directly in computational methods, such as in the design of pile foundations or direct foundations [1]. Additionally, these methods can be successfully applied for qualitative assessment of the substrate, for example, detecting zones of weakness or voids caused by soil suffusion.

Each probing method has its limitations, which means it cannot be used in all soil conditions or construction sites. Therefore, it is beneficial to employ various research methods that complement each other. However, using multiple research methods can also lead to incorrect geotechnical assessment of the investigated soil foundation.

Accurate determination of parameters requires the use of methods calibrated to local conditions and practical interpretations that have been validated. Data from the literature, including those provided in the EC7 appendices, obtained abroad on different soils, are often not satisfactory under Polish conditions [2,3]. Eurocode 7 clearly emphasizes the necessity of using local correlations.

The possibility of correlating the results from static CPTu probing and dynamic DPL probing with the results obtained from the Panda penetrometer appears to be significantly important from a practical standpoint. The main advantages of the penetrometer are its mobility and lightweight design, allowing for testing in virtually any conditions. In Poland, the first two methods are commonly used, while the Panda device is not well-known and therefore is not utilized as a measurement tool in engineering practice. This instrument is being intensively developed and widely used in Western European countries, primarily in France [4,5]. In the relevant Polish literature, we can find few references dedicated to the device, such as [6,7]. Consequently, the authors attempted to evaluate the device’s suitability for geotechnical assessment of the soils present in Poland. The verification of the assumption that the research methods listed above equivalently characterize the soil medium has been undertaken. The convergence of results from multiple methods significantly enhances the reliability and accuracy of the obtained measurements, eliminating the possibility of erroneous interpretations.

2. Penetrometer PANDA

The PANDA cone penetrometer has been manufactured in France since the 1990s [5,8]. The primary objective was to develop a lightweight, compact, and cost-effective dynamic penetrometer. It is both instrumented and autonomous, yet powerful enough to penetrate a wide range of soils up to ten meters deep. The Panda device allows for detailed exploration of layers with varying resistance levels by adjusting the hammering energy and intensity. Its description and operating principles are standardized in the French Standard XP P 94-105 [9]. This standard specifies the application ranges for different soil types and outlines the testing methods, measurement procedures, and result interpretation.

The Panda device comprises six main elements: a hammer, an instrumented anvil, rods, a conical cone, a central acquisition unit (UCA), and an HMI box (TDD). Weighing less than 20 kg, the device is easily transportable and simple to handle.

Table 1. Basic specifications of PANDA apparatus.

Hammer	Mass [kg]	2.0
	Standard drop	Variable (measured)
Anvil	Mass [kg]	2.16
Cone	Area [cm2]	2.0	4.0	10.0
	Angle [°]	90.0	90.0	90.0
	Diameter [mm]	16.0	22.5	35.7
	Tip length [cm]	1.1	1.6	2.5
Extension rods	Mass [kg]	0.586
	Tip length [cm]	0.5
	Diameter [cm]	1.4

presents the dimensions of the PANDA penetrometer. Figure 1 shows the PANDA 2 set during measurements.

The UCA serves to consolidate measurements and data collected from two sensors, records two parameters for each blow of the hammer, the speed of impact and the depth of cone penetration. An accelerometer on the head of the tool measures the speed of impact of the hammer. The depth of penetration is measured by a retractable tape. The HMI box facilitates communication between the operator and the device. The instrumented anvil features adjustable energy driving, enabling the driving process to be tailored to the level of soil compaction. The device automatically calculates the dynamic cone resistance q_d.

The q_d is calculated using the “Dutch formula”, based on the following equation according to French Standards XP P 94-105 [9]:

$$q_d=E{\displaystyle \frac{M}{{\mathit{Ae}}^{\prime }(M+P)}}$$

(1)

where

• q_d—dynamic cone resistance [MPa], E—drive energy [J], A—cone section [m²], e′—penetration [m], M—hammer mass [kg], P—total driven mass (extension rods, anvil) [kg].

The PANDA device operates by manually driving rods into the soil using a hammer. It is advisable to aim for a penetration rate of 2 mm to 20 mm per blow during testing to accurately validate the assumptions of the Dutch formula. The rod has a diameter of 14 mm, and the cone types currently utilized include 2 cm², 4 cm², and 10 cm². The 2 cm² cones are primarily used for compaction assessments in tests performed at depths less than 1.50 m, while 4 cm² cones are suitable for geotechnical investigations at greater depths. The 10 cm² cone is reserved for special applications, and all cone designs are intended to minimize skin friction as much as possible. An average person can generate sufficient penetration force to reach soil layers with resistance levels below 50 MPa, typically in the range of 20 to 30 MPa, and for soundings up to 6 m deep. Additionally, the maximum permissible grain size for these tests is characterized by a diameter D_max of less than 50 mm [10]. The primary parameters obtained during testing include the energy transferred during each impact, the resistance at the cone tip, and the penetration depth of the cone located at the end of the rod. These measurements allow for the creation of high-resolution penetrograms, which depict the ground’s tip resistance as a function of depth (Figure 2).

The dynamic cone resistance q_d is directly utilized in monitoring compaction and conducting soil surveys. Numerous studies have established correlations between dynamic cone resistance and other commonly used geotechnical methods. The comparable methods featured in these studies include CPT, SPT, various types of DCP, and laboratory tests such as the direct shear test. These correlations have shown that q_d can be related to parameters such as E-modulus, cohesion, California Bearing Ratio, undrained shear strength, internal friction angle, apparent cohesion, SPT blow count, and CPT cone penetration resistance [5,6,10,11,12,13].

The latest technological evolutions of this device, called PANDA 3, makes it possible to obtain a complete curve of stress at the tip as a function of penetration for each impact. The PANDA 3 investigation technique provides a load-penetration curve of the soil for each impact. Interpreting this curve allows for the estimation of deformation parameters and wave velocity in the soil [14].

3. Research Methodology

3.1. Test Site

Geomorphologically, the study area is located within the Middle Vistula Valley, specifically on a high river terrace (Otwocki) of the Vistula River (Figure 3). It is situated approximately 3.0 to 3.5 km east of the river. The surface of the area is approximately 5 m above the Vistula River datum, at around 83 m above sea level. The subsoil consists of Quaternary deposits, primarily non-cohesive soils of fluvial origin, mainly sands of various grain sizes, with thicknesses ranging from several to several dozen meters.

3.2. Field Tests

This work analyzes results from field studies conducted at the research node, with a schematic layout of research points shown in Figure 4.

The following tests were conducted at the research node: static CPTu probing, dynamic DPL probing, and PANDA 2 penetrometer probing. The individual testing locations were positioned while maintaining the minimum distances specified in relevant standards [9,15,16]. Test methodology and result interpretation adhered to guidelines provided in those standards. Additionally, drilling was performed during the field studies to determine the type of soils being examined, collect soil samples, and assess the depth of the groundwater table. The profile of the borehole is shown in Figure 5. Beneath the 0.3 m thick layer of topsoil, coarse (non-cohesive) soils occur, consisting according to [17] of fine sands (FSa) up to 3.7 m and medium sands (MSa) up to 5.0 m below the ground surface. Based on the results of the CPTu and DPL probing, the degree of compaction of the tested soils was determined in the range of I_D = 35 ÷ 45%.

The presence of a free groundwater table was observed at a depth of approximately 3.2 m below the ground surface.

Along with in situ tests the laboratory tests were carried out, for which the particle size distributions and typical geotechnical parameters are presented in

Table 2. Geotechnical properties of soils; d₁₀, d₃₀, d₆₀—the effective grain diameter [mm]; d—grain diameter [mm].

Soil	Particle Size Ratio		Fraction Content [%]
	${\displaystyle \frac{{{(\mathit{d}}_{\mathbf{30}})}^{\mathbf{2}}}{{\mathit{d}}_{\mathbf{60}}{\mathit{d}}_{\mathbf{10}}}}$	${\displaystyle \frac{{\mathit{d}}_{\mathbf{60}}}{{\mathit{d}}_{\mathbf{10}}}}$	≤0.063	0.063 < d ≤ 0.20	0.20 < d ≤ 0.63	0.63 < d ≤ 2.0	>2.0
FSa	0.94	1.80	6.0	53.0	30.0	10.0	1.0
MSa	1.13	2.67	1.0	17.0	69.0	12.0	1.0

, respectively. Laboratory tests were carried out in accordance with the procedures described in the ISO 17892-4:2016 [18] technical specification.

4. Statistical Analysis of Research Results

In this chapter, an attempt is made to verify the assumption that the applied research methods, namely the lightweight dynamic penetrometer DPL, the static probing CPTu, and the PANDA 2 penetrometer, can equivalently describe the characteristics of the soil medium. Thus, it is assumed that there is a correlational relationship between the results obtained from the three applied research methods. Taking into account the differences in the measurement techniques and the format of the results obtained by the various devices, the data were averaged over 10 cm sections. The correlational analysis included all research results, starting from the ground surface, assuming that the influence of the lack of overburden in the three analyzed methods is identical. A similar assumption was made regarding groundwater.

The statistical analysis was conducted using Statistica PL software version 13 developed by StatSoft Poland Ltd., Kraków, Poland, according to the procedure described in [19]. The analysis included the values of the cone resistances determined for each research method, collected in three datasets: q_cCPTu, q_dDPL and q_dPanda. The calculated basic descriptive statistics for the variables of the three analyzed datasets are presented in

Table 3. The descriptive statistics of the penetration resistance datasets.

	Number of Measurements n [-]	Mean Value [MPa]	Minimum Value [MPa]	Maximum Value [MPa]	Standard Deviation [MPa]	Coefficient of Variation [%]
qdDPL	150	3.68	0.14	12.55	3.40	92.39
qdPanda	150	2.83	0.58	6.90	1.56	55.12
qcCPTu	150	4.66	0.56	9.82	2.20	47.21

.

It should be noted that there is a very high variability of 92.39% the resistance values obtained from the dynamic DPL (q_dDPL) probing compared to the other methods, for which the variability is lower and more comparable.

Based on the determined average resistance values, it can be stated that:

$${\stackrel{-}{q}}_{\mathit{dPanda}}=0.61{\stackrel{-}{q}}_{\mathit{cCPTu}}$$

(2)

$${\stackrel{-}{q}}_{\mathit{dPanda}}=0.77{\stackrel{-}{q}}_{\mathit{dDPL}}$$

(3)

$${\stackrel{-}{q}}_{\mathit{cCPTu}}=1.27{\stackrel{-}{\mathit{q}}}_{\mathit{dDPL}}$$

(4)

The choice of the type of predicted relationship between the analyzed variables was made based on the scatter plot analysis (Figure 6), which illustrates the relationship between the variables in the three created datasets. A visual assessment of the obtained graphs suggests that the potential correlational relationship is linear.

In the next step of the statistical analysis, the Pearson linear correlation coefficient r was calculated for the analyzed datasets q_cCPTu − q_dPanda and q_dDPL − q_dPanda. Based on the statistical tests conducted, it can be concluded that there is a statistically significant correlation at the significance level α = 0.05, with p = 0.0000 < 0.05, indicating a high correlation, where the Pearson coefficient is r = 0.78 for the dataset q_cCPTu − q_dPanda and a moderate correlation of r = 0.68 for the dataset q_dDPL − q_dPanda. The obtained correlational relationships are described by the formulas:

q_cCPTu = 1.102q_dPanda + 1.543

(5)

The standard error of estimate is S_e = 1.378 MPa.

q_dDPL = 1.483q_dPanda − 0.514

(6)

The standard error of estimate is S_e = 2.495 MPa.

Large standard error values in relation to the average values in the datasets indicate that the correlational relationships should be considered with caution, indicate limited predictive precision in practical applications.

In both analyzed cases, the calculated values of the intercept and the slope coefficient at the accepted significance level α = 0.05 proved to be strongly statistically significant with p = 0.0000. For the analyzed datasets q_cCPTu − q_dPanda, the obtained relationship explains 61% of the observed variability of both variables wit R² = 0.61. In the case of the analyzed datasets q_dDPL − q_dPanda, the obtained relationship explains 46% of the observed variability of both variables with R² = 0.46.

In the next step of the statistical analysis, to verify the correctness of the model, the residual values were analyzed. A random scatter of residuals in the form of a cloud of points, without a clear tendency for their variance to increase (or decrease) as the predicted values rise, as shown in the residuals scatter plot against the predicted values ${\widehat{q}}_{\mathit{cCPTu}}$ and ${\widehat{q}}_{\mathit{dDPL}}$ (Figure 7), supports the linearity of the model with respect to the parameters and confirms the homoscedasticity of the random error component in the analyzed datasets.

To evaluate the assumption of normality of the residual distribution, the normal probability plot of the residuals for the fitted models was analyzed (Figure 8). This plot facilitates a quick visual assessment of how well the residuals conform to a normal distribution; points that align closely along the straight line confirm the normality of the residual distribution.

5. Conclusions

In this article, an experimental study was presented in order to establish an empirical correlation between PANDA penetrometer, DPL probe and static penetrometer CPTu. Within the scope of the in situ tests and statistical analyses carried out, the suitability of the PANDA probe for characterizing the soil medium was verified. The field investigations encompassed natural sandy soils located in the Vistula River valley.

Simple correlation analysis (linear correlation) has been performed and linear models to predict q_c (CPTu) values and q_d (DPL) from measurements of q_d made with Panda are proposed appropriately as q_cCPTu = 1.102q_dPanda + 1.543 and q_dDPL = 1.483q_dPanda − 0.514. In both cases, the coefficient of determination R² is not strong (61% and 46%, respectively), indicating a low consistency in the correlation. Additionally, high standard errors relative to the mean values suggest data dispersion and significant variability in the results. The recommendation that (q_d = q_c) [20] was not observed in the tested natural alluvial sandy soils. Furthermore, the q_d values obtained from DPL probe measurements did not correspond to those determined from the Panda penetrometer. The results for the analyzed datasets were $\stackrel{-}{q}$_dPanda = 0.61$\stackrel{-}{q}$_cCPTu and $\stackrel{-}{q}$_dPanda = 0.77$\stackrel{-}{q}$_dDPL.

While simple, the proposed models are unsatisfactory given the statistical analysis results. The authors note the tested soil’s compaction I_D = 35–45%, classified as loose on the borderline of medium dense may significantly influence results, potentially contributing to the observed variability and weaker correlations. Therefore, the authors suggest further statistical analysis consider more complex models, for example, those with two variables, which account for additional soil properties, such as compaction state, to improve predictions. Investigating the impact of other soil properties (e.g., grain size distribution, moisture content) on the Panda, CPTu, and DPL relationship is also recommended. In the authors’ opinion the correlation equations are only an auxiliary means for rough estimation. Conducting further comparative studies across a wider range of Polish soil types and geological settings should be done to better establish a comprehensive understanding of the Panda penetrometer’s capabilities and limitations.