Usefulness of the CPTU method in evaluating shear modulus G₀ changes in the subsoil

To design and examine the stability of many building structures, the knowledge of small strain shear modulus G₀ is required. In the event of a significant variability in the construction of the subsoil found under the designed structure, it is necessary to continuously assess the changes in modulus G₀ of the studied profiles. Such an assessment can be obtained from the empirical correlation between cone resistance q_c from CPTU and small strain shear modulus G₀. Using this correlation to predict changes in modulus G₀ in the subsoil also allows for the reduction of the cost of field tests and reduction of the number of necessary tests used to directly determine modulus G₀ with SDMT and SCPTU. Because of many independent variables that affect the measured parameters in the process of static penetration, a unique correlation between cone resistance q_c and shear modulus G₀ does not exist, just as in the case of the interrelationship between undrained shear strength from DMT and CPTU (Młynarek et al., 2018). Therefore, it is interesting to identify the factors and their quantitative impact on the correlation between cone resistance q_c and shear modulus G₀. This issue is the objective of this article. Due to the aforementioned large number of variables affecting cone resistance, the analysis was limited to non-cohesive soils of different genesis and preconsolidation effect.

The research was carried out in 5 locations that differed in geological history and allowed the collection of results regarding sediments formed in various depository environments and subjected to various post-sedimentation processes (Fig. 1). Five research sites located in Poland have a complex geological structure. Four of them (Gnojewo, Derkacze, Darłowo and Rzepin) are in the zone of impact of the Weichselian Glaciation, which left moraine deposits covered with fluvioglacial sands.

Figure 1

The grain size distribution of the fluvioglacial sands is very diverse, and it ranges from gravels to fine and silty sands. The layers are generally thin and do not exceed 1.5 m. However, outwash plain ‘sandur’ forms were formed in stages and over hundreds of years, which resulted into a certain variation in the state of these soils and had an impact on the formation of a minor preconsolidation effect in the subsoil. The overconsolidation ratio (OCR) of these soils is estimated within the range of 1–3. The OCR values were determined using the Wierzbicki (2010) method based on the results of CPTU. The obtained values were randomly compared with geological knowledge regarding the history of these soils.

Older sediments, the so-called interglacial sands found below the layer of the youngest moraine clay, were also examined in two locations (Derkacze and Darłowo). These deposits, which developed into the form of medium and fine sands, are characterised by a homogeneous layer structure and high values of OCR reaching 10. The last location, Warsaw, included structures created during the Riss Glaciation. As the examined fluvioglacial deposits in this region rested on moraine clay, they were geologically normally consolidated. In this case, certain effects of ageing (cementation) of the sediment were observed, because the deeper layers showed OCR values characteristic for preconsolidated soils (OCR around 6).

The empirical correlation between cone resistance and shear modulus G₀ is built on the functional parameters that describe two different processes. One process is the process of static penetration, the other one is the course and registration of a seismic wave in the subsoil. The static penetration process is expressed with Eq. (1) (Młynarek, 2007; Młynarek et al., 2018): (1) F(Ps,qc,Vp,Q1,Q2)=0 F\left( {{P_s},{q_c},{V_p},{Q_1},{Q_2}} \right) = 0 where: P_s – measured parameter of CPTU test equivalent, q_c, q_t – cone resistance, V_p – penetration velocity, Q₁ – parameter characterising soil medium, Q₂ – parameter characterising cone.

For non-cohesive soils, parameter Q₂ is written as a function of multiple variables (Lunne et al., 1997; Jamiolkowski et al., 2001): (2) Q2=f1(x1,…,x8) {Q_2} = {f_1}\left( {{x_1}, \ldots ,{x_8}} \right) where: x₁ – effective unit weight of soil, x₂ – grain size characterisation, x₃ – relative density of soil, x₄ – grain coarseness and ageing effect, x₅ – mineralogical type of grain, x₆ – parameter describing stress in the soil, x₇ – parameter defining shear strength (co-dependent on x₁ … x₅), x₈ – preconsolidation stress or OCR.

The quality of the measured cone resistance values also depends on the measurement uncertainty associated with the used test technique (Młynarek, 2010; Lumb, 1974). The impact of the independent variables recorded in parameter Q₁ on the values of cone resistance and measurement uncertainty cannot be separated (Lacasse & Nadim, 1994); hence, the change of e.g. cone geometry, penetration velocity and even the use of probes from different manufacturers (Młynarek, 2010) can lead to different records of the correlation between cone resistance and shear modulus G₀. Equations (1) and (2) justify the statement that there is no unique correlation for non-cohesive soils between cone resistance and modulus G₀. Many authors have documented the impact of variables x₁ … x_n on cone penetration parameters, including cone resistance (e.g. Lunne et al., 1997; Mayne, 2001).

The function that describes the course and registration of a seismic wave and creates the basis for determining shear modulus G₀ is expressed by a simple Eq. (3) (Lunne et al., 1997): (3) G0=ρVs2 {G_0} = \rho V_s^2 where: ρ – soil density, V_s – shear wave velocity.

Equation (3) is supplemented with Eq. (4), which determines the independent variables that affect shear modulus G or G₀ (Hardin, 1978; Lee & Stoke, 1986): (4) G/G0=f2(σ′v0,e0,OCR,S,C,K,T) G/{G_0} = {f_2}\left( {\sigma {'_{v0}},{e_0},OCR,S,C,K,T} \right) where: σ’_v0 – effective vertical stress, e₀ – initial void ratio, OCR – overconsolidation ratio, S – degree of saturation, C – grain characteristics, S – soil structure, T – temperature.

Measurement uncertainty, as in CPTU, has an impact on the determined value of G₀. These uncertainties are related to the measurement technique and seismic wave registration. Research by Foti et al. (2006) showed high recurrence of seismic wave registration in the replication test for one type of the SDMT dilatometer. A separate issue is the conformity assessment of designated moduli G₀ if the test is performed with two different devices. Such situation took place in the conducted research.

During the research, a cone manufactured by AP vd Berg with an seismic module with a single geophone and a Studio Marchetti dilatometer with a seismic module with a pair of geophones located 0.5 m apart were used. To determine the time of arrival of the wave in the case of SCPTU, the pseudo-interval and cross-correlation methods were used. In the case of SDMT, the true interval method and phase shift analysis were applied (ASTM Standard, 2008). Examples of the conducted analysis of the arrival time of the wave are presented in Fig. 2. Determining the time of arrival of the wave allows calculation of the small strain shear modulus G₀ according to the Eq. (3). These results, supplemented with the values of CPTU parameters (q_c, f_s, u₂), formed the basis of the data set used in the analysis (Figs. 3 and 4).

Figure 2

Figure 3

Figure 4

The seismic measurements have been done every 0.5 m or 1.0 m of profile (dependently on the testing site). The CPTU data were averaged within defined geotechnical layers and were correlated with the seismic measurements carried out within each particular layer and depth. Data groups from this set, which were correlated with the depths from which samples were taken for laboratory analyses, were selected for further examination.

The statistical significance of differences between the designated moduli G₀ from both devices can be examined by analysing the trend of modulus G₀ changes with depth (Lumb, 1974). As far as sediments are concerned, Młynarek et al. (2006) showed that the trend of modulus G₀ changes with depth is rectilinear, and the trend equation coefficients do not significantly differ in terms of statistics. This type of analysis was carried out for the examined sands and is presented in Fig. 5. The obtained results prove that SDMT and SCPTU give statistically non-differing assessments of how small strain shear modulus G₀ changes with depth (Fig. 5).

Figure 5

Figure 6 additionally shows the distribution of population of shear moduli G₀ from SCPTU and SDMT in regard to cone resistance q_c, which includes variability of soil grain size, vertical stress, thickness and diversity of origin of non-cohesive soils tested. Figure 6 shows that the modulus values obtained from both studies are located along almost identical trend lines. This fact proves that both techniques consistently register the impact of the parameters listed in Eq. (4) on the variability of modulus G₀. The obtained result also justifies the possibility of using the value of G₀ obtained from both tests to create a correlation between the shear modulus and cone resistance.

Figure 6

Several solutions for Eq. (4) are known in the literature. An example of such correlation is Eq. (5) by Jamiolkowski et al. (1995): (5) G0=480e−1.43σ′v00.22σ′h00.22pa0.66 {G_0} = 480{e^{ - 1.43}}\sigma _{v0}^{'0.22}\sigma _{h0}^{'0.22}p_a^{0.66} where: p_a – atmospheric reference stress in the same unit as G₀, e – void ratio, σ’_v0 – effective vertical stress, σ’_h0 – effective horizontal stress.

In Eqs. (1) and (2), and (3) and (4), the same independent variables related to the ground are found. This fact is an accurate justification for the purpose of constructing the correlation for non-cohesive soils between cone resistance and shear modulus G₀. However, an interesting question remains: how do the variables appearing in Eqs. (2) and (4) affect the correlation between cone resistance and shear modulus G₀? To answer this question, as mentioned in point 2, research was carried out in several locations in Poland. The results allowed an analysis taking into account the variables that define grain characteristic, relative density and soil structure. These variables are associated with different sediment genesis and preconsolidation effect. Preconsolidation stress σ’_p, was used to describe the preconsolidation effect, while grain characteristics were taken into account by performing an analysis in four groups of non-cohesive soils, both normally consolidated and preconsolidated silty sands, fine sands, medium sands and gravels. The second separately analysed issue was the identification and assessment of the significance of the impact of the variables present in Eq. (4) on shear modulus G₀. This analysis was performed again in various groups of non-cohesive soils, and the following variables were taken into account: the degree of thickness instead of the initial void ratio, preconsolidation stress σ’_p and effective vertical stress σ’_v0.

The conducted tests show that the correlation between cone resistance from the SCPTU method and shear modulus G₀ is an effective way to determine changes in this modulus in a non-cohesive subsoil. However, the documented effect of many variables on this correlation results in the need to construct this correlation for individual soil groups because of their grain size and their origin. Taking these variables into account makes it possible to obtain a statistically very favourable assessment of the correlation between cone resistance and shear modulus G₀. Equations (7–12) can be recommended for geotechnical design, as long as they are applied locally. The effect of soil genesis can be taken into account to some extent using the OCR or effective preconsolidation stress σ’_p. Test results also confirmed the strong correlation between modulus G₀ determined from SCPTU and SDMT and soil physical parameters and stress in the subsoil. It is necessary to emphasise that still the best solution is to carry out SCPTU/SDMT to have less uncertainties in G₀.