The Role of Spatial Distribution of Geotechnical Soil Parameters in Site Investigation

The investigated site is located in Bucharest, Romania, and it was analyzed to obtain a geotechnical study for the construction and development of a residential complex. The terrain surface is relatively flat, with absolute elevations of approximately 86.50 m (above Black Sea level). In the studied area, there had been industrial buildings and underground networks that were demolished. At the time of the geotechnical investigations, it was not known whether the building foundations were filled with compacted soil or not.

To characterize the foundation soils from the site, 13 geotechnical boreholes were made with depths ranging from 45 to 60 m, and five CPTs were conducted with depths ranging from 10.50 to 14.50 m (Fig. 1). For the entire site, 630 linear meters of boreholes and approx. 66 linear meters of CPTs have been carried out.

Figure 1:

The following physical and mechanical properties of soils were determined (according to Romanian legislation in force) on samples taken from geotechnical boreholes: 237 grain size distributions, 439 moisture contents, 139 plasticity limits, 92 densities of the mineral skeleton, 119 consolidation tests in oedometer, 140 direct shear tests (consolidated-drained [CD] and consolidated-undrained [CU] types). From the mechanical tests, a total of 253 derived values were obtained for the following parameters: density, dry density, porosity, void ratio, and saturation degree. Based on SPT, 91 values were obtained for characterizing the soils according to their consistency state.

Spatial variation graphs of geotechnical parameters provide an approximate image of the stratification of the investigated site. The final stratification is determined only after analyzing the values obtained from laboratory tests and after the determination of the characteristic values according to NP 122-2010 [8]. According to NP 122-2010, the division into geological layers is based on natural unit weight (γ, kN/m³), moisture content (w, %), consistency index (I_C, -), porosity index (n, %), degree of compaction (I_D, %), and plasticity index (I_P, %). For these parameters, variation coefficients (V_x) are calculated, which must not exceed the values presented in Table 1. In situ and laboratory tests provide measured values of the geotechnical parameters; however, these values cannot be directly used in geotechnical design [9]. Characteristic values are mandatory in geotechnical design, and they are calculated using mathematical statistical methods to ensure a 95% confidence level.

The calculation of variation coefficient [8]: (1) Vx=sxXm=1n−1×∑ Xi−Xm2∑ Xin {V_x} = {{{s_x}} \over {{X_m}}} = {{\sqrt {{1 \over {n - 1}} \times \sum {{{\left( {{X_i} - {X_m}} \right)}^2}} } } \over {{{\sum {{X_i}} } \over n}}} where s_x is the standard deviation of the X_i values, X_i is the measured or derived value resulting from laboratory or onsite test, X_m is the arithmetic mean of the X_i values, and n is the number of X_i values.

It should be noted that this division into layers is based on mathematical statistics, which must be complemented by an appropriate engineering judgment. The coefficient of variation is influenced by both the dispersion of the values and their number. For a large number of laboratory determinations, the dispersion of values can be very large and, nevertheless, the coefficient of variation falls within acceptable limits for the delimitation of a geotechnical layer [10]. Situations may result where, for example, the state of consistency varies from soft to stiff and yet the samples are considered to be part of the same layer.

Table 2 presents a theoretical situation in which the measured values of the consistency index are uniformly distributed in a range of values for which the coefficient of variation is the one recommended for the delimitation of a geotechnical layer, respectively, V_xmax = 0.15. The mean of the firm domain (I_c = 0.625) was chosen as the reference value. It is found that for a small number of determinations (n = 3), they remain in the firm domain, but the lower characteristic value classifies the soil as soft and the upper one as stiff. For 11 determinations uniformly distributed in a range of values that give V_x = 0.15, the layer covers values that classify it from soft to stiff, but the characteristic values are in the firm domain.

It should be mentioned that the consistency index is a physical parameter that classifies the soil as good (I_c > 0.75), average (0.5 < I_c < 0.75), or difficult (I_c < 0.5) foundation soil, which has an important impact in detailing the geotechnical investigation and design, according to NP 074-2022 [9].

From the previously presented statistical simulation, it appears that an engineering judgment is required related to the implications of the classification of geotechnical layers in a certain category.

SURFER is a software program developed by Golden software that specializes in the visualization and analysis of geospatial data. It is commonly used for creating contour maps, 3D surfaces plots, terrain models, and other visual representations of spatial data [11].

The user-friendly interface and diverse functionality make SURFER a popular choice for professionals working with geospatial information. Some of its features and functionalities are: interpolation and extrapolation, 3D visualization, data analysis and manipulation, data import and export, customization, and reporting.

Kriging represents a geostatistical interpolation technique whereby nearby data points are weighted based on their distance from the interpolation location and the level of autocorrelation or spatial arrangement observed for those distances. Optimal weights are computed at each sampling distance to derive the interpolated values. This method was used to realize the spatial (2D) variation of the geotechnical parameters with depth.

Physical measurements can sometimes be inaccurate due to uncertainties inherent in the process, which can compromise the validity of the resulting interpolation. The larger the study area and the greater the amount of data available, the more reliable the variogram tends to be. Conversely, the accuracy of local analysis decreases when the amount of available data is limited. The general equation of Kriging is as follows [12]: (2) Zs=μs+ε′s Z\left( s \right) = \mu \left( s \right) + {\varepsilon ^\prime}\left( s \right) where: Z(s) is the variable of interest, decomposed into a deterministic trend μ(s) and a random, autocorrelated ε′(s). The symbol simply indicates the location (containing x and y coordinates).

The graphs that are presented below, in which the spatial distribution of the different geotechnical parameters is presented, are not used to identify a certain value of a parameter in the foundation soil, but only to visualize the stratification of the foundation soil. The geotechnical parameters that describe each of the geotechnical layers will be established by statistical analysis, according to NP 122-2010 [8] and Eurocode 7 [13, 14].

To identify the stratification of the foundation soil, variation graphs of the main geotechnical parameters with depth are used; these graphs are based on the values measured in laboratory tests. The analyzed parameters are as follows: –

the parameters indicated by NP 122-2010 as mandatory to identify a geotechnical layer, respectively: unit weight, moisture content, consistency index, void ratio, plasticity index (Figs 2–4) and

Figure 2:

Figure 3:

Figure 4:

Figure 5:

Figure 6:

As for the bulk unit weight in natural state, it can be found that it varies in a very wide range, which leads to the idea that the soil has, both horizontally and vertically, large variations in moisture content and porosity. There is some uniformity in terms of the degree of saturation that defines most of the foundation soil as being in a saturated state, but locally, there are also soils classified as being wet, not saturated.

As for the plasticity of the soils, it also varies in a very wide range. The state of consistency is firm to stiff. Even these variations do not provide a vision of the layering of the foundation soil. Because the laboratory tests were programmed uniformly throughout the depth of the boreholes and in sufficient number, which respects the minimum number of samples imposed by NP 074-2022 [9], in these graphs it can be seen that in the depth range of 20–30 m, there are very few determinations of these parameters specific to cohesive soils. This observation indicates that noncohesive soils are intercepted in this depth range in all boreholes.

The values of the oedometric deformation modulus between 200 and 300 kPa classify the soil, according to a classification that was only found in STAS 1243-88 and which has been cancelled, as high, medium, and low compressibility [15].

In a horizontally homogeneous foundation soil, vertical variations of the various parameters presented in Figs 2–6 could be observed and the division into geotechnical layers is visible.

In this particular case, based on the graphs in Figs 2–6, the layers constituting the foundation soil cannot be identified. For this reason, spatial distribution of geotechnical parameters in 2D graphs were generated for three profiles, but only the results from Profile 1 are presented. The variation graphs were generated using the Kriging method in SURFER software. This representation was chosen to facilitate the work of the geotechnical engineer in stratifying the foundation soil.

In Figs 2–6, the 2D spatial distribution graphs of the main geotechnical parameters are presented.

From Fig. 7 to Fig. 10, it can be observed that the foundation soil consists of a succession of cohesive and noncohesive layers as follows: a cohesive layer up to approximately 15.00 m, a noncohesive layer up to approximately 35.00 m, and a cohesive layer followed by another noncohesive layer to the bottom of the boreholes. This stratification is confirmed particularly in Fig. 9c, where the sand layer is clearly defined between 15 and 30 m depth. At the same depth, the noncohesive layer is characterized by the highest values of the internal friction angle, as confirmed in Fig. 10. Based on moisture content variation, it is confirmed that the groundwater table is encountered in the noncohesive layer.

Figure 7:

Figure 8:

Figure 9:

Figure 10:

From the compressibility point of view, zones with high compressibility have been identified at the surface (up to 10 m depth) near boreholes F12 and F8, while at the same depth, in the area with boreholes F5, F10, and F4, soils with medium to low compressibility are encountered (Fig. 10a). This indicates that, in the hypothesis of direct foundation, the constructions in the area with boreholes F12 and F8 can develop differential settlements. The areas defined as having high compressibility correspond to the areas with the lowest unit weight in natural state, as shown in Fig. 7a.

The variation of the physical and mechanical parameters creates a clear picture regarding the vertical and horizontal distribution. On the one hand, areas where the parameters fall within certain domains can be identified at a general level and on the other hand, at local level, areas of geological accidents or change in stratigraphy, where the parameters are significantly different, are clearly visible.

Based on the analysis of spatial variation graphs in SURFER, the measured values from laboratory tests, and the characteristic values required for design, the following stratification has been obtained (Fig. 11): –

Heterogeneous anthropogenic fill from the ground level to a depth of 0.40–3.90 m – identified as a difficult foundation soil; this layer should be removed when the construction begins;

Figure 11:

The groundwater table was intercepted in Layer 2 – noncohesive soil in the form of a pressurized aquifer; at depths of 14.30–19.50 m, it was observed to have an ascending character, stabilizing at 12.10–12.70 m.