Statistical identification of homogeneous soil units for Venice lagoon soils

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1 Statistical identification of homogeneous soil units for Venice lagoon soils M. Uzielli Georisk Engineering, Florence, Italy P. Simonini, S. Cola Department of Hydraulic, Maritime, Environmental and Geotechnical Engineering (IMAGE), University of Padova, Italy ABSTRACT: The paper addresses the identification of soil units which are physically homogeneous in terms of hydro-mechanical response to cone penetration. A moving-window statistical procedure is applied to a number of CPTU-related parameters provided for the Malamocco site in the Venice lagoon. Example criteria for the assessment of homogeneity of soil units are provided. Subjective and objective aspects of the procedure are discussed. 1 INTRODUCTION A large project has been underway since the beginning of the 1980 s to protect the historical city of Venice and its surrounding lagoon from increasingly recurrent flooding. The project involves the construction of movable gates located at the three lagoon inlets. Soil characterization plays a major role in the preliminary typological selection and design of gate foundations. Comprehensive testing programs, including laboratory and in-situ investigations, have been performed in recent years on selected sites in the Venice lagoon to achieve a proper definition of soil profile and properties of sediments. From a compositional perspective, the main characteristic of the Venice lagoon soils is a predominant silt fraction, varying in combination with clay and/or sand with very high degree of interbedding (Simonini et al., 2007). The soils are predominantly alluvial sediments having similar geological origins and a substantially common depositional environment. Despite their limited compositional variation, profiles from in-situ investigations display a considerable fluctuation in the mechanical response of soils with depth. Due to the considerable degree of interbedding of Venetian soils, it is difficult, in practice, to confidently establish whether data from laboratory tests performed on samples and data from in-situ measurements refer to the same stratigraphic unit. Associating results of in-situ and laboratory testing is hindered by a number of factors. The 2 main ones are briefly discussed in the following. First, CPT testing cannot be performed exactly at the same location as a boring. Some horizontal spatial variability invariably exists, however adjacent testing verticals may be. As a consequence, the stratigraphic correspondence between CPT and boring logs is never entirely reliable. Second, CPT results refer to a point value of depth, but are representative of volumes of soil at failure. Measurements are thus influenced by the layering effect, by which the stiffness of the underlying soils and the thickness of underlying layers affects resistance to penetration. This effect is not relevant in boring logs. In heavily interbedded stratigraphies such as Venice lagoon soils, such effect can significantly complicate the association between data from different testing sources. The identification of physically homogeneous stratigraphic units (hereinafter HSUs) is thus an important preliminary phase for site characterization and for the development of correlations between compositional and mechanical properties of soils. 2 REFERENCE DATA SET The Malamocco test site (MTS in Figure 2) is located at the Malamocco inlet. Two of the main aims of the investigations at MTS were: (a) assessment of the performance of characterization methods based on in-situ tests; (b) development of correlations of in-situ testing data with the results of laboratory tests on samples from adjacent locations. A series of investigations, including piezocone tests, were performed at spatially contiguous locations. A continuous borehole was also carried out to obtain a detailed compositional classification. In the present paper, data from the CPTU19 piezocone sounding is used.

2 Figure 2. View of the Venice lagoon with location of the Malamocco test site (Simonini et al. 2007) Ground level in the CPTU19 location is at m below mean sea level, and data measurements (shown in Figure 3) span between depths of 12.61m and 56.92m from mean sea level. Measurement interval is 20mm for a total of 2143 measurement depths. In Figure 3, the erratic profile refers to pore pressure measured between the cone and the friction sleeve [u 2 ]; the solid line is the total vertical overburden stress [σ v0 ]; the dashed line is the effective vertical overburden stress [σ v0 ]; and the dotted line is the hydrostatic pore pressure [u 0 ]. 3 IDENTIFICATION OF PHYSICALLY HOMOGENEOUS SOIL UNITS Statistical theory provides an efficient means of identifying HSUs from geotechnical testing data. Among the most widely diffused geotechnical testing methods, the CPT is possibly the most suitable for statistics-based HSU identification because of the low measurement interval, which results in data sets of high numerosity. 3.1 CPTU-based classification parameters Past research has shown that soil composition and mechanical behavior do not display a one-to-one correspondence (e.g. Zhang & Tumay, 2003). As CPTU testing provides direct information regarding the mechanical response of soil to penetration, physical homogeneity is assessed in terms of soil behavior (i.e. response to cone penetration) rather than composition. The HSUs identified from CPTU data should not be viewed as being necessarily homogeneous from a compositional point of view. Robertson (1990) proposed a three-dimensional classification system which incorporates the three Figure 1. Data plots of CPTU19 from the Malamocco site on the Robertson (1990) charts (1: sensitive, fine-grained; 2: organic soils, peats; 3: clays clay to silty clay; 4: silt mixtures clayey silt to silty clay; 5: sand mixtures silty sand to sandy silt; 6: sands clean sands to silty sands; 7: gravelly sand to sand; 8: very stiff sand to clayey sand; 9: very stiff fine-grained )

3 basic CPTU measurements: cone tip resistance [q c ], sleeve friction [f s ] and the measured pore pressure [u 2 ]. The reference parameters in Robertson s classification system are the pore pressure parameter ratio [BBq], the normalized cone resistance [Q t ] and the normalized friction ratio [F r ]. The pore pressure parameter ratio is given by (Senneset & Janbu, 1985): B ( u2 u0 )/( σ v0 ) = (1) q q t in which q t ( 1 ac ) u 2 = q + (2) c is the cone resistance corrected for unequal end area effects, with a c =0.83 being the cone area ratio pertaining to the specific cone used at the MTS site. Normalized cone resistance and normalized friction ratio are given by, respectively (Wroth, 1984): Q t = ( q t σ v0 ) / ( σ v0 u 0 ) (3) r s /( qt σ v0 F = f ) (4) The three-dimensional system is most frequently implemented by means of the BBq-Q t and F r -Q t charts. The data from the Malamocco site are plotted in such charts as shown in Figure 1, indicating a wide range of soil behavior. Details of the charts can be found in Robertson (1990) and are not provided here. An additional CPTU-related parameter for soil classification is the soil behavior classification index Ic (Jefferies & Davies, 1991), defined as: c [(.47 log Q ) + ( 1.22 log F ) ] I = + (5) 3 t r Such index maps the F r -Q t chart onto a onedimensional scale proposed by Robertson (1990). 3.2 Statistical identification of physical homogeneity Natural soils are inherently complex and heterogeneous materials at all measurement scales, ranging from microstructure to regional scale. Compositional and mechanical properties of soils vary even over limited spatial separation distances. It is therefore necessary to define analysisspecific criteria for an acceptable degree of homogeneity on the basis of the specific engineering problem and of available measurements. Besides verifying the statistical properties of identified HSUs, the validity of the outputs of HSU identification must be assessed on the basis of compatibility with - and utility for - the purpose and scale of the analysis. In the context of the present paper, it is of interest to define homogeneity at stratigraphic scale in view of geotechnical design (i.e. bearing capacity, settlement prediction). Scale should be accounted for in defining the minimum thickness by which a spatial extension can be classified as a HSU, as well as the minimum number of consecutive measurements defining a HSU. Here, a minimum of 10 measurements was set. Samples of 10 or more data have been considered adequate for providing statistics with a confidence level acceptable for geotechnical purposes (e.g. Lacasse & Nadim, 1996; Phoon et al., 2003). In a geotechnical perspective, given the measurement interval of 2cm of the CPTU dataset, the vertical spatial extension of 10 measurements is comparable to the size of a sample from a boring log, from which laboratory test results can be retrieved. A moving-window procedure proposed by Uzielli (2004) is employed to identify HSUs statistically. In the proposed procedure, each position of the moving window defines two semi-windows of equal height above and below a center point. User-defined window statistics are calculated from data lying in the interval z c -W d /2 z z c +W d /2, corresponding to the upper and lower borders of the moving window of height W d centered at depth z c. HSUs are identified on the basis of the comparison between calculated window statistics and user-defined threshold values for the same parameters for a minimum preset number of consecutive measurements. Two types of window statistics were considered for the Malamocco data: range (i.e. difference between maximum and minimum values in data sample) and coefficient of variation (COV, the ratio between the standard deviation and the expected value of a data sample). The top and bottom spatial extents corresponding to the height W d /2 are discarded from each HSU. MTS CPTU 19 cone area: Ac=10 cm 2 Figure 3. Measurements from CPTU 19 at Malamocco

4 The moving window statistical procedure was applied comparatively to different configurations, i.e. scenarios having specific reference statistics and threshold values. A total of 48 analysis configurations were considered. The distinctive features of each configuration, summarized in Table 1, are: (a) the two reference parameters [columns 2, 5]; (b) whether the window statistics related to each reference parameter correspond to its range or coefficient of variation [R or C in columns 3, 6]; and (c) the threshold values assigned for the window statistics [columns 4, 7]. Note that, even if it is not indicated in Table 1, base-10 logarithms of F r and Q t were preferred to the source parameters F r and Q t in the analysis, because in the classification systems and charts such parameters are usually addressed in logscale. Setting a maximum threshold value for window statistics implies setting a tolerance limit for data dispersion and, thus, requiring a certain degree of homogeneity in measured values. Threshold values for ranges were assigned on the basis of Robertson s soil classification charts. The limit values for the coefficient of variation were chosen on the basis of rules of thumb such as the one provided by Harr (1987), by which coefficients of variation below 0.10 are thought to be low, between 0.15 and 0.30 moderate, and greater than 0.30, high. Cone tip resistance, sleeve friction and pore pressure are profoundly different measurements, involving different volumes of soil during penetration. As shown in Table 1, different threshold values were assigned to such parameters, with higher values (indicating greater tolerance) for log(f r ). Sleeve friction is a more erratic parameter, even in homogeneous soils, than cone resistance and pore pressure. The range threshold for I c was established on the basis of Robertson s (1990) table of reference values, by which 0.35 is the minimum range among soil categories. The choice of the moving-window size involves considerations regarding the numerical treatment of data, the physical phenomena occurring during cone penetration and, if available, information regarding the stratigraphic complexity of the specific site under investigation. From the numerical point of view, the choice of the moving-window size (and, consequently, the number of data in a given window configuration) affects window statistics. With larger window size, statistics are less sensitive to outliers and are less biased being calculated from larger samples, but data from layers with different characteristics will be included thus decreasing the geotechnical significance of results: the latter condition may be more evident when the window center is near stratigraphic interfaces. Cone penetration results in soil failure and plastic deformation of a spatial volume of soil. The choice of the moving-window size should take into account Table 1. Scheme and results of analysis configurations Parameter 1 Parameter 2 cnf. (1) par. (2) mt. (3) thr. (4) par. (5) mt. (6) thr. (7) n HSU (8) n ACC (9) 01 BBq R 0.20 Q t C BBq R 0.20 Q t C BBq R 0.40 Q t C BBq R 0.40 Q t C BBq R 0.20 Q t R BBq R 0.20 Q t R BBq R 0.40 Q t R BBq R 0.40 Q t R BBq R 0.20 I c C BBq R 0.20 I c C BBq R 0.40 I c C BBq R 0.40 I c C BBq R 0.20 I c R BBq R 0.20 I c R BBq R 0.40 I c R BBq R 0.40 I c R F R C 0.10 Q t C F R C 0.10 Q t C F R C 0.25 Q t C F R C 0.25 Q t C F R R 0.25 Q t R F R R 0.25 Q t R F R R 0.50 Q t R F R R 0.50 Q t R F R C 0.10 Q t R F R C 0.10 Q t R F R C 0.25 Q t R F R C 0.25 Q t R F R R 0.30 Q t C F R R 0.30 Q t C F R R 0.60 Q t C F R R 0.60 Q t C I c C 0.10 Q t C I c C 0.10 Q t C I c C 0.25 Q t C I c C 0.25 Q t C I c R 0.15 Q t R I c R 0.15 Q t R I c R 0.35 Q t R I c R 0.35 Q t R I c C 0.10 Q t R I c C 0.10 Q t R I c C 0.25 Q t R I c C 0.25 Q t R I c R 0.15 Q t C I c R 0.15 Q t C I c R 0.35 Q t C I c R 0.35 Q t C the spatial extension of the failure zone. Such extension has been quantified in 3-20 cone diameters (i.e cm approximately for a 10cm 2 cone), increasing with soil stiffness (Lunne et al., 1997). Moving-window size should also reflect the sitespecific stratigraphic complexity based on previous knowledge if this is available. In the case of dense stratification with limited layer thicknesses, a large window is more likely to include data from distinct layers, thus reducing the significance of window statistics. On the basis of the above considerations and of literature review, a moving-window size of 0.25m was selected.

5 Figure 4. Homogeneous soil units in best-performing configuration for the Malamocco CPTU19 dataset 3.3 Identification of best-performing configuration As shown in Table 1, the results of HSU identification (presence of HSUs, number, thickness, etc.) depend significantly on the configuration settings. It is of interest to establish which of the configurations should be adopted as reference. As there is no univocal set of homogeneous soil units for any given CPTU profile, the criteria for assessment must be defined by the user. Here, the best-performance criterion was set as the number of HSUs with a COV(I c ) 0.10 and range(i c ) These statistics Table 2. Selected statistics for CPTU classification parameters for the 15 HSUs identified in configuration 16 # n d H μ range μ COV range [m] (BBq) (BBq) (I c ) (I c ) (I c ) refer to the entire HSUs and not to values of window statistics. The aim of the criterion is to provide the highest possible number of soil units with statistics indicating a good level of homogeneity. The criterion reflects a subjective, desired level of homogeneity by the user. Higher threshold values could result in the identification of a different configuration as best-performing, as well as different numbers of HSUs for each configuration. Columns 8 and 9 in Table 1 report, respectively, the total number of HSUs identified in each configuration [n HSU ] and the number of acceptable HSUs [n ACC ]. The configuration denoted by the index 16 (see Table 1) classifies as best-performing with n ACC =14. It should be noted that other configurations display higher values of n HSU. The 15 HSUs from configuration 16 are shown (shaded in gray) in Figure 4. Table 2 reports selected statistics of CPTU classification parameters. Such statistics attest for a good level of homogeneity in terms of mechanical behavior. Only HSU09 is rejected because range(i c )=0.46. Coefficients of variation are not reported for BBq because the mean of such parameter may be close to or equal to zero, thus resulting in a non-informative values of COV. Data from one of the 15 accepted HSUs in configuration 16 are plotted in Figure 5. Data plot in compact clusters in the Robertson charts and show considerable uniformity with depth. The set of iden-

6 Figure 5. Data plots for HSU 12 from configuration 16 tified HSUs include cohesive, intermediate and cohesionless soil behavior types. 4 CONCLUSIONS Statistical identification of physically homogeneous stratigraphic units from CPTU data was performed for the Malamocco site in the Venice lagoon. The sum of the HSUs vertical extension in the bestperforming configuration amounts to 12.05m, accounting for only 27% of the total depth sounded in the considered CPTU test. Such low magnitude, though associated to and reflecting quantitatively - a specific user-defined qualitatively high level of homogeneity, attests for the considerable stratigraphic complexity and variability at the MTS site. REFERENCES Harr, M.E Reliability-based design in civil engineering. New York: McGraw-Hill. Jefferies, M.G. & Davies, M.P Discussion of Soil Classification by the Cone Penetration Test by P.K. Robertson (1990). Canadian Geotechnical Journal 28(1), Lacasse, S. & Nadim, F Uncertainties in characterising soil properties. In C.D. Shackleford, P.P. Nelson and M.J.S. Roth (eds.), Uncertainty in the Geologic Environment: From Theory to Practice, Geotechnical Special Publication No. 58: New York: ASCE. Lunne, T., Robertson, P.K. & Powell, J.J.M Cone penetration testing in geotechnical practice. London: E & FN Spon. Phoon, K.-K., Quek, S.-T. & An, P Identification of statistically homogeneous soil layers using modified Bartlett statistics. Journal of Geotechnical and Geoenvironmental Engineering 129(7), Robertson, P.K Soil classification using the cone penetration test. Canadian Geotechnical Journal 27(1), Senneset, K. & Janbu, N Shear strength parameters obtained from static cone penetration tests. Strength testing of marine sediments; Laboratory and in-situ measurements. Symposium, San Diego, 1984, ASTM Special technical publication, STP 883, Simonini, P., Ricceri, G. & Cola, S Geotechnical characterization and properties of the Venice lagoon heterogeneous silts. In T.S. Tan, K.K. Phoon, D.W. Hight & S. Leroueil (eds.), Proceedings of the 2 nd International Workshop on Characterisation and Engineering Properties of Natural Soils. Singapore, November 29 December 1, The Netherlands: Taylor & Francis, Uzielli, M Variability of stress-normalized CPT parameters and application to seismic liquefaction initiation analysis. Ph.D. thesis. University of Florence, Italy. Wroth, C.P The Interpretation of In Situ Soil Test. 24 th Rankine Lecture, Géotechnique 34(4), Zhang, Z. & Tumay, M.T Non-traditional approaches in soil classification derived from the cone penetration test. Probabilistic Site Characterization at the National Geotechnical Experimentation Sites, ed. G.A. Fenton and E.H. Vanmarcke, ASCE Geotechnical Special Publication No. 121,