Journal of Engineering Geology, Vol.6, No.2, Autumn 2012 & Winter 2013

Uncertainty in Shear Wave Velocity Based on

Standard Penetration Test by Using Error Least Square Model

H. MolaAbasi: Faculty of Engineering, Babol University of

Technology,

*F. Kalantary: School of Civil Engineering, Khajeh Nasir Toosi University of Technology

M. Salahi: Faculty of Mathematical Sciences, University of

Guilan

Received: 26 Aprill 2011 Revised 13 Jan 2013

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Abstract

Shear wave velocity (Vs) is a basic engineering soil property implemented in evaluating the soil shear modulus. Due to a few limitations, sometimes it is preferable to determine Vs indirectly by in situ tests, such as standard penetration test (SPT). However, inaccuracies in measurement or estimation of the influencing parameters have always been a major concern, and thus various statistical approaches have been proposed to subdue the effect of such inaccuracies in predictions of future events. In this article, an innovative approach based on robust optimization has been utilized to enumerate the effect of such uncertainties. In order to assess the merits of the proposed approach a database containing 326 data points of case histories from Adapazari, Turkey were gathered from renowned references. The identification technique used in this article is based on the robust counterpart of the least square problem which is a second order cone problem and is efficiently solved by interior point method. A definition of uncertainty based on frobenius norm of the data is introduced and examined against correlation coefficient of various correlation parameters and optimum values are determined. Finally the results of new correlation are compared with those utilizing a commonly used statistical method and the advantages and possibilities of the proposed correlation over the conventional method are highlighted.

KeyWords: Shear wave velocity; Standard penetration test; Least squares; Uncertainties; Robust optimization; Second order cone.

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*Corresponding author [email protected]

Introduction

Shear wave velocity is a basic engineering soil property for earthquake site response analysis, which is directly related to shear modulus at small shear strain level. Therefore, Vs is one of the indirect methods to evaluate soil modulus. Because of difficulties in soil sampling, the high cost for obtaining the high-quality undisturbed samples which represent confining stress conditions, in situ investigation such as down hole is preferred to laboratory tests. It is preferable to determine Vs directly by in situ tests, such as seismic measurements. Using surface wave velocity measuring techniques, a shear wave velocity profile can be established without boring and penetration [1]. The nondestructive, non-intrusive features make Vs based approach a potentially attractive alternative for characterizing liquefaction resistance in sandy soils [2]. However, this is not always feasible, due to space constraints and, especially in urban areas, high noise levels associated with these tests. Therefore, it is necessary to determine Vs through indirect methods such as SPT and CPT which are commonly used for usual geotechnical site investigations.

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In geotechnical engineering, many design parameters of soil are associated with the standard penetration test (SPT). Standard penetration Test blow counts, NSPT is significant in site investigation, along with other geotechnical parameters such as Vs. There is no theoretical relationship between destructive (e.g. SPT and geotechnical soil parameters) and non-destructive methods (e.g. seismic methods); hence, their association, and evaluation of geotechnical properties, requires empirical correlations, statistical analysis and system identification techniques. The interdependency of factors involved in such problems prevents the use of regression analysis methods such as least square. Inaccuracies in measurement or estimation of the influencing parameters and least square cannot predict Vs correctly. Therefore a new approach “Error Least Square Model” proposed to quantification of the effect of uncertainties on evaluation of correlation parameters in this study. This model is the robust counterpart of the least square model, which is a second order cone program (SOCP) in which, possible uncertainties can be reasonably adjusted [3].

Background to previously proposed correlations

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Many research works can be found in the literature regarding application of NSPT for geotechnical characterization. Imai and Yoshimura [4] studied the relationship between seismic velocities and some index properties over 192 specimens and developed empirical relationships for all soils. Sykora and Stokoe [5] pointed out the geological age. Jafari et al., [6] present detailed historical review on the statistical correlation between NSPT versus Vs in fine grained soils. Some researchers have proposed correlations between NSPT and Vs for different soils, such as sand, silt and clay. Hasancebi and Ulusay [7] studied statistical correlations in sand and clay soil types except for gravels. Ulugergerli and Uyanık [8] investigated statistical correlations using 327 samples and defined the empirical relationship as upper and lower bounds instead of a single average curve for estimating seismic velocities and relative density. Dikmen [9] investigated uncorrected SPT data and presented a correlation for all type of soils. Others have developed correlations which included stress-corrected Vs, energycorrected NSPT (e.g. Pitilakis et al., [10], Kiku et al., [11]), energy- and stress-corrected NSPT, depth (e.g. Tamura and Yamazaki [12]) and fine content (e.g., Ohta and Goto [13]). The shear wave velocity can also provide estimation of effective stress (

) that Mayne et al., [14] suggested in clay soils type. Mayne [15] presents a relationship between the total unit weight (

in terms of Vs and depth (Z) for saturated soils. However, almost all of the studies mentioned above focused on the relationships between uncorrected NSPT and Vs for all soils as well as sand and clay-type soils. Some of these empirical relations have shown in Table.1 Table1. Some of the existing correlations between uncorrected NSPT and Vs.

Ref. Proposed Relation for all soils

Imai and Yoshimura (1975) Vs = 89.9 N0.341

Ohta and Goto (1978) Vs = 85.35 N0.348

Sykora and Stokoe (1983) Vs = 100.5 N0.29

Jafari et al (1997) Vs = 22 N0.85

Kiku et al (2001) Vs = 68.3 N0.292

Jafari et al (2002) Vs = 27 N0.73 (clay type)

Hasancebi and Ulusay (2007) Vs = 90 N0.309

Ulugergerli and Uyanık (2007) a-VSU = 23.291Ln(N)+ 405.61 b-VSL = 52.9 e−0.011N Dikmen (2009) Vs = 58N0.39

a Upper bound b Lower bound

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Overview of database and case histories

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The Kocaeli earthquake by Moment Magnitude of 7.4 had occurred in 1999 and the epicenter was located near the city of Izmit. The fault rupture was physically visible throughout most of the seismically impacted area from Karamürsel to Akayazi. The cause of the earthquake was a multiple rupture process in 140km long western part of 1200 km. In the vicinity of Adapazari peak ground accelerations were recorded at approximately 0.4 g. In the region, as many as 70% of the buildings were subjected to large ground settlements, liquefaction, or subsidence and sea water inundation [16]. As illustrated in Fig.1, the southern shores of Izmit Bay are covered by Holocene deposits except a relatively small area, which was classified geologically as Backpack formation of Companian-Maastrihtien age consisting of marl, mudstone, conglomerate and sandstone. From a sediment logical point of view, the southern shores of Izmit Bay are covered principally by fine-grained sandy deposits which get finer (siltier and more clayey) towards the north into the depths of Izmit Bay. A total of 135 CPT profiles (of which 19 were seismic CPTs) and 46 soil borings with multiple SPT (often at 0.8m spacing) were completed in the city of Adapazari. As shown in Fig.2 soil profiling in the Police station site located on the east shore of Izmit Bay, in the town of Golcuk, the soil liquefaction suspected is considerable [17].

(

http://peer.berkeley.edu/turkey/adapazari/

)

(

http://peer.berkeley.edu/turkey/adapazari/

)

Fig.2. Simplified geological map of Armutlu peninsula (after Goncuoglu [18])

Fig.2. Soil profiling in the Police station site located on the east shore of

Izmit Bay, in the town of Golcuk [17]

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Table3. A sample of the database [16]

Z (m) (N1) 60 FC(%) Vs(m/s)

3.3 6 83 170

17.8 31 80 294

2 6 56 110

2.7 12 53 110

18.2 18 5 262

1.4 4 99 100

9 6 98 200

16.2 13 74 172

6.8 23 14 151

2.6 6 92 253

7.9 40 11 150

14.8 5 98 172

13.2 30 20 179

2.5 13 65 105

2.8 4 99 121

6.5 8 99 95

9 48 5 250

2.6 4 99 85

7.7 39 11 150

17.8 16 12 243

4.1 25 71 306

3.4 4 78 150

The variables considered for the proposed correlations

The dataset, explained in [16] consists of 326 case records for

Adapazari, Turkey. The database, a random sample selection given in Table 3, covers a wide spectrum of soils and seismic parameters, including soil layer depth (Z), corrected SPT blow number (N1 60), FC or Fines Content (% ≤ 75μm) and shear wave velocity (Vs). The objective of selecting above parameter is to limit the disadvantages of

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قیمت: تومان