Development of Empirical Correlations Between Shear Wave Velocity and Standard Penetration Value: A Case Study of Rajshahi District, Bangladesh

In seismic response investigation, shear wave velocity, Vs shows a vigorous role as an input factor. Enormous methodologies have been developed and tested to directly determine this key factor. Direct measurement of Vs is timeconsuming as well as highly expensive. As a result, researchers from different regions have tried to reduce the difficulties associated with the measurement and developed empirical relationships between VS and other geotechnical characteristics of the soil, such as SPT calculation, depth, vertical effective pressure, etc. In this paper, the empirical correlation between shear wave velocity and standard penetration number (SPT-N) has been investigated for several soil categories: all soils, sand, silt and clay-type soils. Study area selected for this analysis are Bagha, Bagmara, Charghat, Durgapur, Godagari, Paba, Puthia, Tanore and Rajshahi City Corporation (RCC) area consisting of 36 borehole dataset. Combining all the data, an approach is made to correlate the Vs with the SPT-N. The square value of the coefficient (R) of correlation shows good agreement with the subsoil. Regression analysis is used to propose an empirical relation for this zone which would be helpful for foundation engineers to have the idea on earthquake response analysis of subsoil.


Introduction
Shear wave velocity (Vs) is the significant parameter for the dynamic characterization and analysis of subsurface. Field measurement of such parameter is expensive as well as time consuming. Vs is estimated as field study and laboratory investigation by using empirical correlations. Laboratory investigation is worked out to determine shear wave velocity with SPT-N value. SPT-N value is locally and internationally available and can be determined very easily in the field.
In the current study, a set of correlation equations between standard penetrations tests (SPT-N values) and shear wave velocity (Vs) for different groups of soils is established for Rajshahi district, Bangladesh. Rajshahi District located in north-western part of Bangladesh beside Padma River. It is a part of the Rajshahi Division and third largest city of Bangladesh. Rajshahi district is divided into 9 Upazila named: Bagha, Bagmara, Charghat, Durgapur, Godagari, Paba, Puthia, Tanore and Rajshahi City Penetration Value: A Case Study of Rajshahi District, Bangladesh Corporation (RCC). Study area selected for this analysis are shown in figure 1.
Empirical correlations have three different advantages i.e., convenience, efficiency and economy. Empirical correlations have been used worldwide but before using it should be checked against validation because these equations are site dependent and some researchers have tried to formulate the equations which may be applicable for all region [1,2]. This analytical research deals with the development of empirical correlations between Vs and SPT-N for different upazillas of Rajshahi and finally for Rajshahi District (RD) collecting four borehole profile from each Upazila, a total of 36 borehole profile.

Development of Empirical Correlations
For evaluation of shear wave velocities and associated geotechnical parameters, the following a power-equation model is practiced widely: Where, A is a constant controlling the amplitude, N is the uncorrected SPT value and B is another constant depending on curvature relationship. Also, it is to be noted here, other factors such as depth, overburden pressure, geological age, fine content and soil types which may also govern or modify the relationships has-not been included in this study. In the present world, Earthquake hazards is one of the crucial issue and Vs in this issue has intensive power to evaluate assessment of any area. Four borehole profiles from each areas in total 36 were utilized for the graphical presentation of existing relations (table 1) with the help of Microsoft Excel 2013. Regression analysis in terms of R squared value is carried out to establish and check the accuracy of the equation for every selected areas for all soils, sands, clays and silts as a power law form (Vs= AN B ). Then, taking all the SPT-N values from these areas (varies from 1 to 49) were plotted for Rajshahi District.

Results and Discussion
It is noticeable from the table that, researchers have given correlations on four distinct category: (a) All soils, (b) Sands, (c) Clay and (d) Silt. Using these correlations given in table 1, following graphs are plotted according to the collected bore log SPT data for Bagha Upazila. Along with graphs, equations and corresponding R 2 value for each category has also been incorporated here. Penetration Value: A Case Study of Rajshahi District, Bangladesh

Conclusions
The developed correlations relating shear wave velocity with SPT value is entirely based on SPT data set available. To quantify liquefaction assessment of the studied area shear wave velocity equations proposed in this study will play a significant role. From the present study, several conclusions can be drawn: 1) The proposed and developed equations are only applicable for the selected areas and Rajshahi District. 2) Number of borehole data set play a dominant role in the estimation of Shear wave velocity. More the number of borehole dataset would give more the accuracy of the regression curves. 3) Using as many equations also give more accuracy curve for the estimation of Vs. 4) The R 2 value shows good agreement with soil type's sand and clay. On the contrary, it also can be shown considering intermediate soil strata.