GROUND RESPONSE ANALYSIS FOR NITK CAMPUS

1. INTRODUCTION:

Seismicity of a region depends on soil characteristics lying above the bedrock. When the wave travels through the different layers of soil, they are amplified and de-amplified in the respect to its properties. The proper study of borehole gives true idea on the profile of soil and helps in ground response analysis. The results obtained helps in dynamic analysis for a structure.

A ground response analysis consists of studying the behavior of a soil or rock layer subjected to an acceleration time history. When dealing with earthquake ground motions, the acceleration time history is usually specified at the bedrock. Examples of response quantities that can be obtained are the acceleration, velocity, displacement, stress, and strain time histories at any layer. Some of the applications of these analyses include liquefaction assessment and seismic risk studies. Different methods of ground response analysis have been developed including one-dimensional (1-D), two-dimensional (2-D), and three dimensional (3-D) approaches. Various modeling techniques like the finite element method are implemented for linear and non-linear analysis. Extended information can be found in Kramer (1996).

Ground response analyses are used to predict ground surface motions for development of design response spectra, to evaluate dynamic stresses and strains for evaluation of liquefaction hazards, and to determine the earthquake induced forces that can lead to instability if earth and earth retaining structures.

Ground response analysis determines the response of the soil deposit due to the motion of the bed rock below it.

One should bear in mind that, Vibrations are generated by man-made and natural disasters .The factors affecting the shaking due to an earthquake at a site are:

·        soil structure interaction,

·        local soil conditions,

·        path of the wave and

·        Location of the source.

Soil acts like a dynamic oscillator and affects the ground motion of the structures constructed on top of it to a great extent. The soil structure interaction has two main parts which comprises of kinematic effect and inertial effect, in the former one the flexibility of the soil will influence the response of the soil structure system, and in the latter one the mass of the structure influences the response of the soil structure system.

2. OBJECTIVES of the research:

1. Investigate 22 boreholes data with SPT test in certain depth, placed in different locations around NITK campus.

2. Analyze ground response analysis for finding Peak Ground Acceleration using EduShake. The bedrock input motion taken from Elcentro (1940) Earthquake.

3. Analyze Model generated for a building in STAAD. The results, i.e. axial force found in each column to be used for foundation design.

4. Modal Analysis, Static Analysis and Dynamic Analysis to be done in LS-DYNA. The Acceleration curve to be used from results obtained from EduShake.

3. Organization of the research:

1. This research gives introduction to the phenomenon of Seismic ground response, the types of ground analysis, basic terminology used, relationship between SPT and shear wave velocity, and modulus reduction curve along with damping curve.

2. It presents detail map of NITK pointing out locations where borehole was placed and the individual soil profile.

3. It gives a detailed view of the EduShake analysis performed with several plots of ground motion, shear stress, shear strain, response spectrum and depth generated according to the input motion used and soil properties obtained from laboratory testing given as an input.

4. It also gives a detailed view of the STAAD analysis performed along with foundation design for column with maximum BM and SF.

5. It gives a detailed view of the LS-DYNA analysis performed with several plots of base shear, roof displacement, Maximum Bending moments and shear force. For dynamic analysis use of ground motion is taken from results obtained in EduShake.

6. It presents the Summary, conclusions, and possibility of extension of this study for further research.

4. Literature Review:

4.1 Terminology Used in Seismic Ground Response:

1. Shear Wave Velocity (Vs):

Shear wave velocity (Vs) is the most commonly measured parameter used in shallow soil geophysics for soil characterization. The importance in its utility is that the particle of motion travels perpendicular to the direction of wave propagation being able to measure the shear properties of the soil skeleton and not the fluids which cannot take shear.

2. Shear Modulus (G):

Shear Modulus (G) is a calculated parameter based on the Vs using the simple elastic relationship G max = V s. The mass density is often estimated or measured by a nearby subsurface sampling or using correlations. Advanced correlations to estimate the value of the dynamic shear modulus are available based on the standard penetration test.

The shear modulus is used to perform more advanced soil modeling, and dynamic response of the soil-structure interactions. Shear modulus at low strain levels as measured by geophysical techniques will provide the elastic parameter for machine foundation analysis or earthquake engineering.

The important utility of this parameter is that it can be used as a varying parameter with respect to strain making the soil response represents the real modulus degradation in soil behavior. This parameter is used in defining the stiffness matrices for finite element analysis of earth structures and foundation soils.

3. Maximum Shear Modulus (G max):

Maximum Shear Modulus (G max) is used to normalize the shear modulus (G) vs. shear strain relationships. These normalized relationships allow the engineer to use well-established degradation curves and scale them to the measured in-situ value of G max. For example, the classic relationships of the shear moduli for cohesion less and cohesive soils are provided in Seed, et al., (1984) and Sun, et al., (1988). In the absence of extensive dynamic soil testing at all ranges of shear strain these curves are used and G max is used as the scaling parameter.

4. Damping Ratio (D):

Damping Ratio (D) is used in several dynamic analysis procedures to provide realistic motion attenuation. This ratio is based on the material damping properties. The damping ratio vs. shear strain relationships for cohesion less and cohesive soils are provided in Seed, et al., (1984) and Sun, et al.,(1988).Since damping ratio is also shear strain dependent, it is required to have several values with strain.

Dynamic analysis results are also influenced by the damping ratio for single and multi degree modal systems. The effects of soil structure interaction also influence the damping of the system making it an area where recent research has focused.

5. Poisson’s Ratio (n):

Poisson’s Ratio (n) is a fundamental parameter that is difficult to measure and it is usually estimated in engineering calculations. The ratio of horizontal to vertical strain is required to relate moduli and strains in a solid body. A suggested range of values for Poisson's ratio for soils is from 0.2 to 0.5, less common values may be as low as 0.1 for loess deposits. This ratio can be calculated [n = E/ (2G-1)] based on laboratory tests at low strains if G and E are obtained from torsional and longitudinal vibration, respectively.

4.2. One dimensional Ground Response Analysis:

The basic idea behind calculated of the seismic ground response, is to find the ground surface (output) motion. Knowing this particular output motion gives edge on designing the anomaly constituting the building parameters and also helps in rendering earth surface features to quite calculative way.

There is different way of calculating ground response. The One-dimensional ground response is more easily conceived. For more accuracy in results two and three dimensional analysis is preferred.

There are two approaches for one-dimensional Ground response analysis:

a. Linear approach

b. Nonlinear approach

In this study, we deal with only linear approach with evaluation of transfer function in one dimensional ground response analysis.

Before explaining mechanism behind response analysis we need to deal with transfer function. There are various parameters such as displacement, velocity, acceleration shear stress and shear strain. To incorporate all of these in our analysis we use transfer function. Although the calculation involves manipulation of complex number, the approach is quite simple (Kramer, 2004).

The steps to be followed are:

a.Represent time history of bedrock (input) motion in Fourier series, using FFT (Fast Fourier Transfer).

b.Multiply this Fourier series with transfer function for individual soil profile one after another.

c. The ground surface (output) motion can then be expressed in the time domain using the inverse FFT.

To say in short transfer function determines how each frequency in the bedrock (input) motion is amplified, or de-amplified, by the soil deposit.

4.3 Standard Penetration Test:

The standard penetration test (SPT) is an in-situ dynamic penetration test designed to provide information on the Geo-technical engineering properties of soil.

Around 1902 Colonel Charles R. Gow, owner of the Gow Construction Co. in Boston, began making exploratory borings using 1-inch diameter drive samplers (Fig. 1). Up until that time, contractors used wash borings with cuttings, similar to the methods presently used in advancing water wells. Mohr developed a slightly larger diameter split- spoon drive sampler and recorded the number of blow counts per foot of penetration on an 18-inch deep sample round, using a 140-lb hammer dropping 30 inches, pushing a 2-inch outside diameter sampler, while recovering a 1-3/8 inch diameter sample. The value recorded for the first round of advance is usually discarded because of fall-in and contamination in the borehole. The second pair of numbers are then combined and reported as a single value for the last 12 inches (1 foot). This value is reported as the SPT blow count value, commonly termed “N”.

Terzaghi and Arthur Casagrande vigorously sponsored adoption of the split spoon sampling procedure through the auspices of ASCE’s Committee on Sampling and Testing of the Soil Mechanics and Foundations Division of ASCE, formed in 1938. The work of this committee was carried out at Harvard by Juul Hvorslev and was standardized in 1940.

Terzaghi’s concept of using “standard” blow counts to estimate soil properties was not realized until 1947, when he sat down with Harry Mohr and developed correlations between allowable bearing pressure and [SPT] blow counts in sands, while completing his draft of Soil Mechanics in Engineering Practice. Later that year Terzaghi christened the 2-inch Gow sampler the “Standard Penetration Test”, in a presentation titled “Recent trends in subsoil exploration”, which he delivered to the 7th Conference on Soil Mechanics and Foundation Engineering at the University of Texas. The first published SPT correlations appeared in Fig. 177 on p. 423 of Soil Mechanics in Engineering Practice (First Ed.) by Terzaghi and Peck, published in 1948.

4.4 Co-relations between corrected N values and Shear Wave Velocity (Vs)

Various studies have been carried out to find the relationships between Vs and Standard penetration test (SPT). Gmax and VS are small-strain properties measured at shear strains on the order of 10-3% or less. Penetration-based tests are typically large-strain measurements associated with failure of the soil surrounding the sampler. Even though Gmax and penetration measurements are affected by soil behavioral factors occurring at opposite ends of the strain spectrum, this common association may be used to develop correlations between the two parameters [Mayne and Rix 1993].

Table shows the history related to study of shear wave velocity

4.5 Early Studies:

The earliest studies between SPT N-value and Vs were performed by Japanese researchers in the 1960s and early 1970s. Their original studies were not available for review; yet, Sykora [1987] provided a brief review of several early studies including Kanai [1966], Shibata [1970], Ohba and Toriuma [1970], and Ohsaki and Iwasaki [1973]. The hammer energy ratio for these studies was not stated. Seed et al. (1985) reported that typical Japanese SPT practices result in approximately 67% of the theoretical SPT free-fall energy.

Kanai [1966] developed a relationship between VS and N-value based on approximately 70 micro tremor measurements which were mainly performed in areas which had a predominant amount of sandy soils. N- Values included in the Kanai data set ranged from approximately 1 to 50 blows per foot (bpf).

Shibata [1970] combined the results of previous studies in the relationship between relative density and N-value and theoretical studies between Vs, relative density, and effective stress of sands into one relationship between Vs and N-value

Ohsaki and Iwasaki [1973] performed statistical analyses for about 200 sets of data from seismic explorations (dominated by down-hole) from all over Japan. Ohsaki and Iwasaki developed relationships between N-value and G. Figure 1 presents a plot of Ohsaki and Iwasaki’s G versus N-value data, as presented in Sykora [1987]. Based on the Ohsaki and Iwasaki shear modulus correlation equation, along with the assumption of a typical unit weight for Japanese soils of 112.4 pcf, Sykora [1987] developed a relationship between SPT N-value and Vs.

Figure 1 Shear Modulus versus SPT N-Value [Ohsaki and Iwasaki 1973]

Imai and Tonouchi [1982] analyzed the largest dataset, containing 1654 data pairs from 386 borings at 250 sites throughout Japan. Imai and Tonouchi developed VS correlation equations based on N-value, soil type, and geologic age. N-values ranged from less than one bpf to nearly 400 bpf.

Seed et al. [1983] developed a relationship for Gmax for sands as a function of N-value based on a review of previous studies. Based on their Gmax equation and an assumed unit weight of 120 pcf, Seed et al. proposed equation for estimating Vs from SPT data. The equation proposed by Seed et al. has been utilized in this project.

Dickenson [1994] studied the relationships between VS and SPT N-values of sandy soils in the San Francisco Bay Area. Dickenson included data from Fumal [1978] as well as new data. The SPT energy ratio was not reported. N-values ranged from approximately 5 to 90 bpf. Dickenson’s dataset and regression equation are shown in Figure 4.5. For comparison, also shows the Sykora and Stoke [1983] equation and the Seed et al. [1983] equation. The three equations are very similar at low SPT N-values. Above approximately 20 bpf Dickenson’s equation plots below the other two, with Seed et al. being the highest.

Figure  Vs versus SPT N-value [Dickenson 1994]

Hasancebi and Ulusay [2007] investigated the relationship between VS and N-value at a site in Yenisehir, Turkey. Yenisehir is located within an alluvial basin. Seismic velocities were measured using seismic refraction. The SPT energy ratio was not reported; however, VS correlation equations were given based on both N and N60. N-values generally ranged from 5 to 45 bpf. Data points and regression equations for All Soils, and clays are presented. Hasancebi and Ulusay also included correlation equations from previous studies: from Sisman [1995]; Equation (4.10) from Iyisan [1996]; from Jafari et al. [1997]; from Kiku et al. [2001]; and from Jafari et al. [2002]. Details of these studies, such as SPT energy ratio and geology, were not reported.

4.6 Dynamic Soil Properties

In the equivalent linear 1-D analysis in EduShake, the dynamic soil properties are defined by the damping ratio and shear modulus degradation curves. Such curves were developed for different soil materials; e.g. curves for sand and clay were proposed by Seed and Idriss (1970) or Seed and Sun (1989), and for gravel by Seed et al. (1986). These curves are shown in Figure. Seed and Idriss (1970) give three curves for lower bound, upper bound and average values. The damping curves for sand with the same range of shear strain are shown. Note that lower bound sand refers to less stiff sand with less damping ratio compared with the upper bound sand at a same shear strain.

In the literature these curves are found for different levels of plastic index for clay and for different confining pressures for sand. It was not a standard practice to report them in the borehole logs done near the investigated sites. For this reason, general curves like those presented here are adopted for this study.

5. Borehole Data Along with Soil Profile

5.1 Layout of NITK campus

5.2 Geographical Terrain of NITK campus:

Borehole terrain for construction of New teaching Block (Adjacent to E&E and IT Building) at NITK Profile 1

Borehole terrain near Boys hostel building (GF + 7 Floors) Profile 2

Borehole terrain for proposed construction near mechanical Department Profile 3

Borehole terrain of New Sports complex at NITK football/cricket ground Profile 4

Construction of Teaching Block campus at western side of NITK campus Profile 5

Borehole terrain near Computer Science building Profile 6

 6. Introduction to Edushake:

EduShake is a public domain program developed to help engineering students understand the mechanics of seismic ground response analysis of horizontally layered soil deposits.

The program is organized into three “managers” - an Input Manager, a Solution Manager, and an Output Manager - and a Report.

Input Manager

The required input data consists of soil profile data and input motion data. The Input Manager provides a series of forms on which the required data can be entered, and on which the desired output can be specified.

Solution Manager

The Solution Manager performs the actual ground response analysis.

Output Manager

The Output Manager allows the user to generate a wide range of plots from plotting time histories, spectra, variations of parameters with depth, and computation of scalar parameters.

Report:

The Report allows the user to keep a record of each analysis. All input data is automatically written to the Report and updated when the Report is accessed.

A brief description of the terms used in our reports is as follows:

Soil Profile

A uniform bulk density of sand having value 18 kN/m2 is assumed for the entire sample space and for all depths. The profile shows the name, thickness, unit weight, and shear wave velocity for each material layer. The profile indicates the depths at which the input motions are applied (with solid red ovals for motions) and the depths at which output is calculated (with solid green ovals for motions).

Input Motion

Input Motion is the input seismic wave that is provided to study the behaviour of the soil in the region. We have used Elcentro earthquake of 1940.

Maximum Number of Iterations

EduShake approximates nonlinear soil behaviour by iterating toward strain compatible soil properties. EduShake will continue until it reaches this limit or until the tolerance criterion is satisfied. For most soil profiles, strain-compatible properties will be reached in a few iterations. Hence we have fixed the Number of Iterations at 5 for all our calculations.

Tolerance Level

As EduShake iterates toward strain-compatible modulus and damping values, the difference between the modulus and damping values from one iteration to the next becomes smaller and smaller. You can specify any error tolerance defined as the maximum percentage change in shear modulus or damping ratio between successive iterations. EduShake will iterate toward strain compatible soil properties until the tolerance criterion is satisfied for all layers or until the maximum number of iterations is reached. The results of many ground response analyses do not change much at tolerance levels below about 5% and EduShake will use this as a default value.

Strain Ratio

The strain ratio is the ratio of effective shear strain to maximum shear strain in each layer. The computed shear strain is an important output parameter because of the strain-dependence of the shear modulus and damping ratio. EduShake takes transient input motions and computes transient output motions. The process of iteration toward strain-compatible modulus and damping values requires comparison of the strains computed in each iteration of EduShake with the strains on which the modulus and damping values are based. Because equivalent linear modulus and damping characteristics are based on laboratory tests with uniform harmonic loading, the transient shear strain computed by EduShake must be converted to an effective shear strain for this comparison. Historically, the strain ratio has often been taken as 0.65.

Response Spectrum

A response spectrum presents the maximum absolute response (acceleration, velocity, or displacement) of single-degree-of-freedom oscillators of different natural periods. As such, it gives a good indication of the potential effects of the ground motion on different structures.

Fourier Spectrum

A transient input motion can be represented, using a Fourier series, as the sum of a series of sine waves with different amplitudes, frequencies, and phase angles. A Fourier amplitude spectrum is a plot of amplitude vs. frequency for each of these sine waves. The Fourier amplitude spectrum illustrates the frequency content of the motion.

Transfer Function

The transfer function is defined as the ratio of the soil surface amplitude to the rock outcrop amplitude.

6.1 Input Motion for Analysis:

Time acceleration curve for ELCENTRO- earthquake with 0.1g as max PGA:

Time acceleration of Elcentro Earthquake used as input motion in bedrock level

RESPONSE SPECTRUM ELCENTRO:

Response spectrum of Elcentro Earthquake

6.2 Details Related to all the Profiles:

There were total 22 boreholes as mentioned earlier. The total location of borehole as shown in terrain is 6. Respective locations have their individual characteristics in terms of ground response analysis.

The following graphs shows individual borehole location with their Peak ground acceleration (PGA). The one with Maximum PGA is selected as our borehole location for further study.

Graph showing PGA at different Borehole no. near boys’ hostel building

Graph showing PGA at different Borehole no. near new teaching block (Adjacent to E &E and IT Building)

Graph showing PGA at different Borehole no. Near teaching block at western side of NITK

Graph showing PGA at different Borehole no. near new sports complex

Graph showing PGA at different Borehole no. near Mechanical Engineering

Graph showing PGA at different Borehole no. near Computer Science building

Comparison between input motion and output motion at layer 1 of Borehole No. 4 near Computer science Building with Maximum PGA 0.325g

Soil profile for BORE HOLE NO. 4 Computer Science building at NITK, Surathkal

6.3 Output

Acceleration Vs time history for ground:

output time acceleration of Layer 1 seen in Borehole No. 4 with max PGA 0.325g

Response spectrum for ground:

Response spectrum in Borehole No. 4

 Depth vs peak acceleration variation:

Depth vs. peak acceleration variation

Amplitude vs Frequency

7. Introduction to STAAD PRO

It is a multipurpose finite element program which is used for several classes of engineering analysis.

The steps followed in STAAD Analysis are:

· Define geometry

· Specify elements

· Define material properties

· Create nodes and number each of them

· Apply boundary conditions

· Attribute load cases and assign particular loads to individual entities

· Check for further specification

· Run analysis

· Select what all results one wants

· Extract results such as displacements, stresses, deformation, mode shapes, stress distribution, etc.

· Use graphical interpretation to have more clear view of the results.

7.1 Types of Structural Analysis:

1. Static Analysis- To determine displacements, stresses, etc. under static loading conditions.

2. Modal Analysis-To calculate the natural frequencies and mode shapes of a structure.

3. Harmonic Analysis-Used to determine the response of a structure to harmonically time varying loads.

4. Transient Dynamic Analysis.

5. Spectrum Analysis.

6. Buckling Analysis.

7.2 Definition of Model:

A model of the structure has been developed in STAAD Pro Vi8 and analysed in detail. The following properties have been used for the structure.

Material Properties

The above properties have been used for the development of all structure elements i.e. beams, columns and slabs.

7.3 Analysis of Structure:

The structure has been analysed for fixed base condition. Both dead load and live load has been applied on the structure.

Loading conditions:

The structure has been analysed with a load case which has both dead load and live load components with factor of safety.

Live load= 2 kN/m3.

Factor of Safety=1.5

The analysis was run successfully and the output file studied.

STAAD Pro model of the Structure showing the supports

The analysis was run successfully and the output file studied.

7.4 Summary of Results:

The summary of the node displacements is as given below:

Bending moment diagram of the structural members under self-weight in fixed base condition:

Diagram showing BMD of the structural members

The analysis also gives us the maximum load transferred by the columns. The columns carrying the maximum load and the magnitude of the axial load are shown in the following figures:

Showing maximum axial force in columns

columns with maximum axial force

The above table shows that columns 164, 165, 184 and 185 transferred maximum axial load so we will now follow foundation design assuming same Axial force.

7.4 Foundation Design

The maximum axial force of columns obtained by STAAD analysis is used to design the foundation.

Maximum axial force experienced by a column= 538.69 kN~560 kN

Area of footing =(560 kN/200kN/m^2)

                          = 2.8 m^2 (1.67m X 1.67m)

Adopt a footing with dimension 1.7m X 1.7m.

Check for One way shear:

Depth (d) = P(L-a)/(2P+700*L)

                = 560(1.7-0.3g)/(2*560 + 700*1.72)

                = 233~ 250mm.

D = 250 + 10 + 75(clear cover)

    = 340mm.

Check for bending:

M = P(L-a)2/(8L)

     =560(1.7-0.3g)2/(8*1.7)

     =70.66 kN.m

D  =  ((70.66*106/(2.76*1700))1/2

     = 109mm<250mm. Hence the design is safe.

8. Introduction to LS-Dyna

LS-DYNA is a software package developed by the Livermore Software Technology Corporation (LSTC). It provides precise calculation of many complex, real life problems, using highly nonlinear transient dynamic finite element analysis (FEA) which indeed uses explicit time integration. Precisely in terms of earthquake analysis, LS-DYNA is a general purpose finite element code for analyzing the large deformation static and dynamic response of structure.

It is widely used by automobile, aerospace, construction, military, manufacturing and bio engineering industries. The outstanding example of LS-DYNA coverage is a simulation of NASA JPL Mass pathfinder landing which has use of airbags to aid in its landing.

The model used for analysis in LS-DYNA is a simple structure featuring use of slabs, beams, columns, footing and incorporating soil profile. The use of soil profile is one with maximum PGA (Peak ground acceleration). The structure length is 26m by 12m with plinth beam at 1.5m from the footing and total height of building 10.5m. The inter-storey height is 3m.

Advantages of using LS-DYNA:

1. Incorporates Nonlinear calculations:

a.Changing boundary conditions (such as contact between parts that changes over time)

b.Large deformations (for example the crumpling of sheet metal parts)

c. Nonlinear materials that do not exhibit ideally elastic behavior (for example thermoplastic polymers)

2. Transient dynamic means it can analyze high speed, short duration events where inertial forces are important. Typical uses include:

a.Automotive crash (deformation of chassis, airbag inflation, seatbelt tensioning,)

b. Explosions (underwater mines, shaped charges,)

c. Earthquake response

8.1 Modeling and Analysis of the Frame Using LS-Dyna

The structure to be analyzed is modeled as a 3-dimensional structure in LS-DYNA . The initial modeling and analysis for LS-DYNA was done in STAAD. The fixed base was taken and foundation design was done. The dimensions incorporated in design were used as benchmark for LS-DYNA.

8.2 Procedure using LS-DYNA for Analysis:

1. Firstly, modeling is done in the element and mesh selecting Shape Mesher. The co-ordinates for entity 4N_shell are entered in the table which appears.

2. The use of element tool for transformation is done after the slab is created.

3. Then the beams are created using element and mesh. The separation of columns and beams is made after the orientation for all the beams is done.

4. The meshing of shell and beams is done by meshing beam into two divisions and shell with 4 divisions.

5. Then footing is created as solid marking nodes simultaneously.

6. The next tab accessed is Model and part. Here, there are commands to assign properties, Specifications, Supports, Load Definitions & Material, boundary, control, damping, database, hourglass, curves, Sections, etc. after selecting Keyword Manager.

a. Assigning properties:

In Keyword Manager, option ‘Mat” is selected which pops up a window. In this window, the dimensions for the columns/beams are defined and the material is selected. After adding various dimensions, they are assigned to the respective beams/columns. There are various methods by which the parameters in LS-DYNA are assigned.

i. Selecting beams and using ‘Assign to Selected beams’

ii. ‘Assign to view’ which will assign that particular parameter to every single item.

iii. ‘Use Cursor to Assign’, where the properties can be assigned by clicking on the beam/nodes/shell.

b. Load:

Body_parts: Body force loads due to a prescribed base acceleration or angular velocity using global axes directions are defined. This data applies to all nodes in the complete problem unless a part subset is specified via the LOAD_BODY_PARTS keyword

c. Section:

Here, the identities to beam, shell and solids are assigned with elements formulation options.

I. Beam: Belytschko-Schwer resultant beam

II. Shell: Belytschko-Tsay

III. Solid: Fully integrated S/R solid intended for elements with poor aspect ratio, accurate formulation

d. Hourglass:

Here hourglass and bulk viscosity properties are referenced via HGID in the *PART command. Standard LS-DYNA viscous form is used as hourglass control type

e. Define:

Curve: Here we define different curves for the structural damping, soil damping, etc.

f. Database:

Binary_D3 Plot: Time interval between output is 0.5sec.

g. Boundary:

After creating model for soil and structure, a boundary constraining the analysis is given. In the model created here boundary exactly 1.5 times the breadth and length to the structure was calculated and the soil profile was created in the either side. Then the use of two boundary parts was done:

i.Boundary_Non_Reflecting:

Non-reflecting boundaries defined with this keyword are only used with three dimensional solid elements. Boundaries are defined as a collection of segments, and segments are equivalent to element faces on the boundary. Non-reflecting boundaries are used on the exterior boundaries of an analysis model of an infinite domain, such as a half-space to prevent artificial stress wave reflections generated at the model boundaries form reentering the model and contaminating the results.

ii.Boundary_SPC_SET:

This is used for constraining the bottom and sides of soil profile. 1 is typed for constraining it along X- direction.

h. Control:

i. Dynamic relaxation:

Initializing stresses and deformation in a model to simulate a preload is done. Examples of preload include load due to gravity. When IDRFLG (Dynamic relaxation flag for stress initialization) is 1, time history output is produced during dynamic relaxation.

ii.Energy:

Provide controls for energy dissipation options.

iii.Termination:

Stops the job. The 5 is entered for termination job in ENDTIM option.

j. Damping:

· Part_mass_set: Parts may be either rigid or deformable. In rigid bodies the damping forces and moments act at the center of mass.

7. Next Step is for Analysis. Model analysis is conducted to find frequency, i.e. Natural frequency and damping factor. Then the calculated Natural frequency is used to run Static Analysis.

8. After Static analysis is done, few switches are made in keyword Manager and the model is made ready for dynamic analysis.

9. The Maximum Peak ground acceleration obtained in Borehole No. 4 located in Computer Science department was used. The acceleration vs. time graph is taken from EduShake analysis and used as input in LS-DYNA.

10. Post Processing: This is the tab which is adjacent to elements tool. After analysis, it will also give an option to switch to post processing mode. In this mode we can see the history plots and ASCII plots. Roof displacements, bending moments, shear forces on any point of the beam or column can be observed simply by selecting those corresponding outputs. We can also view the bending moment diagrams, shear force diagrams and see where max BM or SF occurs. We can also generate reports on respective selected beams. These reports can be sorted in the way the designer wants.

Snapshot of the building model along with soil profile in LS-DYNA

Modelling in LS-DYNA

Keyword Manager

9 RESULTS:

After dynamic analysis was run in LS-DYNA with peak ground acceleration data, the following results were found out:

Base shear plot:

The Base shear generated in respect to time was plotted. All the nodes in which base shear is to be calculated is selected. The force in X-direction in Newton was plotted against time in seconds.

Maximum base shear attained in X-force = 76993N

Minimum base shear attained in X-force = -93689N

Base shear plot in X-direction

Roof displacement:

The displacement of roof with respect to time is plotted. A node A21016 is selected and its displacement with time is plotted.

Roof Resultant displacement with respect to time

Inter-storied drift:

Graphs was plotted for displacement of each floor level with respect to time and maximum and minimum displacement for each floor level was found out.

The table showing the details of inter-storied drift:

Showing inter-storied drift for different floor levels

Bending Moment and Shear force:

The maximum bending moment and shear force for all beam and columns was found out. Then the beam and column with maximum shear force and bending moment was selected to plot the graph with respect to time.

The element A382 which is beam was found to be with maximum shear with 15600N shear resultant.

Maximum Shear resultant in beam A382

The element A19253 which is beam is found to have maximum bending moment with 17836 Nm bending moment.

Maximum bending Moment for beamA19253

The element A548 which is column was found to be with maximum shear with 19508N shear resultant.

Maximum Shear Resultant for columnA548

The element A548 which is column is found to have maximum bending moment with 1 5287 Nm bending moment.

Maximum Bending Moment in column A548

10. Final Conclusion and Remark on the research:

In this project, a study was carried out to determine the peak ground acceleration for the 

• The 22 borehole data around NITK campus was compiled.
• A map of NITK locating all the boreholes was created.
• The soil profile was dominated by presence of sandy silt. Water table was found in a few boreholes at a depth of around 2m.
• The unit weight for different soils was adopted as 18KN/ .
• Correction for overburden pressure (N’) and dilatency correction (N”) due to the presence of water table were carried out for the SPT- N values.
• The equation provided by Seed and Idris (1983) was used to calculate the shear wave velocity in the given terrain.

          Vs=64.1(N)^0.5.

• Shear modulus was obtained using the relationship G=Vs*ρ².
• The soil profile was analyzed using Edu-Shake, in which the soil profile was subjected to a earthquake motion and the responses of these profiles were noted.
• The Elcentro-earthquake (1940) was used to provide the input motion for the purpose of analysis.
• The peak bedrock acceleration (input) of Elcentro earthquake was scaled down to 0.1g from 0.343g.
• All the bore holes were subjected to 1D ground response analysis.
• The peak ground acceleration, Fourier spectrum, and Response spectrum of each borehole was obtained.
• The borehole with the maximum PGA was located (Computer Science building Borehole No. 4). The PGA obtained here was 0.325g.
• A three storied residential building was created using STAAD.
• This structure was subjected to static analysis and the bending moment of all the members of the structure was calculated and plotted
• The axial force in each column was calculated and the maximum value was utilized for the design of foundations of the structure.
• LS-DYNA for was used for the dynamic analysis of the same structure.
• The Peak Ground Acceleration curve obtained from Edu-Shake was used in the dynamic analysis in LS-DYNA
• The bending moment and shear force in all the members of the structure was calculated and the members with maximum shear force and bending moment were noted.
• The Base shear, Roof deflection and the Inter-storied drift were also calculated. 

The conclusions obtained from this study are as follows:

1. The soil profile near Computer Science Department, Borehole No. 4 with weathered rock and sand was found to have the highest peak ground acceleration of 0.325g for the given input earthquake motion.

2. Load at column bases of the proposed model was determined using STAAD Pro software. Isolated footings were designed according to the load parameters obtained at the column base.

3. The response of the structure built on the region having maximum PGA was noted with the help of LS-DYNA. 

4. The bending moment and shear force of all the members subjected to the dynamic load was also calculated using LS-DYNA and the members which have maximum bending moment and shear force were noted.

10.1 Further Scope of the study:

1.  In this study, shear wave velocity is calculated using the relationship given by Seed and Idris (1983). A site specific correlation between Vs and SPT values can be developed.

2. Responses in building with fixed base can be compared with building incorporating soil structure interaction effect.

3. The modulus of reduction and damping curves can be modeled by further lab experiments.

4. The field results can be used to find correlation between SPT (N) and shear wave velocity. The comparison with well known established results around the world can be done.

References:

1. .Dickenson, SE (1994). Dynamic Response of Soft and Deep Cohesive Soils during the Loma Prieta Earthquake of October 17, 1989, PhD thesis, Dept. of Civil and Enviro. Eng., University of California, Berkeley, CA. 
2. · Bernard R. Wair Jason T. DeJong , Department of Civil and Environmental Engineering University of California, Davis Thomas Shantz California Department of Transportation Sacramento, Guidelines for Estimation of Shear Wave Velocity Profiles
3.  Kanai, K (1966). Observation of microtremors, XI: Matsushiro earthquake swarm areas, Bull. Earthq. Res. Inst., Vol. XLIV, Part 3, University of Tokyo, Tokyo, Japan. 
4.  Mayne, PW, and GJ Rix (1993). Gmax-qc relationships for clays, Geotech. Testing J., 16(1):54–60.
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6.  Ohsaki, Y, and R Iwasaki (1973). On dynamic shear moduli and Poisson’s ratio of soil deposits, Soil and Foundations, 13(4):61–73. 
7.  Seed, H. B., I. M. Idriss, and I. Arango. 1983. Evaluation of Liquefaction Potential Using Field Performance Data. J. Geotech. Eng., 109(3):458–482. 
8.  Shibata, T (1970). The Relationship between the N-Value and S-Wave Velocity in the Soil Layer. Disaster Prevention Research Laboratory, Kyoto University, Kyoto, Japan. 
9.  Sykora, DW (1987). Examination of existing shear wave velocity and shear modulus correlations in soils, Department of the Army, Waterways Experiment Station, Corps of Engineers, Miscellaneous Paper GL-87-22. Sykora, DE, and KH Stokoe (1983).
10.  Steven L Kramer, Geotechnical Earthquake Engineering, Pearson Education Inc.