Excerpt

## Table of contents

Abstract

List of symbols

List of figures

List of tables and equations

CHAPTER I

1. Introduction

1.1. General

1.2. Classification of dynamic impact load

2. Description of experiment

3. Parameters and properties

3.1. Direct parameters and properties

3.2. Indirect parameters and properties

3.2.1. Compressive strength of concrete

3.2.2. Average modulus of elasticity of concrete

3.2.3. Average dynamic modulus of elasticity of concrete

3.2.4. Average tensile strength of concrete

3.2.5. Concrete shearmodulus

3.2.6. Elastic (fracture) energy of concrete

3.2.7.Slabgeometry

3.2.8. Bending capacity

3.2.9. Slab rotation and rotation rate

3.2.10. Strain rate

3.2.11. Dynamic compressive and tensile strength of concrete

3.2.12. Penetration depth

3.2.13. Punching cone mass

CHAPTER II

4. Process of data analysis

4.1. Data collection

4.2. Dataprocessing

4.2.1. Data correction

4.2.2. Data transformation

4.2.3. Data conversion

4.2.4. Missing datahandling

4.2.5. Noise data eradication

4.2.6. Data filtering

4.3. Data cleaning

4.4. Data analysis

4.4.1. Characteristic phases

4.4.2. Maximum displacement response

4.5. Datamodeling CHAPTER III

5. State of the art

5.1. Global structural behavior

5.2. Experimental studies

5.2. Analytical modeling

5.3. Numerical modeling

6. Literature review

6.1. 3DoF model

6.2. 2DoF model

6.3. Two-phase model, combination of2DoF and SDoF

7. Effective length of slab span during impact

7.1 Effective span concept by Cotsovos et al.

7.2. Effective span concept by an analysis of slab curvature

7.3. Proposal of new slab dimensions for Leff

8. Analytical model, SDoF proposal

8.1. Stiffness

8.1.1. Determination of stiffness by classical methods

8.1.2. Determination of stiffness by the slab-frequency method

8.2. Effectivemass

8.3. Damping

8.4. Excitation force

8.4.1. Idealization of the excitation load

8.4.2. Normalization and equivalent excitation force (Impactor Slab Interaction; Fourier and Laplace Transformations)

8.5. Analytical procedures for the slab global response

8.5.1. Equation of motion

8.5.2. Correlation between mass drop-height and slab response

8.5.3. Model application steps (algorithms)

9. Numerical integration by Newmark’s method

9.1. Algorithm ofNewmark’s method (average acceleration method)

9.2. Newmark’s method as a verification tool

10. Remarks and recommendations

10.1. Evaluation of the overall behavior of the tested slabs

10.2. Sources of uncertainty

10.3. Enhancement of experiment quality

10.4. Enhancement of analytical model

11. Conclusions

12. Appendix

13. Reference

## Abstract

In the frame of a research program at the TU Dresden, reinforced concrete slabs are tested in a drop-tower. The goal is to obtain a model with which the prediction of the structural behavior of the slabs under high loading rates, depending on different parameters.

The global behavior response of RC slabs (symmetric reinforcement without shear stirrups) due to a hard impact projectile and a strain rate 10-1 [1/s] has been addressed in this project- work.

A complex drop-mass apparatus is used to conduct experiments and investigations on the impact dynamic behavior of RC slabs The focus was on the response stage of the linear elastic field and how to correlate this response stage to the drop-height depending on raw experimental data.

A process of data analysis for hundreds, thousands, or millions of data measurements has been carried out and an analytical model based on a system of single degree of freedom and different simplifications is shown with different verification methods. The model enables predicting bending response due to impact.

The test of 11 slabs with drop-heights (1 to 4 meters) provides the required data to calibrate the analytical model as well as future numerical models.

## List of symbols

Abbildung in dieser Leseprobe nicht enthalten

## List of figures

Fig. 1 : Strain-rate ranges for various load sources

Fig. 2 : Lab instruments and drop-tower

Fig. 3 : Details of the complex mass drop-tower

Fig. 4 : Slab cross-section [mm]

Fig. 5 : Slab’s global response, detailing the response phase being under focus

Fig. 6: Outputs of the lab instrumentations

Fig. 7: Variation of Gf with fc

Fig. 8 : Rotation angle [rad, mm]

Fig. 9: Displacements transformation (mapping)

Fig. 10: Characteristic phases of the slab test

Fig. 11: Slab plan

Fig. 12: Bending displacement response of slab 9

Fig. 13: Global behavior of slabs during the first impact

Fig. 14: System of multiple degrees of freedom

Fig. 15: System of multiple degrees of freedom, Hard impact

Fig. 16: Two-phase model

Fig. 17: Spring properties of K2 for the shear behavior

Fig. 18: Spring properties of K3 for the global bending stiffness

Fig. 19: Slab cross-section [mm]

Fig. 20: Spring properties of K2 for the shear behavior

Fig. 21: Definition of Leff (after Cotsovos)

Fig. 22: Curvature distribution

Fig. 23: Effective length of slab span, slab plan [mm]

Fig. 24: Slab displacements during tMi,i, [mm]

Fig. 25: Proposal of new slab dimensions, slab plan [mm]

Fig. 26: System idealization process

Fig. 27: FE slab model to determine flexural displacements

Fig. 28: Ideal impact excitation

Fig. 29: Real excitation load after idealization process, S8

Fig. 30: Different numbers and shapes of implemented impulses

Fig. 31: Noise data eradication procedure; 9, 4, 2 weighted average methods

Fig. 32: Omitting negative values of accelerations

Fig. 33: Over precise model

Fig. 34: impactor slab interaction by counteract of slab rebound phenomenon

Fig. 35: Fouriertransformation

Fig. 36: Global response of Slab 3/7 by normalized excitation force through Laplace Transformation

Fig. 37: Effects of flexural cracking and punching shear

Fig. 38: Correlating the drop-height to the generated momentum

Fig. 39: Momentum (impulse area) as a function of drop-heights, two proposals

Fig. 40: Slab global response results through the proposed analytical model

Fig. 41: Newmark as a verifier of force records

Fig. 42: Critical drop-height

Fig. 43: interaction between bending behavior and shear failure criteria

Fig. 44: Schematic superimposition of a series of four impulses

Fig. 45: Application of the practical algorithm (analytical model) in Excel spreadsheet

## List of tables and equations

Table 1: Slab ID with respect to its drop-height

Table 2: Characteristic compressive strength of concrete

Table 3: Concrete compressive strength as a function of its age at the test time

Table 4: Rotation rate and strain rate of each slab

Table 5: slab penetration depths of the first mass impact

Table 6: Calibration factors of data1-2 and data2-2

Table 7: Characteristic phases of slab test

Table 8: slab summary of master point displacements

Table 9: Stiffness factor kw for loading in the center [Stiglat et al., 1993]

Table 10: Disagreement of the channels with respect to the excitation load

Table 11: Momentum (impulse area) as a function of drop-heights, two proposals

Table 12 : data 1-2 of slab 3 after processing

Table 13: data 2-2 for slab 3

Table 14: Global bending response over line_0 of slab 9

Abbildung in dieser Leseprobe nicht enthalten

## 1 Introduction

### 1.1 General

The global (bending) response of[1] the concrete slab and the influence of the dynamic effects are investigated in the present project. Its aim on the long-term is to develop an efficient and simple but still adequate design method for new protective slabs which at the same time allows for a reasonable evaluation of existing ones.

Different fields of research are involved in the design of protective slabs against the impact due to object collisions. In this full research program, the following aspects have to be addressed:

- Local behavior close to the impact location (out of the scope of current project-work)

- Global dynamic structural behavior (only the linear field is covered at present)

From a scientific point of view, the dynamic behavior of structures and the corresponding resistance have always been a subject of interest due to the potential military application, e.g. the development of protective shelters and the development of the corresponding weapons to overcome that resistance. For reasons of confidentiality, many research results have not been published or can only be found circuitously [Newmark, 1962], [TM 5-1300, 1990], [Drake et al., 1989]. Today, the focus of research has shifted to protective structures that have to withstand impacts either due to civil activities (e.g. explosions, airplane crashes or ship collisions) or those of natural origin and research results therefore are exchanged more freely.

The design procedure for protective slabs is basically the same as for most other impact problems. The main variables are defined by the different range of impact velocities.

Consequently, the influences of dynamic material properties and inertial forces play a prominent role.

In this work, relevant results derived from corresponding research fields are briefly reported and related to the problem of impacts due to a rigid impacting mass.

In general, impact problems are mainly classified by the impact velocity (low or high velocity) and by the way the kinetic energy is dissipated (soft or hard impact). Depending on the impact velocity and stress rates, a rough classification is proposed for example in [Zukas et al., 1982].

### 1.2 Classification of dynamic impact load

The range up to an impact velocity of 500 m/s is governed by the low velocity regime, which covers most applications of structural dynamics including impact experiments of our case. Typical loading times for low velocity impacts are in the range of milliseconds and the local behavior of such structures interacts with the general deformation stage [Schlütter, 1987]. Commonly, the low-velocity regime is divided into two sub-regimes: up to 50 m/s materials remain basically in the elastic stage and yielding may only occur locally. For impact velocities above 50m/s, materials are expected to behave plastically.

The second important classification concerns soft and hard impacts. By the common definition, for soft impacts the impacting body dissipates most of the kinetic energy while for hard impacts most of the energy is dissipated in the impacted structure.

According to definition, the current experiment should be considered a hard impact, because the protective structure has to dissipate the impact energy by means of deformations. For soft impacts the influence of the structural deformation on the impact procedure is assumed to be small. In reality, of course, all impacts behave somewhere between a soft and a hard impact. The question as to what extent the impact force-time history is influenced by the structural deformations requires further consideration.

Fig. 1 shows typical orders of magnitude of strain rates for different loadings [Schmidt- Hurtienne, 2001]. The results of the current experiment are about a strain rate of 10-1 [s-1]. According to [Toutlemonde et al., 1995], soft impacts lead to strain rates of about 10-4 [s-1] and hard impacts to 10-1 [s-1], respectively.

Abbildung in dieser Leseprobe nicht enthalten

Fig. 1 : Strain-rate ranges for various load sources [Bulletin 65, CEB/fib 2010].

Therefore in short, the classification of the current experiment is:

Heavy mass (508 kg), low velocity (4.43 - 8.75 m/s) and hard impact [Abbildung in dieser Leseprobe nicht enthalten].

## 2 Description of the experiment

The conducted experiment includes testing of 11 slabs (the slab ID: from “1” to “10” belongs to the test series_1 and “11” belongs to the test series_2) with different drop-heights G [1, 4][m] as follows:

Table 1: Slab ID with respect to its drop-height

Abbildung in dieser Leseprobe nicht enthalten

The dimensions of tested slabs are 1.5x1.5x0.3 m with 4 simple supports in corners. The slabs are reinforced with 10 steel rebars ф = 8 mm/m" in two directions and in two levels (symmetric - upper and lower layers) without stirrups. The average cylindrical concrete strength is roughly 50 MPa with density of 2.5 T/m3.

The simply supported slab is installed on a concrete block foundation with a vibration absorber system to isolate the damage effects of the test platform from the surrounding facilities and buildings due to resultant shock waves.

The drop-mass apparatus consists of two masses (508 and 605 Kilograms) collide the slab on two consecutive phases with a flat nose impactor (steel cylinder with a diameter of10 cm).

Two sets of sensor devices (precision value of 10-5 second) are attached to the impactor, slab and supports to monitor accelerations, forces and displacements wherein each set has 6 measuring channels.

A high speed video camera (10,000 frames per second) with an inclination angle is used to record vertical displacements of the slab depending on a black pixels array on the slab"s top surface (spacing of 4 cm between each two pixels).

Abbildung in dieser Leseprobe nicht enthalten

Fig. 2 : Lab instruments and drop-tower

Abbildung in dieser Leseprobe nicht enthalten

Fig. 3 : Details of the complex mass drop-tower

Abbildung in dieser Leseprobe nicht enthalten

Fig. 4 : Slab cross-section [mm]

Abbildung in dieser Leseprobe nicht enthalten

Fig. 5: Slab" global response, detailing the response phase being under focus (linear field); [frm = 0.0001 s]

Abbildung in dieser Leseprobe nicht enthalten

Fig. 6: Outputs of the lab instrumentations

## 3 Parameters and properties

Knowledge of the mechanical properties of concrete and steel, as well as the principles of the interaction between them, is necessary for studying the behavior of reinforced concrete structures.

The reason for reinforcing concrete members is that the tensile strength of concrete is very low, approximately one order of magnitude less than its compressive strength. When tensile stresses occur due to external loading or imposed deformation in concrete members, the material may crack and fail. In reinforced concrete, these tensile stresses are resisted by reinforcing bars crossing crack planes and providing integrity of the members.

In the following treatment of the subject those features of concrete and steel will be briefly reviewed which are essential for analyzing the behavior of concrete structures[2].

### 3.1 Direct parameters and properties:

Basically, some values of properties are available and it is needed to depend on them to drive the other necessary parameters:

Thickness of the slab and dimensions: [Abbildung in dieser Leseprobe nicht enthalten]

Thickness of concrete cover: [Abbildung in dieser Leseprobe nicht enthalten]

Density of concrete: [Abbildung in dieser Leseprobe nicht enthalten]

Poisson"sratioofRC: [Abbildung in dieser Leseprobe nicht enthalten]

Average angle ofRC punching cone in respect to horizon: [Abbildung in dieser Leseprobe nicht enthalten] Longitudinal reinforcement, in 2 directions and 2 layers: [Abbildung in dieser Leseprobe nicht enthalten]

Yield strength of reinforcing steel:[Abbildung in dieser Leseprobe nicht enthalten]

Ultimate strength of reinforcing steel:[Abbildung in dieser Leseprobe nicht enthalten]

Average modulus of elasticity of steel: [Abbildung in dieser Leseprobe nicht enthalten]

Yield strain of steel: [Abbildung in dieser Leseprobe nicht enthalten]

Ultimate strain of steel: [Abbildung in dieser Leseprobe nicht enthalten]

### 3.2 Indirect parameters and properties

#### 3.2.1 Compressive strength of concrete (standard cylinder) f’c[3]

The compressive strength of concrete at an age t depends on the type of cement, temperature and curing conditions. For a mean temperature of 20°C and curing in accordance with EN 12390 the compressive strength of concrete at various ages fcm(t) may be estimated from expressions:

Abbildung in dieser Leseprobe nicht enthalten

where:

fcm(t) is the mean concrete compressive strength at an age of t days.

fcm is the mean compressive strength at 28 days.

ßcc(t) is a coefficient which depends on the age of the concrete t.

t is the age of the concrete in days.

s isa coefficient which depends on the type of cement:

= 0,20 for rapid hardening high strength cements (R) (CEM 42.5R, CEM 52.5)

= 0,25 for normal and rapid hardening cements (N) (CEM 32.5R, CEM 42.5)

= 0,38 for slow hardening cements (S) (CEM 32.5)

According to ACI 209, a study of concrete strength versus time indicates an appropriate general equation for predicting compressive strength at any time:

Abbildung in dieser Leseprobe nicht enthalten

where:

a and b are constants,f’c (28) is a 28-day compressive strength and t in days is the age of concrete. The evaluation of compressive strength with time is of great concern to structural engineers. ACI Committee 209 recommends the following relationship for moist-cured concrete made with normal Portland cement (ASTM Type III): f’c (t) = f’c (28) t/(2.3+0.921)

The used cement for the specimens of the current experiment is none-rapid-hardening CEM III/A, 42.5 and the following given data will be used as initial values to back-calculate the compressive strength in the age of 28 days

Table 2:Characteristic compressive strength of cencerte

Abbildung in dieser Leseprobe nicht enthalten

Table 3: Concrete compressive strength as a function of its age at the test time [MPa]

Abbildung in dieser Leseprobe nicht enthalten

It is conclude that the closet class of concrete strength according to EC2 is 40/50 and it is adopted that are fcm = 50 [MPa] as a mean value of concrete compressive strength for the general calculations and the detailed values of f'c for the advanced calculations which are sensitive tof'c (e.g., strain rate calculations).

#### 3.2.2 Average modulus of elasticity of concrete “Ec”

According to EC2, the Ec for concrete class 40/50 is 35 [GPa].

#### 3.2.3 Average dynamic modulus of elasticity of concrete “Ed”

Lydon and Balendran [Neville, 1997] proposed the following empirical formula:

Abbildung in dieser Leseprobe nicht enthalten

Another empirical relationship is proposed by Swamy & Bandy and is now accepted as part ofBritish testing standard BS8110 Part2:

Abbildung in dieser Leseprobe nicht enthalten

#### 3.2.4 Average tensile strength of concrete “fctm”

According to EC2, the fctm for concrete class 40/50 is 3.5 [MPa]

#### 3.2.5 Concrete shear modulus “G”:

Abbildung in dieser Leseprobe nicht enthalten

#### 3.2.6 Elastic (fracture) energy of concrete “Gf”[4]

The energy dissipated in opening the crack, Gf, or fracture energy, is given by the area underneath the stress displacement curve. For f'c not exceeding 80 [MPa], Model Code 1990 gives an expression for Gf as:

Abbildung in dieser Leseprobe nicht enthalten

where GF0 is a reference fracture energy (which is a function of dg) andf.0 is a reference compressive strength, given as[10] MPa.

It should be noted that Model Code 2010 gives a simplified expression in which GF varies only withf'c and constant with dg, as shown inFig. 7.

Abbildung in dieser Leseprobe nicht enthalten

In this work, the expression found in Model Code 1990 will be used, since this, in the opinion of the authors, is more general.

Abbildung in dieser Leseprobe nicht enthalten

#### 3.2.7 Slab geometry “ds, rs, dsf, rsf, d

Slab diameter and slab radius:

Abbildung in dieser Leseprobe nicht enthalten

Effective slab diameter and effective slab radius due to support effect:

Abbildung in dieser Leseprobe nicht enthalten

Effective depth of the slab “d”: d = h - a - Ф/2 = 300 -25 - 8/2 = 271 [mm]

#### 3.2.8 Bending capacity “MRd"[4]

The moment capacity for a RC section is obtained from simple equilibrium and is given by:

Abbildung in dieser Leseprobe nicht enthalten

where p is the reinforcement ratio at the level being considered (top or bottom) andfy is the steel reinforcement yield stress.

#### 3.2.9 Slab rotation and rotation rate W, W[4]

Model Code 2010 gives expressions for the load-rotation response of a RC slab by using the levels of approximation method. In this instance, a Level II approximation is used, whereby the load-rotation relationship is given by:

Abbildung in dieser Leseprobe nicht enthalten

where rso indicates the position of zero radial bending moment with respect to the support axis (typically taken as ~ 0.22L for flat slabs of span L but this is not the case in the current experiment), Es is the elastic modulus of steel reinforcement, Msd is the average bending moment per unit length in the slab"s column (support) strip and MRd is the average flexural strength per unit length in the column strip. The various terms in Eq. (1) affect the crack width (and thus the rotation). The term rs/d represents the slenderness of the slab while the term Msd/MRd is the bending moment demand ratio. The strain in the reinforcement at yielding is considered by the termfy/Es For internal columns, from the Model Code, Msd is related to the load Vd by:

Abbildung in dieser Leseprobe nicht enthalten

On the other hand, it could be used more simplified formula for the current experiment as a function of the maximum displacement Smax (near to the center of slab):

Abbildung in dieser Leseprobe nicht enthalten

Leff. effective length of slab span and equal 1.7178m (discussed later in section 7)

After that, the rotation angle is divided by the required time to reach max displacement tmax:

Abbildung in dieser Leseprobe nicht enthalten

Fig. 8 : Rotation angle [rad, mm]

#### 3.2.10 Strain rate £[4]

The strain at the crack (assuming the reinforcement is within the elastic domain) can be established by using a strain crack width relationship, such as the square root model suggested by Fernández Ruiz etal.:

Abbildung in dieser Leseprobe nicht enthalten

where Tb,max is the maximum bond stress given by [Abbildung in dieser Leseprobe nicht enthalten] . The square root model for bond is based on the affinity hypothesis of the slip distribution along long anchored bars and neglects the local loss ofbond stiffness and strength due to the formation oflocal diagonal cracks.

The strain-rate è can be determined from Eq. (2) as:

Abbildung in dieser Leseprobe nicht enthalten

At this point, a comment on alternative methods of estimating the strain-rate is in order. A simplified equation is presented in the American UFC 3-340-02 to estimate the strain-rate in the concrete as:

Abbildung in dieser Leseprobe nicht enthalten

where tE is the time duration from the initial impact to the peak response. The results obtained using Eq. (3) and (4) are compared in table 4.

Table 4: Rotation rate and strain rate of each slab

Abbildung in dieser Leseprobe nicht enthalten

#### 3.2.11 Dynamic compressive and tensile strength of concrete

It has been shown by many researchers (e.g.[5] ) that the tensile and compressive strengths of concrete increase with loading rate. A very comprehensive review of experimental data in this respect has been carried out by Cotsovos and Pavlovic[6]. The 1990 and 2010 Model Codes [7, 8, 9] provide relationships which give the increase in strength and modulus with strain-rate.

These relationships are valid for strain rates up to 300/s covering low to moderate impacts. The increases in compressive (f) and tensile ft) strengths are given by Eq. (5) and (6) respectively as:

Abbildung in dieser Leseprobe nicht enthalten

Thus for the current experiment, the concrete may obtain a dynamic increase by 13% forf and a dynamic increase by 25% for fct.

#### 3.2.12 Penetration depth[4]

Punching is a brittle form of failure observed in RC flat slab structures, typically at slab- column connections but also observed in many drop impact tests.

The punching capacity of slab systems has been investigated since the 1950s but most strength models presented in design codes are empirically derived e.g. the American ACI 318-08, the British BS 8110-1 and the European EC 1992-1.

A physically-based mechanical model was proposed in 1988 by Muttoni and subsequently formed the basis for punching shear provisions in various Swiss codes and also in the latest version of the Model Code [7,8].

The model is based on the critical shear crack theory (CSCT) and assumes that the shear strength is governed by the width and the roughness of a shear crack which develops through an inclined compression strut which carries the shear force.

It can be shown that the punching shear capacity decreases with increasing rotation since this implies wider cracks, thus reducing both tensile and aggregate contributions. Further details can be found in Muttoni and Fernández Ruiz for slabs with no transverse reinforcement.

In the current experiment, it has been summarized in Table 5 the penetration depths of the first impact phase depending on an optical method through the test videos.

Table 5: slab penetration depths of the first mass impact

Abbildung in dieser Leseprobe nicht enthalten

#### 3.2.13 Punching cone mass

The average failure angle of shear punching cone is 35° with horizon and the average upper cone diameter is 0.12 [m] . Hence, the punching cone mass is roughly 235 [kg]:

Diameter of upper circle = 0.12m

Diameter oflower circle[Abbildung in dieser Leseprobe nicht enthalten]

Abbildung in dieser Leseprobe nicht enthalten

## 4 The process of data analysis[10]

The process of data analysis includes the following stages in consequence:

1. Data collection.

2. Data processing.

3. Data cleaning.

4. Data analysis.

5. Data modeling.

### 4.1 Data collection

Data is collected from a variety of sources in form of raw data and in our case: the data are collected by means of sensor devices, high speed video camera and minor tests.

In terms of sensors, they supply us with two datasets (data1-2 and data2-2) each dataset contains 8 channels, where channels from 3 to 6 of data1-2 measured by semi-conductor strain- gauges technique and channels from 1 to 4 of data2-2 measured by piezo-electric strain technique, see Table 6.

### 4.2 Data processing

Data initially obtained must be processed or organized for analysis. For instance, this may involve placing data into rows and columns in a table format for further analysis, such as within a spreadsheet or statistical software[11].

Therefore an important step in data analysis is to improve data quality through data processing which includes correction and transformation of available data and handling missed data; besides, weeding out noise data and filtering out of scope data. This is the most critical step in the data value chain; even with the best analysis, junk data will generate wrong results and mislead the research work.

#### 4.2.1 Data correction:

The recorded displacements of the slab need to be subtracted by displacements of the block foundation due to its settlement response to the impact load (vibration / shock absorber system) and this settlement response is available through channel_8 of data1-2.

Moreover, we need to subtract the mean value of natural Eigen vibration recorded by the same channel (ch_8) that we sum up the first 100 measurements before the impact and calculate their average (mean value).

#### 4.2.2 Data transformation[1]:

The recorded slab displacements are deformed values ödef= db because of the inclination of the camera"s axis by an obtuse angle with the zenith (not parallel to the slab surface). Therefore, the deformed values transformed to real valuesö= Ш by applying orthogonality laws as depicted in Fig. 9:

Abbildung in dieser Leseprobe nicht enthalten

#### 4.2.3 Data conversion

The data obtained from sensors are in Volt unit, so we need to convert the measured data by calibration factors provided by instrument technicians as follows:

Table 6 (1 of 2): Calibration factors of data1-2 and data2-2

Abbildung in dieser Leseprobe nicht enthalten

Table 6 (2 of 2): Calibration factors of data1-2 and data2-2

Abbildung in dieser Leseprobe nicht enthalten

#### 4.2.4 Missing data handling

The missed data have been handled by interpolation, extrapolation wherein they are required or in some cases have not been -polated to indicate to the located uncertainty.

#### 4.2.5 Noise data eradication

As mentioned previously about subtracting natural eigen vibrations in section 4.2.1. Besides, The abnormal measurements are weed out from the acceleration records by using a weighted average method (discussed later in section 8.4.1).

#### 4.2.6 Data filtering

A chain is only as strong as its weakest link; therefore, we need tojustify the accuracy of our datasets to match the accuracy of video camera. The accuracy of video camera for all slab tests is 1/10,000 sec with total test-time long G [0.65, 0.11] sec except for slab 7 which is 1/7000 sec[2] with total test-time long 0.04 sec. Furthermore, datasets have the following accuracies and test-time long:

- Data1-2 with the accuracy of 1/100,000 sec and test-time long 5 sec results in 4.5 million measurements in total.

- Data 2-2 with the accuracy of 1/500,000 sec and test-time long 1 sec results in 4.5 million measurements in total.

Hence, datasets (and slab 7) are filtered and unified with the accuracy of 1/10,000 sec and the first impact-time long G [0.011, 0.013] sec. Accordingly, the total measurements are reduced to 1500 instead of millions for each dataset.

As an example in the appendix, a hard copy of slab 3 results is shown in Table 12, 13. The rest of tables are attached as a soft copy due to overwhelming outputs!

### 4.3 Data cleaning

The collected data may be incomplete, contain duplicates or contain errors. The need for data cleaning will arise from problems in the way that data are entered and stored. Data cleaning is the process of preventing and correcting these errors. Latter-in, excluding negative values is necessary sometimes to simulate the physical phenomena more accurately like with acceleration records of the impactor, see Fig. 32.

### 4.4 Data analysis

Once the data is cleaned, it can be analyzed. Analysts may apply a variety of techniques referred to as “exploratory data analysis” to begin understanding the messages contained in the data. The process of exploration may result in additional data cleaning or additional requests for data, so these activities may be iterative in nature. “Data visualization” may also be used to examine the data in graphical format, to obtain additional insight regarding the messages within the data.

#### 4.4.1 Characteristic phases

Abbildung in dieser Leseprobe nicht enthalten

Fig. 10: :nstic phases of the slab test [frm = 0.0001 s]

An optical technique through videos is efficiently adopted to distinguish the characteristic phases of each slab test. The optical technique has had the highest reliability in comparison with the other available data sources represented by an electro technique which tolerate a lot of disturbance. The sensors had some technical problems during experiments which curbed its entrusted role and left a gap patched with the optical instruments.

Characteristic phases of the slab test [frm = 1/10,000 s], see Table 7:

- Start time of first mass impact, ts,Mij

- Start time of second mass impact, tsMR2

- Time of maximum displacement response due to first mass impact, to,Smax

- Duration of first mass impact, tMi, 1= ts,mí,2 - ts,Mi, 1

- Duration until maximum displacement response due to first mass impact, tSmax = to, Smax - ts, Mi, 1

When iť'snot referred to the location of a displacement, it"s assumed in the center of the slab.

**[...]**

^{*} txt files of transformed data were available and given by the supervisor

^{*} the accuracy of slab 7 has been converted to 1/10,000 sec by means of time refinement.

- Quote paper
- Mudar Hamsho (Author), 2015, Investigation on the Behaviour of Reinforced Concrete Slabs under Dynamic Impact Loading, Munich, GRIN Verlag, https://www.grin.com/document/323137

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