Draft - tspace.library.utoronto.ca · This paper investigates the isolation efficacy of geocell reinforced foundation bed infilled with different materials through a series of block

Draft

Effect of Infill Materials on Vibration Isolation Efficacy of Geocell Reinforced Soil Beds

Journal: Canadian Geotechnical Journal

Manuscript ID cgj-2019-0135.R2

Manuscript Type: Article

Date Submitted by the Author: 15-Sep-2019

Complete List of Authors: Venkateswarlu, Hasthi; Indian Institute of Technology Patna, Department of Civil and Environmental EngineeringHegde, Amarnath; Indian Institute of Technology Patna, Department of Civil and Environmental Engineering

Keyword: Geocell, Infill materials, Block resonance test, Peak particle velocity, MSD analogy

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Issue? :Not applicable (regular submission)

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Canadian Geotechnical Journal

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Effect of Infill Materials on the Vibration Isolation Efficacy of Geocell

Reinforced Soil Beds

By

Hasthi Venkateswarlu

Research Scholar, Department of Civil and Environmental Engineering, Indian Institute of

Technology Patna, India, 801106; E-mail: [email protected]

and

A. Hegde

Assistant Professor, Department of Civil and Environmental Engineering, Indian Institute of

Technology Patna, India, 801106; E-mail: [email protected]

Technical paper submitted to Canadian Geotechnical Journal

Corresponding author

A. Hegde

Assistant Professor,

Department of Civil and Environmental Engineering,

Indian Institute of Technology Patna, India-801106.

E-mail: [email protected]

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mailto:[email protected]:[email protected]:[email protected]

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Abstract

This paper investigates the isolation efficacy of geocell reinforced foundation bed infilled with

different materials through a series of block resonance tests. The geocell made with a novel

polymeric alloy (NPA) was used in the experimental investigation. Total, five different cases,

namely, unreinforced, geocell reinforced silty sand, geocell reinforced sand, geocell reinforced

slag, and geocell reinforced aggregate were considered. The presence of geocell has resulted in

improvement of screening efficacy of foundation bed regardless of the infill material. The

displacement amplitude of geocell reinforced bed was reduced by 68%, 64%, 61%, and 59%,

respectively, for aggregate, slag, sand and silty sand infill cases as compared to the unreinforced

condition. The maximum isolation efficiency was observed in the presence of aggregate, among

the four different infill materials. In the presence of aggregate infill, the shear modulus of the

foundation bed was improved by 150%. Similarly, the peak particle velocity and peak

acceleration were reduced by 57% and 48% respectively. Further, the efficacy of mass spring

dashpot (MSD) analogy was studied in predicting the frequency - displacement response of

different reinforced cases. From the analytical study, a significant improvement in damping ratio

of the foundation bed was observed in the presence of geocell reinforcement.

Keywords: Geocell, Infill materials, Block resonance test, Peak particle velocity, Damping ratio,

MSD analogy

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1. Introduction

The concept of soil reinforcement has evolved tremendously in the last four decades. As a result,

different forms of reinforcement materials are available in the market for specific applications.

The basic concept of reinforced earth was discovered by Henry Vidal (1966). The pioneering

work of Binquet and Lee (1975) provided the direction for conducting systematic studies on the

reinforced soil beds. Subsequently, several researchers reported the potential of soil

reinforcement in enhancing the bearing capacity of the soil (Akinmusuru and Akinbolande 1981;

Fragaszy and Lawton 1984; Guido at al. 1986; Shahin et al. 2017). The geosynthetics are one of

the innovative products discovered for reinforcing the soil mass. The invention of geosynthetics

has replaced the utilization of conventional reinforcement materials like steel bars and metallic

strips. The geosynthetics are planar and three dimensional in nature, and are categorized into

different types. The familiar types of geosynthetics include geotextiles, geogrids, geonets,

geocells, and geocomposites. These products have been offering sustainable solutions for the

geotechnical problems since last three decades. Among those products, geogrid and geocell are

primarily preferred for reinforcement application (Hegde and Sitharam 2016). Out of which,

geocell has attained more importance owing to its positive benefits (Satyal et al. 2018).

Geocells are 3-dimensional products manufactured by interconnecting the honeycomb shaped

cells to encapsulate the infill material. In the early 1970s, the US Army Corps of Engineers were

developed these products for the quick mobilization of military vehicles over the sandy soil

(Webster and Alford 1978). Afterward, many researchers have reported the use of geocells in

various civil engineering applications (Pokharel et al. 2010; Hegde 2017). The unique advantage

of geocell is, it offers all round confinement to the infill soil and enhance the stiffness and

strength properties (Koerner 2012; Oliaei and Kouzegaran 2017). Also, the confinement effect of

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geocell on the shear strength behavior of soil was highlighted through triaxial studies (Bathurst

and Karpurapu 1993; Rajagopal et al. 1999; Biabani et al. 2016). Various studies have reported

the benefits of geocell in load supporting applications under monotonic loading conditions

(Tavakoli et al. 2013; Tanyu et al. 2013; Moghaddas Tafreshi et al. 2014; Song et al. 2014;

Hegde and Sitharam 2015a,b,c,d,e; Dutta and Mandal 2016; Hegde and Sitharam 2017).

Nevertheless, several studies investigated the cyclic behavior of geocell supported foundations

(Hegde and Sitharam 2016; Suku et al. 2016; Esmaeili et al. 2017; Correia and Zornberg 2018;

Song et al. 2018).

Generally, sand is used to infill the geocell pockets. Hegde and Sitharam (2015b) studied the

effect of different infill materials on the performance of geocell reinforced soft clay bed under

static loading conditions. The findings revealed that the improvement in load carrying capacity

of clay bed with the increase in the angle of shearing resistance of infill material. Han et al.

(2010) studied the behavior of single geocell reinforced bed with different infill materials under

dynamic loading conditions. From the results, the geocell performance was found better with the

aggregate infill as compared to sand material. Tafreshi et al. (2008) found that the increase in

elastic response of the foundation bed with the increase in density of infill material through a

series of cyclic plate load tests. As of now, research on geocell was constrained to a

strengthening aspect of geotechnical practices under different loading conditions (Hegde 2017).

There is a lack of studies to understand the potential of geocell in the case of isolation of ground

induced vibration.

Nowadays, the isolation of ground borne vibration has become an area of great interest in the

field of geotechnical engineering. The induced vibration from the source is not only problematic

for the structure but also harmful to the surrounding environment. The adverse effects of such

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vibration are ranging from minor cracks to severe damage to the structures. The major damage is

caused by the transmission of vibration energy in the form of surface waves, especially the

Rayleigh wave (Choudhury et al. 2014). The attenuation behavior of these waves is slower than

the body waves (Bose et al. 2018). The open and infilled trench barriers are the commonly

adopted practices for mitigating the amplitude levels of such vibration (Woods 1968; Al-

Hussaini and Ahmad 1996; Murillo et al. 2009; Alzawi and Naggar 2011). Though these

methods are effective, it is tedious to implement in densely populated areas by means of

excavation and transferring of the huge soil mass. Sometimes, it is not viable to excavate the

ground mass due to the presence of buried pipelines and subsidence of adjacent structures. To

avoid such difficulties, enriching the dynamic properties of a foundation bed is an alternate

option for reducing the amplitude of vibration (Gazettas 1991). The study of Hegde and Sitharam

(2016) reported the efficacy of geogrid and geocell in improving the dynamic properties of a soft

clay bed. Various studies described the behavior of geogrid and geotextile reinforced soil in

controlling the amplitude of machine induced vibration (Boominathan et al. 1991; Haldar and

Sivakumar Babu 2009; Heidari and El Naggar 2010; Sreedhar and Abhishek 2015; Clement

2015). Very few have studied the isolation behavior of geocell reinforced beds supporting the

machine foundations. Venkateswarlu et al. (2018a) conducted a field and numerical investigation

of the machine foundation beds reinforced with geogrid and geocell. A significant improvement

in the performance of the foundation bed was observed in the presence of geocell compared to

the planar reinforcement. Venkateswarlu and Hegde (2018) conducted the preliminary numerical

investigation using PLAXIS 2D to increase the knowledge on the behavior of geosynthetics

reinforced bed under machine induced vibration. From the analysis, the lateral spreading of

machine induced vibration was found to arrest in the presence of geocell reinforcement. The

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study of Venkateswarlu et al. (2018b) reported the efficacy of geogrid and geocell in improving

the nonhomogeneous machine foundation bed through FLAC3D based analysis. The realistic soil

profile obtained from the SPT data was used in the study. The study suggested the optimum

width and depth of placement of both the reinforcements for enriching the foundation bed

behavior. Ujjawal et al. (2019) numerically investigated the potential use of cellular confinement

systems in isolating the machine induced vibration. In addition, the study reported the effect of

different geocell properties on the dynamic response of a machine foundation bed.

Based on the available literature, it is observed that the limited studies are available on the topic

of vibration isolation involving the geocells. Hence, the present study investigates the effect of

different infill materials on the vibration mitigation efficacy of geocell reinforced soil bed

through a series of field vibration tests. Four different infill materials, namely, silty sand, sand,

steel slag, and aggregate have been used. The isolation effectiveness has been studied in terms of

change in ground vibration and resonance parameters of the geocell reinforced bed. In addition,

the efficacy of mass spring dashpot (MSD) model in predicting the amplitude versus frequency

response of unreinforced and geocell reinforced bed with different infill materials has been

highlighted. The improvement in damping ratio of foundation bed due to the provision of geocell

reinforced layer with different infill materials has been quantified using the MSD analogy.

2. Material characterization

The properties of various materials used in the present study were divided into three categories,

namely, reinforcement, foundation soil, and infill materials. The neoloy (also referred as NPA)

geocell mattress consists of 330 mm weld spacing and 2150 N cell to cell seam strength was

used as a reinforcement. It can exhibit superior performance over the HDPE (high density poly

ethylene) geocell in terms of thermal expansion, durability, and creep resistance. The ultimate

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tensile strength of the geocell was determined through the tensile strength test based on the

guidelines of ISO 10319 (2015). The geocell section collected between the seam to seam was

used for the testing purpose. Total, three numbers of identical specimens were tested to study the

tensile behavior of a geocell reinforcement. The test was conducted at the loading rate of 12% of

the gauge length of the specimen per minute. The elongation was recorded until the complete

failure of a test specimen. The stress versus strain response of a geocell is shown in Fig. 1. The

maximum tensile strength of the geocell was observed as 23.8 kN/m at the failure strain of 12%.

Further, the slight decrease in peak tensile strength of the specimen was observed up to the strain

value of 33%. In addition to the mechanical behavior, the physical, and endurance properties of

the geocell are summarized in Table 1. The endurance and mechanical properties of the geocell

were provided by the manufacturer.

Further, the surface features such as surface roughness and texture of the geocell were

determined. The surface roughness was measured using a non-contact 3D surface profiler. It

measures the micro-features through the technique of Coherence Scanning Interferometry

(Vangla and Madhavi Latha 2016). The surface roughness of the geocell was measured in terms

of average surface roughness value (Sa) as per the guidelines of ASME-B46.1 (2002). It can be

defined as the arithmetic average of the absolute values of profile height deviations observed

within the evaluation area with respect to a horizontal plane or mean surface area. It is the actual

3D representation of surface roughness with the help of areal measurement. The surface

roughness of the geocell is shown in Fig. 2a. The average surface roughness of the geocell was

observed as 6 micro meters. The surface profiler utilizes an area of 5 mm × 5 mm for this

purpose. Similarly, the surface texture of the geocell was observed using an optical microscope.

The scanned image of the geocell surface is shown in Fig. 2(b). The cup shaped texture was

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observed over the geocell surface. Hegde and Sitharam (2014) was also reported a similar

observation.

The foundation bed was prepared with the locally available sand material (referred as foundation

soil). In accordance with the Unified Soil Classification System, the foundation soil was

classified as silty sand and designated with the symbol SM. In addition to the silty sand, three

different soil materials, namely, river sand, steel slag, and aggregate were used to fill the pockets

of geocell mattress (referred as infill materials). These materials were selected on the basis of

variation in frictional angle. They were classified as SP, SW, and GP respectively, based on the

Unified Soil Classification System (USCS). For the convenience, the river sand (poorly graded

sand) has been referred as sand in the remaining part of the manuscript. The particle size

distribution and the photographic representation of soil materials used in the present study are

shown in Fig. 3. The different properties of infill materials are listed in Table 2.

The triaxial compression test was conducted under a consolidated undrained condition to

determine the elastic modulus of infill materials. To do so, the triaxial specimen of individual

infill material was prepared at the dry unit weight of 17.3 kN/m3. Each material was tested at

three different confining pressures, namely, 100, 200, and 300 kPa. The typical deviator stress

versus axial strain curves of infill materials observed at the confining pressure of 100 kPa is

shown in Fig. 4. From figure, the elastic modulus of infill materials was determined and listed in

Table 2.

3. Experimental investigation

3.1. Block resonance test setup

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The screening effectiveness of geocell reinforced bed with different infill materials was studied

through a series of block resonance tests. The schematic representation of the block resonance

test is shown in Fig. 5(a). The accessories used for conducting the test were concrete block,

mechanical oscillator, DC Motor, vibration meter with the accelerometer, and speed control unit

with sensor assembly. The M20 grade concrete block of 600 mm × 600 mm × 500 mm was used

in the experimental study. The mechanical oscillator used in this study was a Lazen type to

induce sinusoidally varying dynamic force over the concrete block. The concrete block and

oscillator replicate the machine foundation and high-speed rotary machine respectively, in the

real case scenario. The magnitude of a dynamic force induced from the oscillator depends on the

frequency and the eccentric angle between the rotating masses. The DC motor of 6 HP capacity

was used to operate the oscillator at a required frequency. The flexible shaft was used to connect

the DC motor and the oscillator. The operating frequency of a motor was observed and

controlled using a speed control unit. It can measure the frequency of a rotating body with the

help of a non contact type speed sensor. The speed control unit contains a digital counter circuit

to compute the frequency in terms of RPM based on the electrical pulse received from the

sensor. The maximum sensing range of the sensor was 10,000 RPM with a resolution of 1RPM.

It is capable of working from a distance of 2 mm from the objects. In this study, it was connected

at a distance of 1.5 mm from the MS stud (attached to the rotating shaft) of the motor. The

arrangement of a sensor during the test is shown in Fig. 5(b). One end of the sensor was fixed

nearer to the rotating body and the other end connected to the speed control unit. During the test,

the displacement amplitude, velocity, and acceleration of the induced vibration were recorded

through the digital vibration meter. The vibration meter used in this study was portable and

specifically designed for the continuous measurement of vibration parameters. The piezoelectric

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accelerometer was used as a sensing element for this purpose. One end of the accelerometer was

connected with the vibration meter and the other end placed over the concrete block.

3.2. Preparation of reinforced foundation beds

Two different types of reinforced foundation beds were prepared in the present study. One is

unreinforced and the other is a geocell reinforced bed with different infill materials. Both the

conditions were prepared in an excavated test pit of 2 m × 2 m × 1.2 m (length × width × depth).

The dimensions of the foundation bed were selected such that there is no effect of the boundary

on the displacement amplitude of a system (Raman 1975). The existing soil below the foundation

bed (1.2 m to 3 m) was also observed as silty sand. Hence, the top 1.2 m soil was replaced and

reconstructed with the silty sand material. By doing so, the boundary effect was also eliminated

along the depth. The test pit was prepared by layer wise to maintain the uniform density

throughout the depth of the bed. The entire depth was compacted with ten numbers of layers,

having each layer thickness of 12 cm. The approximate compactive effort of 594 kN-m/m3 was

applied over each layer. The compaction was performed at the optimum moisture content of the

soil using a steel rammer of weight 11 kg. Primarily, several trail tests were carried out to study

the moisture content and dry density variation in the foundation bed. Total, nine numbers of

samples were collected for this purpose through the core cutter method, as per the guidelines of

IS 2720-29 (1975). Fig. 6 shows the dry density and moisture content variation of the foundation

bed. The average dry density of the foundation bed was observed as 17.38 kN/m3. Similarly, the

average moisture content was observed as 11.86%. The coefficient of variation for the placement

density and moisture content of the compacted soil mass in the foundation bed was determined

as 0.23% and 0.14% respectively.

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However, the preparation of the geocell reinforced bed was slightly differed as compared to the

unreinforced bed. The geocell was placed at a depth of 0.1B from the ground surface on the

compacted soil as reported in the literature (Hegde and Sitharam 2017). Initially, the geocell

pockets were filled with the aggregate material. Each pocket of the geocell was filled with three

numbers of layers through the tamping process. The cylindrical rod of 16 mm diameter and 600

mm long was used for the tamping purpose. After filling, the average density of the aggregate

was observed as 17.54 kN/m3. The density of the aggregate was measured by dividing the weight

of compacted aggregate in the geocell pocket with the corresponding cell volume. The proper

sequence was followed to avoid the bending and distortion of a geocell wall during the

compaction of aggregate material (Venkateswarlu et al. 2018a). In the other test series, the silty

sand was also compacted with three numbers of layers using Standard Proctor. In order to

maintain the same density for different infill material cases, the density of the aggregate was

considered as a reference. The sand pluviation technique was adopted for filling the geocell

pockets with the sand and steel slag materials. The schematic representation of different

reinforced foundation beds is shown in Fig. 7.

Before filling the sand and slag, trail tests were performed to determine the required height of

fall to achieve the target density. From the trail tests, the required height of fall was determined

as 510 mm and 470 mm, respectively, for the sand and slag materials. The perforated cylindrical

jar was used for the pluviation. The geocell pockets were filled in three numbers of lifts by

varying the height of each lift between 35 mm to 45 mm. The photographs of the preparation of

different reinforced conditions are shown in Fig. 8. While filling, the known volume of

aluminum cups were placed inside the geocell pockets to verify the density of slag and sand

materials (as shown in Fig. 8b). All the precautions were taken to maintain density difference as

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minimum as possible among the infill materials. However, the variation among the densities of

different infill materials was observed as less than 8%. Based on the width of the concrete

footing, soil cover of 0.1B (i.e. 60 mm) was provided after filling all the pockets of geocell

reinforcement. The width of the geocell mattress used in the study was as same as that the length

of the foundation bed (i.e., 3.3 times the width of the concrete block).

The screening behavior of different reinforced cases was studied under rotating mass type

excitation. The different dynamic force conditions were generated over the concrete block

through the change in eccentric setting and frequency of the excitation. The total dynamic force

induced over the concrete block in a vertical mode is determined using,

𝑃(𝑡) = 𝑃0sin (𝜃2) (1)

𝑃0 = 𝑚𝑒𝑒𝜔2 (𝑚𝑒 =𝑊𝑒𝑔 ) (2)

(3)𝑃(𝑡) = 𝑊𝑒𝑔 𝑒𝜔

2𝑠𝑖𝑛(𝜃2)where is the vertical component of the total dynamic force in N, P0 is the total unbalanced 𝑃(𝑡)

dynamic force excited over the footing in N, We is the eccentric weight in the oscillator in kg, e

is the eccentricity of the oscillator in m, is the circular natural frequency in cycles per second, 𝜔

g is the acceleration due to gravity in m/sec2 and is the eccentricity angle in degree. The 𝜃

detailed description about the derivation of above mentioned formulae was mentioned elsewhere

(Das 1992; Richart et al. 1970). During the test, the operating frequency of the oscillator was

varied from 5 Hz to 45 Hz with an increment of 5 Hz. Fig. 9 shows the variation of dynamic

force with the change in frequency and eccentricity angle. The increase in dynamic force was

observed with the increase in eccentricity angle and operating frequency of the oscillator. The

details of the experimental investigation carried out in the present study are summarized in Table

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3. In overall, 30 numbers of field tests were conducted to understand the effect of infill materials

on the isolation behavior of geocell reinforced bed.

3.3. Test procedure

Initially, the concrete block was placed centrally over the leveled surface of the test bed. Prior to

the test, it was left for 18 hours to settle over the foundation bed. A mild steel plate was

connected to the concrete block to facilitate the loading arrangement. The oscillator was placed

over the steel plate and tightened through the nut and bolting arrangement. The proper care was

taken for maintaining the center of gravity of the loading system and the machine foundation in

the same vertical line. The total static weight of 5.6 kN (mass of the foundation and machine

parts) was used in the experimental study. During the test, the flexible shaft was positioned

horizontally to avoid the additional moments developed over the concrete block. To apply

vertical vibration, the oscillator was run slowly through a motor with the help of speed control

unit. It helps to avoid the sudden application of dynamic load over the footing. During the test,

the frequency of the vibration was increased with the range of 0.5 to 1 Hz. It helps to identify the

exact resonance response of different conditions. The displacement amplitude was recorded at

each operating frequency, after the time period of 10 sec using the vibration meter (Kumar and

Reddy 2006; Venkateswarlu et al. 2018a). The piezoelectric accelerometer was placed over the

concrete block to measure the displacement amplitude of vibration for different conditions (as

shown in Fig. 7). Finally, displacement amplitude versus frequency curves were plotted.

4. Results and discussion

The variation of displacement amplitude with the eccentricity angle and frequency of the

excitation for the unreinforced condition is shown in Fig. 10. The increase in displacement

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amplitude was observed with the increase in eccentricity angle. The peak displacement

amplitude at each eccentricity angle represents the occurrence of resonance. The frequency and

displacement amplitude corresponding to the resonance is referred as resonant frequency and

resonant amplitude respectively. The resonant frequency was found to vary between 24.9 Hz to

22.3 Hz, with the increase in eccentricity angle from 10° to 50°. Several researchers reported a

similar observation in the case of unreinforced foundation bed (Baidya and Murali Krishna 2001;

Baidya and Rathi 2004; Kumar and Reddy 2006; Mandal et al. 2012; Swain and Ghosh 2015).

The displacement amplitude versus frequency response of a geocell reinforced foundation bed

with different infill materials is shown in Fig. 11(a)-(d). A significant reduction in peak

displacement of the foundation bed was observed in the presence of geocell reinforcement.

Among the different infill conditions, the minimum resonant amplitude of the foundation bed

was observed for the aggregate infilled case. In the presence of aggregate infill, the reduction in

resonant amplitude of the foundation bed was varied between 69% to 56% with the change in

eccentricity angle from 10° to 50°. The steel slag was exhibited slightly better performance than

the sand infill condition. The better isolation performance of slag was attributed due to its higher

friction angle as compared to the sand material. The performance of silty sand was observed as

similar to the sand material. The increase in stiffness of foundation bed in the presence of geocell

was the reason for the significant reduction in resonant amplitude a system. Several researchers

have made a similar observation (Boominathan et al. 1991; Mandal et al. 2012; Gao et al. 2017;

Venkateswarlu et al. 2018a).

The increase in resonant frequency of the foundation bed was observed in the presence of geocell

reinforcement. The parameter, frequency improvement ratio ( ) was used to quantify the effect 𝐹𝑅

of infill materials on the resonant frequency of a geocell reinforced bed. It can be defined as the

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ratio between the resonant frequency of reinforced condition (Fr) to that obtained in the case of

unreinforced condition (Fu). The variation of frequency improvement ratio with the increase in

the dynamic force level for different infill cases is shown in Fig. 12. It was observed that the FR

found to increase with the increase in dynamic force for all the infill cases. The maximum

improvement was noticed for the geocell with aggregate material. In the presence of aggregate

infill, the FR of the foundation bed was increased by 1.62 times at the eccentric setting of 10°.

Increase in the natural frequency of the foundation bed due to the provision of geocell helps to

avoid the occurrence of resonance in the case of low frequency reciprocating machines. It is

always recommended that the frequency ratio less than 0.5 for the design of foundations

supporting the low frequency machinery (Richart et al. 1970).

The maximum amount of emitted energy from the vibration sources travels in the form of

surface (Rayleigh) waves (Miller et al. 1955; Choudhury et al. 2014; Bose et al. 2018). The

Rayleigh waves are known for causing the major damage of existing structures. Thus, the aim of

all the isolation methods is to mitigate the amplitude of vibration emanated from the source. In

this study, the attenuation behavior of the machine induced vibration was studied in terms of

amplitude reduction factor (Arf). The Arf is defined as the ratio between peak displacement

amplitude of the reinforced condition to the peak displacement amplitude of the unreinforced

condition. The variation in Arf was measured up to the distance of 2 m from the face of a concrete

block with an interval of 0.5 m. In general, the value of Arf should be minimum for better

isolation system (Ahmed et al. 1996). Similarly, the overall system efficacy was determined in

terms of isolation efficiency (IE) or efficiency of isolation. It can be evaluated using the

following equation.

𝐼𝐸 = (1 ― 𝐴𝑟𝑓) × 100 (5)

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The variation of Arf and IE with the distance from the concrete block is shown in Fig. 13 for

different infill cases. The Arf was calculated based on the maximum displacement amplitude of

different conditions obtained at the eccentricity angle of 10°. The reduction in Arf and

improvement in isolation efficiency was observed with the increase in distance from vibration

source, for all the cases. The minimum Arf and the maximum isolation efficiency was observed in

the case of aggregate infill as compared to the other cases. The maximum reduction in Arf was

due to the mobilization of additional confinement in case of geocell with aggregate material.

On the other hand, peak particle velocity (PPV) can be used as the reference parameter to assess

the level of damage caused by ground vibration to the existing structures. It represents the

maximum velocity attained by the soil grains due to the transmission of vibration energy emitted

from the vibration source. In this study, the variation in PPV of the foundation bed in the

presence of geocell with different infill materials was evaluated. The accelerometer was used to

record the change in PPV of different reinforced cases. It can measure the velocity of vibration

up to 200 mm/sec with the resolution of 0.1 mm/sec. Initially, the accelerometer locations were

predetermined and marked over the ground surface from the face of the concrete block. The base

of the accelerometer was made to rest over the ground surface and the other end connected to the

vibration meter. Overall, four accelerometers were placed at the intervals of 0.5 m from the

vibration source. The change in peak particle velocity with the distance for different cases is

shown in Fig. 14. The reported results are corresponding to the resonant frequency of different

conditions at the eccentricity angle of 10°. The reduction in PPV was observed with the increase

in distance from the concrete block in all the cases. The peak particle velocity of the foundation

bed was reduced significantly in the presence of geocell reinforcement. The maximum reduction

in PPV was observed in the case of geocell and aggregate infill material. In the presence of

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aggregate infill, 58% reduction in PPV of the foundation bed was observed at a distance of 0.5 m

from the vibration source.

Similarly, the variation in peak ground acceleration of geocell reinforced bed infilled with

different materials was investigated. The acceleration was also recorded at four measuring points

as described in the measurement of peak particle velocity. The change in acceleration was

studied at two different dynamic force levels, such as 1000 N, and 3000 N. The considered

dynamic forces are corresponding to the frequencies of 20 Hz, and 36 Hz respectively, at an

eccentricity angle of 30° (as per Eq. 3). The attenuation behavior of peak acceleration with the

distance for different reinforced cases is shown in Fig. 15. The variation in acceleration has

shown a nonlinear relationship with the distance for all the cases. It was found to increase with

the increase in dynamic force level. The significant reduction in the acceleration of the

foundation bed was observed in the case of geocell. The maximum reduction in peak

acceleration was observed in the case of aggregate infill as compared to the other cases. In the

presence of aggregate infill, 47% reduction in the acceleration of the foundation bed was

observed at a distance of 0.5 m from the vibration source. The attenuation behavior of the

acceleration depends on the geometric spreading (radiation damping) of the Rayleigh wave and

the material damping (Ulgen and Toygar 2015). The significant reduction of peak acceleration in

the presence of geocell represents the improvement in the damping ratio of the foundation bed.

5. Analytical studies

Over the years, significant advancement has been made in developing mathematical solutions for

vibration problems. Several methods have been developed to predict the dynamic response of a

foundation resting on homogeneous and nonhomogeneous foundation beds. The popular

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analytical studies include elastic half space theory, mass spring dashpot model, and the cone

model. Several studies suggested mass spring dashpot (MSD) model over the other methods due

to simplicity (Baidya and Murali Krishna 2001; Baidya and Rathi 2004; Mandal et al. 2012).

Hence, the MSD model was used for predicting the vibration response of different reinforced

cases considered in the present study.

5.1. Mass Spring Dashpot (MSD) model

In this study, an initiative has been taken to apply the MSD approach for predicting the dynamic

response of geocell reinforced soil beds. The unique advantage of MSD model is the

consideration of stiffness and damping characteristics in a single framework to predict the

response of a system. The machine foundation supporting the rotary machine resting over a half

space is shown in Fig. 16(a). As per MSD analogy, the subsurface is considered to be isotropic

and elastic material. The soil was represented with the linear elastic weight less spring, in which

damping is present. The dashpot was used to represent the damping of a system. The total mass

of a machine and the machine foundation was replaced with the rigid body of mass M. The

idealization of machine foundation system based on MSD model is shown in Fig. 16(b).

The governing equation of motion used to represent the system can be written as,

𝑀𝑍 + 𝐶𝑍 + 𝐾𝑍 = 𝑃(𝑡) (8)

where , , and are the displacement, velocity, and acceleration of vibration respectively, P(t) 𝑍 𝑍 𝑍

is the total dynamic force acting over the footing in a vertical mode and is equal to 𝑚0𝑒𝜔2

, C is the damping coefficient, t is the time variable, and K is the equivalent stiffness. sin (𝜔𝑡)

The displacement amplitude (Z) of vibration for different reinforced cases at each operating

frequency of the machine can be calculated by,

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𝑍 =(𝑚𝑒𝑒𝑀 )( 𝜔𝜔𝑛)

2

(1 ― ( 𝜔𝜔𝑛)2)

2

+ (2𝐷( 𝜔𝜔𝑛))2 (9)

where is the mass of the rotating elements, e is the eccentric distance, is the natural 𝑚𝑒 𝜔𝑛

frequency of the foundation soil system, which is equal to , is the operating frequency of 𝐾 𝑀 𝜔

a machine, and D is the damping ratio. Similarly, the displacement amplitude (Zm) corresponding

to the resonance is computed by,

𝑍𝑚𝑀𝑚𝑒𝑒

=1

2𝐷 1 ― 𝐷2 (10)

The important parameters required for the MSD analysis are damping ratio and shear modulus of

the system. The damping is a mathematical quantity used to replicate the dissipation of vibration

energy in the system. It is a complicated and key parameter for predicting the dynamic response

of a system. The damping of a system subjected to machine induced vibration is majorly

comprised of two parts, namely, material and radiation damping. The material damping is

associated with the hysteresis effect of the material. It ranges from 1 to 10% of the critical

damping (Richart et al. 1970; Baidya et al. 2006). In the case of radiation damping, the

dissipation of induced energy takes place by means of the radiation process. It depends upon

several factors, namely, the size and shape of the foundation, material type, frequency of the

excitation, and weight of the foundation, etc. The radiation damping (Dr) for the foundations

resting on half space can be estimated using,

𝐷𝑟 =0.425

𝐵𝑧 (11)

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𝐵𝑧 = [(1 ― 𝜗)4 ]( 𝑊𝛾𝑟3) (12)where is the modified mass ratio, W is the weight of the foundation, is the unit weight of 𝐵𝑧 𝛾

foundation soil, and r is the equivalent radius of a non circular foundation. The value of Dr can

be as high as 50% of the critical damping (Richart et al. 1970). There is a lack of exact solutions

to find the total damping of a geocell reinforced system. Thus, the varying values of damping

were assumed in the MSD analysis to compare the experimental results. For convenience, the

damping ratio was varied with the increment of 4% in the present study. Various researchers

followed the similar approach for predicting the dynamic response of unreinforced beds (e.g.,

Baidya and Murali Krishna 2001; Baidya et al. 2006; Mandal et al. 2012).

On the other hand, the other parameter influences the dynamic response of a system is the shear

modulus. The various laboratory and field methods available for determining the shear modulus

of soil material. However, IS 5249 (1992) recommends block resonance test for its determination

in order to design the foundations supporting industrial machines. As per Indian Standard code

of practice, the shear modulus is computed using the following equation (Timoshenko and

Goodier 1970).

(13)G = 14r(1 ― μ)ω

2nm

where G is the shear modulus, r is the equivalent radius of the non circular footing, m is the total

mass of the foundation and machine elements, is the natural circular frequency of the 𝜔𝑛

foundation soil system, and is the Poisson’s ratio of the soil mass. The value of Poisson’s ratio 𝜇

was considered as 0.3 for determining the G of different cases. Similarly, the is determined 𝜔𝑛

by,

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(14)𝐾 = 𝜔2𝑛𝑚

where K is the stiffness of the foundation soil system. In this study, the variation in shear

modulus and the magnitude of shear strain with the increase in dynamic force was investigated.

The shear strain was determined by dividing the maximum displacement of the foundation bed

with the width of the machine foundation (Prakash and Puri 1981; Baidya and Murali Krishna

2001). The change in shear modulus and shear strain for different cases is shown in Fig. 17. The

reduction in shear modulus and increase in shear strain was observed with the increase in the

dynamic force level for all the cases. The reduction in G was due to the reduction of resonant

frequency (with the increase in dynamic force) of a system. In the case of geocell reinforced bed

(regardless of infill material), the significant improvement in G was observed as compared to the

unreinforced condition. Particularly, the maximum improvement was noticed in the presence of

aggregate infill as compared to other cases. The maximum reduction in shear strain was the

reason for the higher shear modulus of a system.

The experimental displacement amplitude versus frequency response of different cases

corresponding to the eccentric angle of 500 was considered for the comparison purpose. During

the analytical study, the shear modulus of different cases for the selected condition was chosen

from Fig. 17. Fig. 18 shows the comparison of experimental displacement amplitude versus

frequency response of the unreinforced condition with the MSD analogy. From the comparison,

the experimental results matched well with the results of the analytical study at the damping ratio

of 12%. It indicates that the total damping of the unreinforced condition is approximately 12%. It

also reveals that the radiation damping is possibly present in the system due to the existence of

half space under the foundation bed. Hence, the total damping is considered as 5% material

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damping and 7% radiation damping. Baidya and Rathi (2004) has also followed the similar

separation of total damping for the sand bed resting over the infinite soil mass.

The comparison of experimental frequency versus displacement amplitude of the geocell

condition (with different infill materials) with the MSD model is shown in Fig. 19. The

experimental resonant frequency of geocell and silty sand infill case was agreed with the MSD

results at the damping ratio of 26% (as shown in Fig. 19a). It reveals that the significant

improvement in the damping ratio of the foundation bed in the presence of geocell

reinforcement. The observed damping is a combination of 5% material damping and 21%

radiation damping. The reasonable agreement between the dynamic response of geocell with

sand infill and MSD response was observed at the damping ratio of 28% (as shown in Fig. 19b).

It indicates that the total damping is a combination of 5% material damping and 23% radiation

damping. From Fig. 19(c), the experimental results of geocell with slag infill case has shown

reasonable agreement with that obtained from the analytical study at the damping ratio of 32%.

Thus, the observed total damping is a combination of 5% material damping and 27% radiation

damping. Similarly, the good agreement between the experimental response of geocell with

aggregate infill case and the MSD model was observed at the damping ratio of about 36%. The

total damping can be divided as 5% material damping and 31% radiation damping. From the

analytical comparison, the maximum damping ratio was observed in the case of geocell and

aggregate infill as compared to the other cases. In the presence of geocell and aggregate infill,

the improvement in the total damping of the foundation bed was observed by 200%. The increase

in damping ratio in the presence of stiff layer nearer to the machine foundation was also reported

by Baidya et al. (2006) and Mandal et al. (2012). A sample calculation to determine the

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displacement amplitude of a reinforced foundation bed at 500 eccentricity angle has been

illustrated in Annexure 1.

6. Conclusions

The effect of infill materials on the screening performance of geocell reinforced bed supporting

the machine foundation was investigated in the present study. Four different materials, namely,

silty sand, sand, slag, and the aggregate were used as the infill materials. From the experimental

results, the significant improvement in isolation efficacy of foundation bed was observed in the

presence of geocell, regardless of the infill material. The resonant amplitude of the foundation

bed was reduced by 68%, 64%, 61%, and 59%, respectively, when the geocell infilled with

aggregate, slag, sand, and silty sand materials. Similarly, the resonant frequency was increased

by 1.62 times for aggregate, 1.53 times for slag, 1.48 times for sand, and 1.42 times for silty sand

materials. The test results revealed that the comparable isolation performance between the sand

and silty sand infill materials. It indicates that the silty sand can perform as effectively as sand

infill material. The steel slag has shown higher isolation performance as compared to the sand

infill material. Hence, the utilization of steel slag (industrial waste) is a good substitute for

natural aggregates to improve the isolation behavior of geocell reinforced bed. Among four

different materials, the maximum reduction in ground vibration parameters of the foundation bed

was observed in the case of aggregate infill material. In the case of aggregate infill, the reduction

in PPV of the foundation bed was observed as 58% at a distance of 0.5 m from the footing face.

Similarly, 47% reduction in peak ground acceleration of the foundation bed was observed. The

analytical comparison revealed that the significant improvement in the total damping of the

foundation bed in the presence of geocell. The total damping for different cases was observed as

12%, 26%, 28%, 32%, and 36%, respectively, for unreinforced, silty sand, sand, slag, and

(b)

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aggregate infill materials. The higher damping ratio of the aggregate infill case resulted the

maximum reduction in ground vibration parameters of the foundation bed. In overall, higher

angle of shearing resistance of infill material resulted the maximum isolation performance of the

geocell reinforced foundation bed.

Annexure 1

In this section, a sample calculation has been provided to determine the displacement amplitude

of a reinforced foundation bed using MSD analogy.

Known parameters:

Reinforced case considered : Geocell reinforced bed with sand infill

Resonant frequency for the considered case, Fr in Hz : 34.5 (obtained from field vibration test)

The operating frequency assumed, f in Hz : 20

Contact area of the concrete footing, A in m2 : 0.6 m × 0.6 m

Total weight of vibrating mass and footing, W in kN : 5.5

Total weight of footing, Wf in kN : 4.32

Eccentric distance, e in m : 0.0019

The eccentric weight, We in kN : 0.491

Poisson’s ratio of the foundation soil, 𝜗 : 0.3

The acceleration due to gravity, g in m/sec2 : 9.81

Eccentric angle : 50°

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The essential steps followed for the determination of the displacement amplitude (Z) are illustrated

below:

The displacement amplitude corresponding to the operating frequency is obtained by,

𝑍 =(𝑚𝑒𝑒𝑀 )( 𝜔𝜔𝑛)

2

(1 ― ( 𝜔𝜔𝑛)2)

2

+ (2𝐷( 𝜔𝜔𝑛))2

Calculating and substituting the values of each parameter in the equation,

m 0.17 mm𝑚𝑒𝑒𝑀 =

(0.491) × 0.0019(5.5) = 0.00017 =

where and M are the masses of rotating element and vibrating mass respectively.𝑚𝑒

Determination of the circular frequency of rotating mass, ω = 2 × 𝜋 × 𝑓 = 2 × 𝜋 × 20

Hz= 125.66

Natural circular frequency, 𝜔𝑛 =𝑘𝑀

where k is the soil stiffness. It can be determined by,

𝑘 =4𝐺𝑟0

(1 ― 𝜗)

where, and G are equivalent radius of concrete footing and shear modulus respectively. The 𝑟0

following Equation is used to determine the equivalent radius of the concrete footing.

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m𝑟0 =𝐴𝜋 =

0.6 × 0.6𝜋 = 0.3385

The shear modulus (G) is selected from the shear modulus versus eccentric setting plot presented

in Fig. 17 of the revised manuscript.

From Fig. 17, G = 12.0807 MN/m2 = 12080 KN/m2

Therefore, kN/m𝑘 =4 × 12080 × 0.3385

(1 ― 0.3) = 23366.17

= Hz𝜔𝑛 =𝑘𝑀

23366.17 × 9.815.5 = 204.15

Assuming the damping ratio (D) value of 28%,

Finally, the displacement amplitude, Z = 0.17 × (125.66204.15)

2

(1 ― (125.66204.15)2)2

+ (2 × 0.28 × (125.66204.15))2

= 0.08534 mm

In the similar lines, displacement amplitudes of other reinforced cases are calculated and are

shown in Table 4.

Notations

The following notations are used in this paper:

A contact area of the concrete footing (m2)

Ar displacement amplitude of reinforced condition (mm)

Aun displacement amplitude of unreinforced condition (mm)

Arf amplitude reduction factor

b width of the geocell reinforcement (m)

B width of the concrete footing (m)

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Bz modified mass ratio

C damping coefficient (dimensionless)

D damping ratio (%)

Dr radiation damping (%)

e eccentric distance between center of mass and the center of rotation (m)

E Young’s modulus (MPa)

fnz natural frequency of the foundation soil system (Hz)

P(t) the dynamic force excited over the footing in a vertical mode (N)

Po total dynamic force (N)

f operating frequency (Hz)

FR frequency improvement factor (dimensionless)

Fr resonant frequency of the reinforced soil system (Hz)

Fu resonant frequency of the unreinforced soil system (Hz)

g acceleration due to gravity (m/sec2)

G shear modulus (MPa)

GS stands for ground surface

IE isolation efficiency (%)

K stiffness of the soil (kN/m)

M mass of the vibrating block, oscillator and motor (kg)

m centre of gravity of the rotating mass

me eccentric mass weight (kg)

MSD stands for mass spring dashpot model

N geocell seam strength (N)

c centre of rotation

PPV peak particle velocity (mm/sec)

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𝑟0 equivalent radius (m)

Sa average surface roughness (µm)

t time duration (sec)

𝑍, 𝑍, 𝑎𝑛𝑑 𝑍 acceleration, velocity, and displacement amplitude of the vertical vibration in mm/sec2, mm/sec, and mm respectively.

W total weight of vibrating mass (kN)

Wf weight of the concrete footing (kN)

𝜔 circular frequency in cycles (rotations) per minute

𝜔𝑛 natural frequency of the foundation soil system (cycles per minute)

Z displacement amplitude (mm)

Zm peak displacement amplitude (mm)

ν Poisson’s ratio (dimensionless)

𝜃 eccentricity angle (degrees)

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Timoshenko S.P., and Goodier, J.N. 1970. Theory of elasticity, 3rd edn. McGraw-Hill, New York.

Ujjawal, K.N., Venkateswarlu, H., and Hegde, A. 2019. Vibration isolation using 3D cellular

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Ulgen, D., and Toygar, O. 2015. Screening effectiveness of open and in-filled wave barriers: A

full-scale experimental study. Construction and Building Materials, 86: 12-20.

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Draft

List of Figures

Fig. 1. Stress versus strain response of NPA geocell

Fig. 2. Surface features of the geocell reinforcement

Fig. 3. Particle size distribution of infill materials

Fig. 4. Deviator stress versus axial strain response of infill materials with the triaxial

compression test setup

Fig. 5. Block resonance test setup: (a) schematic representation; and (b) arrangement of non-

contact speed sensor

Fig. 6. Variation in compaction parameters of the foundation bed: (a) dry density; and

(b) moisture content

Fig. 7. Schematic representation of the reinforced foundation beds

Fig. 8. Preparation of different reinforced conditions: (a) geocell filled with silty sand;

(b) partially filled geocell with sand; (c) partially filled geocell with steel slag; and

(d) geocell filled with aggregate

Fig. 9. Variation of dynamic force with the change in frequency and eccentricity angle

Fig. 10. Displacement amplitude versus frequency response of unreinforced condition

Fig. 11. Displacement amplitude versus frequency response of a geocell with different infill

conditions: (a) silty sand; (b) sand; (c) steel slag; and (d) aggregate

Fig. 12. Variation of frequency improvement factor for different infill cases

Fig. 13. Variation in Arf and IE with the distance for different infill cases

Fig. 14. Variation of PPV with the change in distance for different infill conditions

Fig. 15. Variation of peak acceleration with the distance for different cases: (a) at 1000 N;

and (b) at 3000 N

Fig. 16. The idealization of field problem into a single degree freedom system: (a) actual

scenario; and (b) MSD representation

Fig. 17. Variation in shear modulus and shear strain for different reinforced cases

Fig. 18. Comparison of experimental response with the MSD analogy for the unreinforced

condition

Fig. 19. Comparison between the experimental and analytical results: (a) geocell with silty

sand infill; (b) geocell with sand infill; (c) geocell with steel slag infill; and

(d) geocell with aggregate infill

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Draft0 5 10 15 20 25 30 35 40

02468

101214161820222426

Tens

ile lo

ad (k

N/m

)

Axial strain (%)

Fig. 1. Stress versus strain response of NPA geocell

Fig. 2. Surface features of the geocell reinforcement

(a) Surface roughness (b) Texture of geocell

Sa = 6 µm

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Draft Fig. 3. Particle size distribution of infill materials

Aggregate Steel slag

Sand Silty sand

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Draft0 2 4 6 8 10 12

0

400

800

1200

1600

2000

Silty sandSandSteel slagAggregate

Dev

iato

r stre

ss (k

Pa)

Axial strain (%)

Fig. 4. Deviator stress versus axial strain response of infill materials with the triaxial compression test setup

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Draft

Fig. 5. Block resonance test setup: (a) schematic representation; and (b) arrangement of non-contact speed sensor

1200 mm

2000 mm

600 mm

500 mm

Mechanical oscillator

Eccentricity control unit

Accelerometer

Vibration meter

DC Motor

Concrete block

Reinforced foundation bed

Flexible shaftRotating shaft

Non contact type speed

sensor

rpm indicator

Speed control unit

Subsurface

GS

Geocell

d

DC Motor MS stud

Rotating shaft

Non-contact speed sensor

(b)

(a)

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Draft

Fig. 6. Variation in compaction parameters of the foundation bed: (a) dry density; and (b) moisture content

(a)

(b)

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Draft(b) Geocell reinforced condition

B

∞

Subsurface

Foundation Soil

GS

0.3

B

Infill Material Geocell

Concrete Footing

b

0.2

B

1.7

B

Dynamic Excitation

B

∞

Subsurface

Foundation Soil

GS

Concrete Footing

2B

Dynamic Excitation

(a) Unreinforced condition

Fig. 7. Schematic representation of the reinforced foundation beds

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Draft

Fig. 8. Preparation of different reinforced conditions: (a) geocell filled with silty sand; (b) partially filled geocell with sand; (c) partially filled geocell with steel slag; and

(d) geocell filled with aggregate

(a)

(c)

(b)

(d)

Aluminum cups

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Draft0 10 20 30 40 50

0

0.5

1

1.5

2

2.5

3

3.5

10°20°30°40°

Dyn

amic

forc

e (k

N)

Frequency (Hz)

Eccentricity angle

Fig. 9. Variation of dynamic force with the change in frequency and eccentricity angle

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Draft0 10 20 30 40 500

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

10°20°30°40°

Dis

plac

emen

t am

plitu

de (m

m)

Frequency (Hz)Fig. 10. Displacement amplitude versus frequency response of unreinforced condition

Eccentricity angle

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Draft

0 10 20 30 40 50

0

0.1

0.2

0.3

0.4

10°20°30°40°

Dis

plac

emen

t am

plitu

de

(mm

)

Frequency (Hz) 0 10 20 30 40 50

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

10° 20°30° 40°50°

Dis

plac

emen

t am

plitu

de (m

m)

Frequency (Hz)

0 10 20 30 40 50

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

10° 20°30° 40°50°

Dis

plac

emen

t am

plitu

de (m

m)

Frequency (Hz) 0 10 20 30 40 50

0

0.05

0.1

0.15

0.2

0.25

0.3

10° 20°30° 40°50°

Dis

plac

emen

t am

plitu

de (m

m)

Frequency (Hz)

Fig. 11. Displacement amplitude versus frequency response of a geocell with different infill conditions: (a) silty sand; (b) sand; (c) steel slag; and (d) aggregate

(a) (b)

(c)

Eccentricity angle Eccentricity angle

Eccentricity angle

(d)

Eccentricity angle

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Draft

12

0 20 40 601.3

1.4

1.5

1.6

1.7

Geocell+Silty sandGeocell+SandGeocell+Steel slag

Freq

uenc

y im

prov

emen

t fac

tor (

F R)

Eccentricity angle (°)

Fig. 12. Variation of frequency improvement factor for different infill cases

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13

0 0.5 1 1.5 2 2.50

0.1

0.2

0.3

0.4

0.5

60

65

70

75

80

85

Geocell+Silty sandGeocell+SandGeocell+Steel slagGeocell+Aggregate

Am

plitu

de re

duct

ion

fact

or (A

rf)

Isol

atio

n ef

ficie

ncy

(%)

Distance from the vibration source (m)

Fig. 13. Variation in Arf and IE with the distance for different infill cases

0 0.5 1 1.5 2 2.52

4

6

8

10

12

14

16UnreinforcedGeocell+Silty sandGeocell+SandGeocell+Steel slagGeocell+Aggregate

Peak

par

ticle

vel

ocity

(mm

/sec

)

Distance from the source (m)

Fig. 14. Variation of PPV with the change in distance for different infill conditions

Isolation efficiency Arf

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14

0 0.5 1 1.5 2 2.50

0.5

1

1.5

2

2.5

3

3.5


Peak

acc

eler

atio

n (m

/sec

2 )

Distance from vibration source (m)

0 0.5 1 1.5 2 2.50

1

2

3

4

5

6

7

8


Peak

acc

eler

atio

n (m

/sec

2 )

Distance from vibration source (m)

Fig. 15. Variation of peak acceleration with the distance for different cases: (a) at 1000 N; and (b) at 3000 N

(a)

(b)

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15

KC

Rigid mass (M)

Z

Foundation bed: G, and

Subsurface

GS

(a) (b)

Rotary machine

Vertical dynamic force

Machine foundation

m

ce θ

ω

me

Fig. 16. The idealization of field problem into a single degree freedom system: (a) actual scenario; and (b) MSD representation

0 10 20 30 40 50 600

4

8

12

16

20

24

28

2

3

4

5

6

7

8

9

10

11

12UnreinforcedGeocell + SandGeocell + SlagGeocell + AggGeocell + Silty sand

Shea

r mod

ulus

(MN

/m2 )

Shea

r stra

in (×

10-4

)

Eccentric setting (°)

Fig. 17. Variation in shear modulus and shear strain for different reinforced cases

Shear modulus Shear strain

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16

0 10 20 30 40 500

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1ExperimentalD=8%D=12%D=16%

Dis

plac

emen

t am

plitu

de (m

m)

Frequency (Hz)

Fig. 18. Comparison of experimental response with the MSD analogy for the unreinforced

condition

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Draft

17

0 10 20 30 40 50

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35


Dis

plac

emen

t am

plitu

de (m

m)

Frequency (Hz) 0 10 20 30 40 50

0

0.05

0.1

0.15

0.2

0.25

0.3


Dis

plac

emen

t am

plitu

de (m

m)

Frequency (Hz)

0 10 20 30 40 50

0

0.05

0.1

0.15

0.2

0.25

0.3


Dis

plac

emen

t am

plitu

de (m

m)

Frequency (Hz) 0 10 20 30 40 50

0

0.05

0.1

0.15

0.2

0.25


Frequency (Hz)

Dis

plac

emen

t am

plitu

de (m

m)

Fig. 19. Comparison between the experimental and analytical results: (a) geocell with silty sand infill; (b) geocell with sand infill; (c) geocell with steel slag infill; and (d) geocell with aggregate infill

(a) (b)

(c) (d)

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1

List of Tables

Table 1. Properties of the geocell reinforcement

Table 2. Properties of different infill materials

Table 3. Details of the field study

Table 4. Summary of displacement amplitude calculation for different reinforced cases

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2

Table 1. Properties of the geocell reinforcement

Properties/Parameter Details/Values ReferencePhysical properties

Polymer composition Neoloy or Novel Polymeric AlloyCell depth (mm) 120Strip thickness (mm) 1.53Cell wall surface Textured and perforatedPercentage of open area on the surface (%) 16Hole diameter on the surface (mm) 10Number of cells per square meter 39Density (g/cm3) 0.95 (±1.5%) ASTM D1505 (2010)

Mechanical propertyCell seam strength (N) 2150 (±5%) ASTM D4437 (2013)

Endurance propertiesCoefficient of thermal expansion (ppm/0C) 400 ASTM D5885 (2015)

≥100 ASTM D3895 (2014)Oxidation induction time (minutes)Creep reduction factor

Draft

3

Table 2. Properties of different infill materials

Property/Parameter Silty sand Sand Steel slag AggregateGravel (>4.75 mm) 1 6 8 100

Sand (75 µm – 4.75 mm) 84 92 88 0Fines content (

Draft

4

Table 4. Summary of displacement amplitude calculation for different reinforced cases

Reinforced case

ParameterUnreinforced

Geocell+ Silty sand

Geocell+ Steel slag

Geocell+ Aggregate

Equivalent radius, in m𝑟0 0.3385 0.3385 0.3385 0.3385

Shear modulus, G in kN/m2 5600 11380 12780 14110

Soil stiffness, K in kN/m 10832.46 22012.17 24720.17 27292.77

Natural circular frequency, in Hz𝜔𝑛 139.09 198.16 209.98 220.64

Circular frequency, in Hz (operating 𝜔frequency of 20 Hz)

125.66 125.66 125.66 125.66

Damping ratio assumed (%) 12 26 32 36

Displacement amplitude, Z in mm 0.4595 0.0942 0.0766 0.0656

Page 57 of 57



Documents

Draft - tspace.library.utoronto.ca · This paper investigates the isolation efficacy of geocell reinforced foundation bed infilled with different materials through a series of block