Recent developments in constructions have heightened the need for protecting existing buried infrastructure. New roads and buildings may be constructed over already existing buried infrastructures e.g. buried utility pipes, leading to excessive loads threatening their stability and longevity. Additionally applied loads over water mains led to catastrophic damage, which result in severe damage to the infrastructure surrounding these mains. Therefore, providing protection to these existing buried infrastructure against increased loads due to new constructions is important and necessary. In this research, a solution was proposed and assessed, where the protection concept would be achieved through the inclusion process of geogrid-reinforcing layers in the soil cover above the buried infrastructure. The controlling parameters for the inclusion of geogrid-reinforcing layers was assessed experimentally and numerically. Twenty-three laboratory tests were conducted on buried flexible and rigid pipes under unreinforced and geogrid-reinforced sand beds. All the investigated systems were subjected to incrementally increasing cyclic loading, where the contribution of varying the burial depth of the pipe and the number of the geogrid-reinforcing layers on the overall behaviour of the systems was investigated. To further investigate the contribution of the controlling parameters in the pipe-soil systems performance, thirty-five numerical models were performed using Abaqus software. The contribution of increasing the amplitude of the applied cyclic loading, the number of the geogrid-reinforcing layers, the burial depth of the pipe and the unit-weight of the backfill soil was investigated numerically. The inclusion of the geogrid-reinforcing layers in the investigated pipe-soil systems had a significant influence on decreasing the transferred pressure to the crown of the pipe, generated strains along its crown, invert and spring-line, and its deformation, where reinforcing-layers sustained tensile strains. Concerning rigid pipes, the inclusion of the reinforcing-layers controlled the rebound that occurred in their invert deformation. With respect to the numerical investigation, increasing the number of the reinforcing-layers, the burial depth of the pipe and the unit-weight of the backfill soil had positive effect in decreasing the generated deformations, stresses and strains in the system, until reaching an optimum value for each parameter. Increasing the amplitude of the applied loading profile resulted in remarkable increase in the deformations, stresses and strains generated in the system. Moreover, the location of the maximum tensile strain generated in the soil was varied, as well as the reinforcing-layer, which suffered the maximum tensile strain. / Government of Egypt

[pt] O presente estudo teve como principal objetivo demonstrar que fibras derivadas da reciclagem de garrafas PET (Polietileno Tereftalato), confeccionadas com 100 porcento do resíduo, pela indústria têxtil, podem ser uma boa alternativa se utilizadas como reforço de solos, quando submetidos a diferentes níveis de cargas. Buscando uma melhor aplicabilidade para este material, foram executados ensaios de compressão triaxial drenados em laboratório, bem como ensaios de prova de carga em placa e também com simulação de um talude em modelo físico reduzido, para a determinação do comportamento mecânico de uma areia e do compósito areia-fibras PET. Para os ensaios triaxiais drenados, foram utilizadas fibras PET com dois títulos (correspondente ao diâmetro das fibras) e comprimentos distintos (1,4 dtex com 38 mm e 3,3 dtex com 56 mm), inseridas aleatoriamente na massa de solo, onde foi utilizado o teor de 0,5 porcento de fibras, em relação ao peso seco do solo, teor de umidade de 10 porcento e densidade relativa de 50 porcento. Os resultados mostraram que o comportamento da areia pura é influenciado pela adição de fibras PET, melhorando os parâmetros de resistência, como o intercepto coesivo e o ângulo de atrito, definidos pelo critério de Mohr-Coulomb. O compósito reforçado com as fibras PET de menor título e menor comprimento apresentou um maior ganho na resistência ao cisalhamento, mas ambos os compósitos, em comparação ao solo não reforçado, apresentaram uma maior resistência. Para os ensaios de prova de carga em placa e para a simulação do talude, ambos realizados em modelo físico reduzido, foram utilizadas as fibras de menor título e menor comprimento como elemento de reforço. Observa-se que a inserção das fibras PET melhora o comportamento carga-recalque da areia pura, onde o compósito reforçado apresenta uma maior capacidade de suporte e a redução dos recalques, bem como uma mudança na propagação e formação das fissuras ao redor da placa. Na simulação do talude, a inserção das fibras PET promove uma alteração completa no mecanismo de ruptura ocorrido no compósito, quando comparado à ruptura da areia pura. Ressalta-se o emprego positivo das fibras PET para aplicação como reforço de solos em obras geotécnicas (como por exemplo, em camadas de aterros sanitários, aterros sobre solos moles, reforço de taludes, base de fundações superficiais e controle de erosão), além de eliminar problemas atuais de disposição de resíduos, dando um fim mais nobre a este material, com benefícios ambientais, sociais e econômicos. / [en] The main objective of this study was to demonstrate that fibers derived from the recycling of PET (Polyethylene Terephthalate) bottle, 100 percent made from the residue by the textile industry, can be a good alternative if used as reinforcement of soil, when submitted to different load levels. Looking for a better applicability for this material, were executed drained triaxial compression tests in laboratory, as well as plate load tests, also with slope simulation in a reduced physic model, to evaluate the mechanical behavior of a sand and a composite sand-PET fibers. For the drained triaxial tests, were used PET fibers with two different titles (corresponding to the fiber diameters) and lenghts (1,4 dtex com 38 mm e 3,3 dtex com 56 mm), distributed randomly in the soil mass, where was used a fiber contente of 0,5 percent by relation to the soil s dry weight, moisture content of 10 percent and relative density of 50 percent. The results showed that the pure sand behavior was influenced by the addition of PET fibers, improving the strenght parameters as the cohesion intercept and the friction angle, defined by the Mohr-Coulomb criteria. The composite reinforced with PET fibers with minor title and lenght presented a better improvement in the shear strenght, but both composites, compared to the non reinforced soil, showed greater resistence. For the plate load tests and for the slope simulation, both performed in a reduced physic model, it was used the fiber with minor title and lenght as reinforcement element. The addiction of PET fibers improve the load-settlement behavior of the sand, where the reinforced composite shows a greater bearing capacity, a reduction of the settlements and a change in the propagation and formation of fissures around the plate. In the slope simulation, the addiction of PET fibers promove a complete alteration in the rupture mechanism that occurred in the composite, when compared to the rupture of the pure sand. It is highlighted the positive use of PET fibers for application as soil reinforcement in geotechnical works (as an example, in landfill layers, embankment on soft soil, slope reinforcement, base of shallow foundations and erosion control), eliminating current problems of waste disposal, giving a noble end to this material, with environmental, social and economical benefits.

Geosynthetic reinforced soil (GRS) is a soil improvement technology in which closely spaced horizontal layers of geosynthetic are embedded in a soil mass to provide lateral support and increase strength. GRS is popular due to a relatively new application for bridge support, as well as long-standing application in mechanically stabilized earth walls. Several different GRS design methods have been used, and some are application-specific and not based on fundamental principles of mechanics. Because consensus regarding fundamental behavior of GRS is lacking, numerical and mathematical analyses were performed for laboratory tests obtained from the published literature of GRS under triaxial compression in consolidated-drained conditions. A three-dimensional numerical model was developed using FLAC3D. An existing constitutive model for the soil component was modified to incorporate confining pressure dependency of friction angle and dilation parameters, while retaining the constitutive model's ability to represent nonlinear stress-strain response and plastic yield. Procedures to obtain the parameter values from drained triaxial compression tests on soil specimens were developed. A method to estimate the parameter values from particle size distribution and relative compaction was also developed. The geosynthetic reinforcement was represented by two-dimensional orthotropic elements with soil-geosynthetic interfaces on each side. Comparisons between the numerical analyses and laboratory tests exhibited good agreement for strains from zero to 3% for tests with 1 to 3 layers of reinforcement. As failure is approached at larger strains, agreement was good for specimens that had 1 or 2 layers of reinforcement and soil friction angle less than 40 degrees. For other conditions, the numerical model experienced convergence problems that could not be overcome by mesh refinement or reducing the applied loading rate; however, it appears that, if convergence problems can be solved, the numerical model may provide a mechanics-based representation of GRS behavior, at least for triaxial test conditions. Three mathematical theories of GRS failure available in published literature were applied to the laboratory triaxial tests. Comparisons between the theories and the tests results demonstrated that all three theories have important limitations. These numerical and mathematical evaluations of laboratory GRS tests provided a basis for recommending further research. / Ph. D.

Design of retaining structures depends upon the load which is transferred from backfill soil as well as external loads and also the resisting capacity of the structure. The traditional safety factor approach of the design of retaining structures does not address the variability of soils and loads. The properties of backfill soil are inherently variable and influence the design decisions considerably. A rational procedure for the design of retaining structures needs to explicitly consider variability, as they may cause significant changes in the performance and stability assessment. Reliability based design enables identification and separation of different variabilities in loading and resistance and recommends reliability indices to ensure the margin of safety based on probability theory. Detailed studies in this area are limited and the work presented in the dissertation on the Optimum design of retaining structures under static and seismic conditions: A reliability based approach is an attempt in this direction. This thesis contains ten chapters including Chapter 1 which provides a general introduction regarding the contents of the thesis and Chapter 2 presents a detailed review of literature regarding static and seismic design of retaining structures and highlights the importance of consideration of variability in the optimum design and leads to scope of the investigation. Targeted stability is formulated as optimization problem in the framework of target reliability based design optimization (TRBDO) and presented in Chapter 3. In Chapter 4, TRBDO approach for cantilever sheet pile walls and anchored cantilever sheet pile walls penetrating sandy and clayey soils is developed. Design penetration depth and section modulus for the various anchor pulls are obtained considering the failure criteria (rotational, sliding, and flexural failure modes) as well as variability in the back fill soil properties, soil-steel pile interface friction angle, depth of the water table, total depth of embedment, yield strength of steel, section modulus of sheet pile and anchor pull. The stability of reinforced concrete gravity, cantilever and L-shaped retaining walls in static conditions is examined in the context of reliability based design optimization and results are presented in Chapter 5 considering failure modes viz. overturning, sliding, eccentricity, bearing, shear and moment failures in the base slab and stem of wall. Optimum wall proportions are proposed for different coefficients of variation of friction angle of the backfill soil and cohesion of the foundation soil corresponding to different values of component as well as lower bounds of system reliability indices. Chapter 6 presents an approach to obtain seismic passive resistance behind gravity walls using composite curved rupture surface considering limit equilibrium method of analysis with the pseudo-dynamic approach. The study is extended to obtain the rotational and sliding displacements of gravity retaining walls under passive condition when subjected to sinusoidal nature of earthquake loading. Chapter 7 focuses on the reliability based design of gravity retaining wall when subjected to passive condition during earthquakes. Reliability analysis is performed for two modes of failure namely rotation of the wall about its heel and sliding of the wall on its base are considering variabilities associated with characteristics of earthquake ground motions, geometric proportions of wall, backfill soil and foundation soil properties. The studies reported in Chapter 8 and Chapter 9 present a method to evaluate reliability for external as well as internal stability of reinforced soil structures (RSS) using reliability based design optimization in the framework of pseudo static and pseudo dynamic methods respectively. The optimum length of reinforcement needed to maintain the stability against four modes of failure (sliding, overturning, eccentricity and bearing) by taking into account the variabilities associated with the properties of reinforced backfill, retained backfill, foundation soil, tensile strength and length of the geosynthetic reinforcement by targeting various component and system reliability indices is computed. Finally, Chapter 10 contains the important conclusions, along with scope for further work in the area. It is hoped that the methodology and conclusions presented in this study will be beneficial to the geotechnical engineering community in particular and society as a whole.

The EC Landfill Directive (1999), which is enforced in England and Wales through the Landfill (England and Wales) Regulations (2002), has increased the technical challenge associated with the design and construction of landfill containment systems, in particular those on steep side slopes. Increased numbers of lining system components, varied configurations, and complex loading scenarios require advanced analysis tools to facilitate design. This project involved the development of advanced numerical modelling techniques, based on the FLAC finite difference modelling code. The analysis toolbox can be used to predict the behaviour of multilayered geosynthetic and soil lining systems, during and after staged construction. The model can include non-linear interface and geosynthetic axial properties, represent complex loading, including downdrag from the waste mass, whilst retaining the flexibility to represent varied geometries and include engineered support structures. Whilst numerical modelling is becoming increasingly commonplace in commercial design, there is little evidence of the validation of numerical models with field or experimental data. Validation of the analysis toolbox described in this document was conducted by back analysis of published data, modelling of landfill failure mechanisms, and comparisons to large scale laboratory testing. Design of field scale instrumentation has also been carried out as part of this project. The influence of interface shear strength variability has been assessed through the compilation of a comprehensive database, and the effect of this variability on lining system behaviour assessed through reliability based analyses. This has shown probability of failures may be higher than proposed limiting values when adopting traditional accepted factors of safety. A key area of interest identified during the project was the requirement for support, potentially through reinforcement, of the geological barrier. The inclusion of randomly reinforced fibres in bentonite enhanced soil has shown the potential for increased strength, without adverse effects on hydraulic barrier performance. ii Additionally, the influence of geomembrane seams on lining system integrity has been investigated, showing that fusion welded seams can result in stress concentration and extruded seams can cause significant stress concentration.

[pt] O presente trabalho tem como objetivo a implementação e avaliação de um modelo constitutivo para solos reforçados com fibra (compósito). A principal característica do modelo constitutivo implementado é que cada material (matriz de solo e fibra) segue sua própria lei constitutiva e ao mesmo tempo interagem entre si. Utilizando um algoritmo explícito, são implementados os modelos Cam Clay Modificado e Lade-Kim para a matriz de solo, cuja verificação é feita mediante o programa PLAXIS 2D e curvas tensão-deformação obtidas da literatura, respectivamente. Posteriormente, é adicionado o comportamento da fibra no desenvolvimento das tensões no compósito e verificado mediante a comparação das curvas tensão-deformação com as apresentadas por Diambra et al. (2013). As linguagens de programação utilizadas neste trabalho foram duas, a primeira é a utilizada no programa MATLAB, onde os códigos dos modelos são verificados e validados em relação à um conjunto de ensaios triaxiais de areia reforçada com fibra. Posteriormente foi usada a linguagem de programação FORTRAN para incluir o modelo constitutivo para solo reforçado com fibras no programa de elementos finitos ABAQUS, através da sub-rotina UMAT. Porém, para a implementação na sub-rotina UMAT os códigos dos modelos implementados no MATLAB sofrem algumas modificações com a finalidade de que o ABAQUS consiga compilar e representar adequadamento o comportamento do modelo constitutivo, mediante a correta utilização de vetores e propriedades desta. Finalmente, são modelados ensaios triaxiais drenados para verificar que a implementação mediante a sub-rotina UMAT é satisfatória. / [en] The present work aims to implement and evaluate a constitutive model for fiber-reinforced soils (composite). The main characteristic of the constitutive model implemented is that each material (soil and fiber matrix) follows its own constitutive law and at the same time interact with each other. Using an explicit algorithm, the Cam Clay Modified and Lade-Kim models are implemented for the soil matrix, verified by the PLAXIS 2D software and stress-strain curves obtained from the literature, respectively. Later, it is included the behavior of the fiber in the development of the stresses in the composite and verified by the comparison of the stress-strain curves with those presented by Diambra et al. (2013). The programming languages used in this work were two, the first one is the one used in the MATLAB program, where the codes of the models are verified and validated in relation to a set of triaxial tests of fiber-reinforced sands. Later the programming language was converted into FORTRAN to include the constitutive model for fiber reinforced soil in the ABAQUS finite element software, through the UMAT subroutine. However, for the implementation in the UMAT subroutine the codes of the models implemented in MATLAB undergo some modifications in order that ABAQUS can compile and represent adequately the behavior of the constitutive model through the correct use of vectors and its properties. Finally, drained triaxial tests are modeled to verify that the implementation through the UMAT subroutine is satisfactory.

The various aspects of the 3D cellular confinement systems (geocells) subjected to static loading are comprehensively studied with the help of experimental and numerical studies. The performances of the geocells were separately studied in both sand and clay beds. Laboratory tests were performed on single as well as multiple cells. The behavior of 3D-cells made of different materials such as Novel polymeric alloy, geogrids and bamboo were compared. Moreover, the performances of the geocells were compared with other forms of geosynthetic reinforcements namely, geogrids and the combination of geocells and geogrids. In addition to comprehensive experimental study, 2-dimensional and 3-dimensional numerical modelling efforts are also presented. A Realistic approach of modelling the geocells in 3D framework has been proposed; which considers the actual curvature of the geocell pockets. An Analytical equation has been proposed to estimate the increase in the bearing capacity of the geocell reinforced soft clay beds. Similarly, a set of equations to estimate the stress and strains on the surface of the geocells subjected to compressive loading were also proposed. A case study highlighting the innovative use of the geocell foundation to support the embankment on soft settled red mud has been documented in the thesis. A new and emerging application of geocell to protect underground utilities and the buried pipelines has been proposed. At the end, behavior of the geocell under cyclic loading has also been discussed. Firstly, laboratory model tests were performed to understand the behavior of the geocells in sand and clay beds. Test results of unreinforced, geogrid reinforced, geocell reinforced, and geocell reinforced with additional planar geogrid at the base of the geocell cases were compared separately for sand and clay beds. Results revealed that the use of geocells increases the ultimate bearing capacity of the sand bed by 2.9 times and clay bed by 3.6 times. Provision of the basal geogrid increases the ultimate load carrying capacity of the sand and clay bed by about 3.6 times and 4.9 times, respectively. Besides increasing the load carrying capacity, provision of the planar geogrid at the base of the cellular mattress arrests the surface heaving and prevents the rotational failure of the footing. Geocells contribute to the load carrying capacity of the foundation bed, even at very low settlements. In addition, the effect of infill materials on the performance of the geocell was also studied. Three different infill materials, namely aggregate, sand and local red soil were used in the study. Results suggest that the performance of the geocell was not heavily influenced by the infill materials. Out of which aggregate found to be slightly better than other two infill materials. Further, 2-dimensional numerical studies using FLAC2D (Fast Lagrangian Analysis of Continua in 2D) were carried out to validate the experimental findings. The equivalent composite approach was used to model the geocells in 2-dimensional framework. The results obtained from the FLAC2D were in good agreement with the experimental results. However, in the sand bed, FLAC2D overestimated the bearing pressure by 15% to 20% at higher settlements. In addition, the joint strength and the wall deformation characteristics of the geocells were studied at the single cell level. The study helps to understand the causes for the failure of the single cell in a cellular confinement system. Experimental studies were conducted on single cells with cell pockets filled up with three different infill materials, namely, silty clay, sand and the aggregates. The results of the experimental study revealed that the deformation of the geocell wall decreases with the increase in the friction angle of the infill material. Measured strain values were found to be in the range of 0.64% to 1.34% for different infill materials corresponding to the maximum applied bearing pressure of 290 kPa. Experimental results were also validated using FLAC3D. Findings from the numerical studies were in accordance with the experimental results. A simple analytical model based on the theory of thin cylinders was also proposed to calculate the accumulated strain of the geocell wall. This model operates under a simple elastic solution framework. The proposed model slightly overestimates the strains as compared to experimental and numerical values. A realistic approach of modelling the geocells in 3-dimensional (3D) framework has been proposed. Numerical simulations have been carried out by forming the actual 3D honeycomb shape of the geocells using the finite difference package FLAC3D. Geocells were modeled using the geogrid structural element available in the FLAC 3D with the inclusion of the interface element. Geocells, foundation soil and the infill soil were modeled with the different material model to match the real case scenario. The Mohr Colombo model was used to simulate the behavior of the sand bed while modified Cam clay was used to simulate the behavior of the clay bed. It was found that the geocells distribute the load in lateral direction to a relatively shallow depth as compared to unreinforced case. More than 50% reduction in the stress in the presence of geocells and more than 70% reduction in the stress in the presence geocells with basal geogrid were observed in sand and clay beds. The numerical model was also validated with the experimental studies and the results were found to be in good agreement with each other. The validated numerical model was used to study the influence of various properties of the geocells on the performance of the reinforced foundation beds. The performance of the foundation bed was directly influenced by the modulus and the height of the geocells. Similarly, the pocket size of the geocell inversely affected the performance of the reinforced beds. The geocell with textured surface yielded better performance than the geocell with smooth surface. A case history of the construction of a 3 m high embankment on the geocell foundation over the soft settled red mud has been documented. Red mud is a waste product from the Bayer process of Aluminium industry. The reported embankment is located in Lanjigharh (Orissa) in India. The geotechnical problems of the site, the design of the geocell foundation based on experimental investigation and the construction sequences of the geocell foundations in the field are discussed. Based on the experimental studies, an analytical model was also developed to estimate the load carrying capacity of the soft clay bed reinforced with geocell and the combination of geocell and geogrid. The solution was established by superimposing the three mechanisms viz. lateral resistance effect, vertical stress dispersion effect and the membrane effect. By knowing the pressure applied on the geocell, tensile strength of the geogrid and the limiting settlement, the increment in the load carrying capacity can be calculated. The analytical model was validated with the experimental results and the results were found to be in good agreement with each other. The results of the experimental and analytical studies revealed that the use of the combination of geocell and the geogrid is always beneficial than using the geocell alone. Hence, the combination of geocell and geogrid was recommended to stabilize the embankment base in Lanjigharh. Over 15,000 mof embankment base was stabilized using geocell foundation. The foundation work was completed within 15 days using locally available labors and the equipment. Construction of the embankment on the geocell foundation has already been completed. The constructed embankment has already sustained two monsoon rains without any cracks and seepage. Like Aluminum tailings (redmud), geocell foundations can also be used in various other mine tailings like zinc, copper etc. Geocell foundation can offer potential solutions to storage problems faced by various mining industries. The thesis also proposes a potential alternative to the geocells in the form of bamboocells in order to suit the Indian scenario. Indian has the 2nd largest source of bamboo in the world. The areas particularly rich in bamboo are the North Eastern States, the Western Ghats, Chattisgarh and Andaman Nicobar Islands. The tensile strength and surface roughness of the bamboo was found to be 9 times and 3 times higher than geocell materials. In order to use the bamboo effectively, 3D cells (similar to geocells) and 2D grids (similar to geogrids) are formed using bamboo known as bamboocells and bamboogrids respectively. The idea behind forming bamboocells is to extract the additional confining effect on the encapsulated soil by virtue of its 3-dimensional shape. The laboratory investigations were performed on a clay bed reinforced with natural (bamboo) and commercial (geosynthetics) reinforcement materials. The performance of bamboocells and bamboogrids reinforced clay beds were compared with the clay bed reinforced with geocells and geogrids. The ultimate bearing capacity of the bamboocell and bamboogrid reinforced clay bed was found to be 1.3 times that of reinforced with geocell and geogrid. The settlement of the clay bed was reduced by 97% due to the insertion of the combination of the bamboocell and bamboogrid as compared to the unreinforced clay bed. The bamboo was treated chemically to increase the durability. The performance of the bamboo was reduced by 15-20% after the chemical treatment; still the performance was better than its geosynthetic counterparts. Analytical studies revealed that the 3% of the ultimate tensile strength of the bamboogrid was mobilized while resisting the footing load. The study also explored the new and innovative applications of the geocells to protect underground utilities and buried pipelines. The laboratory model tests and the numerical studies were performed on small diameter PVC pipes, buried in geocell reinforced sand beds. In addition to geocells, the efficacy of only geogrid and geocell with additional basal geogrid cases were also studied. A PVC (Poly Vinyl Chloride) pipe with external diameter 75 mm and thickness 1.4 mm was used in the experiments. The vehicle tire contact pressure was simulated by applying the pressure on the top of the bed with the help of a steel plate. Results suggest that the use of geocells with additional basal geogrid considerably reduces the deformation of the pipe as compared to other types of reinforcements. Further, the depth of placement of pipe was also varied between 1B to 2B (B is the width of loading plate) below the plate in the presence of geocell with additional basal geogrid. More than 50% reduction in the pressure and more than 40% reduction in the strain values were observed in the presence of reinforcements at different depths as compared to the unreinforced beds. Further, experimental results were validated with 3-dimensional numerical studies using 3D FLAC. Good agreement in the measured pipe stain values were observed between the experimental and numerical studies. In addition, the results of the 1-g model tests were scaled up to the prototype case of the shallow buried pipeline below the pavement using the appropriate scaling laws. The efficacy of the geocells was also studied under the action of cyclic loading. The laboratory cyclic plate load tests were performed in soft clay bed by considering the three different cases, namely, unreinforced, geocell reinforced and geocell with additional basal geogrid reinforced. The coefficient of elastic uniform compression (Cu) was evaluated from the cyclic plate load tests for the different cases. The Cu value was found to increase in the presence of geocell reinforcement. The maximum increase in the Cu value was obtained for the case of the clay bed reinforced with the combination of geocell and the geogrid. The results of the laboratory model tests were extrapolated to prototype foundation supporting the low frequency reciprocating machine. The results revealed that, in the presence of the combination of geocell and the geogrid the natural frequency of the foundation-soil system increases by 4 times and the amplitude of the vibration reduces by 92%.