Finite Element Analysis And Analytical Method

Finite Element Analysis And Analytical Method Stone columns are widely used as a ground improvement technique especially in construction of shallow foundations. The main concern in the application of stone columns rely on how well it performs, which involves reducing the overall settlement of the stone column. This project mainly investigates the comparison and contrast between finite element analysis and analytical method in modelling stone columns, whereby settlements of the stone columns are checked whether it is consistent. Finite element analyses were carried out by axisymmetric modelling of the stone column using 15-noded triangular elements with the software package PLAXIS. A drained analysis was conducted using Mohr-Coulombs criterion for soft clay, stones and sand. Analytical data used to compare the settlement was found according to the design method published by Heinz J. Priebe (1995). Both methods were compared by varying parameters such as modulus of deformation of the column to sand ratio, area ratio, stress, diameter, and friction angle of stone column that signifies different soil conditions. It is challenging to find a site with acceptable ground conditions for construction of structures such as buildings, bridges, etc. Often the bearing capacity of the soil would not be sufficient to support the loads of the structures nor would it be in a workable condition for the employees to build the structure. The need for the use of such land with weak cohesive soil strata has been a challenge for design engineers. Although the design of piles foundation can meet all the design necessities, extensive lengths of piles needed eventually results in vast increase of cost of the overall project. Therefore, it is a necessity that the ground conditions must be improved to allow the buildings and heavy construction. A number of ground improvement techniques have been developed over the past fifty years. Main concern of these techniques includes creating stiff reinforcing elements to the soil mass, which results in a soil that has a higher bearing capacity. Out of the various techniques available for ground improvement, the stone column has been widely used. Stone columns (also known as granular columns, granular piles or sand columns) are used to improve soft ground by increasing the load bearing pressure of the soil and reducing settlement of the foundation of structures, embankments, etc. Although these structures are permissible for a relatively large settlement, it is necessary that the settlement be minimized for maximum safety. There have been several ways for installing stone columns depending on the design, local practice and availability of equipment. Among which, the most general methods are the vibro-replacement method and vibro-displacement or vibro-compaction methods. Vibro-replacement technique of stone column is a process whereby large sized columns of compacted coarse aggregates are installed through the weak soil by means of special in-depth vibrators. This can be carried out either with the dry or wet process. In the dry process, a hole of desired depth is drilled down in to the ground by jetting a vibroflot. Upon extraction of the vibroflot, the borehole must be able to stand open. The densification of the soil will be a result of the vibrator near the bottom of the vibroflot. In the wet process, the vibroflot will form a borehole that is of larger diameter than the vibrator and it requires continuous supply of water. As a result the uncased hole is flushed out and filled with granular soil. Th e main difference between wet and dry process is the absence of continuous jetting water during the initial formation of the borehole in the dry process. The performance of the stone columns is not measurable by simple investigations. However, analytically, the efficiency of this composite system that consists of stone column and soil interactions can be assessed by separate consideration of significant parameters as proposed by Priebe (1995) [1]. Stone column technique has proven successful in improving many applications. Such applications include slope stability of both natural slopes and embankments. Construction of such embankments can commence immediately after the installation of stone columns (Vibro Stone Columns, 2009) [2]. Other advantages include increasing bearing capacity of ground, reducing total and differential settlements, reducing the liquefaction potential of sands. The main disadvantage of the stone column technique is its ability to induce bulging failure on the upper part of the stone column. In-situ field tests (cone penetration test and full scale footing test) before construction and after construction of stone columns have shown significant improvements in the soil (J. T. Blackburn, J. K. Cavey, K. C. Wikar, and M. R. Demcsak., 2010) [3]. In a study of the behaviour of stone columns, (Mitchell J.K., and Huber T.K., 1985) [4], by using finite element analysis, had proved that the installation of stone columns leads to a 30-40% reduction in settlement of the values expected that of an untreated ground. 1.2 Objectives The main objective of this project is to show that the analytical method used to design stone columns and the finite element method used to model the stone column numerically, has comparable total and differential settlement. The analysis also provide the understanding of the influence on settlement by varying parameters such as modulus of deformation of the column to sand ratio (Ec/Es), Area ratio (Ac/A), stress à Ã†â€™0, diameter D, and friction angle of stone column ÃŽÂ ¦c, and finally comparing them against the Priebe analytical approach. The objectives of the project are to: study the existing analytical and numerical theories related to stone column modelling develop an axisymmetric simulation of the stone columns by using finite element method, and compare the settlement difference with the analytical results by altering various parameters related to settlement change. This project uses the finite element software package PLAXIS to simulate the stone column numerically and the design method proposed by Heinz J. Priebe (1995) [1] for the analytical results. 1.3 Organization of the research paper In addition to the abstract, list of figures and notation, acknowledgement, and table of contents, this dissertation is divided to six chapters: The first chapter consists of introduction and background of stone columns where it briefly summarizes the installation methods, some of the advantages and disadvantages of the stone columns. The second chapter describes the study of existing analytical and numerical theories regarding modelling stone columns. In this chapter, other than the main findings from the theories, the full procedure of Priebe (1995) method of modelling stone column has been reviewed. Third chapter describes how the stone column was modelled using the PLAXIS software, including the assumptions made and technical data used in different models. The fourth chapter shows the results obtained from the analysis compared to the analytical method proposed by Priebe (1995). The results are presented using necessary graphs and charts. The fifth chapter includes the conclusion of the project and provides recommendations for further studying. The final chapter lists out the references used in this project. The Appendix contains documents such as the Risk Assessment, Diary of the work progress, and the any additional tables and figures of the analysis. CHAPTER TWO 2. LITERATURE REVIEW Many researchers in this field have made their effortless contribution studying the behaviour of stone columns numerically and analytically. Most of the numerical analyses were conducted using finite element analysis, whereas analytical method is derived from a series of equations. Some of the main findings from researchers related to this study are reviewed below. 2.1 Analytical Models 2.1.1 Alamgir, Miura, Poorooshasb, and Madhav, (1996) Alamgir et al. (1995) proposed a simple theoretical approach to evaluate the deformation behaviour of uniformly loaded ground reinforced by columnar inclusions. The displacements of the soil and stone columns are obtained by considering the elastic deformation of both soil and column. A typical column-reinforced ground and column soil unit (Fig. 2.1) where the column is considered to be cylinder, of height H and diameter of dc (=2a where a is the radius) The deformation at a cross section within the column, wcz, is assumed to be constant throughout whereas the deformation of the surrounding soil, wrz, increases from the soil column surface towards the outer boundary of the unit cell (Fig. 2.2). This denotes that since the column soil interface is elastic and no slip occurs, the displacements of the soil and the column at interface can be assumed to be equal. The deformation of the surrounding ground, wrz, is assumed to follow: where wrz is the displacement of the soil element at a depth z and at a radial distance r, wcz is the displacement of the column element at a depth z, ÃŽÂ ±cz and ÃŽÂ ²c are the displacement parameters, a and b are the radii of column and unit cell, respectively, r is the radial distance measured from the center of the column. The column and the surrounding soil were discretized in to a number of elements as shown in Fig. 2.3. The interaction shear stresses and stresses on the column and the soil were obtained by using equilibrium of vertical forces within the medium (Fig. 2.4). Successively the displacement of the column and soil were obtained by solving equations by applying the linear deformation characteristics of the soil. Therefore, the deformation of the jth element of the column, Wcj was obtained as: where à ¢Ã‹â€ Ã¢â‚¬  H is the height of a single element, Es and Ec are the modulus of deformations of soil and column material respectively, vs is the Poissons ratio of the soil, and à Ã†â€™cj is the normal stress acting at the top of the jth element of the column. Due to the symmetry of load and geometry, the shear stress at the outside boundary of the unit cell is zero, which subsequently leads to an equation for ÃŽÂ ²c Furthermore, the compression of the soil element adjacent to the boundary of unit cell (N,jth element of the soil), wsNj was derived as: where à Ã†â€™sNj is the normal stress acting at the top of the element, n is the spacing ratio b/a, à ¢Ã‹â€ Ã¢â‚¬  R is à ¢Ã‹â€ Ã¢â‚¬  r/a and à ¢Ã‹â€ Ã¢â‚¬  r is (b-a)/n. By using the displacement compatibility and substituting r/a=n-à ¢Ã‹â€ Ã¢â‚¬  R/2, Eq. [2.1] can be written as: Finally, solving the equations 2.2, 2.3, 2.4, and 2.5 can lead to the displacement parameter The settlement profiles, the shear stress distribution, and the load sharing from the above mention method was compared against a simple finite element analysis as shown in Fig. 2.5, Fig. 2.6, and Fig. 2.7. It is seen that the results obtained shows a reasonable agreement between the two methods and can be used as a useful method to determine the settlement of the stone columns. 2.1.2 Priebe (1995) Priebe (1995) proposed a design method to assess the behaviour of stone columns that uses an improvement factor which stone columns improve the performance of the subsoil in comparisons to the state without columns. The above statement was best described using the following relationship: According to this improvement factor, the deformation modulus of the composite system is increased respectively settlements are reduced. A unit cell of area A is considered which consists of a single column with the cross section area Ac. Calculation of the improvement factor was done by assuming that: The stone column to be of incompressible material The stone column is installed within a rigid layer The bulk densities of the stone column and soil are also neglected. Hence, according to Priebes approach, column cannot fail in end bearing and any settlement of the load area results in a bulging of the column, which remains constant all over its length. The improvement of a soil achieved by the presence of stone columns is evaluated based on the assumption that the column material shears from the beginning whilst the surrounding soil reacts elastically. Additionally, the coefficient of earth pressure amounts to K=1 by assuming that the soil to be displaced already during the column installation to such a degree that its preliminary resistance corresponds to the liquid state. Using the above criterion the basic improvement factor n0 is expressed as: where = Improvement factor Ac = Area of the stone column A = Grid area of the single unit = Poissons ratio = Coefficient of active earth pressure for the stone column material = Friction angle of the stone column material Since a Poissons ratio of 1/3 is adequate for the state of final settlement in most cases, the results of the evaluation is expressed as basic improvement factor n0 and substituting 1/3 as Poissons ratio, which leads to the following equation. The relation between the improvement factor n0, the area ratio A/Ac and the friction angle of the backfill material is illustrated in figure 2.8 below. The compacted backfill material of the stone column is still compressible. Due to this reason, applied load of any amount will lead to settlements that are unconnected with bulging of the columns. Subsequently, compressibility of the column is integrated by adding up an additional area ratio (A/Ac) as a function of the constrained moduli of the columns and soil Dc/Ds and is provided in the Fig. 2.9. The improvement factor as a result of the consideration of the column compressibility is represented by n1, as shown in the equation: where and Furthermore, for =1/3 can be found using the equation below The additional loads due to the bulk densities of the soil and columns decrease the pressure difference asymptotically and reduce the bulging correspondingly. Subsequently, multiplying the basic improvement factor by a depth factor could incorporate the effect of the bulk density, which is given by: where, fd = Depth factor K0C = Coefficient of earth pressure at rest for stone column material = Bulk density of the soil = Layer thickness Pc = Pressure within the column along the depth Figure 2.10 shows the influence factor y as a function of the Area ratio A/Ac and can be used to approximate the depth factor. The figure considers the same bulk density for the columns and soil, which may not be true in most cases. Therefore as a safety measure, the lower value of the soil should be always considered. Using the above depth factor fd, a more enhanced improvement factor can be defined that considers the effects of the overburden pressure, and therefore is represented by n2 where it can be related by the following equation: The depth factor is limited so that the settlement of the columns resulting from their inherent compressibility does not exceed the settlement of the composite system. This is because as the depth increases, the support by the soil reaches such an extent that the column do not bulge anymore. The first compatibility control where the depth factor is limited is applied when the existing soil is stiff or dense and is given by: The second compatibility control is required since should not be considered even if it may result from the calculation. This second control relates to the maximum value of the improvement factor nmax and is applied when the existing soil is loose or soft. Both compatibility controls can be determined using figure 2.11 below. Finally, the total settlement of a single or a strip footing can be assessed using the above series of equations. The design results from the performance of an unlimited column grid below an unlimited load area. For the unimproved ground, the settlement can be found using the equation: where, sà ¢Ã‹â€ Ã… ¾ = Total settlement p = Pressure exerted by the above structure d = Depth of the stone column Ds = Constrained modulus of the soil Similarly, the total settlement of the improved ground, where the improvement factor is incorporated, can be found by dividing the settlement by n2, which is shown below: This method is one of the most common and well-known method of designing stone columns and has been widely used all over the world because of its simplicity. Moreover, in comparison with the other methods, it shows a much wider behaviour of the stone column by assuming the stone column and surrounding soil as a composite system. 2.2 Numerical Models 2.2.1 A.P. Ambily and Shailesh R. Gandhi (2007) Ambily and Shailesh (2007) studied the behaviour of stone columns by comparing experimental and Finite Element analysis on a single stone column and a group of 7 columns. Laboratory experiments were carried out on a stone column of 100mm diameter surrounded by soft clay in cylindrical tanks of 500mm high with diameter varying from 210 to 420 mm for a single column test and from 210 835 mm for a group of 7 columns. This represents the required unit cell area of soft clay around each stone column. Pressure cells attached to the loading plate were used to measure the stress intensity of the column and the soil as shown in figures 2.12 and 2.13. Furthermore, it is also assumed the stone columns are installed in a triangular pattern. The load deformation behaviour of the column/treated soil was studied by applying vertical load for both cases; column only loading and entire area loading, and observed for equal intervals of settlements until failure occurs. After a series of procedure, the shapes of the tested columns are obtained. It is clearly seen in Fig. 2.14 that bulging mode of failure only occurs in the case of column alone loaded, and not in the case of entire area loaded. Finite Element analysis was conducted using 15-noded triangular elements with the software package PLAXIS, to compare the load-settlement behaviour with the model test and the laboratory experiment. The analysis was carried out using a stone column of diameter 25 mm and 225 mm high, which was made at the center of the clay bed and loaded with a plate of diameter two times the diameter of the stone column. The axisymmetric finite element mesh to represent the single stone column and the group of stone columns are shown in Fig. 2.15 and Fig. 2.16 respectively. Likewise the laboratory experiment, finite element analyses were done for column alone loaded and entire area loaded case for s/d=3. The results of these simulations (Fig. 2.17) shows that failure by bulging occurs in column alone loaded case, which also agrees with the results from laboratory experiment. The comparison of the experimental results and finite element analysis data shows significant consistency in both methods. The comparisons made by A.P. Ambily and Shailesh R. Gandhi include the effect of shear strength, Cu (Fig. 2.18) and the effect of s/d (Fig. 2.19) on the behaviour of stone columns. Additionally, the effect of surcharge on stress settlement behaviour (Fig. 2.20) and effect of s/d and ÃŽÂ ¦ on the stiffness improvement factor (Fig. 2.21) was compared between both methods. These tests have also shown similar behaviour. The stiffness improvement factor (ÃŽÂ ²) was calculated as the ratio of the stiffness of treated and untreated ground, and beyond s/d = 3, it shows no significant improvement. The analysis was extended to study the effect of the angle of internal friction of stones by varying the ÃŽÂ ¦ as 35, 40, 43, and 45o for varying values of s/d ranging from 1.5 4. From the results shown in Fig. 2.22, it is confirmed that this relationship is valid for any shear strength values of surrounding soil. Furthermore, the comparisons between a single column and group of 7 columns were found as in Fig. 2.23. Both experimental and finite element method results reveal comparable behaviour regarding the ultimate load and load deformation relationship. To ensure that this proposed design method agrees with the existing theories, this study was compared with the existing theories as shown in Fig. 2.24 and Fig. 2.25. The result shows a slightly higher stiffness improvement factor (ÃŽÂ ²) for an area ratio more than 4 and a lower value for an area ratio less than 4 compared to Priebe (1995). 2.3 Summary The studies mentioned above show comparable results and have been adopted by many engineers and contractors. However, not many researchers had compared Priebes analytical model with finite element method. Therefore, the finite element analysis carried out in this project will be compared to the design method proposed by Priebe (1995), since it gives a much broader overview of the composite system consisting of the stone column and soil interactions and moreover it is the most common and improved analytical method used by the design engineers around the globe. CHAPTER THREE 3. METHODOLOGY 3.1 Introduction Different methods of modelling stone columns numerically have been implemented in the past. Among those, the most simplest and common type of numerical modelling is using finite element method. In fact, studies have shown that the settlements predicted from the finite element analysis shows comparable results that of the values gained from actual field tests (Kirsch, F. 2009). Numerical calculations are usually complex and most of the time is impossible to conduct without means of dedicated software. Likewise, in this research project, PLAXIS software is used to carry out the finite element analyses. 3.2 PLAXIS software The main computer software used in this investigative project is PLAXIS Professional Version 8.2. PLAXIS is a comprehensive package for finite element analyses for geotechnical applications. It allows simulating the soil behaviour by using soil models. The software employs a graphical user interface that makes it simple to use and also provide the ability to input the necessary parameters such as different soil layers, structural elements, variety of loadings, and boundary conditions through CAD drawing procedures. It allows discretizing the soil component into either 6-noded or 15-noded triangular elements whereby 15-noded triangles provides high stress results for complex problems. The software also allows automatic generation of 2D finite element meshes that can be further refined according to the choice of analysis. In addition to that, the software comes with a very useful feature named Staged Construction. This feature allows the models to be simulated at different stages by ac tivating and deactivating clusters of elements, application of loads, etc. One of the advantages of this software is the ability to generate the results quickly with minimum errors. The output results include values for stresses, strains, settlements, and structural forces together with the plots of different curves such as, load-displacement curve, stress-strain diagrams, and time-settlement curve. 3.3 Finite Element Modelling Finite element analysis was conducted to compare the load-settlement behaviour of the stone column. A two dimensional axisymmetric analysis was carried out since the investigation concerns a single unit of stone column using Mohr-Coulombs criterion for clay and stone column. 15-noded discretization was used for more precise results. The initial vertical stress due to gravity has been considered in this analysis. Similarly, the stress due to column installation, which often depends on the method of construction, is also considered in this analysis. Assumptions made in the finite element modelling: The soil is assumed to be homogenous, infinite and behaves as Mohr-Coulomb model. The ground water table is at the same level as the stone column and clay layer, meaning the stone column and clay layer is submerged in the water. Hence, effect of ground water condition should be taken into account. The base of the clay layer is rigid, i.e., full fixity at the base of the geometry (ux=0, uy=0) and roller conditions at the vertical sides (ux=0, uy=free) boundary conditions are shown in Figure 3.1(a). Assumed that deformation of the column is mainly by radial bulging and no significant shear is possible. Therefore, interface element between stone column and clay has not been used. Mitchell, J. K., and Huber, T. R. (1985) also carried out similar type of finite element analysis without the inclusion of the interface element. 3.4 Geometrical Parameters The dimensions of the PLAXIS model are shown in Figure 3.1(b). H is the height of the column, which varies between 10m, 20m, and 30m. D is the diameter of the stone column, which has a typical value of 1m, in all the models except for the model to check the influence of diameter and spacing. Equivalent diameter De depends on the spacing between stone columns as well as the arrangement pattern of the columns. The value of De was calculated by considering the following Influence Area methods. 3.4.1 Influence Area Methods There are several methods for calculating the equivalent diameter around the stone column, which depends greatly on the spacing, diameter, and pattern of installation of the stone column. Two methods were considered in this investigation. 3.4.1.1 Equivalent Area method The equivalent area method simply equates the area of the grid spacing with that of the cross sectional area of column to find the influence area around the stone column. The following example gives a better understanding of the above statement. Example: Grid spacing of the column = 1.5 X 1.5 meters (square grid) Therefore, Diameter of stone column = Finally, Where, De is the equivalent diameter around the stone column. 3.4.1.2 Unit cell method (Balaam Booker, 1981) Unit cell consists of the column and the surrounding soil within the zone of influence of the column. The unit cell has the same area as the actual domain and its perimeter is shear free and undergoes no lateral displacement. Balaam Booker (1981) relates the diameter of the unit cell to the spacing of the columns as: where, De is the equivalent diameter (for square grid) S is the spacing of the stone column Similarly the different geometrical patterns due to column arrangements are shown in the Figure 3.2. Both methods reviewed above gives relatively similar magnitudes. However, Priebes analytical method concerns more on unit cell area. Hence, for this investigation Equivalent Area method is used to model the influence are in PLAXIS. 3.5 Mesh Refinement Test Mesh generation has a great influence in the accuracy of the model. Generally, the finer the mesh the more accurate the result would be. However, this is not true for every case. Therefore a simple test using PLAXIS was conducted to check the effect of mesh refinement. Initially, mesh generation was set to coarse (around 100 elements), utilized as global coarseness of model. The test was carried out by comparing it with the refined mesh (around 500 elements). Moreover, the mesh is further refined which in PLAXIS is set to very fined (around 1000 elements). The generated meshes are shown in Figure 3.3. followed by the time-displacement graph showing the comparison between coarse, medium, fine and very fine mesh refinements. (Figure 3.4) From the above graph it can be seen that the four curves gives comparable results. However, the coarse, medium, and fine meshes give very similar results compared to the very fine mesh refinement. The objective here was to get the lowest value for the displacement since the improved ground due to the installation of stone column would eventually lead to a reduced settlement. Therefore, the finest mesh refinement gives the most precise result. Even though it takes a substantial amount of time to simulate using the most finest meshing, for this investigation, models had been simulated using the very fine mesh option. 3.6 Input Parameters Varying the soil parameters can alter soil characteristics. Most important outcome by altering these parameters is deformation that leads to settlement. Such parameters that have major impact on settlement includes, material type, spacing of stone columns, diameter of influence area, diameter of stone column, elastic modulus of both column and soil, depth of the soil layer, Poissons ratio for both column material and soil, Unit weights of the materials, cohesion, friction angle, etc. Soil and material properties are shown in Table 3.1. Note that the effective stress cohesion, c of the stone column is given a small nonzero value to avoid numerical complications. The majority of the above parameters are considered for only one type of test model and are varied for different model tests. The varied parameters such as elastic modulus of soil and column, friction angle, spacing between columns and influence area around the stone column are reviewed in the following section. 3.7 Test Models The main objective of this project is comparing both analytical and numerical method using Priebes analytical approach and finite element analysis as numerical solution. This can only be achieved by developing multiple models and simulations to obtain a range of values to compare with, which would lead to a more solid conclusion. Three constitutive models were considered for the representation of the following three cases. A clay layer of 30 m, which has a stone column of height 10 m installed. A clay layer of 30 m, which has a stone column of height 20 m installed. A clay layer of 30 m, which has a stone column of height 30 m installed. Note that 1 and 2 are floating columns that are not extended to bedrock or hard layer, which in stone column installation is a rare case, yet installed occasionally. Each of the above tests was carried out by varying the spacing between columns, which would alter the s/d relationship together with the Ac/A ratio. Further tests were carried out to check the influence of stress à Ã†â€™0, diameter D, modulus of deformation of the column to sand ratio Ec/Es and friction angle of stone column ÃŽÂ ¦c using the third case and compared them against the Priebe analytical approach. The summary of test models is given in the Tables 3.2. All the tests were carried out in 3 stages. Install the stone column: Just after the stone column is installed Apply Load: Just after the load is applied to the column Consolidation: After the consolidation process completed to a minimum pore pressure of 1kPa In the all cases the materials were idealized as the Mohr-Coulomb model with the characteristic linear-elastic-perfectly plastic behaviour and the failure criteria defined by the strength parameters given in tables below. Table 3.2 Summary of Model tests Model Test Description Constants Variables 1 Influence of column height on settlement (case 1, 2, and 3) à Ã†â€™0 = 100 kPa Ac/A = 0.2 ÃŽÂ ¦c = 40o Ec/Es = 20 Heigh

Othello: Religious Motifs Essay

Othello: Religious Motifs BY Cherrry678 Relationships in which people allow themselves to be manipulated through their weaknesses are truly flawed and have a great potential for failure. These relationships can become tainted by Jealousy and rumours nurtured by deceitful individuals. Such is the situation in Shakespeare’s Othello, which depicts the tragic downfall of an apparently perfect relationship. Shakespeare uses images of heaven in the beginning of the play to emphasize the seemingly flawless love between Othello and Desdemona. Furthermore, as the play progresses, the Juxtaposition etween heaven and hell is used to represent the manipulative powers of Iago over Othello revealing the weaknesses of Desdemona and Othello’s relationship. As a result, the twisted heaven and hell imagery used near the end of Othello reflects the eventual break down of Othello and Desdemona’s marriage. Thus, in Shakespeare’s Othello, the connotation of the religious motifs throughout are used to develop the idea that even the most loving couples have their flaws leaving them vulnerable to the destructive powers of Jealousy brought on by the manipulative influences of others, resulting in suspicion and ultimately betrayal. The seemingly perfect love between Othello and Desdemona is initially emphasized by Shakespeare’s use of heavenly images. Through images of heaven, Othello’s passionate love for Desdemona is revealed. After being accused by Brabantio of using enchantments to win over his daughter’s love, Othello swears against it assuring their love is true: And till she come, as truly as to heaven I do confess the vices of my blood, So Justly to your grave ears I’ll present How did I thrive in this fair ladys love, And she in mine (1. 3. 122-126). Othello swears on heaven that his love for Desdemona and her love for him is not a esult of witchcraft, but the result of an honest love for one another. The image of heaven is used to emphasize that Othello believes that the love between him and Desdemona is as pure as heaven itself. To call their love heavenly shows an exaggerated passion between the two further emphasizing the appearance of their perfect union. Similarly, Desdemona feels that the love between her and Othello is destined to be, and through Shakespeare’s use of divine imagery this point is emphasized. Upon arriving in Cyprus, Desdemona and Othello are reunited for the first time since their Journey: â€Å"The heavens forbid/ But that our loves and comforts hould increase/ Even as our days do grow†(2. 1. 190-192). For Desdemona to pray that nothing come between them and their eternal happiness shows a great deal of passion. Furthermore, to believe that their love will only die if they die highlights the certainty in which Desdemona feels that their love is more than Just a coincidence, but rather fate itself. The intensity of Desdemona’s feelings for Othello adds to the idea that their marriage is ideal. Moreover, images of the soul illustrate Desdemona’s love and her willingness to risk her entire being to be with Othello. When confronted bout her love for Othello, Desdemona reveals that [her] heart’s subdued/ Even to the very quality of [her] lord. [She] saw Othello’s visage in his mind, Did [she her] soul and fortunes consecrate (1. . 250-254). â€Å"From the beginning, Desdemona has viewed love as a risk and challenge. She has violently uprooted herself from her father’s protection and the conventional expectations of Venetian society†¦ â€Å"(Thomas Neely 96). Desdemona believes that a life full of risks and unknown dangers is worth living if she is by Othe llo’s side. This complete devotion of body and soul reveals Desdemona’s feelings of loyalty towards Othello. The rendering of her soul; her whole entire being, wholly to Othello emphasizes the impeccable love between the two of them. Thus, through heavenly images the apparently perfect union between Desdemona and Othello is portrayed throughout the first scenes of the play. Despite the apparent perfect relationship between Othello and Desdemona, the flaws within their marriage are revealed through lagds manipulative powers as illustrated by the Juxtaposition of heaven and hell. Shakespeare uses lagds character to bring about the doubt in Othello and Desdemona’s perfect heavenly love through mages of hell. During his first soliloquy, part of lagds plan is revealed: â€Å"l have’t! It is engender’d! Hell and night/ Must bring this monstrous birth to the world’s light†(l . . 392-393). Desdemona and Othello’s relationship is represented as the good in the world; the light. For their relationship is that of perfection, they both love and trust each other with a deep passion. However, Iago is the opposite of this heavenly light and with him comes hell and corruption. When the c haracters meet, the sense of perfection is lost and human faults come into play. Furthermore, the Juxtaposition f heaven and hell illustrates that Iago is the tempter in Othello and Desdemona’s relationship. After giving Cassio advice on how to approach Othello regarding his job, Iago reveals his true plan: Divinity of hell! When devils will the blackest sins put on, They do suggest at first with heavenly shows, AS I do now (2. 3. 321-324). By comparing himself to a devil that appears innocent, Iago is revealing his ability to deceive those around him with a fapde of kindness. â€Å"To interpret Iago as a devil in turn implies Iago is more than that: a fiend whose fiendishness remains unproven in [the] play†¦ (Christofides 19). Furthermore, the contrast of the heaven and hell further highlights the Machiavellian nature of Iago that allows him to manipulate those around him without feeling remorse. Consequently, Iago tricks Othello into believing he is an honest man, thus, giving him the ability to manipulate Othello. Moreover, there is a lack of trust between Othello and Desdemona which is made evident through comparisons to the devil. Clearly, Othello is suspicious of something when he accuses Desdemona’s hand of being â€Å"hot, hot, and moist† and require[ing] a sequester from liberty, fasting and prayer, uch castigation, exercise devout; For here’s a young and sweating devil here that commonly rebels (3. 4. 34-39). By accusing Desdemona of having a moist hand, a symbol of amorous nature, he is accusing her of being unfaithful. Othello believes that Desdemona is a devil who needs to repent for the crimes she has committed against him. However, Othello has no proof that she has done any harm; he is simply accusing her based on lies told to absence of trust within their marriage. As a result, perverse images of heaven are used to show that lagds trickery has caused Othello to give up on those he loves. While Iago fills Othello’s head with lies of Desdemona and Cassio together, Othello comes to the conclusion that â€Å"†¦ is true†¦. [and] [a]ll [Othellds] fond love thus doles] [he] blow to heaven. ‘ ‘Tis gone†(3. 3. 444-446). By believing what Iago says to be the truth in such a brash manner, a lack of confidence in Othello is revealed. This lack of confidence causes Othello to doubt other aspects of his life such as his relationship with Desdemona allowing Iago to further manipulate Othello. Therefore, Iago has the power to make Othello believe that Desdemona is being unfaithful to him thus, ausing Othello to lose all hope in his marriage. This loss of love is reflected through Othello’s loss of religion. Therefore, lagds manipulative influences expose the true weaknesses within Othello and Desdemona’s relationship which is reflected through contrasting images of the divine and damned. Furthermore, due to their marriage’s weaknesses, the eventual breakdown of Othello and Desdemona’s relationship is reflected through twisted heaven and hell imagery. Through the ironic use of divine images it is shown that when he is overcome by Jealousy, Othello’s sense of Justice becomes twisted. When confronted by Emilia, Othello gives reason as to why he killed Desdemona: Cassio did top her. Ask they husband else. O, I were damn’d beneath all depth in hell But what I did proceed upon Just grounds -ro this extremity (5. 2. 136-139). Othello’s sense of morality is corrupted; he believes that he is Justified in killing Desdemona because of her betrayal. â€Å"Here, Othello Judges on behalf of God†¦ but, of course, the audience knows Desdemona has been misjudged, that the sword of justice should rightly 21) for Desdemona is innocent. Othello has been tricked by Iago into believing that he has the authority to choose what is right nd wrong. He then uses this authority misguidedly, resulting in the breakdown of his character and eventually his relationship with Desdemona. Additionally, the ironic reference to damnation further depicts Just how twisted his morality is; for he believes that what he did was truly Just. Moreover, Shakespeare illustrates the contrast between Othello’s assumed morality and his true crime by once more using images of heaven and hell. After Desdemona is dead, her virtuous nature is compared to Othello’s: â€Å"O, the more angel she,] And you the blacker devil! â€Å"(5. 2. 130-131). Othello lacks confidence within himself due to his differences, hich is emphasized through the use of a racial comment. However, these differences had meant nothing in the beginning, for the love between him and Desdemona was too strong. Consequently, Othello lets these differences get to him allowing Iago to manipulate him into losing the morality and honour he first possessed, reducing him to evil; a devil in comparison to Desdemona. Resulting in the further breakdown of Othello and Desdemona’s relationship. Ultimately, as a result of distrust and Jealousy Othello betrays Desdemona, as is depicted through the use of religious images. Emilia reveals to Othello the true tragedy of his crime: â€Å"This deed of thine is no more worthy heaven/ Than thou wast worthy her†(5. 2. 160-161). Othello so overcome by Jealousy and anger is no longer associated with heavenly his entire marriage to Desdemona and ultimately leading to his betrayal of her. However, since Desdemona is still associated with heavenly images, it emphasizes her loyalty which in contrast further underlines Othello’s flaws and the tragedy of his betrayal. Thus, through twisted images of heaven and hell Othello’s betrayal of Desdemona and its consequential ruin of their relationship is portrayed. The shift from positive to negative connotation of the religious motif throughout Othello is used to develop the idea that even the most loving couples can have their flaws manipulated by others allowing them to be overcome by Jealousy, resulting in a lack of trust and ultimately betrayal. In the beginning, heavenly images are used to illustrate an almost perfect love between Othello and Desdemona. Later, near the middle of Othello, the playwright uses contrasting images of heaven and hell to represent lagds manipulative powers over Othello revealing the flaws within Othello nd Desdemona’s relationship. Thus, the ironic use of heaven and hell imagery near the end of the play mirrors the tragic breakdown of Othello and Desdemona’s marriage. Since relationships are not perfect they can become easily tainted when left to the deceitful will of others. For when people allow their weaknesses to rule over their lives true tragedy ensues. It is up to those individuals to decide whether or not to let the lies brought about by others to affect them or not. This is the decision that ultimately determines the strength of a relationship, not the number of flaws within it.

Business Plan For A Business - 1223 Words

An important first step when starting your own business is to prepare a business plan. A business plan is a written document describing your business future. It tells potential investors and customers what your goals are for the company and how you plan to achieve that. You will need to define your business, products and services, operating procedures and the route your company intends to take to achieve the goals that are set forth. This information summarizes the sense of your business in a single document. Business plans are inherently strategic because it shows that you’ve thought about every detail and challenge that comes with starting a business in California. You can show people that you have a roadmap for how you will start the business and have it continuously move forward. A well thought out plan is also extremely helpful if your company needs funding from loans or venture capitalists. Below are a few tips on what to include in a good business plan! Executive Summary/Mission Statement Within the overall outline of the business plan, the executive summary will follow the title page. Your executive summary is a snapshot of your business plan as a whole and touches on your company profile and goals. It briefly tells the reader where your company currently is, where you want to take it and how, and why your business ideal is exceptionally qualified to succeed, especially if you are in a highly competitive market. Although this section will appear first in yourShow MoreRelatedBusiness Plan For A Business998 Words   |  4 PagesIntroduction Prior to initiating a business, it is necessary for the management and the people involved to make sure that a proper business plan is set out in order to understand the needs of the business. In addition to this, it should also be made sure that the market is properly analysed and all the competitors are studied before taking any step related to the new business. 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Review current menu in terms of business focus 2. Get staff feedback 3. Get customer feedback 4. Point out restaurant goals and business 5. Write menu redesigning proposal 6. Get restaurant owners approval 7. Initiate stake holder support 8. Get stake holders approval and contribution 9. Redesign new menu 10. Trail with restaurant stake holders 11. Modify the trail menu 12. Mass print the modified RESOURCES 1. Restaurant business plan, current menu, current and historical sales report

How to Get Into an Ivy League School

If you are hoping to attend one of the Ivy League schools, youre going to need more than good grades. Seven of the eight Ivies have made the list of the most selective colleges in the country, and acceptance rates range from 6% for Harvard University to 15% for Cornell University. Applicants who are admitted have earned excellent grades in challenging classes, demonstrated meaningful involvement in extracurricular activities, revealed leadership skills, and crafted winning essays. All Ivy League schools should be considered reach schools. A successful Ivy League application is not the result of a little effort at application time. It is the culmination of years of hard work. The tips and strategies below can help make sure your Ivy League application is as strong as possible. Develop the Foundation for Ivy League Success Early The Ivy League universities (and all universities for that matter) will consider your accomplishments in 9th through 12th grades only. The admissions folks will not be interested in that literary award you got in 7th grade or the fact that you were on the varsity track team in 8th grade. That said, successful Ivy League applicants build the foundation for an impressive high school record long before high school. On the academic front, if you can get into an accelerated math track while in middle school, this will set you up to complete calculus before you graduate from high school. Also, start a foreign language as early as possible in your school district, and stick with it. This will put you on track to take an Advanced Placement language class in high school, or to take a dual enrollment language class through a local college. Strength in a foreign language  and completing math through calculus  are both important features of the majority of winning Ivy League applications. You can get admitted without these accomplishments, but your chances will be diminished. Its not too early to begin college preparation in middle school — this can help you understand the numerous ways in which a strong middle school strategy can help set you up for Ivy League success. When it comes to extracurricular activities in middle school, use them to find your passion so that you begin ninth grade with focus and determination. If you discover in middle school that drama, not soccer, is what you truly want to be doing in your after school hours, great. Youre now in a position to develop depth and demonstrate leadership on the drama front when youre in high school. This is hard to do if you discover your love of theater in your junior year.   Craft Your High School Curriculum Thoughtfully The most important piece of your Ivy League application is your high school transcript. In general,  youll need to take the most challenging classes available to you if you are going to convince the admissions folks that you are prepared to succeed in your college coursework. If you have a choice between AP Calculus or business statistics, take AP Calculus. If Calculus BC is an option for you, it will be more impressive than Calculus AB. If you are debating whether or not you should take a foreign language in your senior year, do so (this advice assumes that you feel you are capable of succeeding in these courses). You should also be realistic on the academic front. The Ivies dont, in fact, expect you to take seven AP courses in your junior year, and trying to do too much is likely to backfire by causing burn out and/or low grades. Focus on core academic areas — English, math, science, language — and make sure you excel in these areas. Courses such as AP Psychology, AP Statistics, or AP Music Theory are fine if your school offers them, but they dont carry the same weight as AP Literature and AB Biology.   Also, keep in mind that the Ivies recognize that some students have more academic opportunities than others. Only a small fraction of high schools offer a challenging International Baccalaureate (IB) curriculum. Only larger, well-funded high schools can offer a wide breadth of Advanced Placement courses. Not all high schools make it easy to take dual enrollment courses at a local college. If youre from a small rural school without many academic opportunities, the admissions officers at the Ivy League schools take your situation into consideration, and measures such as your SAT/ACT scores and letters of recommendation will be even more important for evaluating your college readiness. Earn High Grades You are likely wondering which is more important: high grades or challenging courses?  The reality for Ivy League admissions is that you need both. The Ivies will be looking for lots of A grades in the most challenging courses available to you. Also, keep in mind that the applicant pool for all of the Ivy League schools is so strong that the admissions offices are often not interested in weighted GPAs. Weighted GPAs play an important and legitimate role in determining your class rank, but the reality is that when  admissions committees are comparing students from around the world, they will consider whether or not that A in AP World History is a true A or if it is B that was weighted up to an A. Realize that you dont need straight A grades to get into the Ivy League, but every B on your transcript is lessening your chance  of admission. Most successful Ivy League applicants have unweighted GPAs that are up in the 3.7 range or higher (3.9 or 4.0 is more common).   The pressure to earn straight A grades can sometimes cause applicants to make bad decisions when applying to highly competitive colleges. You should not  write a supplemental essay explaining why you got a B in one course in your sophomore year. There are, however, a few situations in which you should explain a bad grade. Also, keep in mind that some students with less-than-stellar grades get admitted. This can be because they have an exceptional talent, come from a school or country with different grading standards, or have legitimate circumstances that made earning A grades extremely challenging. Focus on Depth and Achievement in Your Extracurricular Activities There are hundreds of endeavors that count as extracurricular activities, and the reality is that any of them can make your application shine if you have demonstrated true depth and passion in your chosen activity. In general, think of extracurriculars in terms of depth, not breadth. A student who acts a minor role in a play one year, plays JV tennis one spring, joins yearbook another year, and then joins Academic All-Stars senior year is going to look like a dabbler with no clear passion or area of expertise (these activities are all good things, but they dont make for a winning combination on an Ivy League application). On the flip side, consider a student who plays euphonium in County Band in 9th grade, Area All-State in 10th grade, All-State in 11th grade, and who also played in the school symphonic band, concert band, marching band, and pep band for all four years of high school. This is a student who clearly loves playing her instrument and will bring that interest and passion to the campus community.   Show That You Are a Good Community Member The admissions folks are looking for students to join their community, so they clearly want to enroll students who care about the community. One way to demonstrate this is through community service. Realize, however, that there is no magic number here — an applicant with 1,000 hours of community service may not have an advantage over a student with 300 hours. Instead, make sure you are doing community service that is meaningful to you and that truly makes a difference in your community. You may even want to write one of your supplemental essays about one of your service projects. Earn High SAT or ACT Scores None of the Ivy League schools are test-optional, and SAT and ACT scores still carry a bit of weight in the admissions process. Because the Ivies draw from such a diverse pool of students from around the world, standardized tests truly are one of the few tools the schools can use to compare students. That said, the admissions folks do recognize that financially advantaged students have an advantage with the SAT and ACT, and that one thing these tests tend to predict is a familys income. To get a sense of what SAT and/or ACT scores youre going to need to get into an Ivy League school, check out these graphs of GPA, SAT and ACT data for students who were accepted, waitlisted, and rejected: BrownColumbiaCornellDartmouth Harvard Penn PrincetonYale The numbers are rather sobering: the great majority of admitted students are scoring in the top one or two percentiles on the SAT or ACT. At the same time, youll see that there are some outlying data points, and a few students do get in with less-than-ideal scores. Write a Winning Personal Statement Chances are youre applying to the Ivy League using the Common Application, so youll have five options for your personal statement. Its a good idea to research your Common Application essay options, and understand that your essay is extremely crucial. An essay that is riddled with errors or focuses on a trivial or clichà © topic could land your application in the rejection pile. At the same time, realize that your essay doesnt need to focus on something extraordinary. You dont need to have solved global warming or saved a bus full of 1st-graders to have an effective focus for your essay. More important than what you write about is that you focus on something important to you and that your essay is thoughtful and self-reflective.   Put Significant Effort Into Your Supplemental Essays All of the Ivy League schools require school-specific supplemental essays in addition to the main Common Application essay. Dont underestimate the importance of these essays. For one, these supplemental essays, much more than the common essay, demonstrate why you are interested in a specific Ivy League school. The admissions officers at Yale, for example, arent just looking for strong students. They are looking for strong students who are truly passionate about Yale and have specific reasons for wanting to attend Yale. If your supplemental essay responses are generic and could be used for multiple schools, you havent approached the challenge effectively. Do your research and be specific. The supplemental essays are one of the best tools for demonstrating your interest in a specific university.   Ace Your Ivy League Interview Youre likely to interview with an alum of the Ivy League school to which you are applying. In truth, the interview isnt the most important part of your application, but it can make a difference. If you stumble to answer questions about your interests and your reasons for applying, this can certainly damage your application. Youll also want to make sure that you are polite and personable during your interview. In general, Ivy League interviews are friendly exchanges, and your interviewer wants to see you do well. A little preparation, however, can help. Be sure to think about the most common interview questions, and work to avoid typical interview mistakes. Apply Early Action or Early Decision Harvard, Princeton, and Yale all have a single-choice early action program. Brown, Columbia, Cornell, Dartmouth, and Penn have early decision programs. All of these programs allow you to apply to just a single school through the early program. Early decision has additional restrictions in that if you are admitted, you are obligated to attend. You should not  apply early decision if you are not 100% positive that a specific Ivy League school is your top choice. With early action, however, its fine to apply early if theres a chance you will later change your mind. If youre on target for Ivy League admission (grades, SAT/ACT, interview, essays, extracurriculars), applying early is the best tool you have for improving your chances significantly. According to early and regular admit rates for the Ivy League schools, you are four times more likely to get into Harvard by applying early than applying with the regular applicant pool. Factors That You Cant Control If you start early and prepare accordingly, there are many aspects of the application process you can work to your favor. There are, however, a couple factors in the Ivy League admissions process that are outside of your control. Its great if these factors work in your favor, but if they dont, dont fret — the majority of accepted students do  not  have these advantages. First is legacy status. If you have a parent or sibling who attended the Ivy League school to which you are applying, this can work to your advantage. Colleges tend to like legacies for a couple reasons: they will be familiar with the school and are likely to accept an offer of admission (this helps with the universitys yield); also, family loyalty can be an important factor when it comes to alumni donations. You also cant control how you fit into the universitys efforts to enroll a diverse class of students. Other factors being equal, an applicant from Montana or Nepal is going to have an advantage over an applicant from New Jersey. Similarly, a strong student from an under-represented group will have an advantage over a student from a majority group. This may seem unfair, and its certainly an issue that has been debated in the courts, but most selective private universities operate under the idea that the undergraduate experience is enriched significantly when the students come from a wide range of geographical, ethnic, religious, and philosophical backgrounds. A Final Word Before you embark on the application process, Ivy League applicants should ask themselves, Why the Ivy League? Perhaps not surprisingly, many times the answer is often far from satisfactory: family pressure, peer pressure, or just the prestige factor. Keep in mind that there is nothing magical about the eight Ivy League schools. Of the thousands of colleges in the world, the one that best matches your personality, academic interests, and professional aspirations is very likely  not  one of the eight Ivies.   Every year youll see the news headlines heralding that one student who got into all eight Ivies. The news channels love to celebrate these students, and the accomplishment is certainly impressive. At the same time, a student who would thrive in the bustling urban environment of Columbia would probably not enjoy the rural location of Cornell. The Ivies are remarkably different, and all eight are not going to be a great match for a single applicant. Also keep in mind that there are hundreds of colleges that deliver exceptional educations (in many cases better undergraduate educations) than the Ivies, and many of these schools will be much more accessible. They may also be more affordable since the Ivies do not offer any merit-based financial aid (although they do have excellent need-based aid).   In short, make sure you truly do have good reasons for wanting to attend an Ivy League school, and recognize that failure to get into one is not failure: you are likely to thrive at the college you do choose to attend.