# Comparison Between Finite Element Analysis And Analytical Method Engineering Essay

Stone columns are widely used as a land betterment technique particularly in building of shallow foundations. The chief concern in the application of rock columns rely on how good it performs, which involves cut downing the overall colony of the rock column.

This undertaking chiefly investigates the comparing and contrast between finite component analysis and analytical method in patterning rock columns, whereby colonies of the rock columns are checked whether it is consistent. Finite element analyses were carried out by axisymmetric modeling of the rock column utilizing 15-noded triangular elements with the package bundle PLAXIS. A drained analysis was conducted utilizing Mohr-Coulomb ‘s standard for soft clay, rocks and sand. Analytical informations used to compare the colony was found harmonizing to the design method published by Heinz J. Priebe ( 1995 ) . Both methods were compared by changing parametric quantities such as modulus of distortion of the column to sand ratio, country ratio, emphasis, diameter, and clash angle of rock column that signifies different dirt conditions.

It is disputing to happen a site with acceptable land conditions for building of constructions such as edifices, Bridgess, etc. Often the bearing capacity of the dirt would non be sufficient to back up the tonss of the constructions nor would it be in a feasible status for the employees to construct the construction. The demand for the usage of such land with weak cohesive dirt strata has been a challenge for design applied scientists. Although the design of hemorrhoids foundation can run into all the design necessities, extended lengths of hemorrhoids needed finally consequences in huge addition of cost of the overall undertaking. Therefore, it is a necessity that the land conditions must be improved to let the edifices and heavy building.

A figure of land betterment techniques have been developed over the past 50 old ages. Main concern of these techniques includes making stiff reenforcing elements to the dirt mass, which consequences in a dirt that has a higher bearing capacity. Out of the assorted techniques available for land betterment, the rock column has been widely used.

Stone columns ( besides known as farinaceous columns, farinaceous hemorrhoids or sand columns ) are used to better soft land by increasing the burden bearing force per unit area of the dirt and cut downing colony of the foundation of constructions, embankments, etc. Although these constructions are allowable for a comparatively big colony, it is necessary that the colony be minimized for maximal safety.

There have been several ways for put ining rock columns depending on the design, local pattern and handiness of equipment. Among which, the most general methods are the vibro-replacement method and vibro-displacement or vibro-compaction methods. Vibro-replacement technique of rock column is a procedure whereby big sized columns of compacted coarse sums are installed through the weak dirt by agencies of particular in-depth vibrators. This can be carried out either with the prohibitionist or wet procedure. In the dry procedure, a hole of coveted deepness is drilled down in to the land by gushing a vibroflot. Upon extraction of the vibroflot, the borehole must be able to stand unfastened. The compaction of the dirt will be a consequence of the vibrator near the underside of the vibroflot. In the moisture procedure, the vibroflot will organize a borehole that is of larger diameter than the vibrator and it requires uninterrupted supply of H2O. As a consequence the uncased hole is flushed out and filled with farinaceous dirt. The chief difference between moisture and dry procedure is the absence of uninterrupted gushing H2O during the initial formation of the borehole in the dry procedure.

The public presentation of the rock columns is non mensurable by simple probes. However, analytically, the efficiency of this composite system that consists of rock column and dirt interactions can be assessed by separate consideration of important parametric quantities as proposed by Priebe ( 1995 ) [ 1 ] .

Stone column technique has proven successful in bettering many applications. Such applications include slope stableness of both natural inclines and embankments. Construction of such embankments can get down instantly after the installing of rock columns ( Vibro Stone Columns, 2009 ) [ 2 ] . Other advantages include increasing bearing capacity of land, cut downing entire and differential colonies, cut downing the liquefaction potency of littorals. The chief disadvantage of the rock column technique is its ability to bring on convex failure on the upper portion of the rock column.

In-situ field trials ( cone incursion trial and full graduated table picking trial ) before building and after building of rock columns have shown important betterments in the dirt ( J. T. Blackburn, J. K. Cavey, K. C. Wikar, and M. R. Demcsak. , 2010 ) [ 3 ] . In a survey of the behavior of rock columns, ( Mitchell J.K. , and Huber T.K. , 1985 ) [ 4 ] , by utilizing finite component analysis, had proved that the installing of rock columns leads to a 30-40 % decrease in colony of the values expected that of an untreated land.

## 1.2 Aims

The chief aim of this undertaking is to demo that the analytical method used to plan rock columns and the finite component method used to pattern the rock column numerically, has comparable sum and differential colony. The analysis besides provide the apprehension of the influence on colony by changing parametric quantities such as modulus of distortion of the column to sand ratio ( Ec/Es ) , Area ratio ( Ac/A ) , stress I?0, diameter D, and clash angle of rock column I¦’c, and eventually comparing them against the Priebe analytical attack.

The aims of the undertaking are to:

analyze the bing analytical and numerical theories related to lapidate column patterning

develop an axisymmetric simulation of the rock columns by utilizing finite component method, and

compare the colony difference with the analytical consequences by changing assorted parametric quantities related to colony alteration.

This undertaking uses the finite component package bundle PLAXIS to imitate the rock column numerically and the design method proposed by Heinz J. Priebe ( 1995 ) [ 1 ] for the analytical consequences.

## 1.3 Organization of the research paper

In add-on to the abstract, list of figures and notation, recognition, and tabular array of contents, this thesis is divided to six chapters:

The first chapter consists of debut and background of rock columns where it briefly summarizes the installing methods, some of the advantages and disadvantages of the rock columns.

The 2nd chapter describes the survey of bing analytical and numerical theories sing patterning rock columns. In this chapter, other than the chief findings from the theories, the full process of Priebe ( 1995 ) method of patterning rock column has been reviewed.

Third chapter describes how the rock column was modelled utilizing the PLAXIS package, including the premises made and proficient informations used in different theoretical accounts.

The 4th chapter shows the consequences obtained from the analysis compared to the analytical method proposed by Priebe ( 1995 ) . The consequences are presented utilizing necessary graphs and charts.

The 5th chapter includes the decision of the undertaking and provides recommendations for farther perusal.

The concluding chapter lists out the mentions used in this undertaking.

The Appendix contains paperss such as the Risk Assessment, Diary of the work advancement, and the any extra tabular arraies and figures of the analysis.

## Chapter TWO

## 2. LITERATURE REVIEW

Many research workers in this field have made their effortless part analyzing the behavior of rock columns numerically and analytically. Most of the numerical analyses were conducted utilizing finite component analysis, whereas analytical method is derived from a series of equations. Some of the chief findings from research workers related to this survey are reviewed below.

## 2.1 Analytic Models

## 2.1.1 Alamgir, Miura, Poorooshasb, and Madhav, ( 1996 )

Alamgir et Al. ( 1995 ) proposed a simple theoretical attack to measure the distortion behavior of uniformly loaded land reinforced by columnar inclusions. The supplantings of the dirt and rock columns are obtained by sing the elastic distortion of both dirt and column. A typical column-reinforced land and column dirt unit ( Fig. 2.1 ) where the column is considered to be cylinder, of height H and diameter of District of Columbia ( =2a where a is the radius )

The distortion at a cross subdivision within the column, wcz, is assumed to be changeless throughout whereas the distortion of the environing dirt, wrz, increases from the dirt column surface towards the outer boundary of the unit cell ( Fig. 2.2 ) . This denotes that since the column dirt interface is elastic and no faux pas occurs, the supplantings of the dirt and the column at interface can be assumed to be equal. The distortion of the environing land, wrz, is assumed to follow:

where wrz is the supplanting of the dirt component at a deepness omega and at a radial distance R, wcz is the supplanting of the column component at a deepness omega, I±cz and I?c are the supplanting parametric quantities, a and B are the radii of column and unit cell, severally, R is the radial distance measured from the centre of the column.

The column and the environing dirt were discretized in to a figure of elements as shown in Fig. 2.3. The interaction shear emphasiss and emphasiss on the column and the dirt were obtained by utilizing equilibrium of perpendicular forces within the medium ( Fig. 2.4 ) .

Successively the supplanting of the column and dirt were obtained by work outing equations by using the additive distortion features of the dirt. Therefore, the distortion of the jth component of the column, Wcj was obtained as:

where a?†H is the tallness of a individual component, Es and Ec are the modulus of distortions of dirt and column stuff severally, V is the Poisson ‘s ratio of the dirt, and I?cj is the normal emphasis moving at the top of the jth component of the column.

Due to the symmetricalness of burden and geometry, the shear emphasis at the outside boundary of the unit cell is zero, which later leads to an equation for I?c

Furthermore, the compaction of the dirt component adjacent to the boundary of unit cell ( N, jth component of the dirt ) , wsNj was derived as:

where I?sNj is the normal emphasis moving at the top of the component, N is the spacing ratio b/a, a?†R is a?†r/a and a?†r is ( b-a ) /n.

By utilizing the supplanting compatibility and replacing r/a=n-a?†R/2, Eq. [ 2.1 ] can be written as:

Finally, work outing the equations 2.2, 2.3, 2.4, and 2.5 can take to the supplanting parametric quantity

The colony profiles, the shear emphasis distribution, and the burden sharing from the above reference method was compared against a simple finite component analysis as shown in Fig. 2.5, Fig. 2.6, and Fig. 2.7. It is seen that the consequences obtained shows a sensible understanding between the two methods and can be used as a utile method to find the colony of the rock columns.

## 2.1.2 Priebe ( 1995 )

Priebe ( 1995 ) proposed a design method to measure the behavior of rock columns that uses an betterment factor which rock columns better the public presentation of the undersoil in comparings to the province without columns. The above statement was best described utilizing the undermentioned relationship:

Harmonizing to this betterment factor, the distortion modulus of the composite system is increased severally colonies are reduced.

A unit cell of country A is considered which consists of a individual column with the cross subdivision country Ac. Calculation of the betterment factor was done by presuming that:

The rock column to be of incompressible stuff

The rock column is installed within a stiff bed

The majority densenesss of the rock column and dirt are besides neglected.

Hence, harmonizing to Priebe ‘s attack, column can non neglect in terminal bearing and any colony of the load country consequences in a bulging of the column, which remains changeless all over its length.

The betterment of a dirt achieved by the presence of rock columns is evaluated based on the premise that the column stuff shears from the beginning whilst the environing dirt reacts elastically. Additionally, the coefficient of earth force per unit area sums to K=1 by presuming that the dirt to be displaced already during the column installing to such a grade that its preliminary opposition corresponds to the liquid province. Using the above standard the basic betterment factor n0 is expressed as:

where

= Improvement factor

Ac = Area of the rock column

A = Grid country of the individual unit

= Poisson ‘s ratio

= Coefficient of active Earth force per unit area for the rock column stuff

= Friction angle of the rock column stuff

Since a Poisson ‘s ratio of 1/3 is equal for the province of concluding colony in most instances, the consequences of the rating is expressed as basic betterment factor n0 and replacing 1/3 as Poisson ‘s ratio, which leads to the undermentioned equation.

The relation between the betterment factor n0, the country ratio A/Ac and the clash angle of the backfill stuff is illustrated in figure 2.8 below.

The compacted backfill stuff of the rock column is still compressible. Due to this ground, applied burden of any sum will take to colonies that are unconnected with bulging of the columns. Subsequently, squeezability of the column is integrated by adding up an extra country ratio ( A/Ac ) as a map of the forced moduli of the columns and dirt Dc/Ds and is provided in the Fig. 2.9.

The betterment factor as a consequence of the consideration of the column squeezability is represented by n1, as shown in the equation:

where

and

Furthermore, for =1/3 can be found utilizing the equation below

The extra tonss due to the majority densenesss of the dirt and columns decrease the force per unit area difference asymptotically and cut down the bulging correspondingly. Subsequently, multiplying the basic betterment factor by a deepness factor could integrate the consequence of the majority denseness, which is given by:

where,

fd = Depth factor

K0C = Coefficient of earth force per unit area at remainder for rock column stuff

= Bulk denseness of the dirt

= Layer thickness

Personal computer = Pressure within the column along the deepness

Figure 2.10 shows the influence factor Y as a map of the Area ratio A/Ac and can be used to come close the deepness factor. The figure considers the same majority denseness for the columns and dirt, which may non be true in most instances. Therefore as a safety step, the lower value of the dirt should be ever considered.

Using the above deepness factor fd, a more enhanced betterment factor can be defined that considers the effects of the overburden force per unit area, and hence is represented by n2 where it can be related by the undermentioned equation:

The deepness factor is limited so that the colony of the columns ensuing from their built-in squeezability does non transcend the colony of the composite system. This is because as the deepness additions, the support by the dirt reaches such an extent that the column do non pouch any longer. The first compatibility control where the deepness factor is limited is applied when the bing dirt is stiff or dense and is given by:

The 2nd compatibility control is required since should non be considered even if it may ensue from the computation. This 2nd control relates to the maximal value of the betterment factor nmax and is applied when the bing dirt is loose or soft.

Both compatibility controls can be determined utilizing figure 2.11 below.

Finally, the entire colony of a individual or a strip terms can be assessed utilizing the above series of equations. The design consequences from the public presentation of an limitless column grid below an limitless burden country. For the unimproved land, the colony can be found utilizing the equation:

where,

sa?z = Total colony

P = Pressure exerted by the above construction

vitamin D = Depth of the rock column

Ds = Constrained modulus of the dirt

Similarly, the entire colony of the improved land, where the betterment factor is incorporated, can be found by spliting the colony by n2, which is shown below:

This method is one of the most common and well-known method of planing rock columns and has been widely used all over the universe because of its simpleness. Furthermore, in comparing with the other methods, it shows a much wider behavior of the rock column by presuming the rock column and environing dirt as a composite system.

## 2.2 Numeric Models

## 2.2.1 A.P. Ambily and Shailesh R. Gandhi ( 2007 )

Ambily and Shailesh ( 2007 ) studied the behavior of rock columns by comparing experimental and Finite Element analysis on a individual rock column and a group of 7 columns.

Lab experiments were carried out on a stone column of 100mm diameter surrounded by soft clay in cylindrical armored combat vehicles of 500mm high with diameter changing from 210 to 420 millimeter for a individual column trial and from 210 – 835 millimeter for a group of 7 columns. This represents the needed unit cell country of soft clay around each rock column. Pressure cells attached to the lading home base were used to mensurate the emphasis strength of the column and the dirt as shown in figures 2.12 and 2.13. Furthermore, it is besides assumed the rock columns are installed in a triangular form.

The burden distortion behavior of the column/treated dirt was studied by using perpendicular burden for both instances ; column merely lading and full country burden, and observed for equal intervals of colonies until failure occurs. After a series of process, the forms of the tested columns are obtained. It is clearly seen in Fig. 2.14 that pouching manner of failure merely occurs in the instance of column entirely loaded, and non in the instance of full country loaded.

Finite Element analysis was conducted utilizing 15-noded triangular elements with the package bundle PLAXIS, to compare the load-settlement behavior with the theoretical account trial and the laboratory experiment. The analysis was carried out utilizing a rock column of diameter 25 millimeter and 225 millimeter high, which was made at the centre of the clay bed and loaded with a home base of diameter two times the diameter of the rock column. The axisymmetric finite component mesh to stand for the individual rock column and the group of rock columns are shown in Fig. 2.15 and Fig. 2.16 severally.

Similarly the research lab experiment, finite component analyses were done for column entirely loaded and full country loaded instance for s/d=3. The consequences of these simulations ( Fig. 2.17 ) shows that failure by pouching occurs in column entirely loaded instance, which besides agrees with the consequences from laboratory experiment.

The comparing of the experimental consequences and finite component analysis information shows important consistence in both methods. The comparings made by A.P. Ambily and Shailesh R. Gandhi include the consequence of shear strength, Cu ( Fig. 2.18 ) and the consequence of s/d ( Fig. 2.19 ) on the behavior of rock columns. Additionally, the consequence of surcharge on emphasis colony behavior ( Fig. 2.20 ) and consequence of s/d and I¦ on the stiffness betterment factor ( Fig. 2.21 ) was compared between both methods. These trials have besides shown similar behavior. The stiffness betterment factor ( I? ) was calculated as the ratio of the stiffness of treated and untreated land, and beyond s/d = 3, it shows no important betterment.

The analysis was extended to analyze the consequence of the angle of internal clash of rocks by changing the I¦ as 35, 40, 43, and 45o for changing values of s/d runing from 1.5 – 4. From the consequences shown in Fig. 2.22, it is confirmed that this relationship is valid for any shear strength values of environing dirt.

Furthermore, the comparings between a individual column and group of 7 columns were found as in Fig. 2.23.

Both experimental and finite component method consequences reveal comparable behavior sing the ultimate burden and burden distortion relationship. To guarantee that this proposed design method agrees with the bing theories, this survey was compared with the bing theories as shown in Fig. 2.24 and Fig. 2.25. The consequence shows a somewhat higher stiffness betterment factor ( I? ) for an country ratio more than 4 and a lower value for an country ratio less than 4 compared to Priebe ( 1995 ) .

## 2.3 Drumhead

The surveies mentioned above show comparable consequences and have been adopted by many applied scientists and contractors. However, non many research workers had compared Priebe ‘s analytical theoretical account with finite component method. Therefore, the finite component analysis carried out in this undertaking will be compared to the design method proposed by Priebe ( 1995 ) , since it gives a much broader overview of the composite system dwelling of the rock column and dirt interactions and moreover it is the most common and improved analytical method used by the design engineers around the Earth.

## Chapter THREE

## 3. Methodology

## 3.1 Introduction

Different methods of patterning rock columns numerically have been implemented in the past. Among those, the most simplest and common type of numerical modeling is utilizing finite component method. In fact, surveies have shown that the colonies predicted from the finite component analysis shows comparable consequences that of the values gained from existent field trials ( Kirsch, F. 2009 ) . Numeric computations are normally complex and most of the clip is impossible to carry on without agencies of dedicated package. Likewise, in this research undertaking, PLAXIS package is used to transport out the finite component analyses.

## 3.2 PLAXIS package

The chief computing machine package used in this fact-finding undertaking is PLAXIS Professional Version 8.2. PLAXIS is a comprehensive bundle for finite component analyses for geotechnical applications. It allows imitating the dirt behavior by utilizing dirt theoretical accounts. The package employs a graphical user interface that makes it simple to utilize and besides provide the ability to input the necessary parametric quantities such as different dirt beds, structural elements, assortment of burdens, and boundary conditions through CAD drawing processs. It allows discretizing the dirt constituent into either 6-noded or 15-noded triangular elements whereby 15-noded trigons provides high emphasis consequences for complex jobs. The package besides allows automatic coevals of 2D finite component meshes that can be farther refined harmonizing to the pick of analysis. In add-on to that, the package comes with a really utile characteristic named Staged Construction. This characteristic allows the theoretical accounts to be simulated at different phases by triping and deactivating bunchs of elements, application of tonss, etc. One of the advantages of this package is the ability to bring forth the consequences rapidly with minimal mistakes. The end product consequences include values for emphasiss, strains, colonies, and structural forces together with the secret plans of different curves such as, load-displacement curve, stress-strain diagrams, and time-settlement curve.

## 3.3 Finite Element Modelling

Finite component analysis was conducted to compare the load-settlement behavior of the rock column. A two dimensional axisymmetric analysis was carried out since the probe concerns a individual unit of rock column utilizing Mohr-Coulomb ‘s standard for clay and rock column. 15-noded discretization was used for more precise consequences. The initial perpendicular emphasis due to gravitation has been considered in this analysis. Similarly, the emphasis due to column installing, which frequently depends on the method of building, is besides considered in this analysis.

Premises made in the finite component modeling:

The dirt is assumed to be homogeneous, infinite and behaves as Mohr-Coulomb theoretical account.

The land H2O tabular array is at the same degree as the rock column and clay bed, intending the rock column and clay bed is submerged in the H2O. Hence, consequence of land H2O status should be taken into history.

The base of the clay bed is stiff, i.e. , full fastness at the base of the geometry ( ux=0, uy=0 ) and roller conditions at the perpendicular sides ( ux=0, uy=free ) – boundary conditions are shown in Figure 3.1 ( a ) .

Assumed that distortion of the column is chiefly by radial bulging and no important shear is possible. Therefore, interface component between rock column and clay has non been used.

Mitchell, J. K. , and Huber, T. R. ( 1985 ) besides carried out similar type of finite component analysis without the inclusion of the interface component.

## 3.4 Geometric Parameters

The dimensions of the PLAXIS theoretical account are shown in Figure 3.1 ( B ) . H is the tallness of the column, which varies between 10m, 20m, and 30m. D is the diameter of the rock column, which has a typical value of 1m, in all the theoretical accounts except for the theoretical account to look into the influence of diameter and spacing. Equivalent diameter De depends on the spacing between rock columns every bit good as the agreement form of the columns. The value of De was calculated by sing the undermentioned Influence Area methods.

## 3.4.1 Influence Area Methods

There are several methods for ciphering the tantamount diameter around the rock column, which depends greatly on the spacing, diameter, and form of installing of the rock column. Two methods were considered in this probe.

## 3.4.1.1 Equivalent Area method

The tantamount country method merely equates the country of the grid spacing with that of the cross sectional country of column to happen the influence country around the rock column. The undermentioned illustration gives a better apprehension of the above statement.

Examples:

Grid spacing of the column = 1.5 Ten 1.5 metres ( square grid )

Therefore, Diameter of rock column =

Finally,

Where, De is the tantamount diameter around the rock column.

## 3.4.1.2 Unit cell method ( Balaam & A ; Booker, 1981 )

Unit cell consists of the column and the surrounding dirt within the zone of influence of the column. The unit cell has the same country as the existent sphere and its margin is shear free and undergoes no sidelong supplanting. Balaam & A ; Booker ( 1981 ) relates the diameter of the unit cell to the spacing of the columns as:

where, De is the tantamount diameter

( for square grid ) S is the spacing of the rock column

Similarly the different geometrical forms due to column agreements are shown in the Figure 3.2.

Both methods reviewed above gives comparatively similar magnitudes. However, Priebe ‘s analytical method concerns more on unit cell country. Hence, for this probe Equivalent Area method is used to pattern the influence are in PLAXIS.

## 3.5 Mesh Refinement Test

Mesh coevals has a great influence in the truth of the theoretical account. By and large, the finer the mesh the more accurate the consequence would be. However, this is non true for every instance. Therefore a simple trial utilizing PLAXIS was conducted to look into the consequence of mesh polish.

Initially, mesh coevals was set to coarse ( around 100 elements ) , utilised as planetary saltiness of theoretical account. The trial was carried out by comparing it with the refined mesh ( around 500 elements ) . Furthermore, the mesh is further refined which in PLAXIS is set to really fined ( around 1000 elements ) . The generated meshes are shown in Figure 3.3. followed by the time-displacement graph demoing the comparing between coarse, medium, all right and really all right mesh polishs. ( Figure 3.4 )

From the above graph it can be seen that the four curves gives comparable consequences. However, the coarse, medium, and all right meshes give really similar consequences compared to the really all right mesh polish. The aim here was to acquire the lowest value for the supplanting since the improved land due to the installing of rock column would finally take to a reduced colony. Therefore, the finest mesh polish gives the most precise consequence.

Even though it takes a significant sum of clip to imitate utilizing the most all right engagement, for this probe, theoretical accounts had been simulated utilizing the really all right mesh option.

## 3.6 Input Parameters

Changing the dirt parametric quantities can change dirt features. Most of import result by changing these parametric quantities is distortion that leads to colony. Such parametric quantities that have major impact on colony includes, stuff type, spacing of rock columns, diameter of influence country, diameter of rock column, elastic modulus of both column and dirt, deepness of the dirt bed, Poisson ‘s ratio for both column stuff and dirt, Unit weights of the stuffs, coherence, clash angle, etc. Soil and stuff belongingss are shown in Table 3.1. Note that the effectual emphasis coherence, c ‘ of the rock column is given a little nonzero value to avoid numerical complications.

Table 3.1 Properties of Soil and Stone column

Material

Material type

## I?

( kN/m3 )

## I?sat

( kN/m3 )

## V ‘

## Tocopherol

( kPa )

## kh=kv

( m/s )

## degree Celsiuss ‘

( kN/m3 )

## I¦ ‘

( deg )

Stone column

Drained

19

20

0.25

60000

1×10-3

0.1

40

Clay

Undrained

15

15

0.33

3000

1×10-9

10

0

The bulk of the above parametric quantities are considered for merely one type of trial theoretical account and are varied for different theoretical account trials. The varied parametric quantities such as elastic modulus of dirt and column, clash angle, spacing between columns and influence country around the rock column are reviewed in the undermentioned subdivision.

## 3.7 Test Models

The chief aim of this undertaking is comparing both analytical and numerical method utilizing Priebe ‘s analytical attack and finite component analysis as numerical solution. This can merely be achieved by developing multiple theoretical accounts and simulations to obtain a scope of values to compare with, which would take to a more solid decision.

Three constituent theoretical accounts were considered for the representation of the undermentioned three instances.

A clay bed of 30 m, which has a stone column of tallness 10 m installed.

A clay bed of 30 m, which has a stone column of tallness 20 m installed.

A clay bed of 30 m, which has a stone column of tallness 30 m installed.

Note that 1 and 2 are drifting columns that are non extended to bedrock or hard bed, which in rock column installing is a rare instance, yet installed on occasion.

Each of the above trials was carried out by changing the spacing between columns, which would change the s/d relationship together with the Ac/A ratio. Further trials were carried out to look into the influence of emphasis I?0, diameter D, modulus of distortion of the column to sand ratio Ec/Es and clash angle of rock column I¦’c utilizing the 3rd instance and compared them against the Priebe analytical attack.

The sum-up of trial theoretical accounts is given in the Tables 3.2. All the trials were carried out in 3 phases.

Install the rock column: Merely after the rock column is installed

Apply Load: Merely after the burden is applied to the column

Consolidation: After the consolidation procedure completed to a minimal pore force per unit area of 1kPa

In the all instances the stuffs were idealized as the Mohr-Coulomb theoretical account with the characteristic linear-elastic-perfectly fictile behavior and the failure standards defined by the strength parametric quantities given in tabular arraies below.

Table 3.2 Summary of Model trials

Model Test

Description

Constants

Variables

1

Influence of column tallness on colony

( instance 1, 2, and 3 )

I?0 = 100 kPa

Ac/A = 0.2

I¦’c = 40o

Ec/Es = 20

Height = 10 m

= 20 m

= 30 m

2

Influence of spacing between columns on colony by changing the Ac/A for three instances

I?0 = 100 kPa

Ec/Es = 20

I¦’c = 40o

Ac/A = 0.35

= 0.20

= 0.13

= 0.09

Height = 10 m

= 20 m

= 30 m

3

Influence of D and spacing on Settlement by changing the spacing of the 1m and 1.5m Defense Intelligence Agency rock columns

H = 30 m

I?0 = 100 kPa

Ec/Es = 30

I¦’c = 40o

D = 0.8 m

= 1 m

= 1.2 m

Spacing = 1.5 m

= 2 m

= 2.5 m

= 3 m

4

Influence of Ec/Es ratio on colony by transporting out exemplary trial 2 with I?0 as 50 kPa

for 3 values of Ec/Es

I?0 = 50 kPa

H = 30 m

I¦’c = 40o

Ec/Es = 60000/3000 = 20

= 75000/2500 = 30

= 100000/2500 = 40

5

Influence of I¦’c on colony by transporting out exemplary trial 2 with I?0 as 50 kPa for 3 values of I¦’c

H = 30 m

I?0 = 50 kPa

Ec/Es = 30

I¦’c = 35o

I¦’c = 40o

I¦’c = 45o

6

Influence of emphasis on colony before betterment and after betterment by increasing the I?0

H = 30 m

Ac/A = 0.20

I¦’c = 40o

Ec/Es = 20

I?0 = 50 kPa

= 70 kPa

= 85 kPa

= 100 kPa

## 3.8 Priebe Models

To transport out the Priebe theoretical accounts, a Microsoft Excel spreadsheet was prepared based on the Priebe ‘s attack of stone column design reviewed in Section 2.1.2. The input parametric quantities harmonizing to the PLAXIS theoretical accounts were used to get the consequences.

For instance 1 and 2 where rock column is non extended until the bedrock, the spreadsheet was modified to distinguish between the two beds. The colony of bed 1, which had the rock column installed was calculated usually. The colony of bed 2, which had untreated clay was calculated by utilizing the clay belongingss as rock belongingss in the spreadsheet. The sum-up of the spreadsheet can be referred in Appendix.

## Chapter FOUR

## 4. RESULTS AND DISCUSSIONS

## 4.1 Model Test 1: Influence of Height of Stone column

The first theoretical account trial was carried out to verify the three instances mentioned in subdivision 3.7, which is the influence of different highs of rock column, installed in same deepness of clay bed. The graph bespeaking the colony alteration for the three instances is plotted in Figure 4.1. The highs of the column tested in this theoretical account were 10m, 20m, and 30m. As the deepness of column additions, volume of the treated land additions and becomes stiffer than the untreated land. Therefore, colony lessenings.

As seen from the above graph, Both PLAXIS analysis and Priebe method are in good understanding to the fact that the addition of height additions the colony. However, for the 10m and 20m columns the colony values were 545.68 millimeters and 410.98 millimeters severally for the Priebe method and 762 millimeter and 601 millimeters severally for the PLAXIS analysis. The difference between the Priebe method and PLAXIS analysis is chiefly due to the partial inclusion of rock column in the clay bed. Harmonizing to the Priebe method, it was assumed that the base of the rock column should be stiff. However, in the instance of 10m and 20m rock columns, the base is elastic and can displace farther through the untreated land. In comparing, for the instance of 30m rock column installed in 30m of clay, PLAXIS analysis and Priebe method gave colonies values of 271 millimeters and 263 millimeter severally, which is extremely comparable.

## 4.2 Model Test 2: Influence of Area Ratio ( Ac/A )

Area ratio Ac/A, which is expressed as the ratio of the rock column country with the entire country of the influence part, was examined by using a surcharge of 100kPa to the 10m, 20m and 30m deep rock columns of different spacing. The country ratio depends both on spacing and diameter of the column. With a fixed diameter of 1m, as the spacing of the rock column additions from 1.5m to 3m, the country ratio decreases from 0.35 to 0.09.

## 4.2.1 10m rock column

The graph of country ratio against colony for 10m deep rock column is plotted in Figure 4.2. For the