Investigation of Subgrade Reaction Coefficient in Sandy Soil

Numerical ventilation of subaction reaction coefficient in sandy contaminates

Adel Asakereh1, Hassan Jamali2*, Masoud mossafa1

1 Civil Department, University of Hormozgan, Bandar Abbas, Iran

2Young Inquiryers and Elite Club, Sabzevar Branch, Islamic Azad University, Sabzevar,

Abstract

The contaminate-groundlabor interaction is undivided of the most importancey issues in geotechnical engineering relating to contaminate action counter aspect attacking. Winkler’s example is the primary and undesigningst process ce regarding the contaminate-groundlabor interaction. Becaconservation to cunningate the coefficient of the subaction reaction of the contaminate antecedently sharp make is indispensablely importancey, so, tentative, analytical and numerical processs keep been contemplated. This inquiry chose a reason idiosyncrasy that is in Bandar Abbas (Iran). Purpose is to collate the contemplated tentative cemulae ce determining the coefficient of the subaction reaction with its similar appraises resulting from the actional examples. Terminable multiply multiplyition was manufactured by Plaxis software and importancey parameters were contemplated by the engineers. Results profession increasing standing tranindividuality leads to a lessen in the coefficient of the subaction reaction attribuconsultation to increasing attack area which results in increasing precipitation. It is rest that increasing each of the power parameters of the contaminate can be expected to keep an good-natureds on increasing the subaction reaction, although this acception depends on standing transection. To-boot in sand contaminates, the contaminate cohesion good-naturedss on the acception of the subaction reaction coefficient aggravate than the inner attrition intention.

Keywords: Buoyantity coefficient, Involve restation, Subaction reaction coefficient, Bandar Abbas City, Terminable multiply multiplyition

  1. Introduction

The contact of involve restations has a desire truth. This fashion of restation has professionn a very good-natured-natured exploit in make-overring composition ceces to the reason. Floatingly in most predicaments, engineers conservation a firm appraise ce the subaction reaction coefficient to awaken the involve pliant restations. This firm is gained from geotechnical experiments such as platter attacking. Frequent inquiryers keep premeditated contaminate ebb and the subaction reaction coefficient using platter attacking cupel [1-9].

Nomenclatures

B

Tranindividuality of standing (m)

Minimum ultimate bulk of standing(m)

c

Cohesion (kPa)

d

Platter animalism (m)

Df

Embedment profoundness of restation(m)

Contaminate buoyantity modulus (kPa)

EI

Flexural rectilinearity of standing (kN.m2)

EA

Axial rectilinearity of standing (kN.m2)

Climax of ith lamina (m)

If , Is, Id

Dimensionless coefficients

ks

Subaction Reaction Coefficient (kN/m3)

m

Firm coefficients

P

Perpendicular hurry (kPa)

Greek Symbols

v

Poisson ratio

Perpendicular Dismemberment (m)

Intention of attrition (Degree)

Item importance (kN/m3)

Tedious item importance (kN/m3)

The contact of a regular reaction coefficient aggravate every of the restation media neglecting the stipulations of a continuum ce the contaminate and the good-naturedss of slice in the contaminate laminas. Undivided of the primary issues in sharp and careful the restations is the climax of contaminate-groundlabor interaction. It is very importancey to con-aggravate contaminate action counter the superficial attacks. Contaminate action depends on frequent constituents such as humidity gratified, hebetude, multiplyicle-forming azoic fashions, atom bulk, atom rule, grading flexion, floating propound of the purify, purify truth, pore hurry, saturation aim, permeability scold, spell, and sky. In dispose to con-aggravate the contaminate-groundlabor interaction, frequent inquiryers keep tried to question contaminate action counter the imposed attackings to confront a example ce it. The involveerial example is a involvehematical relative ce describing the purify-purify behaviour of a smevery multiply of the environment.

As previously mentioned, contaminate action depends on frequent constituents it is yieldingly intricate to afford a example including the good-naturedss of every constituents. Thus in solving the climaxs of contaminate-groundlabor interaction, some properties of the contaminate are usually exclusive to afford a undesigningr example with lackinger parameters. Since the contaminate at a macroscopic lamina is braveed as a continuum, the undesigningst potential propound we brave the contaminate as a rectilinear, homogenous and harmonious buoyant semi-space. In such a predicament, the contaminate achieve keep brace parameters Poisson coefficient and the buoyant modulus. The primary and undesigningst example ce investigating the contaminate and restation interaction is a example offered by Winkler in 1867 [10]. In this example, the deformation of any aim of the contaminate reason is kindred to the aim purify appraise and the good-natureds of the purifyes and the changes in other aims are aggravatelooked. In this example, contaminate is replaced with a cemal of rebellious springs with a restricted slang coefficient. Thus, singly undivided only parameter is braveed ce the contaminate, that is, the subaction reaction coefficient represented by ks. Undivided of the most adequate properties of this example is its discontinuous action [9]. The subaction modulus is referable attribuconsultation attribuconsultation attribuconsultation attribuconsultation attribuconsultation attribuconsultation attribuconsultation attribuconsultation attribuconsultation attribuconsultation attribuconsultation attribuconsultation a primary contaminate nature and its bulk depends on frequent constituents including the rule of the restation, the slang of the restation slab, the rule of the attacking on the restation, the profoundness of the attacked area beneath the reason exterior, and the spell. As such, it is referable attribuconsultation attribuconsultation attribuconsultation attribuconsultation attribuconsultation attribuconsultation attribuconsultation attribuconsultation attribuconsultation attribuconsultation attribuconsultation attribuconsultation firm ce a dedicated fashion of contaminate, making the nature of a only unconcealed appraise ce cunning a challenging business [11]. Consequently, inquiryers keep suggested irrelative restraintms to cunningate this parameter and irrelative cemulae keep been offered ce determining ks.

Frequent inquiryers keep labored on the circumspection of subaction reaction coefficient. Ismail [12] premeditated the contacts of the fictitious neural networks (ANN) and the undesigning-multiple retirement multiplyition to ceetell the deformation modulus and the coefficient of the subaction reaction of the compacted contaminates from the compaction parameters (such as climax tedious hebetude (MDD) optimum humidity gratified (OMC), reason tedious hebetude (FDD), and reason humidity gratified (FMC)). Ding [13] collated impure regular processs ce determining the coefficient of the subaction reaction including the cupel process, Lis process, MIDAS process, and terminable multiply process. He professioned that the cupel process is the undivided preferred by the cunningers, that the tangential coefficient should be in a place of undivided to brace-third of the typical coefficient. The inner cece of subfashion makes can be gained by the cupel process and mitigated by a amendment constituent that is 1.05. Barmenkova et al. [14] carried extinguished circumspections of platters on an buoyant establishment with wavering and firm coefficients of subaction reaction. In this tract, the circumspection of platters bending was carried extinguished by the terminable multiply process. The results were collated ce irrelative examples of platters on an buoyant establishment. Ce a brace-lamina platter on an buoyant establishment, which had hostility in the drawing, the results of circumspection to-bootk into recital the acception of the climax of the higher make.

Kobayashi et al. [15] adapted the subaction reaction coefficient ce a restation contaminate in an known pier using an adequate Kalman ooze (EKF) reasoned on measurements enslaved during in situ even attacking cupels on a stuck. The numerical results would afford conservationful knowllaterality ce the advenient cunning of known piers and their restations. Liao [16] reviewed the limitations of sunbarren undesigning and multifarious-sided processs suited ce estimating the coefficient of subaction reaction k, and open a innovating process using the results of the drawinge purify terminable multiply analyses of a attacked ray or slab contingent on the exterior of a homogeneous buoyant contaminate lamina.

Although frequent studies keep been carried extinguished on determining the subaction reaction coefficient, the reliance on frequent parameters leads to elevate parametric studies. Tentative and speculative cemulas ce determining ks are reasoned on suited reasons from scant residences with some assumptions, so it is potential ce them referable attribuconsultation attribuconsultation attribuconsultation attribuconsultation attribuconsultation attribuconsultation attribuconsultation attribuconsultation attribuconsultation attribuconsultation attribuconsultation attribuconsultation to keep adequate nicety in every areas. Therefore, determining the subaction reaction coefficient in restricted areas such as Bandar Abbas city and tribute of the good-naturedsive parameters on subaction reaction coefficient is indispensable. Besides, the Increasing in standing width, acceptions good-naturedsive profoundness. Therefore, favor of ks in standing with aggravate width is aggravate multifarious-sided in-particular in laminaed contaminate, becaconservation ks gained from platter attack cupel is irrelative from ks subordinate vericonsultation attacking of make. Thus ventilation of the standing width and the power parameters of the contaminate on ks is needed. Performing platter attack cupels with wide transections is valuable and intricate, thus the confer-upon con-aggravate conservations terminable multiply software of Plaxis to question the good-natureds of the aforementioned parameters.

Parametric studies on subaction reaction coefficient of sand contaminate in Bandar Abbas city are lacking, so this tract conservations geotechnical reasons of a residence in Bandar Abbas city (Iran) to cunningate subaction reaction coefficient by using of speculative, tentative relatives and numerical processs. Besides, the good-naturedss of the power parameters (c,) and B on subaction reaction coefficient are questiond to-boot. This con-aggravate is carried extinguished by using and identifying numerical processs and ensuring the exactness of the software. Numerical multiplyition has been dundivided by terminable multiply process using Plaxis software [17].

  1. Analytical processs of subgrades reaction coefficient

In dispose to gain ks, undivided can unconcealedly engage platter attacking, connection, triaxial, and CBR cupels and tentative and theoretic relatives affordd by inquiryers [18]. Among them, platter attacking cupeling and the tentative process are braveed the most sordid processs. In this tract, tentative and theoretic processs are braveed. There are irrelative relatives including Vesic [19], Biot [20], and Bowles [6] as courteous as relatives resulting from buoyant assumption from buoyantity assumption to cunningate subaction reaction coefficient.

Biot [20] solved the climax of an interminable ray on a rectirectistraight buoyant subaction and affordd Eq. (1) ce subaction reaction coefficient.

(1)

Vesic [19] open Biot’s labor [20] and suggested Eq. (2) ce the relative betwixt ks and buoyant idiosyncrasy of contaminate:

(2)

He to-boot professioned the unlikeness betwixt Winkler process and continuum does referable attribuconsultation attribuconsultation attribuconsultation attribuconsultation attribuconsultation attribuconsultation attribuconsultation attribuconsultation attribuconsultation attribuconsultation attribuconsultation attribuconsultation yield 10 percent. Bowles [6] professioned the numerical appraise of in inferior predicament may be resembled by 1, and in most predicaments subaction reaction coefficient is gained by Eq. (3):

(3)

Using buoyantity assumption is another restraintm to resemble ks. By reformulating the buoyant ebb in crosswise restation, we gain the aftercited [21]:

(4)

These appraises are cunningated reasoned on consultations in the buoyant ebb individuality of basic contaminate workman harmonys. “m” is the coefficient which is resembling to 1, 2 and 4 ce hole, laterality, and disposition, respectively. ks is adapted in holes pretentious m = 1 from Eq. (4) and it is sunbarren by 0.5 to gain k lateralitys or by 0.25 to gain ks dispositions. According to the aggravatehead argument, it can be seen that there are irrelative cemulae to cunningate contaminate subaction reaction coefficient.

  1. Unconcealed and geotechnical properties of the contaminate

The residence of the residential- markeconsultation structure is located to the west multiply of Bandar Abbas city in Iran (Fig. 1) with seven foots aggravate the reason foot (parking cetune). The profoundness of the restation precipitation is resembling to the climax of the restation as 1 meter and no reasonwater action was observed until the object of the trench profoundness. In dispose to veritableize the subordinatereason laminas, five boreholes were scooped (three 15-meter boreholes and brace 20-meter boreholes) using a rotary control deed. During contaminate boring, some samples were extracted ce laboratory experiments. After quantity of the reason exercise, the extracted samples were cupeled ce grading, Atterberg limits, humidity gratified of the eventual contaminate, and manifest scrape cupel. The studies on the laminas of the residence contaminate profession the contaminate fashion in the restation subaction is primarily silty sand (SM) from the reason resemblingize down to the profoundness of 8 meters, and the contaminate fashion is bad-grained sand (SP) from the profoundness of 8 meters beneath.

Fig. 1. Location of Bandar Abbas city.

Regarding the reason and laboratory experiments in dispose to cunningate the lamina of contaminate ebb and the inclination cleverness of the residence contaminate, the required parameters were selected from the five scooped boreholes as professionn in Consultation 1. The reasons of the samplings is suited down to 20 meters low. The contaminate fashion was dedicated down to the profoundness of the restation good-natureds (environing 30m). Aggravateover, the contaminate importance at the 20 to 30 m profoundness (lamina 11) has braveed as entity firm.

Consultation 1. Contaminate properties of the residence

No. of Laminas

Dep. (m)

Contaminate Fashion

SPT (Ncor.)

ω (%)

c (kPa)

φ (˚)

γ (kN/m3)

γd(kN/m3)

1

0-2

SM

21

4.1

0

29

17

16.3

2

2-4

SM

17

16.6

0

29.1

18.6

16.23

3

4-6

SM

24

14.9

0

28.8

18.6

16.18

4

6-8

SM

33

15.2

0

30.4

18.9

16.4

5

8-10

SP

38

23.7

0

32.4

20.1

16.24

6

10-12

SP

39

18.1

0

31.2

19.4

16.42

7

12-14

SP

47

24.2

0

31.2

20.6

16.58

8

14-16

SP

50

19.8

0

30

20

16.69

9

16-18

SP

50

19.2

0

32

20

16.77

10

18-20

SP

50

18.8

0

32

20

16.83

11

20-30

SP

50

18.8

0

32

20

16.83

Equations (5) and (6) were conservationd to cunningate the buoyantity modulus of the contaminate [6]:

(5)

Ce unsaturated sands, and

(6)

Ce saturated sands.

Thus, the buoyantity modulus ce each of the contaminate laminas is adapted reasoned on the aggravatehead cemulae and the results are professionn in Consultation 2.

Consultation 2. Buoyantity modulus of the contaminate laminas

No. of Laminas

SPT (Ncor.)

Es (kPa)-dry

1

21

18000

2

17

16000

3

24

19500

4

33

24000

5

38

26500

6

39

27000

7

47

31000

8

50

32500

9

50

32500

10

50

32500

11

50

32500

  1. Numerical multiplyition procedure

First, the results of Brian Anderson et al. [22] were awakobject with Plaxis to identify the software. Brian Anderson et al. [22] manufactured in situ cupeling and numerical ventilation ce ceetelling precipitation of unprofound restations. Accordingly, a 1.8 m tranindividuality particularized standing was statically attack cupeled. Prior to composition, in situ rule insight cupel (SPT), cundivided insight cupeling (CPT), dilatometer (DMT), and hurrymeter (PMT) and laboratory cupels were manufactured to cunningate engineering properties of the contaminate. A reinforced round 1.8 m tranindividuality 0.6 m bulky particularized standing was unnatural using a corrugated pipe coupler as a cem. To aggravatecome a unsubstantial unyielding lamina exterior covering, the standing was embedded 0.6 m into the reason. The reasonwater consultation was at 1.7 m from the reason exterior, as illustrated in Fig. 2. Static attack was 222 kPa. Attribuconsultation to the proportion, half of standing with the width of 0.5 B is exampleed asymmetrically. Avoiding proviso good-naturedss, a 6.5Ã-5 m example was selected. The example profoundness was enslaved as 6.5 m, that is resemblely resembling to 4B=6.8 m and the width of the example was enslaved as 5 m, that is resemblely resembling to 3B [23] . Results proved that the dismemberment did referable attribuconsultation attribuconsultation attribuconsultation attribuconsultation attribuconsultation attribuconsultation attribuconsultation attribuconsultation attribuconsultation attribuconsultation attribuconsultation attribuconsultation gain the boundaries in the multiplyition. To question the snare dependency, a compute of certainty analyses were conducted through the certainty con-over. The example intervening 1971 nodes and 235 multiplys. The proviso lines were defined as the scant deformation in even manifestion and permitted deformation in perpendicular manifestion, and scant deformations twain in even and perpendicular manifestions at the inferior proviso as professioned in Fig. 3. Certainty analyses proved that with resolute bulk and snareing, errors would be negligible. In dispose to do the exampleing with terminable multiply process, the 15-node triangular multiply was conservationd according to Fig. 4. Consultation 3 confer-upons the input parameters conservationd ce the FEM analyses. Figure 5 confer-upons applied purify-precipitation diagram gained from Plaxis in this con-aggravate and harmony to a aim located subordinate platter. There was a negligible unlikeness betwixt brace diagrams, so Plaxis was suiconsultation ce multiplyition.

Fig. 2. Geometry and snare of the certainty example.   

Fig. 3. Contaminate-standing line of certainty example [22].

Fig. 4. 15-node triangular multiply.

Consultation 3. Contaminate properties conservationd in certainty according to [22].

Bottom(m)

(kN/m3)

(deg)

E(Mpa)

c(kPa)

1.64

18.9

31.4

14.5

0

2.5

17.3

30.1

12.5

0

3.17

15.7

28.6

10.50

0

6.5

14.2

27.1

8.5

0

Fig. 5. Applied purify-precipitation diagram.

After software certainty, the example was open ce determining the subaction reaction coefficient of Bandar Abbas city and parametric con-over. In the created example (which intervening 2011 nodes and 256 multiplys), the attacking was regular and, a stubborn restation was braveed in every phases of multiplyition. Example profoundness should be senior than 4B and example width senior than 3B ce irrelative transections. Since it was intended to con-aggravate the good-natureds of restation tranindividuality on determining the appraise of subaction reaction coefficient, an asymmetric example was conservationd in the software ce contaminate exampleing. The bearing parameters of the unconcealed properties (damp and tedious restricted importance) and the bearing parameters of the contaminate hindrance (c,) ce every contaminate laminas were conservative from Consultation 1. Regarding the results of the experiments and inquiryes and the reliability of the open numerical example with the results, and regarding the contaminate fashion of the residence (sand contaminate), Mohr-Coulomb actional example ce the contaminate was conservationd in this inquiry. Since in Mohr-Coulomb actional example the purify-purify relative is fulfilled manifestly by the contaminate buoyantity coefficient, thus in entering the reasons of the contaminate buoyantity coefficient as undivided of the input parameters, the reasons of Consultation 2 were conservationd. The appraises of the dilation intention in every laminas were conducive to be 0. Regarding the properties of the structure in this plan and the lamina of the imposed attacking (dull and speed attack), the appraise of the imposed hurry on the contaminate was conducive to be 120 kN/m2 where the platter multiply (with the particularized restation properties) was conservationd to make-over this attack to the exampleed contaminate. Among the most importancey properties of the multiply, it could be referred to its flexural unyieldingness (EI) and its axis unyieldingness (EA). These brace parameters can be conservationd to gain the platter animalism that is the delegated-to-others of the restation animalism in this predicament. Regarding the firm animalism of the restation by 1 meter in this inquiry, irrelative appraises would be gained ce EI and EA in irrelative examples according to the Eqs. (7) and (8) [24]. Since the exampleing was dundivided with asymmetric process, thus half of the tranindividuality of the vericonsultation restation was exampleed, and the exampleing was dundivided in manifestion of x-axis, three spells aggravate than the restations tranindividuality (3B), and in the manifestion of y-axis resembling to the compute of the laminas mentioned in Consultation 1. Aggravateover, Consultation 4 professions the parameters needed ce determining the platter input parameters into Plaxis software.

d= ½ deq

(7)

(8)

Fig. 6. Geometry of the example.

Consultation 4. Platter parameters

EI (kNm2/m)

EA (kN/m)

E (kPa)

Df(m)

Var.

Var.

2.5Ã-107

1

  1. Results and argument

Seven examples were open ce irrelative appraises of restation tranindividuality (8, 10, 12, 14, 16, 18, and 20 m). Then, they were awakobject by terminable multiply process using Plaxis. Becaconservation of axis manifest purify in Plaxis, restation is braveed as a flay with B/2 of tranindividuality and 1 m, orthogonal to the drawinge as professionn in Fig. 6. Amount of perpendicular dismemberment in disposition and beneath of the restation (sections are in disposition and 1 meter beneath the aggravatehead subaction of contaminate example) is gained according to the attack cunningated by the composition multiplyition (120 kN/m2). The contaminate subaction reaction coefficient is adapted by Eq. (9) ce any appraises of restation tranindividuality [25]:

(9)


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