Determine the Stress Calculating Mode of Sliding Failure of Soil Mass under the Push-Extend Multi-under-Reamed Pile

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1 Engineeing, 014, 6, Published Online Apil 014 in SiRes. Deteine the Stess Calulating Mode of Sliding Failue of Soil Mass unde the Push-Extend Multi-unde-Reaed Pile Yongei Qian, Xuezhe Chen, Xuewen Xie Jilin Jianzhu Univesity, Changhun, China Eail: Reeived 7 Novebe 013; evised 7 Deebe 013; aepted 5 Januay 014 Copyight 014 by authos and Sientifi Reseah Publishing In. This wok is liensed unde the Ceative Coons Attibution Intenational Liense (CC BY). Abstat Though the analysis of the sliding failue fo of soil ass unde the beaing push-extend eaed of Push-extend Multi-unde-eaed Pile, in the pape, the law of oulob-moh is used to establish a stess funtion and the theoy of the sliding line is used to establish Pandtl egional stess field, whih deteines the stess alulating ode of soil ass and povides a theoetial basis fo a futhe study of this type of pile ultiate beaing apaity of soil ass. Keywods The Push-Extend Multi-unde-Reaed Pile; Sliding Failue; the Beaing Push-Extend Reaed; Calulating Mode 1. Intodution The failue pefoane of the foundation is the slide of soil ass, when the soil ass is sliding, we an usually find the though sliding sufae (o alled slip line). So the stength of the soil ass is atually the elative sliding esistane between one pat of the soil ass and the othe, whih is the shea stength, and essentially is the fition between soil ass and soil ass. So the shea stength of soil ass is in onfoity with the law of fition. Beause it is the fition of the sae kind of ateial between diffeent pats, in ode to distinguish it fo the fition between diffeent ateials, it is known as the intenal fition, the oesponding oeffiient alled intenal fition oeffiient. Aoding to the analysis of theoy and the expeiental eseah on the failue ehanis of pile soil of the Push-extend Multi-unde-eaed Pile, the esults show that the destution of the soil ass unde the plate also oplies with the law above and belongs to the sliding failue, and that the ultiate beaing apaity of the soil ass an be solved by the theoy of slip line. Theefoe, this atile uses the How to ite this pape: Qian, Y.M., Chen, X.Z. and Xie, X.W. (014) Deteine the Stess Calulating Mode of Sliding Failue of Soil Mass unde the Push-Extend Multi-unde-Reaed Pile. Engineeing, 6,

2 theoy of slip line to deteine onfos to the stess alulating ode of failue odes of soil unde the Pushextend Multi-unde-eaed Pile [1].. The Law of Coulob-Moh At pesent, the ost suessful failue theoy is to use stess to define the failue, in soil ehanis, the soil ass shea failue is often based on the theoy of oulob Moh stength. This theoy onsides that if the shea stess of any setion is equal to the shea stength of the ateial, then ateial appeas failue. As shown in Figue 1, this figue paints the stess Moh ile when ateial auses daage in the ule of oulob, when the intenal foe on oss setion and the oesponding Moh ile inside the bounday, failue ous. The failue sufae of Moh ile is usually alled slip plane (o line), the aute angle that eah othe fos is 90, both failue on the oss setion of noal stess and sheaing stength eet the law of oulob-moh, that is: = tan []. Syboli ules: The sybols of noal stess and shea stess at any setion of sybols, aoding to the usto(the ight hand spial ule), when the dietion of otation is lokwise, noal stess to tensile stess is positive, Shea stess to tensile stess and the ode of shea stess satisfies the oksew ule is positive. Signifiane of sybol: As shown in Figue 1, the inteept between failue envelope and vetial oodinates is, whih is alled ohesive ateial (o ohesion). The slope angle of the failue envelope is alled the angle of intenal fition, is alled the shea stength index of soil ass, and is an ipotant ehanial indexes of soil ass. 3. The Establishent of Stess Funtion As shown in Figue 1, the adius of the Moh ile whih is oesponded to the failue sufae is os 1 ( 1+ 3), so: 1( 1 3) = os 1( 1 31) (1) We get: 1 + sin os 1 3 = 1 1 That is: ( tanϕ+ 1+ tan ϕ ) ( 1 3 = tanϕ+ 1+ tan ϕ ) Let ( ) k = tan + 1+ tan, then the above foula is: So Let k = k () k = (3) 1 f = k, so k1 3 = f (4) 3 1 (, ) Figue 1. The stess Moh ile when it is daaged. 55

3 Aoding to the foula (3), we get: 1+ os f = = 1 1 (5) 4. Coulob Hypothesis Aoding to the law of Coulob, in the stess field, on the failue sufae whee eah othe ae in a 900 aute angle, shea stess point to the opposite way to the intesetion edges. As shown in Figue, a and b ae two positive and negative failue sufaes espetively. Explode stess to the stess on failue sufae, as shown in Figue 3(a) and Figue 3(b) ae two positive and negative failue sufaes. Make the failue sufae t axis, use Catesian oodinates (t, n) to show stess field, as shown in Figue 4, a and b ae two positive and negative failue sufaes. So the stess field is: n = nt = = tanϕ (6) (positive) t = tanϕ = ( 1+ tan ϕ) tanϕ n = nt = = ( tan ϕ) t = tanϕ = ( 1+ tan ϕ) tanϕ (7) (negative) (a) Figue. The stess pitues of two positive and negative failue sufaes /os /os (a) (b) /os /os Figue 3. The two positive and negative exploded views of failue sufaes. (b) t t n n (a) Figue 4. Stess field unde the atesian oodinates. (b) 56

4 If is the aveage stess in the sufae, = ( + ) Aoding to Moh ile, we get = tan + (8) os 3 = tan (9) os ( ) = tan = 1+ tan tan (10) 5. The Satisfied Yield Condition in Failue Sufae (Stess Condition) In Moh ile, the adius whih is oesponded to the failue sufae os 1 ( 1+ 3), an be ex- pessed as osϕ sinϕ, thus, we an alulate the stess on the abitay setion. Supposed that the inluded angle between one sufae and the failue sufae is, and the stess on the sufae ae X, Y, Xy. As shown in Figue 5. Aoding to Moh ile, we get: ( ) π x = + os os( ) = ot + ( ot) 1 sin ( + ) (11) In the sae way: ( ) y = ot + ( ot ) 1 + sin + (1) ( ) ( ) xy = ot os + (13) If the known stesses on abitay sufae ae x, xy, fo the loation of failue sufae and stess. In ode to xy alulate easily, lead in β angle, as shown in Figue 5, take tan β = into foula (11) (13), we get: ot Siplified as os( β) ot ( + ) ( ) os tan β = 1 sin + sin β + =, get and stess on the failue sufae: x ot = + tan os 1 sin = +, aoding to foula (10), we get: ( ) ( + ) 6. The Satisfied Equilibiu Condition on Failue Sufae At fist, hoose a siple daaged aea whih is statially adissible, aoding to failue fo of soil ass x χ χy y χ ( χ, -χy ) 3 1 β ( χ, χy) (, ). os Figue 5. Stess pitue on abitay sufae in Moh ile. 57

5 unde the pile, hoose Pandtl egion. Take two sets of uves, one is logaithi spial line with inlination angle, the othe is the pola ays, we an also get the 900- set of uves, as shown in Figue 6. Coinide axis and t axis whih ae in Figue 4, we get: = = ± ( tan) = ( 1+ tan ) tan Establish pola oodinate and take the infinitesial body, as shown in Figue 7, Aoding to Figue 7, establish the equilibiu diffeential equation, due to = 0, we get: d + d ( d) d d d d d d + d d d kdd = 1 we get: k = 0 1 In the sae way, we get: k = 0 Take foula (14) into equation, ignoe the gavity, ( 1 tan ) tan ( tan ) + ϕ ϕ 1 ϕ tan ϕ tanϕ ± + = 0 ( tan) 1 tan ± ± = 0 Take tan (16) + (15), we get: = 0, explain that along the failue staight line, is a onstant. Aod- ± tan = 0. ing to foula (16), we get: ( ) (15) (16) Figue 6. The stess field in pandtl egional. 0 d y k χ k + + d d + d + d d Figue 7. Stess diaga of the infinitesial body unde pola oodinate. 58

6 Then we get: Take (17) into (14), we get: = ± tan e ± ± tan = e + ot (17) tan 7. Conlusions Beause the failue fo of the soil ass unde the beaing push-extend eaed of Push-extend Multi-undeeaed Pile belongs to the sliding failue, thus, the theoy of the sliding line an be put in use to analysis the stess unde the destution of the soil ass. Though the analysis of the theoy above, the law of Coulob- Moh is used to establish a stess funtion, and aoding to the yield ondition and equilibiu ondition and so on, applying Pandtl egional stess field, deteines the alulation odel of the stess of the soil ass unde the beaing push-extend Multi-unde-eaed Pile. tan Noal stess = ± tan e ± On the basis of the foula above, obining plasti potential theoy and vitual wok piniple an deteine ultiate beaing apaity of the soil ass unde the push-extend Multi-unde-eaed Pile, then an deteine the alulation odel of the beaing apaity of single pile futhe. Aknowledgeents ± tan = e + ot shea stess This wok was finanially suppoted by National Natual Siene Foundation of China (51784). Refeenes [1] Qian, Y.M., Wang, R.Z. and Yin, X.S. (01) The Siulated Analysis in the Copute on the Effet of Pile and Soil Woking Togethe about the Push-Extend Multi-unde-Reaed Pile. Advaned Mateial Reseah, , [] Qian, Y.M., Wang, R.Z. and Yin, X.S. (011) Testing Study on the Shape of the Beaing Push-extend Reaed Affeting the Beaing Capability of the Pile. Ahitetue Tehnology, 4, (in Chinese) 59