Analysis on horizontal bearing capacity based on catastrophe theory of anti-slide micropiles

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1 Vietrock15 an ISRM specialized conference Vietrock Marc 15, Hanoi, Vietnam Analysis on orizontal bearing capacity based on catastrope teory of anti-slide micropiles YimingXiang a *, Wanxue Long a and HaiSi b a GuizouProivincial Communications Planning Survey & Design Institute Co., Ltd.,Guiyang, Cina b Scool of Civil Engineering,Beijing Jiaotong University, Beijing, Cina * Abstract Te destruction of te micro piles belongs to te scope of te catastrope teory under te orizontal force of te landslide. In tis study, te function of te landslide trust to te micro piles is treated as te gatering process of te elastic energy. In te process of bending and deformation of te micro pile, wen te energy accumulates to a certain tresold, te instability will be occurred in te micro piles. Firstly, te cusp catastrope teory will be applied to te landslide reinforcement micro pile buckling critical load of damage in te study. We establis te micro pile at te top free and te bottom build-in cases, wic is te micro pile buckling nonlinear cusp catastropic model in line wit te engineering caracteristics. Moreover, we also introduce micro pile instability energy potential function and te bifurcation set equation, in tis way, te micro pile limit bearing capacity formula is obtained. In te landslide using te micro pile to reinforcement, te anti-sliding experiment is conducted. We compare te results of te cusp catastrope teory and te results of te validation. Te results sow tat te catastrope teory to study te level of te micro anti-slide pile bearing force is feasible, wic as a certain engineering value. Keywords:Catastrope teory, Micropiles, Lateral capacity bearing, Field test, Engineering application 1. Introduction Micro pile, also called as te root pile, was proposed by Lizzi(Andrew ZB, 6) in Italy in 195s. Furtermore, te ole bored pile wit a small diameter are firstly developed and utilized by Fonddile(Juran H.et al., 1996) company. Te diameter is generally 1 ~ 3 cm and te lengt/diameter ratio is more tan 3. Moreover, te pile is composed by te reinforcement materials and te cement mortar grouted by te pressure or te small stone concrete. As a new type of supporting tecnology, te micro pile as experienced wit te rapid development and te wide application in te engineering practice, wic is mainly applied in te embankment engineering, deep foundation, warf, anti-seismic reinforcement of te buildings and te landslide treatment etc. (S. Isam.et al.,1; J.D. Nelson et al., 1; M. Esmaeili et al., 13; Yan J. K. et al., 11; Liu H. et al., 13). Nowadays, te supporting tecnology of te micro anti-slide pile as musroomed, but te teory of te anti-sliding mecanism and related design is immature, wic seriously lags beind te engineering application (Liu H. et al., 13). Especially in te process of te anti- sliding trust, tere is little discussions about te orizontal bearing capacity wen it is under te load effect of te level. Tis tesis takes te advantages of te micro piles to researc on te anti-sliding pile bearing capacity of te micro piles. Furtermore, it as acieved some researc results in te researc of te micro piles against sliding mecanism and orizontal load force calculation, including te metod of beam on elastic foundation,p - y curve metod, te ultimate ground resistance metod, te double parameters improvement metod of te elastic subgrade reaction metod and te numerical simulation metod (Wang M. et al.,; Sun S.W. et al., 13; Broms B.B., 1964; Sun K.M., 1994; Rajasree S.S. et al., 1). In tis paper, te micro piles are used in te treatment of te landslide control. Te destruction of te micro piles belongs to te scope of te catastrope teory under te orizontal force of te landslide (Feng J. et al.,6). First of all, we analyze te orizontal bearing capacity of te micro pile under te influence factors of te landslide trust. Te catastrope teory is introduced into te micro

2 Vietrock15 an ISRM specialized conference Vietrock Marc 15, Hanoi, Vietnam pile buckling damage levels to determine te critical load. We ave establised te micro pile buckling sarp point Mutation model wit te free top and fixed bottom. It is concluded tat te calculating formula of te orizontal critical load. Pusing te micro pile test is also carried out. Troug ierarcical load test, we study te caracteristics and distribution pattern of te micro-pile body bending moment in te loading process of eac row. From te ierarcical load, we ave a basic understanding of te anti- trust mecanism of te micro pile composite structure. We also compare te orizontal load test results wit te field test by te catastrope teory to verify te feasibility of tis metod.. Te analysis model based on catastrope teory.1 Te introduction of te catastrope teory Catastrope teory, on te basis of te teory of structural stability, put forward a new criterion of instability criterion. Te application of te current workis te relatively sopisticated cusp catastrope teory model; it is made up of two stable points and an unbalanced point wit te equilibrium evolution. Te mutation appens at te turning point to establis a new equilibrium (Cen Y.H.,9). Terefore, tis paper is accordance wit te micro pile in te level border instability failure process and use te cusp catastropic model to analyze.. Nonlinear te establisment of te cuspcatastropic model Cusp catastropic model is put forward by Zeeman(Pang Y. et al., ;Zeeman E. 19). Its function standard formula is as follows: ( x) x ux vx (1) 4 Were, x is te state variables, u and v are te controlvariables. Te equation of a surface of te correspondingequilibrium position sould meet te followingcondition: 3 ( x) x ux v () Te vertical tangent of te surface is namely tattere are two lines on te profile of equilibrium. Tepoint set S of te vertical tangent is: ( x) 3x u (3) In te formula (3), te points wic are around tecritical points of te curve are called as te catastropepoints. Te formula () and (3) divided by x is to constitutete bifurcation set equation in te parameter space: 3 4u 7v (4).3 Te analysis of te micro piles critical condition in buckling and mutation According to te cusp catastropic model todetermine te bifurcation set equation (4), wen,te root pile is in a stable region and te pile is stable; wen, it means tat pile is not in te steadystate. Wen crossing te borderline, mutations appen.at tis time,u,, te equation (4) as tree realroot, one of te smallest is te critical value of te micropile orizontal bearing capacity. 3. Te flat bearing capacity of te micro pile analysisbased on cusp catastrope teory 3.1 Te establisment of te mecanics model Te micro-pile is used to treat landslide. Teanti-sliding effect can be sowed in two aspects: firstly,te micro piles are under te larger force of slidingsurface to enance te capacity of te sear slide.secondly, te formation of te anti-sliding body of tepile and soil and te collaborative resistance landslidetrust (Wu W.P. et al., 9). In te analysis of te micro pile orizontalbearing capacity, te pile soil system is simplifiedfirstly wit mecanics, tus we make te followingassumptions (assuming te simplified model is sown infigure 1: (1) Te parts below te sliding surface are fixed inte bedrock. Te sliding surface is te fixed constraint.if we assume te micro pile above part of te landslideis under te uniform landslide trust; () Te micro-pile connects wit cap troug tefixed contact form. Te landslide trust is put on temicro pile, because te micro pile is constricted by tecap wic is not fixed. But tere is certain

3 Vietrock15 an ISRM specialized conference Vietrock Marc 15, Hanoi, Vietnam displacement,so te tree rows of tiny pile is simplified for te freetop and te fixed bottom in te forms of constraint; (3) Te anti-sliding mecanism of te root pilecomposite structures is analyzed according to teprinciple of pile - soil interaction. Pile1 Pile Pile3 Slip surface m Fig. 1.Hypotesis model of micropiles composite structure. 3. Te micro-pile at te top of freedom, te bottom of te built-in outburst cusp Because te micro-pile connects fixedly wit cap topbeam, te top beam is as a rigid member wit onlyorizontal displacement. Te orizontal displacement ofte top beam is equal. And te micro pile below te slipsurface part is fixed in te bedrock, wile te slidingsurface is fixed constraint. Terefore, we put te treerows in accordance wit te free top and te bottomembedded solid as our analysis basis as sown in figure. Beam Te ground p(x) q(x) Trust from Landslide Slip surface Micro- pile Fig..Micropiles simplified mecanical model of top-free and bottom-fixed. (1) Determination of te potential function On tebasis of te ypotesis mecanics model, we can get tetotal potential energy of te mecanics model system,and ten we build te expression of potential functionand use te matematical metod to turn it into testandard accurate expression of te cusp catastropicmodel. Te axis deflection line of te micro pile is asfollows: ( x) 1 cos s L (5) Were, ω is te deflection of te axis midpoint ofte micro pile, s is arc lengt, L is te lengt of telandslide surface above. Te potential function of testandard form is: ( x) U1 U W1 (6) Were, U 1 is te bending strain of te micro pile, U is te increased potential energy of te system, and W 1 is te orizontal force. By te principle of mecanics of elasticity, we know te bending strain of te micro pile system is: 1 EI U1 ( x) 1 ( x) dx (7)

4 Vietrock15 an ISRM specialized conference Vietrock Marc 15, Hanoi, Vietnam Were, E is te micro pile elastic modulus, I is te moment of inertia of te micro pile, is te lengt of te micro piles above te landslide surface. Te increased potential energy of te system is as follows: ( ) a ( ) ( ) 1 ( ) 1 () U p x R q x dx f L x x dx Were, p(x) is te level soil resistance of x, R a is te critical value of orizontal bearing capacity of pile, and q is te orizontal load of te micro pile by te landslide. W 1 is te power of te orizontal pressure: 1 W 1 p( x) Ra q ( L x) ( x) dx (9) Ten, te standard form of potential function is: 1 a EI ( x) ( x) 1 ( x) dx p( x) R q ( x) dx 1 a f ( L x) 1 ( x) 1 dx p( x) R q ( L x) ( x) dx Were f is te force between te pile and soil, f=dμ, d is te pile s circumference, μis soil force per unitarea of te pile side. We assume te p(x) as te orizontal resistance of x, tat is to say, p(x)=kw i bin wic k is te lateral resistance coefficient. And we assume tat te ground is, wit te increase of te dept, terefore, k=m(-x), b is te calculating widt, m is te orizontal resistance coefficient of pile lateral soil. Wen te soil is composed of several layers, mis: m1 1 m ( 1 ) m3 (1 3 ) 3 m (11) ( 1 3 ) Te formula wit te Taylor series x= is to expand in place. After simplified, te potential function of standard form of te micro pile composite system is as follows: 64EI (1 ) ( q km R 3 kml) d ( x) 3L L L 4 4 EI a 6 3 km(16 ) 3L 4L Transform te above formula, and assume: ( q km Ra )(4 ) 3L 4 64EI 4 EI (1 ) ( q km Ra 3 kml) d 3L u L L 64EI km(16 ) ( q km Ra )(4 ) 3L v 4 3L 4L 64EI ()Te determination of critical load of te micro pile Terefore, according to te critical condition of te micro pile buckling mutation, we know tat te sufficient and necessary condition for te micro pile system is as follows: (1) (1) (13) u After making furter derivation, it can know tat: 3 4u 7v (14)

5 Vietrock15 an ISRM specialized conference Vietrock Marc 15, Hanoi, Vietnam a 3 4u 7v 4 3 EI 1 L q km R 3kml d Terefore, te micro piles system is free in te top, wile te bottom is embedded wit bearing capacity of te solid and te critical assumptions. Under te condition of, and Δ=, tree equations can be obtained. Te root wit minimum value of te tree root is taken as te critical load values of te micro-pile. 4. Field test 4.1 Te condition of sites Te landslide of a igway is medium type wit wide About -1m, lengt 16m, te tickness of te front about 5m, central part 1-15m, back part 3.5-.m, te average tickness of te landslide about 1 m and te total volume of landslide about 16, m3. Te factors of landslide are typical wit te slope facing te empty and te steep slope. Te features of landslide appearance are obvious. Te back as tensile cracks. Te two sides ave te pinnate crack. Te front is flanked by sear seam wit te ballooning of extrusion forming crack and radioactive cracks. In its reinforcement design, it adopts steel tube of te micro piles to make te reinforcement. 4. Te principle of te test Experiment uses te metod of jack ierarcical load. Te micro piles composite structure is analyzed te wole process from te load to te destruction. Wat s more, we also analyze te governance mecanism and limit state of eac row of micro pile structure in landslide treatment, te stress of eac row and te eart pressure cange of te landslide mass situation. Te inspection of te installation of te micro piles before and after and eart pressure force box is to monitor te force of eac row of te micro pile. We use te pipe steel bar meter weld on te micro pile to measure te deformation of pile body and te approximation measurement of installing te side inclined tube. Under te orizontal load of te eart pressure, we test te forces between eac pile before and after pile soil. Te steel bar meter is applied to measure te deformation and stress of te inclined tube pile body. Test model diagram is as sown in figure 3, and te arrangement of te test site root pile composite structure is as sown in figure 4..5m (15) Inclinometer tube Trust 1# # 3# 4# 5# 6# Reinforced stress meter Eart pressure cells Fig. 3.Te scematic drawing of test model on micropiles composite structure. Fig. 4.Site layout of micropiles composite structure. 4.3 Te experimental materials (1) Grouting micro steel pipe piles Te test te in-situ uses te micro pile of te reinforcement. Te grouting coagulation Soil strengt grade is C5. Te micro pile lengt cooses te landslide segment, wic is m lengt. Te pile diameter is 15mm and te tube diameter is 5mm. te main reinforcement pile cooses 3 root,

6 Vietrock15 an ISRM specialized conference Vietrock Marc 15, Hanoi, Vietnam reinforced steel pipes. Te microcap sets C3 concrete capping beam wit te beam.5m eigt and 1.5m widt. Te micro-pile section is as sown in figure 5: Fig. 5.Micropiles sectional drawing. () Te field test of te soil Te material of te landslide is mainly sediments on te surface of te mountain, te soil pysical and mecanical properties and te indicators is as in te table 1. (3) Te experimental process and data acquisition In accordance wit te requirements for load test, te test IS conducted wit grade 11 effective load, using te two gauges to record te data. And te average works as te final result. Wen on te 1t Level (96 t) load, te counterforce device occurs damages. Tereby, te test finises. Te load of te destruction is te Horizontal limit load. At te maximum bending moment section, te steel of te tensile zone yielding is te corresponding load. Table 1Mecanical parameters of in-situ rock. Parameter Elastic modulus (MPa) Poisson's ratio Density (kn/m 3 ) Material coesive force (kpa) Material frictional angle ( ) Mudstone Silty clay Te comparison and analysis of te experimental results According to te result of experiment and te calculation based on te catastrope teory, we draw te orizontal load - displacement gradient curve as sown in figure 5. As we can see from te figure, since te micro pile combination structure is under te action of orizontal force, te critical and ultimate load metod is used to determinate te critical orizontal load test of pile group wic is 13 kpa; It is concluded tat te critical level of te load for catastrope teory calculation is close to kpa, and test te pase wic furter validate te reliability of te orizontal sliding resistance of te micro pile based on catastrope teory model. Te mutations teory is used to calculate te critical bearing capacity Displacement gradient (mm/kpa )Horizontal load(kpa ) Displacement gradient (mm/kpa )Horizontal load(kpa ). a)te orizontal bearing capacity by testb) Te orizontal bearing capacity by catastrope teory Fig. 6.Te relationsip of orizontal load and displacement gradient. 6. Conclusions Tis paper focuses on te composite structure of micro pile in te treating te landslide control, te cusp mutation teory is used to analyze te critical load by te miniature pile buckling. We set up te

7 Vietrock15 an ISRM specialized conference Vietrock Marc 15, Hanoi, Vietnam free top, but te bottom is in te consolidation, te sarp point mutation of te micro pile buckling destruction can be acieved. Wit te researc, we can get te following conclusions: (1)By set up te free top, but te bottom is in te consolidation, te cusp catastropic model can be reaced. We also derive energy potential function and bifurcation set equation of te micro pile instability, we conclude level limit bearing capacity formula of te micro pile. ()By make te comparison of te limit orizontal loads between te cusp catastrope teory model and te field experiment. We can draw an conclusion, based on te analysis of te catastrope teory model value and field test value, te limit orizontal load is similar, wic verifies e feasibility of te orizontal bearing capacity of pile model based on catastrope teory. It as certain teoretical and engineering practical value.. Acknowledgements Te autors gratefully acknowledge te support of National & Local United Engineering Laboratory of Mountain Traffic Disaster Prevention and Control Tecnology. References Andrew ZB, 6, Load transferrin micropiles for slope stabilization from tests of large-scale pysical models, University of Missouri-Columbia, -. JuranH., BenslimaneA., Bruce D. A., 1996, Slope stabilization by micropile reinforcement,landslides. S. Isam. A. Hassa and S. Mamed, 1, 3D elastoplastic analysis of te seismic performance of inclined micropiles, Computers and Geotecnics, (39):1-7. J.D. Nelson, R.W. Scaut and D.D. Overton, 1, Design procedure and considerations for piers in expansive soils, J. Geotec. Geoenviron.Eng, (13): M. Esmaeili, M. G. Nik and F. Kayyer, 13, Experimental and numerical study of micropilesto reinforce ig railway embankmentsmortezaesmaeili, Int. J. Geomec, (13): Yan J.K., Yin Y.P. and MEN Y.M., 11, Model test study of landslide reinforcement wit micropile groups, Cina Civil Engineering Journal, 44(4): 1-1. Liu H., Zou P.D. and Zang Y.F, 13, Model test of anti-sliding mecanism of micro-pile combined structure, Rock and Soil Mecanics, 34(1): Wang M., Lou Z.G. and Li J.X.,, Numerical analysis of m metod for single pile under lateral loading, Rock and soil mecanics, 3(1): 3-3. Sun S.W., Wang J.C. and Bian X.L., 13, Design of micropiles to increase eart slopes stability, J. Cent. Sout Univ, (): Broms B.B., 1964, Lateral resistance of piles in coesive Soil, Journal of te Soil Mecanics and Foundations Division, 9(): Sun K.M.,1994, A numerical metod for laterally loaded piles, Computers and Geotecnics, (16): Rajasree S.S. and SITHARAM T.G., 1, Nonlinear finite-element modeling of batter piles under lateral load, Journal of Geotecnical and Geoenvironmental Engineering, 17(7): FengJ., Zou D.P. and Jiang N., 6, A model for calculation of internal force of micropile system to reinforce bedding rock slope, Cinese Journal of Rock Mecanics and Engineering, 5(): 4-. Cen Y.H., Wang X.Q. and Liu H.L., 9, Bucking critical load analysis of Y style vibro-pile based on cusp catastrope teory, Engineering Mecanics, 6(4): Pang Y., Wang Z.Q.,, Catastrope Teory in te system of rock dynamic instability, Beijing: Science Press,. Zeeman E. and C. Bifurcation, 19, Catastropes and Turbulence, New Directions in Applied Matematics, New York: Springer-Verlag, Wu W.P., Zou P.D. and Wang H.L., 9, Model based on experimental researc micropile structural reinforcement slope, Subgrade Engineering, (7):