Abstract:The underground space in urban areas is frequently congested with utilities,including pipelines and conduits,that are affected by underground ,tunneling.This paper carries out finite element(FE)analys to investigate the effects of tunneling-induced ground movement on pipelines,with special attention to the different soil respons to uplift and downward pipe–soi雅思作文
l relative movements.A ries of numerical parametric studies with900FE simulation runs in total is performed to encompass various combinations of ground ttlement profiles,pipe dimensions,material properties,pipe burial depth,and soil properties that are typical for utility pipelines and tunnel construction in urban areas.The results are summarized in a dimensionless plot of relative pipe–soil stiffness versus ratio of maximum pipe curvature to maximum ground curvature,which can be ud to directly estimate the maximum pipe bending strain and(or)to directly asss the tunneling-induced risk to pipelines.The FE results and dimensionless plot are validated against field and centrifuge test re-sults reported in the literature.Effect of pipeline orientation with respect to the tunnel centerline is explor
ed.It might be un-conrvative if design analysis only considers the ca that the pipeline is perpendicular to the tunnel centerline.
Key words:finite element analysis,ground movements,dimensionless plot,pipe safety criteria,pipeline orientation.
Rsum:La partie souterraine des zones urbaines comprend frquemment un grand nombre de commodits,incluant des pipelines et conduites,qui sont affectes par la construction souterraine,par exemple le creevading
ument de tunnels.Cet article prnte des analys parlments finis(EF)ralis dans le but d’tudier les effets des mouvements du sol induits par le creument de tunnels sur les tuyaux,avec une attention spciale sur les diffrentes rpons du sol en raction aux mouve-ments relatifs sol-tuyau vers le haut et vers le bas.Unetude paramtrique numrique,avec un total de900simulations EF, est rali afin de couvrir diffrentes combinaisons de profils de tasment du sol,de dimension du tuyau,de proprits des matriaux,de profondeur d’enfouisment du tuyau,et de proprits des sols qui sont typiques des conduites de commo-dits et de construction de tunnels dans les zones urbaines.Les rsultats sont rsums dans un graphique sans dimension de la rigiditrelative tuyau-sol versus le ratio de la cambrure maximale du tuyau sur la cambrure maximale du sol.Ce gra-phique peuttre utilispour estimer directement la dformation duela flexio
n maximale du tuyau et(ou)pourvaluer di-rectement le risque pour les pipelines dau creument de tunnels.Les rsultats d’EF et le graphique sont validsl’aide de rsultats d’essais sur le terrain et en centrifuge prnts dans la littrature.L’effet de l’orientation du pipeline lon la ligne centrale du tunnel est explor.Il mble que l’analy de conception n’est pas conrvatrice si l’on considre ule-ment le cas ole pipeline est perpendiculairela ligne centrale du tunnel.
Mots‐cls:analy parlments finis,mouvements du sol,graphique sans dimension,critres de scuritdes tuyaux,orien-tation du pipeline.
[Traduit par la Rdaction]
Introduction
The underground space in urban areas is frequently con-gested with utilities,including pipelines and conduits,that are affected by underground construction, e.g.,tunneling. Tunneling-induced ground movements cau pipeline defor-mation that may disrupt the conveyance of important rvices and ,water,gas,electric power,and telecom-munications)and threaten the safety and curity of urban ,flooding and leakage of combustible gas from ruptured or leaking mains).The interaction between under-ground utility pipelines and the surrounding soil has attracted
growing rearch attention ,Rajani et al.1996; Rajani and Tesfamariam2004;Hawlader et al.2006),partic-ularly the tunneling-induced ground movement effect on buried ,Attewell et al.1986;Vorster et al. 2005;Klar et al.2005,2007,2008;Marshall et al.2010; Wang et al.2010,2011).To evaluate the effects of tunneling-induced ground movements on underground util-ities,it is necessary to(i)characterize the distributed ttle-ment at shallow depths typical of most utilities,and (ii)account rationally for the interaction between
pipeline
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and soil associated with tunneling-induced patterns of soil 榧子
movement.In addition,the evaluation results should be vali-dated against obrvations from field and(or)centrifuge tests.
There has been substantial work performed on the charac-terization of ground movement patterns caud by tunneling.
A Gaussian approximation is commonly ud to describe the three-dimensional shape of the ttlement profile,particularly the distribution of ttlement transver to the longitudinal axis of the tunnel.Such approximation has been shown to compare favorably with field measurements reported by many ,Peck1969;O’Reilly and New 1982;New and O’Reilly1991;Mair et al.1993;New and Bowers1994)and with model test results in , Chapman et al.2007).Analytical methods have been devel-oped to evaluate the buried pipeline respons to tunneling-induced ground movements,such as Winkler-bad methods (e.g.,Attewell et al.1986;Wang et al.2010)and continuum ,Klar et al.2005;Vorster et al.2005). Although the methods are different in many aspects,they share one common assumption,that is,the pipe–soil interac-tion is identical in both uplift and downward pipe move-ments.It has been well recognized,however,that soil resistance to pipe uplift is different from that associated with
downward movements of pipes,particularly for pipes buried at shallow depths(Trautmann and O’Rourke1983;Commit-tee on Gas and Liquid Fuel Lifelines1984;Trautmann et al. 1985;Honegger and Nyman2004).In addition,previous
studies focud on the alignment where the tunnel centerline is perpendicular to the pipeline longitudinal axis.Pipelines in reality,however,may interct the tunnel centerline at an an-gle that varies from0(parallel)to90(perpendicular). This paper carries out finite element(FE)analys to in-vestigate the effects of tunneling-induced ground movement on pipelines,devoting special attention to the different soil respons to uplift and downward pipe movements and pipe-line orientation with respect to the tunnel centerline.It starts with brief reviews on ground movements induced by tunnel-ing and the different soil resistances to uplift and downward pipe movements.Then,the FE analys are performed,and their results are validated against results from full-scale field and centrifuge tests.Subquently,a ries of FE parametric studies is carried out,and its results are summarized in a di-mensionless plot to facilitate estimation of pipe respons to tunneling-induced ground movement.Finally,the effect of pipeline orientation with respect to the tunnel centerline is explored.
Tunneling-induced ground movements
Figure1shows a schematic view of tunneling-induced ground ttlement,S(x,y),at horizontal ground , XY plane)where the tunnel centerline is positioned along the X ,y=0)(Attewell et al.1986).The S(x,y)can be expresd as(New and O’Reilly1991)
1 Sx;yS max
2exp
y2
2i2
erf
xX f
i
ffiffiffi
2
p
!
erf
xX s
i
ffiffiffi
2
p
!
"#
where S max is the maximum ttlement;i is the distance be-tween the tunnel centerline and the inflection point of the t-tlement trough;erf(x)is the error function;and X s and X f are the starting and final locations of the tunnel face,re-spectively.For locations that are far away from the starting and final locations of the tunnel face,the ttlement S(y) along the transver direction of the tunnel ,x is constant)can be simplified as(e Fig.1b)
2 SyS max exp
y2
2i2
Such Gaussian approximation of ground ttlement profiles has been shown to compare favorably with field measure-ments reported by many ,Peck1969; O’Reilly and New1982;New and O’Reilly1991;Mair et al. 1993;New and Bowers1994)and with model test results in ,Chapman et al.2007).
Pipe–soil interaction
As the tunneling-induced movements occur in soil sur-rounding existing pipelines,distributed loads are impod in the pipelines through the soil.To evaluate the effects of tunneling-induced ground movements on underground pipe-lines,it is necessary to account rationally for the pipe–soil interaction,which is different and depends on the direction of the pipe–soil relative movements.Figure2shows force–displacement respons of pipe–soil interactions for up-Fig.1.Three-dimensional view of tunneling-induced ground ttle-ment:(a)three-dimensional view;(b)cross ction A–A(modified after Attewell et al.1986).
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ward pipe movement (Fig.2a )and downward pipe movement (Fig.2b ).Although the elastoplastic force –displacement re-spons in Figs.2a and 2b em similar,and are both fre-quently simplified using a linearly elastic and perfectly plastic model (i.e.,the dashed lines in Fig.2),the maximum resistance forces (i.e.,q u and q d for upward and downward pipe movements,respectively)and their associated thresholds of pipe –soil relative displacements (i.e.,d ru and d rd for up-ward and downward pipe movements,respectively)are quite different.The maximum resistance force,q u ,for pipe uplift is frequently estimated as (Trautmann and O ’Rourke 1983;Committee on Gas and Liquid Fuel Lifelines 1984;Traut-mann et al.1985;Honegger and Nyman 2004),3
q u N v g HD
where N v is a dimensionless uplift factor estimated from de-sign charts (Committee on Gas and Liquid Fuel Lifelines 1984),g is the soil bulk unit weight,H is the burial depth to pipe center,and D is the pipe outer diameter.The typical range of d ru required for the full mobilization of q u is propor-tional to the value of H (i.e.,0.005–0.015H for sands,0.1–0.2H for clays (Committee on Gas and Liquid Fuel Lifelines 1984)).In contrast,the bearing capacity equation for strip foundations is commonly ud to estimate the maximum re-sistance force,q d ,for downward pipe movement,4
q d g HN q D 1
2
g D 2N g
where N q and N g are Vesic ’s bearing capacity factors for ver-tical strip footings.The typical range of d rd required for the full mobilization of q d is proportional to the value of D (i.e.,0.10–0.15D for both sands and clays (Committee on Gas and Liquid Fuel Lifelines 1984)).
In general,the value of q u differs substantially from the q d value.Consider,for example,a steel pipe,with D =0.165m and wall thickness T =5mm,buried in den sand with H =1.58m,soil bulk unit weight g =20kN/m 3and friction angle f 0=40.As utility pipelines are typically buried at shallow depths and above the ground water table,the soil properties ud in this work correspond to tho under dry conditions.Bad on the friction angle and ratio of depth to diameter,the design chart gives an N v value of 7.8.In addi-tion,N q and N g are estimated to be 64.2and 95.5,respec-tively.Using eq.[女孩的英文怎么写
3]and eq.[4]results in q u =38.7kN/m and q d =361.7kN/m;they differ by about one order of mag-nitude.Note that previous studies (e.g.,Klar et al.2005;Vor-ster et al.2005;Wang et al.2010)have shown that pipeline displacement at the center of a ttlement trough is smaller than the corresponding ground ttlement at the same loca-tion.This leads to relative upward pipe movement
s in this re-gion,as oppod to the rela百岁老人祝寿贺词
tive downward pipe movement that occurs in other regions where the pipeline displacement is larger than or equal to the corresponding ground ttlement at the same location.As different pipe –soil relative move-ments with opposite directions occur along the pipeline,proper evaluation of tunneling-induced ground movement ef-fects on buried pipelines requires rational treatment of differ-ent soil respons to uplift and downward movements.FE analysis with explicit consideration of such different pipe –soil interactions is carried out in this work and described in the next ction.
Finite element analysis and its validation
FE analysis is carried out in this work to investigate tun-neling-induced ground movement effects on pipelines,using the software package ABAQUS (2006).As illustrated in Fig.3,continuous pipe gments and pipe –soil interactions are simulated explicitly in the FE analysis.Beam elements with pipe cross ctions are ud to simulate pipe gments我们自己的英文
,and the pipe –soil interaction is modeled by pipe –soil interaction (PSI)elements in ABAQUS.The PSI element in ABAQUS is formulated according to the American Society of Civil Engi-neers (ASCE)Guidelines for the ismic design of oil and gas pipeline systems (Committee on Gas and Liquid Fuel Lifelines 1984)and models explicitly the different soil re-spons to uplift and downward movements using two pa-rate nonlinear force
–displacement relationships in uplift and downward movements (e Fig.2),respectively.Similar to Winkler-bad methods,the tunneling-induced ground dis-placements are impod on the PSI elements as distributed displacement boundary conditions.
FE analysis is carried out to simulate a full-scale field test reported by Takagi et al.(1984).A国庆节作文600字作文
13.5m long steel pipe with D =0.165m and T =5mm was buried at a depth of 1.5m to the top of the pipe (i.e.,H =1.58m)before the advancement of a 2.42m radius tunnel at a depth of 8.35m.The pipe was aligned along the transver direction of the tunnel centerline,and the pipe length at the left-or right-hand side of the centerline was 7.3or 6.2m,respectively.Soil bulk unit weight and friction angle are g =20kN/m 3and f 0=40,respectively.The steel pipe has a Young ’s modulus E =210GPa and Poisson ’s ratio n =0.3.As mentioned in the previous ction,q u =38.7kN/m and q d =361.7kN/m.The d
ru
Fig.2.Force –displacement respon of pipe –soil interaction:(a )up-ward movement;(b )downward movement.
Wang et al.
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and d rd are estimated as d ru =0.01H =0.011.58m =15.8mm and d rd =0.1D =0.1165mm =16.5mm,respectively.Figure 4a shows the measured ground ttlement due to tunneling.The measured ground ttlement can be reasonably approximated by eq.[2]with S max =0.045m and i =2.51m.The simulated pipe deflection from the FE anal-ysis is shown by a dashed line in Fig.4a .The
pipe is rela-tively flexible with respect to the surrounding soil,and the pipe deflection at the center of the ttlement trough is smaller than the ground ttlement,resulting in relative pipe uplift in this region.This agrees well with the aforemen-tioned results from previous studies (e.g.,Klar et al.2005;Vorster et al.2005;Wang et al.2010,2011).
Takagi et al.(1984)installed many strain gauges at the pipe crown and invert along the buried pipe.Figure 4b shows the measured pipe strain along this 13.5m long pipe,as well as the FE simulation results.As the pipe is slightly asymmet-ric with respect to the tunnel centerline,the be4s店服务顾问
nding moment and pipe strain obtained from the FE simulation are also slightly asymmetric.The strain distribution obtained from the FE analysis is consistent with that from a strain gauge measurement along the pipe.The maximum strains occur be-low the center of the ttlement trough for both FE results and field measurements.This agrees well with results from previous studies (e.g.,Attewell et al.1986;Klar et al.2005;Vorster et al.2005;Wang et al.2010,2011).The good agreement among results from FE analysis,field test,and previous studies shows that,with a given ground ttlement profile (i.e.,i and S max ),pipe dimension (i.e.,D and T ),pipe material properties (i.e.,E and n ),pipe burial depth (i.e.,H ),and soil properties (i.e.,g and f 0),the FE analysis in this work simulates the pipe –soil –tunnel interaction reasonably well.Then,a ries of FE parametric studies is
carried out to investigate systematically the effect of tunneling-induced ground movements on underground pipes,as described in the next ction.
Parametric study
The numerical parametric study contains 900FE simula-tion runs to encompass various combinations of ground t-tlement profiles,pipe dimensions,material properties,and soil properties that are typical for utility pipelines and tunnel
construction in urban areas.Table 1summarizes the ground ttlement profiles in the parametric study.The values of i and S max vary from 2to 6m and from 0.025to 0.3m,re-spectively.As summarized in Table 2,six reprentative pipes are considered,with D and T varying from 0.14to 1.02m and from 6to 26mm,respectively.Two common material types (i.e.,steel and ductile iron)for continuous pipes are simulated in the parametric study,and their respec-tive E and n values are summarized in Table 3.Three differ-ent soil conditions,(i.e.,loo,medium,and den sand)are considered in the parametric study,and the soil friction an-gle,f 0,and bulk unit weight,g ,vary,respectively,from 30to 40and 16.0to 20.0kN/m 3,as shown in Table 4.The pipe burial depth to the top of the pipe varies from 0.9to 1.5m,which are typical for utility pipelines in urban areas.Dimensionless plot of relative pipe –soil stiffness versus curvature ratio
The results of 900FE runs are summarized in Fig.5with two
dimensionless parameters,k pmax /k gmax and [E p I p /(K 0:9u K 0:1d i 4
)](S max /i )0.5.k pmax is the maximum pipe curvature that occurs right below the S max or above the tunnel centerline,and it is expresd as 5
k pmax
M max E p I p
where M max is the the maximum pipe bending moment;E p is the pipe ’s Young ’s modulus;and I p is the moment of inertia of a pipe ction.k pmax can be ud conveniently to estimate maximum pipe bending strain,3pmax ,as 6
3pmax D
2
k pmax
k gmax is the maximum ground curvature that occurs at the lo-cation of S max or above the tunnel centerline.Using eq.[2]leads to an expression of k gmax as 7
k gmax
S max i 2
The vertical axis in Fig.,k pmax /k gmax ),therefore,rep-rents the ratio of the resulting pipe respons to their re-spective tunneling-induced ground movements.The horizontal
axis in Fig.5,[E p I p /(K 0:9u K 0:1d i 4)](S max /i )0.5,is the relative
pipe –soil stiffness,where K u and K d are the soil subgrade modulus in upward and downward relative pipe –soil move-ments,respectively.They are expresd as 8
K u
q u d ru
and K d
q d d rd
Figure 5plots the data pairs of k pmax /k gmax and [E p I p /(K 0:9u K 0:1d i 4)](S max /i )0.5S max =i
0:5from the 900FE runs as open squares.The data points in Fig.5reveal a relationship that
k pmax /k gmax decreas from one to zero as [E p I p /(K 0:9u K 0:1d i 4
)](S max /i )0.5increas from about 1.010–5to about 1.0102.
When the relative pipe –soil stiffness [E p I p /(K 0:9u K 0:1d i 4)](S max /i )
0.5is small (i.e.,<1.010–4),the pipe is relatively flexible with re-spect to its surrounding soil.The pipe,therefore,deforms coinci-dentally with the ground ttlement,and k pmax ≈k gmax or k pmax
/
Fig.3.An illustration of finite element analysis of pipeline re-spons to tunneling-induced ground movement.
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Can.Geotech.J.Vol.48,2011
k gmax approaches one.When the relative pipe –soil stiffness [E p I p /(K 0:9u K 0:1d i 4)](S max /i )
0.5is large (i.e.,>10),the pipe is relatively rigid with respect to its surrounding soil,and the pipe deflection caud by movement of the surrounding soil is minimal,result-ing in k pmax /k gmax ≈0.
Regression analysis on the 900data points in the figure was then carried out,and it was found that they can be repre-
0–8
–6
–4
–2024
6
8
P i p e d e f l e c t i o n o r g r o u n d s e t t l e m e n t (m )
–3.010
–1.0101.0103.0105.010
7.0109.010P i p e s t r a i n ,e
–12.0
–9.0–6.0
–3.00.03.06.09.012.0
B e n d i n g m o m e n t ,M (k N m )
(b)(a)Pipe length, x (m)
Pipe length, x (m)
Fig.4.Validation of finite element analysis results:(a )ttlement;(b )strain.
Table 1.Summary of ground ttlement profiles in FE para-metric study.i (m)S max (m)20.0250.0500.0750.1000.2000.30030.0250.0500.0750.1000.2000.30040.0250.0500.0750.1000.2000.3006
0.025
0.0500.0750.1000.2000.300
Table 2.Summary of pipe dimension in FE parametric study.Pipe dimension Pipe 1Pipe 2Pipe 3Pipe 4Pipe 5Pipe 6Diameter,D (m)
0.140.270.510.610.81 1.02Wall thickness,T (mm)
6
6
10
10
13
26
Table 3.Summary of pipe material properties in FE parametric study.Material type Young ’s modulus,E (GPa)Poisson ’s ratio,n Steel
2100.3Ductile iron
84
0.3
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