A Different View on TBM Face Equilibrium in Permeable Ground

Transcription

1 A Differet View o TBM Face Equilibrium i Permeable Groud Tiago Gerheim Souza Dias Ghet Uiversity, Ghet, Belgium Adam Bezuije Ghet Uiversity, Ghet, Belgium ad Deltares, Delft, the Netherlads ABSTACT The costructio of mechaized tuels i soft groud has evolved sigificatly over the last 0 years, especially i the cotrol of the face pressure ad the closure of the soil-liig void to reduce the iduced settlemets. O the other had, several mechaisms of the TBM excavatio cycle are still ot take ito accout for routie desig calculatios, such as the icremet of water pressures i frot of the tuel face, the flow of excavatio fluids aroud the shield, the dyamic equilibrium betwee the grout pressures ad the excavatio covergece, amog others. This paper discusses specifically the issue of face pressures ad how several mechaisms, which are routiely ot cosidered, ca be easily verified ad icorporated ito the state-of-practice of desig. INTODUCTION The stability of udergroud excavatios is traditioally assessed through aalytical solutios based o the lower boud theorem of plasticity (Atkiso ad Potts 1977; Mühlhaus 1985) or the limit equilibrium method (Aagostou ad Kovári 1994; Messerli et al. 010). These methodologies deped o the tuel geometry, certai groud parameters ad the support pressure. Whe covetioal costructio methods are used, the iteral support pressure is a abstract represetatio of the combied effects of partial excavatio, groud reiforcemet, ad the differet support elemets. The use of closed-face tuel borig machies (TBM) chaged this perspective, as the magitude of pressures actig o the excavatio boudary could be cotrolled i a more direct way. I frot of the TBM the groud is excavated as the cutterhead rotates ad the cuttig tools scrape the groud from the tuel face while additives are ijected to coditio the material. Water, polymers, betoite, ad foam ca be used as additives uder differet coditios (Thewes et al. 01). The looseed groud with additives, herei referred to as the mixture, flows through the opeigs at the cutterhead ad ito the excavatio chamber. This mixture is kept pressurized to support the face. These ad all other TBM processes ca be actively cotrolled through the operatio of mechaical or hydraulic systems that make up the machie. It is self-evidet that for each of these TBM actios there will be a reactio from the groud to achieve equilibrium. However, this last poit is frequetly overlooked, resultig i idealized cocepts of how mechaized tuelig works. Most importatly, these frameworks fail to explai importat features of groud respose that have bee observed i the field (Bezuije ad Talmo 008; Dias ad Bezuije 015). Noetheless, it is fair to say that this is somethig geerally kow ad discussed i the specialized academic commuity. However, to the 1

2 authors kowledge, most projects still use these idealized cocepts, with a few exceptios of challegig projects (Aime et al. 004; Kaalberg et al. 014) ad post-mortem ivestigatios of projects that did ot go as expected. Therefore, a realistic improvemet i the desig practice of mechaized tuels i soft groud would be to uderstad why that is the case ad how these models ca be icorporated ito the state-of-practice. I this paper, the framework describig the mechaisms aroud the face of a TBM will be discussed. The first poit to be recogized is that the supportig mixture is the medium through which the machie forces are trasferred to the face of the tuel. I earth pressure balace (EPB) machies, the mixture is composed of the excavated soil ad additives, ad is removed from the chamber mechaically, through a screw coveyor. I slurry pressure balace (SPB) ad mixshield machies, the mixture is mostly composed of a slurry suspesio, ad is removed through a hydraulic circuit. The chambers of mixshield machies are divided by a submerged wall, i a workig chamber, completely filled with slurry, ad a pressure chamber, partially filled with a pressurized air bubble that cotrols the pressure at the chamber ad prevets sigificat fluctuatios. STESS TANSFE The structure of the mixture is very importat to the uderstadig of how the face pressure is trasferred to the tuel face. The slurry suspesios i SPB ad mixshield machies, which ca be extracted through a hydraulic circuit, are ormally more fluid tha the paste cosistecy ecessary to cotrol the pressure gradiet alog the screw coveyor o EPB machies. However, i both cases, the mixture presets a ope matrix, where the solid particles are i a suspesio with egligible effective stresses. The rheology ca the be cosidered equivalet to a fluid ad, as the mixture flows slowly, viscous forces ca be disregarded. These fluid mixtures ca oly support isotropic stress states, represeted by a equivalet scalar pressure. Adversely, the udisturbed groud at the tuel face will, i most cases, be stadig uder a aisotropic stress state, set by the coefficiet of earth pressure at rest (k 0). Therefore, it is fudametally ifeasible to trasfer a face pressure that will match the i situ stress of the groud i every directio. Take, as a example, a pressure that matches the vertical stress at the tuel roof, as show i Figure 1. The same pressure will be actig at the horizotal directio, where the horizotal stress i groud is probably of a differet magitude. The same is true at the tuel ivert, where a perfect balace caot eve be attaied i the vertical directio, because of the differeces betwee the volumetric weight of the mixture ad the groud. As a cosequece, the tuel face will always udergo stress icremets, ad the associated strais. Alog the radial directio, the excavated perimeter ca either cotract or expad. If it cotracts while i cotact with the cutterhead, a additioal volume of groud will be excavated. For a expaded sectio, there will be a gap betwee the groud ad the cutterhead. This allows the supportig mixture to flow aroud the shield depedig o the pressure at the face ad the grout pressure at the back of the shield. Aother poit to cosider is that if volumetric strais are iduced i a saturated groud, they will geerate icremets of pore water pressure that will lead to cosolidatio. Of course, the time frame for dissipatio will deped o the groud permeability ad draiage coditios.

3 v z pz h z supportig mixture p z D h z D z z D v z D v h Figure 1. Differeces betwee the stress states of the supportig mixture (fluid solid lies) ad the groud (solid dashed lies) i the vertical v ad horizotal h directios. The fact that the supportig mixture has such a loose matrix that it acts as a fluid raises the questio of whether the face pressure should be cosidered by its hydraulic head or just as a total stress boudary. Here, a parallel is ormally traced with diaphragm walls (slurry walls), where the supportig fluid creates a impermeable layer o which the fluid pressure is applied ad the hydraulic head is dissipated. I this way, the pressure ca be trasferred to the groud without chagig the hydraulic boudary coditios. The same thig should occur at the TBM face, through the so-called filter cake. However, oe should cosider that the groud at the tuel face is costatly beig removed while the filter cake is beig formed, which ca affect the process. This problem was idetified whe excess pore pressures were measured i frot of SPB (Bezuije et al. 001; 1999) ad EPB machies (Bezuije 00), revealig that the ideal process of cake formatio is ot always achieved ad depeds o the properties of the groud, the additives ad the excavatio speed (see Figure for example measuremets). To quatify these effects, oe must first uderstad how the supportig fluid creates a impermeable layer o the groud. The pressure i the supportig fluid must be higher tha the water pressure i the groud, iducig the fluid to flow ito the groud. The fluid carries suspeded material that clogs the groud pores, reducig its permeability. As far as this process is cocered, the foam bubbles used to coditio permeable soils o EPB TBMs have the same purpose as the slurry particles o SPB ad mixshield TBMs. The secod step is to quatify the gradiet iducig the flow from the face. A aalytical formulatio ca be derived (Bezuije 00; Bezuije et al. 001), based o the approximatio that there is a costat ifiitesimal hydraulic source at every poit i the tuel face. This distributed head is defied with referece to the i situ water pressure. By equatig the volumetric flow rate from the source (A=dr.r.dθ) with the flow rate at a certai radial distace (s) alog a semi-spherical domai i frot of the tuel (A=.π.s²), oe obtais: d 4.. s q. r. d. dr k.. ds (1) 3

4 excess pore pressure - φ (kpa) SPB SPT - Fit EPB EPB - Fit 0 x x SPB EPB φ distace from tuel face - x (m) Figure. Measuremets of excess pore water pressure i frot of SPB ad EPB tuels i permeable groud. where q is the discharge from the poit source, assumed costat all over the tuel face. By itegratig Equatio 1 alog the followig limits: ϕ=[ϕ(s), ]; s=[s, ]; r=[0,]; θ=[0,π], ad defiig, oe obtais: s x r x 0 x x where ϕ 0 is the icremetal piezometric head at the tuel face (x=0). From Equatio it is possible to calculate the hydraulic gradiet at the tuel face as: () d dx x0 0 The peetratio velocity ca the be defied as: x x k. v p 0. 1 x0 0 where is the groud porosity ad k is the groud hydraulic coductivity to the peetratio fluid. If the peetratio velocity (v p) is smaller tha the TBM drillig velocity the the excavatio tools will be scrapig deeper tha the slurry/muck peetratio ad 0 will be equal to the face pressure. O the other had, whe v p is larger tha the TBM drillig velocity a impermeable layer will be formed. However, excess pore pressures will still occur i frot of that layer, as the layer moves through the groud at a rate equal to the TBM drillig velocity. For this coditio Equatio 4 ca also be used, but ow the peetratio velocity (v p) is kow (equal the TBM drillig velocity) ad the icremetal piezometric head 0) ca be calculated, resultig i a value smaller tha the pressure i the mixig chamber. (3) (4) 4

5 V Air/Water t=0 Foam (Water + Surfactats) Foam Water Foam Water Vi Solids Solids Solids Solids (a) iitial (b) dry (c) saturated o flow (d) saturated flow Figure 3. epresetative volumetric elemets for the solid, water ad foam phases i a supportig mixture. This situatio occurred durig drillig of the N/S lie i Amsterdam (Kaalberg et al. 014), where the measured excess pore pressure close to the TBM was oly 40% of the applied excess pressure i the mixig chamber. This process is explaied more i detail i Bezuije (016). There are some recet attempts to simulate this process umerically with a model for the slurry peetratio withi a umerical groudwater flow calculatio (Zizka et al. 015). PHASE BALANCE IN THE MIXTUE The icremets of pore water pressure i frot of the tuel ad the cosequet water outflow ca have a sigificat impact o foam coditioig, which depeds heavily o the amout of water i the supportig mixture. The foam is formed by mixig a surfactat solutio, which presets a certai liquid volume (QL), with compressed air. This forms a structure where gas is trapped i the foam bubbles. The volume of foam (QF) is used to calculate the foam expasio ratio (FE=QF/QL), dividig it by the origial liquid volume of the solutio, ad the foam ijectio ratio (FI=QF/QS), dividig it by the volume of excavated groud (QS). Oce the foam bleds ito the supportig mixture, its additioal volume will icrease the iitial porosity of the mixture ( 1), described i Figure 3a, to a porosity that is suitable for the TBM operatio ( ). For a iitially dry mixture, the foam will occupy the air spaces (Figure 3b), so the volume of foam eeded to icrease the porosity from 1 to ca be calculated as: V ( dry) F 1 Vi 1 If the groud is origially saturated, oe must cosider the possibility that the face pressure will iduce groudwater flow from the face, i which case the iitial amout of water will be reduced or eve icreased, depedig o the flow coditios. Cosiderig the hypothesis that there is o water flow (Figure 3c), the ecessary volume of foam ca be calculated as: 1 (5) 5

6 V ( o flow) F Vi 1 For the case where water flows out of the mixture (Figure 3d), the ecessary volume of foam ca be calculated as: ( flow) V V V V FW F i W i where the Foam Water eplacemet atio (FW) is defied as the volume of water that flows out of mixture over the iitial volume of water. Usig Equatios 5, 6 ad 7 oe ca calculate the ecessary foam ijectio ratio (FI) for these three coditios. A detailed calculatio example is preseted i the ext sectio. FACE STABILITY Nowadays, the most commoly used method to assess the stability of a mechaized tuel is the limit equilibrium wedge stability aalysis (Aagostou ad Kovári 1994; Messerli et al. 010). The miimum required face pressure is composed of two parts: oe to guaratee the wedge stability (S), cosiderig effective stresses; ad aother to support the water pressures (W). The first part (S, see Figure 4) depeds o the vertical forces due to the overlyig prism (V) ad self-weight of the wedge (G), ad o the shear resistace alog the vertical triagular walls of the wedge (T). The magitude of the resultat alog the iclied plae () is ukow. However, its directio at limit equilibrium is φ, the frictio agle of the groud, with respect to the ormal vector. Therefore, it is possible to calculate equilibrium alog the directio perpedicular to, based o the wedge agle (θ), so that ca be igored. eferrig to the trigoometric scheme i Figure 4, oe ca derive the followig, where the wedge agle (θ) should be set to maximize the value of S: 1 V G. T.cos S (8) ta si For a hydrostatic distributio of water pressure, the compoets V, G ad T ca be calculated explicitly. It should be oted that Terzaghi s archig theory is ofte used to alleviate the overburde of the prism to calculate the V compoet. There are cotrastig views o how the horizotal stresses should be calculated for that, so the authors decided ot to cosider this effect herei. Therefore the three compoets ca be calculated as follows: k. D T Zt. D ta V ' (9) v 3 D. ta G. ' (10).ta.ta ' D. ' 3 0 v Zt where σ v(zt) is the vertical effective stress at the depth of the tuel crow ad γ is the volumetric weight of the soil immersed i water. The compoet to support the water pressures (W) ca also be calculated explicitly, multiplyig the hydrostatic pressure at the depth of the tuel ceterlie by the area of the wedge (D²). However, as (6) (7) (11) 6

7 V+G PWP Zt Zw φ V+G xt θ S 0 1 x0=d.taθ x4 dy D D φ θ+φ -1 θ D θ θ+φ φ S θ x Figure 4. Geometry ad scheme of forces for the limit equilibrium wedge stability aalysis discussed i the previous sectio, the distributio of pore water pressure i frot of a TBM is ofte ot hydrostatic durig drillig. The differece betwee the face pressure ad the hydrostatic pressure creates a groudwater flow patter that ca be roughly described with Equatio. This chages the face pressure calculatio, as the water pressure reduces the effective stresses to compute V, G ad T, which i tur reduce the required effective support (S), while it also icreases the support ecessary for the water pressure (W). This iterative balace ca be calculated by discretizig the wedge area alog the vertical directio (dy). Each slice of the wedge will be icremetally shorter (dy taθ) i the horizotal directio. By itegratig Equatio from x=0 to x=x i, ad dividig the result by x i, oe ca obtai the average icremet of water pressure at each level i from 0 to (see Figure 4). The resultat expressio is: avg i 1 1 xi xi l xi xi. x i. xi This pressure is the used to recalculate the vertical effective stress actig alog the wedge, rememberig that φ deotes a pressure icremet over the hydrostatic pressure. The prism compoet (V) ca still be calculated through Equatio 9, cosiderig the icremet of pore water φ 0 avg calculated with Equatio 1. O the other had, the compoets of self-weight (G) ad side frictio (T) have to be calculated discretely, as i: T k G D. 0 i1.ta. x i x i i1 1 '. x i x dy. i Fially, the compoet for the support of the water pressure (W) ca be calculated cosiderig the pressure icremet alog the iclied edge of the wedge, usig Equatio for x=x i. The resultat will be 1 v i ' '. v i v i1 ' v i1 l (1) (13) (14) 7

8 the itegral of these values, summed with the hydrostatic pressure, alog the y directio ad the thickess of the wedge (D). For both cases, the resultat F=S+W is scaled to the circular area of the tuel. There are several rules of thumb to determie the operatioal face pressure of the machie. For ow, a safety margi of 10 kpa above the miimum pressure will be cosidered. This operatioal pressure is the verified agaist the possibility of blowout, cosidered to occur whe the pressure exceeds the vertical total stress at the tuel crow plus the weight of the supportig mixture from the roof to the tuel ceterlie. EXAMPLE Cosider the followig: A tuel of 10 m i diameter with the crow at a depth of 0 m; the groud volumetric weight is 18 kn/m³ ad k 0=0.5; the groudwater level is at the surface ad the volumetric weight of the mixture is 1 kn/m³. First cosider that a impermeable layer ca be formed, durig stad still for example, ad that the groudwater remais hydrostatic. I this case, the effective support (S) is maximized at a wedge agle (θ) of. 0 with the followig compoets: V=6530 kn; G=163 kn; ad T=1100 kn, resultig i S=391 kn. The water support (W) is 5 MN, resultig i a operatioal support pressure of 99 kpa, which is less tha the blowup limit of 40 kpa. Here is where the traditioal desig would stop. By simple geostatic calculatios oe ca assess the total horizotal ad vertical stresses alog the tuel boudary. The ormal stress ca the be calculated through a coordiate trasformatio operatio ad compared with the face pressure distributio (Figure 5). Oe ca see that the face pressure falls short of matchig the ormal boudary stresses, which will iduce the excavatio to coverge. To aalyze the hydraulics of the face pressure trasfer, oe ca start by usig Equatio 3 to calculate the hydraulic gradiet at the tuel face. The face pressure is 49 kpa above the hydrostatic pressure at the tuel ceter, so the hydraulic gradiet is aroud 1 (i = ϕ 0/ = 5 m/5 m = 1). Assumig a graular material with a permeability of 10-5 m/s ad a porosity of 0.4, oe ca the use Equatio 4 to calculate the water peetratio velocity from the mixture to the groud (v = k.i/ = 0.05 mm/s). This velocity ca be assumed a upper boud to the peetratio of slurry or foam bubbles, which will always have a higher viscosity tha water. A typical TBM drillig velocity is 1 mm/s. Therefore, for this set of parameters, oe ca easily see that, durig drillig, the supportig fluid will ot be able to peetrate further tha the depth that is scraped away durig each cutterhead rotatio. Aother way to look at this is to cosider the rotatio speed of the cutterhead. Take, for example, a rotatio speed of 3 rpm, ad cosider that each poit alog the face is scraped two times per revolutio. This meas that the supportig fluid ca peetrate 0.5 mm i the 10 secods it remais i cotact with the groud before it is removed. Other studies have scaled this dissipatio by the ratio betwee the peetratio depth ad the maximum thickess of the filter cake, through which the whole pressure differece is dissipated (Broere ad va Tol, 000). However, cosiderig that a regular filter cake is stable at the scale of cetimeters, it is fair to say that the dissipatio through a layer of 0.5 mm will be egligible. Therefore, the whole pressure differece is used i Equatio to assess the field of pore water pressure icremets ahead of the face. Through the iterative methodology described i the previous sectio, the ew wedge equilibrium is set at a wedge agle (θ) of with the followig compoets: V=5411 kn; G=1351 kn; ad T=917 kn, resultig i S=356 kn. The effective support is 40% less tha for the hydrostatic case. The water, 8

9 Height/Diameter SY0 SX0 P0 FP Stresses (kpa) Stresses (kpa) Figure 5. Example calculatio for the face pressures (FP) ad i situ stresses (SX-horizotal, SY-vertical, P0-ormal to the boudary) aroud the tuel perimeter. support (W), o the other had, is 31 MN, 3% higher tha before. Their combied effect requires a operatioal face pressure of 34 kpa, which is less tha the blowup limit of 40 kpa. Aother cosideratio is the volume of water that flows out of the supportig mixture. Cosiderig a Darcy velocity of m/s through the area of the tuel face, the flow rate is about m³/s. A certai FI eeds to be specified to take the porosity of the saturated groud from the origial 0.4 to about 0.5. If o flow is cosidered, a FI=0% should suffice (Equatio (6)). However, the water flow rate represets about 5% of the iitial water i the amout of muck excavated i a certai time (FW=0.05). Therefore, a FI=% is ecessary to compesate for the water loss (Equatio (7)). CONCLUSION The way the processes aroud TBM operatios are uderstood is costatly evolvig, helpig desigers ad cotractors to achieve more reliable tuelig systems. However, the quatitative models that represet these processes are frequetly disregarded i geeral desig ad face stability aalyses. This paper preseted oe step of a geeral approach to icorporate these models i the state-of-practice. A differet view regardig the equilibrium coditios aroud the face of a TBM was preseted, through aalysis of the followig: the stresses aroud the face, alog the cross sectio, ad the logitudial directio; the field of pore water pressure icremets i frot of a TBM where o filter cake could be formed; the phase balace i the supportig mixture, of special cocer to desig foam ijectios; ad fially the assessmet of face stability, where the icremet of pore water pressure will ormally require a higher support pressure at the face. The example that was preseted illustrates the relative magitude of these factors for the chose parameters. Other coditios ca possibly reach differet results. However, the poit of this study is to show that these aalyses ca provide a objective ad accessible framework for the state of practice, where ay coditio or set of parameters ca be processed ad the results aalyzed for a more realistic desig of the TBM excavatio cycle. 9

10 ACKNOWLEDGMENTS The first author would like to ackowledge the fiacial support of the Brazilia esearch Agecy CNPq. EFEENCES Aime,., Aristaghes, P., Autuori, P., Miec, S m diameter tuellig uder Netherlads Polders. I: ITA World Tuel Cogress Udergroud Space for Sustaiable Urba Developmet, Sigapore. Aagostou, G., Kovári, K The face stability of slurry-shield-drive tuels. Tuellig ad Udergroud Space Techology 9: Atkiso, J.H., Potts, D.M Stability of a shallow circular tuel i cohesioless soil. Géotechique 7: Bezuije, A. 00. The ifluece of soil permeability o the properties of a foam mixture i a TBM. I: Geotechical Aspects of Udergroud Costructio i Soft Groud - 4th Iteratioal Symposium, Toulouse, Frace. Bezuije, A Moitorig pressures ad deformatios aroud a TBM. To be published i: 13th Iteratioal Coferece Udergroud Costructio Prague, Prague, Czech epublic. Bezuije, A., Pruiksma, J.P., va Meerte, H.H Pore pressures i frot of tuel, measuremets, calculatios ad cosequeces for stability of tuel face. I: Iteratioal Symposium o Moder Tuelig Sciece ad Techology, Kyoto, Japa. Bezuije, A., Schamiee, P.E.L., Kleija, J.A Additive testig for earth pressure balace shields. I: 1th Europea Coferece o Soil Mechaics ad Geotechical Egieerig, Amsterdam, The Netherlads. Bezuije, A., Talmo, A.M Processes aroud a TBM. I: Geotechical Aspects of Udergroud Costructio i Soft Groud - 6th Iteratioal Symposium, Shaghai, Chia. Broere, W., va Tol, A.F Ifluece of Ifiltratio ad Groudwater Flow o Tuel Face Stability. I: Geotechical Aspects of Udergroud Costructio i Soft Groud - 3rd Iteratioal Symposium, Tokyo, Japa. Dias, T.G.S., Bezuije, A TBM Pressure Models Observatios, Theory ad Practice. I: XV Pa- America Coferece o Soil Mechaics ad Geotechical Egieerig, Bueos Aires, Argetia. Kaalberg, F.J., uigrok, J.A.T., De Nijs, TBM face stability ad excess pore pressures i close proximity of piled bridge foudatios cotrolled with 3D FEM. I: Geotechical Aspects of Udergroud Costructio i Soft Groud - 8th Iteratioal Symposium, Seoul, South Korea. Messerli, J., Pimetel, E., Aagostou, G Experimetal study ito tuel face collapse i sad. I: 7th Iteratioal Coferece o Physical Modellig i Geotechics, Zurich, Switzerlad. Mühlhaus, H.B Lower boud solutios for circular tuels i two ad three dimesios. ock Mechaics ad ock Egieerig 18:37 5. Thewes, M., Budach, C., Bezuije, A. 01. Foam coditioig i EPB tuelig. I: Geotechical Aspects of Udergroud Costructio i Soft Groud - 7th Iteratioal Symposium, ome, Italy. Zizka, Z., Thewes, M., Popovic, I Aalysis of slurry pressure trasfer o the tuel face durig Excavatio. I: ITA World Tuel Cogress SEE Tuel - Promotig Tuellig i SEE egio, Dubrovik, Croatia. 10