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Assessment and control of metro-construction induced settlement of a pile-supported urban overpass
Available online at www.sciencedirect.com
Tunnelling and Underground Space Technology 23 (2008) 300–307
Tunnelling and Underground Space Technology incorporating Trenchless Technology Research
www.elsevier.com/locate/tust
Assessment and control of metro-construction induced settlement of a pile-supported urban overpass Yanyong Xiang *, Zhiping Jiang, Haijian He School of Civil Engineering, Beijing Jiaotong University, Beijing 100044, China Received 25 November 2006; received in revised form 24 May 2007; accepted 22 June 2007 Available online 13 August 2007
Abstract A metro station in Beijing, consisting of two separate parallel platform tunnels, has been constructed in close range below a pile-supported overpass of a major municipal artery built more than a decade ago. In order to assure the normal operation and integrity of the overpass as well as smooth and safe tunneling, the condition and status quo settlement capacity of the overpass is assessed via structural measurements and analysis, and on the basis of which, criteria on allowable additional settlements of pile foundations are established. The probable additional settlements of the pile foundations caused by tunneling and dewatering are estimated by using empirical and theoretical analyses and numerical simulations of the construction process in combination with in situ monitoring data, and anti-settlement underpinning piles are installed to control the predicted excessive adverse effects of tunneling. The major conclusions include: (1) the surcharge effect from an existing structure in or on the ground may enhance the effect of tunneling on ground deformation, and thus should be taken into account when estimating the delimitations of zones of tunneling influence and the degree of closeness of an existing structure; (2) when tunneling in close range to an existing urban overpass supported on pile foundations, the general control procedure should consist of assessment of the contemporary capacity of the superstructure, establishment of criteria for and prediction of dewatering and tunneling-induced ground surface and pile foundation settlements, and, if necessary, execution of reinforcement measures; (3) in situ monitoring data close to areas sensitive to tunneling should be employed to adapt theoretical analysis and calibrate numerical models; (4) rational settlement criteria and mitigation measures should be worked out through consideration of the local composition of the superstructure of the overpass, as well as the type and depth of the pile foundations; and (5) a time period after installation may be needed for the underpinning piles to be effective in counteracting the settlement effect of tunneling. Ó 2007 Elsevier Ltd. All rights reserved. Keywords: Tunneling; Dewatering; Urban overpass; Pile foundation; Settlement; Underpinning
1. Introduction A metro station in Beijing has been constructed within close range to an existing pile-supported overpass of a major urban artery. The main body of the metro station, about 10–12 m below the ground surface, is composed of two separate parallel north–south tunnels, connected through three east-west passenger and equipment galleries, and serviced by three drift-shafts for ventilation. Tunneling is conducted via ground pre-treatments, multiple-phased
*
Corresponding author. E-mail address: [email protected] (Y. Xiang).
0886-7798/$ - see front matter Ó 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.tust.2007.06.008
excavations and supports, aimed at preventing excessive settlements of the nearby pile foundations. Referring to Fig. 1, the present study is concerned with the two northern ventilation drifts of the metro station, to which the in situ cast reinforced concrete piles of the existing urban overpass are extremely close, and, as shown in Fig. 2, the western 59# foundation rests upon relatively shorter piles whose tips are well above the drift floor, while the eastern 60# foundation upon two shorter and two longer piles, and the transverse reinforced concrete cap beam is rigidly connected with the two reinforced concrete piers. In order to assure the normal operation and integrity of the overpass as well as smooth and safe tunneling, a
Y. Xiang et al. / Tunnelling and Underground Space Technology 23 (2008) 300–307
cap beam
northeast vent tunnel
foundations for main road
cap beam
60# foundation 59# foundation
left station line passenger gallery
cap beam
foundations for left access road
shaft
foundations for right access road
cap beam cap beam
northwest metro entrance
Fig. 1. Plane schematic of metro tunneling and five most sensitive existing urban overpass cap beams on pairs of piers supported on piles.
procedure as shown in Fig. 3 for assessment and control of metro-tunneling effects on piled urban overpass structures in close range is executed, and the key components and conclusions of the work are presented as follows. 2. Degree of closeness and status quo settlement capacity of the overpass The content and degree of investigation and subsequent appraisal of an existing urban overpass and its foundation should be decided consistent with the relative degree of closeness of the foundation to tunneling. The range of tunneling influence hinges upon factors of a physical nature, including tunnel shape and size, embedded depth, geology and hydrogeology, ground treatment, excavation, primary
301
supporting and permanent lining methods, as well as upon factors of somewhat subjective nature, such as the technical know-how, craftsmanship and management effectiveness of the construction group, etc. In addition, surcharge from existing structures in or on the ground may also play an important role. Illustrated in Fig. 4 is a conceptualization of zones of tunneling influence and possible compositions of a piled overpass structure. Determination of the tunneling effect and the degree of closeness of an existing structure should take into consideration the surcharge effect of the structure. Evidently this is difficult, and a feasible remedy would be to make empirical, theoretical and numerical estimations. An existing structure in the ground exerts two types of mechanical effects, one as additional stiffness, and the other as surcharge, and since the volume of the structure would in general be relatively small and thus passively follow the movement of the ground, the surcharge effect is more significant. Referring to Fig. 4, the net vertical as well as horizontal separations of the existing structure from tunnel excavation, Dv and Dh, are the main factors of consideration, and the angle of the slip plane and the height of the natural arch should be determined by calculating the effects of both tunneling and surcharge of the structure. Even though in greenfield conditions, b = 45° //2 and hc = (b c/c)/ktg/, based on Terzaghi’s theory of earth pressure on tunnel lining, with c, k, c and / denoting, respectively, the unit weight, coefficient of lateral earth pressure at rest, cohesion and angle of internal friction of the soil, the surcharge from an existing structure in or on the ground may result in expansion of zones I and II, as may be inferred using the depiction in Fig. 5 by virtue of Janssen’s silo theory (Kolymbas, 2005). Illustrated in Fig. 5, both the vertical earth pressure (equivalent to the portion of gravity that is unsupported by arching) and the portion of gravity supported by arching increase with depth, with the former asymptotically approaching chc,
Fig. 2. West-east cross section of the ventilation tunnels (including the pilot tunnels) and the super- and sub-structures of the existing urban overpass (m).
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Degree of closeness: judge the degree of closeness between metro tunnel and existing overpass
Overpass superstructure Overpass substructure
Inspection of upper structure,pier,cap,beam
Characterization of tunneloverpass spatial relationship
Tunnel and pile profiles
Structural modal test and evaluation of material deterioration Estimation of pretunneling pile settlement
Tunnel and upper structure planes
Evaluation of current state of overpass
Degree of influence Predict effect of metro construction on overpass structure
Estimation of bearing mode and capacity of pile foundation
Ground settlement Dewatering influence
Absolute settlement of overpass foundation
Construction influence
Differential settlement of nearby foundations
Stop construction and take measures to reduce risk
Criteria for control of ground surface and overpass settlements
Yes
Construction management procedures
In-situ measured settlement > Maximum allowable settlement
Yes
No
No
In-situ measured settlement > Alerting settlement
In-situ measured settlement > Warning settlement Yes
Take precautionary mearures and predict effects
Construction continues
No
Halt tunneling, take adjustment-reinforcement measures and predict effects
Fig. 3. Flow chart for characterization, prediction and control of tunneling effects on urban piled overpass.
Fig. 4. Zones of influence above and lateral to tunnel excavation (zone I – ground within slip planes and natural arch, experiencing plastic flow or collapse; zone II – ground bounded by slip planes, natural arch and boundary of tunneling influence, experiencing elastic deformation; zone III – ground free from tunneling influence, maintaining the primitive state prior to excavation; the symbol b denotes the half-width of the natural arch, and the radius of the silo when considering Janssen’s silo theory as described in Kolymbas, 2005).
and the surcharge at the ground surface induces an decreasing-with-depth increment in the vertical earth pressure under greenfield conditions. Similar soil behavior may be imagined if there is in-ground surcharge from an existing buried structure.
In reference to Fig. 4, it is worthy to note that soil friction serves as the sole driving mechanism for soil arching, as manifested by the expression of height of the natural arch, hc (if / = 0 , hc = 1, meaning no arching is possible). When the thickness of the overburden, hs, is adequately
Y. Xiang et al. / Tunnelling and Underground Space Technology 23 (2008) 300–307
γhc
γ hc
q σ
σ
1
1
303
allowable for any two neighboring piers with simply supported beams along the longitudinal (road) direction, the maximum permissible tunneling-induced differential settlement for the transverse frame composed of two piers and a rigidly connected cap beam shown in Fig. 2 is prescribed to be 5 mm.
2
3. Dewatering and tunneling-induced pile foundation settlement σs
δσ σ=γz
z
σ=γ z + q
z
1 σ=γhc(1-e-z/h ) 2 σ=γhc+(q-γhc)e-z/h σs gravity supported by arching δσ surcharged-induced load increment unsupported by arching b -c/γ b hc= . h= . k tgφ k tgφ Fig. 5. Vertical earth pressure along depth with ground surface being either free of or with surcharge (based on Janssen’s silo theory as described in Kolymbas, 2005; r denoting vertical earth pressure which is equivalent to the portion of gravity unsupported by arching, z depth, q strength of surcharge, b silo radius and b = (wt/2 + httgb) with Terzaghi’s theory of earth pressure on tunnel lining, with c, k, c and / denoting, respectively, the unit weight, coefficient of lateral earth pressure at rest, cohesion and angle of internal friction of the soil).
large, the influence of tunneling would be confined to below the ground surface, and zone II, as characterized by the height of the influence boundary above the tunnel crown, hi, delineates the range within which soil arching takes place. Let z95 represent the depth where the vertical earth pressure r equals 95% of chc under greenfield condition, then when the tunnel is deep enough, the characteristic thickness of zone II, hi–hc, would equal z95 with a 5% round off. Similar inference applies for other prescribed percentages. Based on an assessment of the degree of closeness of the pile foundations, the content and degree of investigation for different portions of the overpass are selected for appraisal of the status quo settlement-resistant capacity of the overpass. Referring to Fig. 4, the composition of a substructure group of an overpass, including type of members, type of connections between members as well as the composition and working condition of the member materials, and the pre-tunneling settlement of the substructure should be taken into account when prescribing criteria of permissible tunneling-induced settlement. A rigid or continuous connection would demand a lower criterion than simply supported connection, when other conditions are similar. For the overpass concerned herein, although a maximum of differential settlement of 20 mm is considered
Empirical, theoretical and numerical methods are employed to assess the additional pile foundation settlements induced by dewatering and tunneling for construction of the ventilation drifts, and the main bodies of these methods are presented as follows. 3.1. Estimation of dewatering-induced settlement Assuming that the consolidation of the soil in-between the initial and the depressed phreatic surfaces occurs immediately after the pumping drawdown, that there is no soil loss, and that the soil below the drawdown surface experiences no consolidation, the final dewatering-induced soil settlement may be estimated as the compression of the soil strata, for sandy and clayey soils, respectively: ds ¼
X Dri Bi X DB2 c w i ; Esi 2Esi i i
ð1Þ
ds ¼
X ai Dri Bi X ai DB2 c w i ; 1 þ e 2ð1 þ e Þ 0i 0i i i
ð2Þ
where ds denotes the dewatering-induced final soil settlement; cw the unit weight of water; ai, Bi, e0i and Esi stand for soil compressibility, thickness, void ratio and effective compression modulus, respectively; Dri and DBi for dewatering-induced increment in effective stress and dewatered thickness of soil, respectively. The above expressions involve two approximations: Bi DBi, Dri DBicw/2. Dewatering-induced settlement would exert negative skin friction on nearby piles and cause additional pile settlements, two situations of which may be distinguished as sketched in Fig. 6. Referring to Chen and Xiang (2006), a simplified theoretical approach is employed for estimating the pile settlement induced by dewatering in phreatic zone: (i) the Neuman (1972, 1973, 1974) model of pumping in an unconfined aquifer, to calculate the dynamic drawdown distribution; (ii) a simplified effective stress method, to estimate the corresponding soil consolidation settlement, the final value of which may be checked by using Eqs. (1) and (2); (iii) the Randolph and Wroth (1978) pile–soil interaction model, to estimate the additional negative skin friction on the pile shaft; and (iv) a semi-theoretical pile foundation settlement model (China Ministry of Construction, 2002), to predict the temporal evolution of the dewatering-induced pile settlement, dp, for case (a) and (b), respectively:
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z
h ; u ¼ 4ð1 mÞeR2 2 x þ h2 Z 1 p 2 exp 2 ðx nÞ dndg; u¼ r ðgÞ H rðgÞ
Q
τ
d l
τ wc
lp
rp
H rc r
z
Q τ
d
τ
rp
lp w c lw
l H rc r Fig. 6. Effects of dewatering on a nearby pile: (a) wc 6 lp, (b) wc > lp (s denotes the dewatering-induced negative skin friction on pile shaft, wc drawdown at pile center, lp the pile length below the initial phreatic surface, and lw the distance between the pile base and the depressed piezometric surface below) (after Chen and Xiang, 2006).
dp ¼ w dp ¼ w
m X plm cw w2c ð2m 1Þ ðzj aj zj1 aj1 Þ; 2ðm 1ÞabEsj ln 20 j¼1 m X j¼1
þ
ð3aÞ
plcw l2p ð2m 1Þ ðzj aj zj1 aj1 Þ 2ðm 1ÞabEsj ln 20
cw ðlp þ wc Þ lw ; 2Es
ð3bÞ
where a and b denote the length and width of the pile foundation base, respectively; m denotes the Poisson’s ratio of the representative soil surrounding the pile shaft; Esj denotes the modulus of compression of the jth layer of soil below the pile tip; zj the distance of the bottom of the jth soil layer below the pile tip; aj a coefficient for the averaged incremental stress over the range of zj, w an empirical coefficient, and m the number of soil layers adequate for calculation of pile settlement.
ð5Þ ð6Þ
where i denotes the horizontal distance from the tunnel centerline to the point of inflection of the ground settlement trough, Vs the volume of settlement trough per unit distance of tunnel drive; m Poisson’s ratio, h depth of tunnel axis, and e = w/R with w and R representing the uniform radial convergence of the excavation boundary and the equivalent tunnel radius, respectively; x and z stand for the coordinate axes originated at the ground surface, and aligned in the transverse and vertical directions to the tunnel drive, respectively, (n, g) refers to the (x, z) location of an elemental ground loss volume, dndg, H cross-sectional ground loss distributed on the excavation surface for an infinitely long tunnel, and r = g/tgb characterizes the radius of the influence zone, with b being the angle of influence. The formulations, physical assumptions, mathematical expressions and applications of several theoretical solutions, in conjunction with the Peck formula, for calculation of tunneling-induced ground movement are comparatively analyzed in Xiang (2006), and trial calculations using comparable parameter values indicate that these theoretical and empirical formulas may produce similarly shaped but quite discrepant ground surface settlements, implying that rational adaptations to field conditions are essential to successful predictions. For the empirical and theoretical formulas (4)–(6), the i parameter is estimated for sandy and clayey soils, respectively, the Vs, e and H parameters are calculated by using the area of convergence of the tunnel cross section, and the b parameter by estimating the lateral extent of in situ monitored ground surface settlement trough. As illustrated in Fig. 7, the tunnel of a horse-shoe shaped cross section is conceptualized into an equal-area circular tunnel with an equivalent uniform convergence such that the total ground loss is equal to the in situ measurement value. Rankine’s theory of active limit state of equilibrium of soil is employed to check how much percentage of the pile shaft is within the soil wedge possibly in an active limit state as influenced by tunneling. If such percentage is larger than 50%, the soil settlements calculated using the empirical and theoretical formulas may be considered as conservative estimates of pile settlement.
3.2. Empirical and theoretical estimations of tunnelinginduced settlement
3.3. Numerical simulation of tunneling effects
An empirical formula as proposed by Peck (1969) and two theoretical solutions as in Sagaseta (1987) and Yang et al. (2004), respectively, are employed for predicting ground surface settlement induced by tunneling: Vs x2 u ¼ pffiffiffiffiffiffi exp 2 ; ð4Þ 2i 2pi
Referring to Fig. 8, the ventilation drifts are constructed via a 12-stage procedure dubbed as pilot tunnel and pilearch-beam method. A three-dimensional numerical simulation of the staged tunneling process is performed. The soil strata, based on borehole logs, is considered by using the Mohr–Coulomb plasticity model, while the shotcrete primary support, the transverse bracing and the secondary
Y. Xiang et al. / Tunnelling and Underground Space Technology 23 (2008) 300–307
305
Fig. 7. Conceptual model for empirical and theoretical estimations of ground settlement (m).
pilot tunnels
concrete fill
cast in-situ reinforced concrete piles
cap beams
2nd excavation
1st excavation
1st bracing
lining are considered as elastic. Grouting effect is taken into account by using increased soil modulus. The numerical model is first calibrated against available monitoring data by manually making parameter adjustments, and then employed for predictive calculations. A parametric sensitivity analysis indicates that with the excavation and construction procedure, the material properties of the soil strata and the primary support exert the most significant influence on the settlements of the nearby pile foundations. Monte-Carlo simulations are conducted to study the probabilistic distributions of the differential settlement between the 59# and 60# foundations and the reliability of the pier-beam structure, due to the probabilistic material parameters of the local soil strata and the primary support inferred from site and laboratory test data and experience. The performance function can be expressed as: Zð~ hÞ ¼ RðxÞ Sð~ hÞ;
ð7Þ
where R stands for the allowable ultimate differential settlement between the 59# and 60# foundations in conformity with the material and composition, symbolized by x, of the cap beam and its connection with the 59# and 60# piers, S the differential settlement between the 59# and 60# foundations induced by metro tunneling, and Z the performance function, both of which are characterized in a probabilistic framework as a function of a random vector, ~ h, representing the probabilistic material parameters of the local soil strata and the primary support.
2nd bracing 3rd excavation 4th excavation & 3rd bracing
crown lining
4. Control of overpass settlement
middle slab
bottom slab
Fig. 8. Numerically simulated sequential construction stages of the ventilation drift: (1) pilot tunnel excavation, (2) bored piling within the pilot tunnels, (3) beam capping the piles, (4) backfilling the void behind the cap beams, (5)–(8) sequential top-down excavations and transverse bracings, (9)–(12) sequential upward removal of bracings and casting of bottom slab, side wall, middle slab and crown as permanent lining.
Based on in situ monitoring data, the empirical, theoretical, deterministic and probabilistic numerical analyses of the effects of dewatering and tunneling on the settlements of adjacent pile foundations, a judgment is made that the differential settlement of the 59# and 60# pile foundations, when the tunnel construction finishes, would induce a bending moment in the cap beam exceeding the capacity allowed by its material and composition. Subsequently, it is decided that precautionary anti-settlement measures should be taken in order to maintain the smooth and safe operation of the overpass while allowing normal metro tunneling advance. Underpinning of the 59# foundation
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Y. Xiang et al. / Tunnelling and Underground Space Technology 23 (2008) 300–307
installed to furnish extra bearing capacity to the existing piles of the 59# foundation during the installation of the underpinning piles, as shown in Fig. 10. Shown in Figs. 11 and 12 are the settlement histories of the 59# and 60# foundations and the differential settlement between these two foundations, respectively, from which one may see that after underpinning, the 59# foundation has exhibited an appreciable amount of additional settlement prior to settling similarly as the 60# foundation, and the differential settlement continues increasing and assumes significantly larger values roughly between 540 and 570 days of tunneling, after which the settlements of the two foundations largely parallel with each other, resulting in relatively insignificant differential settlement. This phenomenon demonstrates that it may take a while after installation for the underpinning piles to start effectively counteracting the settlement effect of tunneling, and that the underpinning has made the underpinned 59# foundation eventually behave like the 60# foundation.
centerline of simply supported beams cap beam interim support of steel frames ground surface cap of the 59# piled foundation
cap of the 60# piled foundation
Fig. 9. Schematic of ground-surface based temporary support steel frames for the overpass.
I
by means of additional piles tipped an adequate distance below the metro tunnel floor is deemed necessary, whilst in-tunnel measures, including pre-grouting and strong primary support, are undertaken. As illustrated in Fig. 9, interim ground support consisting of steel frames is
10.91 8.91
1.0
3
2.60 2.0
6.
9.47
R1 =0 .
23.0
3 6.
original piles R2 =0 .5
north
augmented cap
original cap
75
10.91
original piles and cap
1.0
45
45
underpinning piles
underpinning piles
I
augmented cap 10.91
I-I cross section
plane
pile foundation settlement (mm)
Fig. 10. Precautionary underpinning of the 59# pile foundation (m).
2 0 -2 0 -4 -6 -8 -10 -12 -14 -16 -18 -20 -22
tunneling progress (day) 30
60
90 120 150 180 210 240 270 300 330 360 390 420 450 480 510 540 570 600 630 660 690 720 750 780
60# foundation settlement start of underpinning end of underpinning
59# foundation settlement
differential pile-foundation settlement(mm)
Fig. 11. Temporal evolvement of the 59# and 60# foundation settlements.
9 8 7 6 5 4 3 2 1 0
start of underpinning
0
30 60
end of underpinning
90 120 150 180 210 240 270 300 330 360 390 420 450 480 510 540 570 600 630 660 690 720 750 780
tunneling progress (day)
Fig. 12. Differential settlement of the 59# foundation with respect to the 60# foundation.
Y. Xiang et al. / Tunnelling and Underground Space Technology 23 (2008) 300–307
5. Summary For a Beijing metro station construction near a more than a decade old pile-supported urban overpass, a procedure of assessment and control of metro-tunneling effects on urban piled overpass structures in close range has been carried out, which involves applications of empirical, theoretical and numerical predictions as well in situ monitoring schemes. In order to ensure the normal operation and integrity of the overpass as well as smooth and safe tunneling, the condition and status quo settlement capacity of the overpass are assessed via on-site measurements and computer modeling, the probable additional settlements of the pile foundations caused by tunneling and dewatering in the vicinity are estimated by using in situ monitoring data, empirical and theoretical analyses and numerical simulations of the construction process, and on the basis of which, allowable limit settlements of ground surface and pile foundations are established and anti-settlement underpinning is executed to control the adverse effects of metro construction. In situ monitoring data indicated that the post-underpinning pile foundation exhibited an appreciably larger amount of additional settlement prior to behaving like the nearby non-underpinned pile foundation, with both foundations experiencing similar tunneling influences. The major conclusions may be summarized as follows: (1) the surcharge effect from an existing structure in or on the ground would enhance the effects of tunneling on ground deformation, and thus should be taken into account when estimating the delimitation of zones of tunneling influence and the degree of closeness of an existing structure; (2) for metro tunneling in close range to an existing urban overpass supported on pile foundations, the general control procedure should consist of assessment of the contemporary capacity of the superstructure, prediction of tunneling and dewatering-induced ground surface and pile foundation settlements, establishment of criteria for distinctively constraining ground surface and pile founda-
307
tion settlements, and, if necessary, execution of reinforcement measures; (3) in situ monitoring data close to the sensitive areas should be employed to adapt theoretical analysis and calibrate numerical models; (4) settlement criteria and mitigation measures should be worked out through considering the local composition of superstructure of the overpass, as well as the type and depth of the pile foundations; and (5) as indicated by post-underpinning monitoring data, it may take a while after installation before the underpinning piles to effectively counteract the effect of tunneling. References Chen, S., Xiang, Y., 2006. A procedure for theoretical estimation of dewatering-induced pile settlement. Computers and Geotechnics 33 (4– 5), 278–282. China Ministry of Construction, 2002. Code for Design of Building Foundation (GB50007 – 2002) (in Chinese). Kolymbas, D., 2005. Tunneling and Tunnel Mechanics – A Rational Approach to Tunneling. Springer-Verlag, Berlin. Neuman, S.P., 1972. Theory of flow in unconfined aquifers considering delayed response of the water table. Water Resources Research 8 (4), 1031–1045. Neuman, S.P., 1973. Supplementary comments on theory of flow in unconfined aquifers considering delayed response of the water table. Water Resources Research 9 (4), 1102–1103. Neuman, S.P., 1974. Effect of partial penetration on flow in unconfined aquifers considering delayed gravity response. Water Resources Research 10 (2), 303–312. Peck, R.B., 1969. Deep excavations and tunneling in soft ground. In: State of the art report, 7th International Conference on Soil Mechanics and Foundation Engineering, Mexico City, pp. 225–290. Randolph, M.F., Wroth, C.P., 1978. Analysis of deformation of vertically loaded piles. Journal of Geotechnical Division 104 (GT12), 1465–1488. Sagaseta, C., 1987. Analysis of undrained soil deformation due to ground loss. Geotechnique 37 (3), 301–320. Xiang, Y., 2006. An evaluation of theoretical solutions for prediction of ground movements due to shallow tunneling in soil. ASCE Geotechnical Special Publication No. 155, Underground Construction and Ground Movement, pp. 296–303. Yang, J.S., Liu, B.C., Wang, M.C., 2004. Modeling of tunneling-induced ground surface movements using stochastic medium theory. Tunneling and Underground Space Technology 19, 113–123.
Tunnelling and Underground Space Technology 23 (2008) 300–307
Tunnelling and Underground Space Technology incorporating Trenchless Technology Research
www.elsevier.com/locate/tust
Assessment and control of metro-construction induced settlement of a pile-supported urban overpass Yanyong Xiang *, Zhiping Jiang, Haijian He School of Civil Engineering, Beijing Jiaotong University, Beijing 100044, China Received 25 November 2006; received in revised form 24 May 2007; accepted 22 June 2007 Available online 13 August 2007
Abstract A metro station in Beijing, consisting of two separate parallel platform tunnels, has been constructed in close range below a pile-supported overpass of a major municipal artery built more than a decade ago. In order to assure the normal operation and integrity of the overpass as well as smooth and safe tunneling, the condition and status quo settlement capacity of the overpass is assessed via structural measurements and analysis, and on the basis of which, criteria on allowable additional settlements of pile foundations are established. The probable additional settlements of the pile foundations caused by tunneling and dewatering are estimated by using empirical and theoretical analyses and numerical simulations of the construction process in combination with in situ monitoring data, and anti-settlement underpinning piles are installed to control the predicted excessive adverse effects of tunneling. The major conclusions include: (1) the surcharge effect from an existing structure in or on the ground may enhance the effect of tunneling on ground deformation, and thus should be taken into account when estimating the delimitations of zones of tunneling influence and the degree of closeness of an existing structure; (2) when tunneling in close range to an existing urban overpass supported on pile foundations, the general control procedure should consist of assessment of the contemporary capacity of the superstructure, establishment of criteria for and prediction of dewatering and tunneling-induced ground surface and pile foundation settlements, and, if necessary, execution of reinforcement measures; (3) in situ monitoring data close to areas sensitive to tunneling should be employed to adapt theoretical analysis and calibrate numerical models; (4) rational settlement criteria and mitigation measures should be worked out through consideration of the local composition of the superstructure of the overpass, as well as the type and depth of the pile foundations; and (5) a time period after installation may be needed for the underpinning piles to be effective in counteracting the settlement effect of tunneling. Ó 2007 Elsevier Ltd. All rights reserved. Keywords: Tunneling; Dewatering; Urban overpass; Pile foundation; Settlement; Underpinning
1. Introduction A metro station in Beijing has been constructed within close range to an existing pile-supported overpass of a major urban artery. The main body of the metro station, about 10–12 m below the ground surface, is composed of two separate parallel north–south tunnels, connected through three east-west passenger and equipment galleries, and serviced by three drift-shafts for ventilation. Tunneling is conducted via ground pre-treatments, multiple-phased
*
Corresponding author. E-mail address: [email protected] (Y. Xiang).
0886-7798/$ - see front matter Ó 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.tust.2007.06.008
excavations and supports, aimed at preventing excessive settlements of the nearby pile foundations. Referring to Fig. 1, the present study is concerned with the two northern ventilation drifts of the metro station, to which the in situ cast reinforced concrete piles of the existing urban overpass are extremely close, and, as shown in Fig. 2, the western 59# foundation rests upon relatively shorter piles whose tips are well above the drift floor, while the eastern 60# foundation upon two shorter and two longer piles, and the transverse reinforced concrete cap beam is rigidly connected with the two reinforced concrete piers. In order to assure the normal operation and integrity of the overpass as well as smooth and safe tunneling, a
Y. Xiang et al. / Tunnelling and Underground Space Technology 23 (2008) 300–307
cap beam
northeast vent tunnel
foundations for main road
cap beam
60# foundation 59# foundation
left station line passenger gallery
cap beam
foundations for left access road
shaft
foundations for right access road
cap beam cap beam
northwest metro entrance
Fig. 1. Plane schematic of metro tunneling and five most sensitive existing urban overpass cap beams on pairs of piers supported on piles.
procedure as shown in Fig. 3 for assessment and control of metro-tunneling effects on piled urban overpass structures in close range is executed, and the key components and conclusions of the work are presented as follows. 2. Degree of closeness and status quo settlement capacity of the overpass The content and degree of investigation and subsequent appraisal of an existing urban overpass and its foundation should be decided consistent with the relative degree of closeness of the foundation to tunneling. The range of tunneling influence hinges upon factors of a physical nature, including tunnel shape and size, embedded depth, geology and hydrogeology, ground treatment, excavation, primary
301
supporting and permanent lining methods, as well as upon factors of somewhat subjective nature, such as the technical know-how, craftsmanship and management effectiveness of the construction group, etc. In addition, surcharge from existing structures in or on the ground may also play an important role. Illustrated in Fig. 4 is a conceptualization of zones of tunneling influence and possible compositions of a piled overpass structure. Determination of the tunneling effect and the degree of closeness of an existing structure should take into consideration the surcharge effect of the structure. Evidently this is difficult, and a feasible remedy would be to make empirical, theoretical and numerical estimations. An existing structure in the ground exerts two types of mechanical effects, one as additional stiffness, and the other as surcharge, and since the volume of the structure would in general be relatively small and thus passively follow the movement of the ground, the surcharge effect is more significant. Referring to Fig. 4, the net vertical as well as horizontal separations of the existing structure from tunnel excavation, Dv and Dh, are the main factors of consideration, and the angle of the slip plane and the height of the natural arch should be determined by calculating the effects of both tunneling and surcharge of the structure. Even though in greenfield conditions, b = 45° //2 and hc = (b c/c)/ktg/, based on Terzaghi’s theory of earth pressure on tunnel lining, with c, k, c and / denoting, respectively, the unit weight, coefficient of lateral earth pressure at rest, cohesion and angle of internal friction of the soil, the surcharge from an existing structure in or on the ground may result in expansion of zones I and II, as may be inferred using the depiction in Fig. 5 by virtue of Janssen’s silo theory (Kolymbas, 2005). Illustrated in Fig. 5, both the vertical earth pressure (equivalent to the portion of gravity that is unsupported by arching) and the portion of gravity supported by arching increase with depth, with the former asymptotically approaching chc,
Fig. 2. West-east cross section of the ventilation tunnels (including the pilot tunnels) and the super- and sub-structures of the existing urban overpass (m).
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Degree of closeness: judge the degree of closeness between metro tunnel and existing overpass
Overpass superstructure Overpass substructure
Inspection of upper structure,pier,cap,beam
Characterization of tunneloverpass spatial relationship
Tunnel and pile profiles
Structural modal test and evaluation of material deterioration Estimation of pretunneling pile settlement
Tunnel and upper structure planes
Evaluation of current state of overpass
Degree of influence Predict effect of metro construction on overpass structure
Estimation of bearing mode and capacity of pile foundation
Ground settlement Dewatering influence
Absolute settlement of overpass foundation
Construction influence
Differential settlement of nearby foundations
Stop construction and take measures to reduce risk
Criteria for control of ground surface and overpass settlements
Yes
Construction management procedures
In-situ measured settlement > Maximum allowable settlement
Yes
No
No
In-situ measured settlement > Alerting settlement
In-situ measured settlement > Warning settlement Yes
Take precautionary mearures and predict effects
Construction continues
No
Halt tunneling, take adjustment-reinforcement measures and predict effects
Fig. 3. Flow chart for characterization, prediction and control of tunneling effects on urban piled overpass.
Fig. 4. Zones of influence above and lateral to tunnel excavation (zone I – ground within slip planes and natural arch, experiencing plastic flow or collapse; zone II – ground bounded by slip planes, natural arch and boundary of tunneling influence, experiencing elastic deformation; zone III – ground free from tunneling influence, maintaining the primitive state prior to excavation; the symbol b denotes the half-width of the natural arch, and the radius of the silo when considering Janssen’s silo theory as described in Kolymbas, 2005).
and the surcharge at the ground surface induces an decreasing-with-depth increment in the vertical earth pressure under greenfield conditions. Similar soil behavior may be imagined if there is in-ground surcharge from an existing buried structure.
In reference to Fig. 4, it is worthy to note that soil friction serves as the sole driving mechanism for soil arching, as manifested by the expression of height of the natural arch, hc (if / = 0 , hc = 1, meaning no arching is possible). When the thickness of the overburden, hs, is adequately
Y. Xiang et al. / Tunnelling and Underground Space Technology 23 (2008) 300–307
γhc
γ hc
q σ
σ
1
1
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allowable for any two neighboring piers with simply supported beams along the longitudinal (road) direction, the maximum permissible tunneling-induced differential settlement for the transverse frame composed of two piers and a rigidly connected cap beam shown in Fig. 2 is prescribed to be 5 mm.
2
3. Dewatering and tunneling-induced pile foundation settlement σs
δσ σ=γz
z
σ=γ z + q
z
1 σ=γhc(1-e-z/h ) 2 σ=γhc+(q-γhc)e-z/h σs gravity supported by arching δσ surcharged-induced load increment unsupported by arching b -c/γ b hc= . h= . k tgφ k tgφ Fig. 5. Vertical earth pressure along depth with ground surface being either free of or with surcharge (based on Janssen’s silo theory as described in Kolymbas, 2005; r denoting vertical earth pressure which is equivalent to the portion of gravity unsupported by arching, z depth, q strength of surcharge, b silo radius and b = (wt/2 + httgb) with Terzaghi’s theory of earth pressure on tunnel lining, with c, k, c and / denoting, respectively, the unit weight, coefficient of lateral earth pressure at rest, cohesion and angle of internal friction of the soil).
large, the influence of tunneling would be confined to below the ground surface, and zone II, as characterized by the height of the influence boundary above the tunnel crown, hi, delineates the range within which soil arching takes place. Let z95 represent the depth where the vertical earth pressure r equals 95% of chc under greenfield condition, then when the tunnel is deep enough, the characteristic thickness of zone II, hi–hc, would equal z95 with a 5% round off. Similar inference applies for other prescribed percentages. Based on an assessment of the degree of closeness of the pile foundations, the content and degree of investigation for different portions of the overpass are selected for appraisal of the status quo settlement-resistant capacity of the overpass. Referring to Fig. 4, the composition of a substructure group of an overpass, including type of members, type of connections between members as well as the composition and working condition of the member materials, and the pre-tunneling settlement of the substructure should be taken into account when prescribing criteria of permissible tunneling-induced settlement. A rigid or continuous connection would demand a lower criterion than simply supported connection, when other conditions are similar. For the overpass concerned herein, although a maximum of differential settlement of 20 mm is considered
Empirical, theoretical and numerical methods are employed to assess the additional pile foundation settlements induced by dewatering and tunneling for construction of the ventilation drifts, and the main bodies of these methods are presented as follows. 3.1. Estimation of dewatering-induced settlement Assuming that the consolidation of the soil in-between the initial and the depressed phreatic surfaces occurs immediately after the pumping drawdown, that there is no soil loss, and that the soil below the drawdown surface experiences no consolidation, the final dewatering-induced soil settlement may be estimated as the compression of the soil strata, for sandy and clayey soils, respectively: ds ¼
X Dri Bi X DB2 c w i ; Esi 2Esi i i
ð1Þ
ds ¼
X ai Dri Bi X ai DB2 c w i ; 1 þ e 2ð1 þ e Þ 0i 0i i i
ð2Þ
where ds denotes the dewatering-induced final soil settlement; cw the unit weight of water; ai, Bi, e0i and Esi stand for soil compressibility, thickness, void ratio and effective compression modulus, respectively; Dri and DBi for dewatering-induced increment in effective stress and dewatered thickness of soil, respectively. The above expressions involve two approximations: Bi DBi, Dri DBicw/2. Dewatering-induced settlement would exert negative skin friction on nearby piles and cause additional pile settlements, two situations of which may be distinguished as sketched in Fig. 6. Referring to Chen and Xiang (2006), a simplified theoretical approach is employed for estimating the pile settlement induced by dewatering in phreatic zone: (i) the Neuman (1972, 1973, 1974) model of pumping in an unconfined aquifer, to calculate the dynamic drawdown distribution; (ii) a simplified effective stress method, to estimate the corresponding soil consolidation settlement, the final value of which may be checked by using Eqs. (1) and (2); (iii) the Randolph and Wroth (1978) pile–soil interaction model, to estimate the additional negative skin friction on the pile shaft; and (iv) a semi-theoretical pile foundation settlement model (China Ministry of Construction, 2002), to predict the temporal evolution of the dewatering-induced pile settlement, dp, for case (a) and (b), respectively:
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z
h ; u ¼ 4ð1 mÞeR2 2 x þ h2 Z 1 p 2 exp 2 ðx nÞ dndg; u¼ r ðgÞ H rðgÞ
Q
τ
d l
τ wc
lp
rp
H rc r
z
Q τ
d
τ
rp
lp w c lw
l H rc r Fig. 6. Effects of dewatering on a nearby pile: (a) wc 6 lp, (b) wc > lp (s denotes the dewatering-induced negative skin friction on pile shaft, wc drawdown at pile center, lp the pile length below the initial phreatic surface, and lw the distance between the pile base and the depressed piezometric surface below) (after Chen and Xiang, 2006).
dp ¼ w dp ¼ w
m X plm cw w2c ð2m 1Þ ðzj aj zj1 aj1 Þ; 2ðm 1ÞabEsj ln 20 j¼1 m X j¼1
þ
ð3aÞ
plcw l2p ð2m 1Þ ðzj aj zj1 aj1 Þ 2ðm 1ÞabEsj ln 20
cw ðlp þ wc Þ lw ; 2Es
ð3bÞ
where a and b denote the length and width of the pile foundation base, respectively; m denotes the Poisson’s ratio of the representative soil surrounding the pile shaft; Esj denotes the modulus of compression of the jth layer of soil below the pile tip; zj the distance of the bottom of the jth soil layer below the pile tip; aj a coefficient for the averaged incremental stress over the range of zj, w an empirical coefficient, and m the number of soil layers adequate for calculation of pile settlement.
ð5Þ ð6Þ
where i denotes the horizontal distance from the tunnel centerline to the point of inflection of the ground settlement trough, Vs the volume of settlement trough per unit distance of tunnel drive; m Poisson’s ratio, h depth of tunnel axis, and e = w/R with w and R representing the uniform radial convergence of the excavation boundary and the equivalent tunnel radius, respectively; x and z stand for the coordinate axes originated at the ground surface, and aligned in the transverse and vertical directions to the tunnel drive, respectively, (n, g) refers to the (x, z) location of an elemental ground loss volume, dndg, H cross-sectional ground loss distributed on the excavation surface for an infinitely long tunnel, and r = g/tgb characterizes the radius of the influence zone, with b being the angle of influence. The formulations, physical assumptions, mathematical expressions and applications of several theoretical solutions, in conjunction with the Peck formula, for calculation of tunneling-induced ground movement are comparatively analyzed in Xiang (2006), and trial calculations using comparable parameter values indicate that these theoretical and empirical formulas may produce similarly shaped but quite discrepant ground surface settlements, implying that rational adaptations to field conditions are essential to successful predictions. For the empirical and theoretical formulas (4)–(6), the i parameter is estimated for sandy and clayey soils, respectively, the Vs, e and H parameters are calculated by using the area of convergence of the tunnel cross section, and the b parameter by estimating the lateral extent of in situ monitored ground surface settlement trough. As illustrated in Fig. 7, the tunnel of a horse-shoe shaped cross section is conceptualized into an equal-area circular tunnel with an equivalent uniform convergence such that the total ground loss is equal to the in situ measurement value. Rankine’s theory of active limit state of equilibrium of soil is employed to check how much percentage of the pile shaft is within the soil wedge possibly in an active limit state as influenced by tunneling. If such percentage is larger than 50%, the soil settlements calculated using the empirical and theoretical formulas may be considered as conservative estimates of pile settlement.
3.2. Empirical and theoretical estimations of tunnelinginduced settlement
3.3. Numerical simulation of tunneling effects
An empirical formula as proposed by Peck (1969) and two theoretical solutions as in Sagaseta (1987) and Yang et al. (2004), respectively, are employed for predicting ground surface settlement induced by tunneling: Vs x2 u ¼ pffiffiffiffiffiffi exp 2 ; ð4Þ 2i 2pi
Referring to Fig. 8, the ventilation drifts are constructed via a 12-stage procedure dubbed as pilot tunnel and pilearch-beam method. A three-dimensional numerical simulation of the staged tunneling process is performed. The soil strata, based on borehole logs, is considered by using the Mohr–Coulomb plasticity model, while the shotcrete primary support, the transverse bracing and the secondary
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305
Fig. 7. Conceptual model for empirical and theoretical estimations of ground settlement (m).
pilot tunnels
concrete fill
cast in-situ reinforced concrete piles
cap beams
2nd excavation
1st excavation
1st bracing
lining are considered as elastic. Grouting effect is taken into account by using increased soil modulus. The numerical model is first calibrated against available monitoring data by manually making parameter adjustments, and then employed for predictive calculations. A parametric sensitivity analysis indicates that with the excavation and construction procedure, the material properties of the soil strata and the primary support exert the most significant influence on the settlements of the nearby pile foundations. Monte-Carlo simulations are conducted to study the probabilistic distributions of the differential settlement between the 59# and 60# foundations and the reliability of the pier-beam structure, due to the probabilistic material parameters of the local soil strata and the primary support inferred from site and laboratory test data and experience. The performance function can be expressed as: Zð~ hÞ ¼ RðxÞ Sð~ hÞ;
ð7Þ
where R stands for the allowable ultimate differential settlement between the 59# and 60# foundations in conformity with the material and composition, symbolized by x, of the cap beam and its connection with the 59# and 60# piers, S the differential settlement between the 59# and 60# foundations induced by metro tunneling, and Z the performance function, both of which are characterized in a probabilistic framework as a function of a random vector, ~ h, representing the probabilistic material parameters of the local soil strata and the primary support.
2nd bracing 3rd excavation 4th excavation & 3rd bracing
crown lining
4. Control of overpass settlement
middle slab
bottom slab
Fig. 8. Numerically simulated sequential construction stages of the ventilation drift: (1) pilot tunnel excavation, (2) bored piling within the pilot tunnels, (3) beam capping the piles, (4) backfilling the void behind the cap beams, (5)–(8) sequential top-down excavations and transverse bracings, (9)–(12) sequential upward removal of bracings and casting of bottom slab, side wall, middle slab and crown as permanent lining.
Based on in situ monitoring data, the empirical, theoretical, deterministic and probabilistic numerical analyses of the effects of dewatering and tunneling on the settlements of adjacent pile foundations, a judgment is made that the differential settlement of the 59# and 60# pile foundations, when the tunnel construction finishes, would induce a bending moment in the cap beam exceeding the capacity allowed by its material and composition. Subsequently, it is decided that precautionary anti-settlement measures should be taken in order to maintain the smooth and safe operation of the overpass while allowing normal metro tunneling advance. Underpinning of the 59# foundation
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installed to furnish extra bearing capacity to the existing piles of the 59# foundation during the installation of the underpinning piles, as shown in Fig. 10. Shown in Figs. 11 and 12 are the settlement histories of the 59# and 60# foundations and the differential settlement between these two foundations, respectively, from which one may see that after underpinning, the 59# foundation has exhibited an appreciable amount of additional settlement prior to settling similarly as the 60# foundation, and the differential settlement continues increasing and assumes significantly larger values roughly between 540 and 570 days of tunneling, after which the settlements of the two foundations largely parallel with each other, resulting in relatively insignificant differential settlement. This phenomenon demonstrates that it may take a while after installation for the underpinning piles to start effectively counteracting the settlement effect of tunneling, and that the underpinning has made the underpinned 59# foundation eventually behave like the 60# foundation.
centerline of simply supported beams cap beam interim support of steel frames ground surface cap of the 59# piled foundation
cap of the 60# piled foundation
Fig. 9. Schematic of ground-surface based temporary support steel frames for the overpass.
I
by means of additional piles tipped an adequate distance below the metro tunnel floor is deemed necessary, whilst in-tunnel measures, including pre-grouting and strong primary support, are undertaken. As illustrated in Fig. 9, interim ground support consisting of steel frames is
10.91 8.91
1.0
3
2.60 2.0
6.
9.47
R1 =0 .
23.0
3 6.
original piles R2 =0 .5
north
augmented cap
original cap
75
10.91
original piles and cap
1.0
45
45
underpinning piles
underpinning piles
I
augmented cap 10.91
I-I cross section
plane
pile foundation settlement (mm)
Fig. 10. Precautionary underpinning of the 59# pile foundation (m).
2 0 -2 0 -4 -6 -8 -10 -12 -14 -16 -18 -20 -22
tunneling progress (day) 30
60
90 120 150 180 210 240 270 300 330 360 390 420 450 480 510 540 570 600 630 660 690 720 750 780
60# foundation settlement start of underpinning end of underpinning
59# foundation settlement
differential pile-foundation settlement(mm)
Fig. 11. Temporal evolvement of the 59# and 60# foundation settlements.
9 8 7 6 5 4 3 2 1 0
start of underpinning
0
30 60
end of underpinning
90 120 150 180 210 240 270 300 330 360 390 420 450 480 510 540 570 600 630 660 690 720 750 780
tunneling progress (day)
Fig. 12. Differential settlement of the 59# foundation with respect to the 60# foundation.
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5. Summary For a Beijing metro station construction near a more than a decade old pile-supported urban overpass, a procedure of assessment and control of metro-tunneling effects on urban piled overpass structures in close range has been carried out, which involves applications of empirical, theoretical and numerical predictions as well in situ monitoring schemes. In order to ensure the normal operation and integrity of the overpass as well as smooth and safe tunneling, the condition and status quo settlement capacity of the overpass are assessed via on-site measurements and computer modeling, the probable additional settlements of the pile foundations caused by tunneling and dewatering in the vicinity are estimated by using in situ monitoring data, empirical and theoretical analyses and numerical simulations of the construction process, and on the basis of which, allowable limit settlements of ground surface and pile foundations are established and anti-settlement underpinning is executed to control the adverse effects of metro construction. In situ monitoring data indicated that the post-underpinning pile foundation exhibited an appreciably larger amount of additional settlement prior to behaving like the nearby non-underpinned pile foundation, with both foundations experiencing similar tunneling influences. The major conclusions may be summarized as follows: (1) the surcharge effect from an existing structure in or on the ground would enhance the effects of tunneling on ground deformation, and thus should be taken into account when estimating the delimitation of zones of tunneling influence and the degree of closeness of an existing structure; (2) for metro tunneling in close range to an existing urban overpass supported on pile foundations, the general control procedure should consist of assessment of the contemporary capacity of the superstructure, prediction of tunneling and dewatering-induced ground surface and pile foundation settlements, establishment of criteria for distinctively constraining ground surface and pile founda-
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tion settlements, and, if necessary, execution of reinforcement measures; (3) in situ monitoring data close to the sensitive areas should be employed to adapt theoretical analysis and calibrate numerical models; (4) settlement criteria and mitigation measures should be worked out through considering the local composition of superstructure of the overpass, as well as the type and depth of the pile foundations; and (5) as indicated by post-underpinning monitoring data, it may take a while after installation before the underpinning piles to effectively counteract the effect of tunneling. References Chen, S., Xiang, Y., 2006. A procedure for theoretical estimation of dewatering-induced pile settlement. Computers and Geotechnics 33 (4– 5), 278–282. China Ministry of Construction, 2002. Code for Design of Building Foundation (GB50007 – 2002) (in Chinese). Kolymbas, D., 2005. Tunneling and Tunnel Mechanics – A Rational Approach to Tunneling. Springer-Verlag, Berlin. Neuman, S.P., 1972. Theory of flow in unconfined aquifers considering delayed response of the water table. Water Resources Research 8 (4), 1031–1045. Neuman, S.P., 1973. Supplementary comments on theory of flow in unconfined aquifers considering delayed response of the water table. Water Resources Research 9 (4), 1102–1103. Neuman, S.P., 1974. Effect of partial penetration on flow in unconfined aquifers considering delayed gravity response. Water Resources Research 10 (2), 303–312. Peck, R.B., 1969. Deep excavations and tunneling in soft ground. In: State of the art report, 7th International Conference on Soil Mechanics and Foundation Engineering, Mexico City, pp. 225–290. Randolph, M.F., Wroth, C.P., 1978. Analysis of deformation of vertically loaded piles. Journal of Geotechnical Division 104 (GT12), 1465–1488. Sagaseta, C., 1987. Analysis of undrained soil deformation due to ground loss. Geotechnique 37 (3), 301–320. Xiang, Y., 2006. An evaluation of theoretical solutions for prediction of ground movements due to shallow tunneling in soil. ASCE Geotechnical Special Publication No. 155, Underground Construction and Ground Movement, pp. 296–303. Yang, J.S., Liu, B.C., Wang, M.C., 2004. Modeling of tunneling-induced ground surface movements using stochastic medium theory. Tunneling and Underground Space Technology 19, 113–123.