Settlement Of The Surface

19 Settlement of the surface

19.1 Estimation of settlement Apart from the assessment of stability, the determination of settlements at the surface is very important in tunnelling. However, in geotechnical engineering, deformations can be forecast with less accuracy than stability. This is mainly because the ground has a nonlinear stress-strain-relationship, so that one hardly knows the distribution of the stiffnesses. We consider here some rough estimations of the settlement of the ground surface due to the excavation of a tunnel. One should be aware of their limited accuracy. For the determination of the distribution of the surface settlements let us take first Lam´ e’s solution (see Equ. 14.8) of the problem of a cylindrical cavity in a weightless elastic space, loaded by the hydrostatic stress σ∞ . We regard the vertical displacement uv of the ground-surface shown in Fig. 19.1.

Fig. 19.1. Vertical displacement at the ground surface

The vertical component uv of the displacement u reads uv =

H ·u . r

(19.1)

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19 Settlement of the surface

With r2 = H 2 + x2 we obtain from Lam´ e’s solution uv =

r2 H σ∞ − p · 20 2 2G H +x

.

(19.2)

The maximum settlement uv,max is obtained at x = 0, and the distribution of the settlement reads: uv =

uv,max 1 + (x/H)2

.

This distribution1 is not realistic, when compared with measurements.2 It is also inconsistent, because it uses a solution for the full space for a problem of the halfspace. A more realistic description of the measured settlement is obtained according to Peck by the Gauss-distribution uv = uv,max · e−x

2

/2a2

.

The parameter a (standard deviation) is to be determined by adjustment to measurements. It equals the x-coordinate at the inflection point of the Gausscurve. It can be estimated with the diagram of Peck (Fig. 19.2)3 or according to the empirical formula:4 2a/D = (H/D)0.8

.

(19.3)

D is the diameter of the tunnel and H is the depth of the tunnel axis (Fig. 19.3). For clay soils is a ≈ (0, 4 . . . 0, 6)H, for non-cohesive soils is a ≈ (0, 25 . . . 0, 45)H. Another estimation of a is given in table 19.1.5

1

It also follows from more complicated computations for a linear-elastic material, see A. Verruijt and J.R. Booker: Surface settlements due to deformation of a tunnel in an elastic half space. G´eotechnique 46, No. 4 (1996), 753-756 2 see e.g. J.H. Atkinson and D.M. Potts: Subsidence above shallow tunnels in soft ground. Journal of the Geotechnical Engineering Division, ASCE, Volume 103, No. GT4, 1977, 307-325 3 Peck, R.B., Deep excavations and tunnelling in soft ground. State-of-the-Art report. In Proceedings of the 7th International Conference on Soil Mechanics and Foundation Engineering, Mexico City, State-of-the-Art Volume, 1969, 225-290 4 M.J. Gunn: The prediction of surface settlement profiles due to tunnelling. In ’Predictive Soil Mechanics’, Proceedings Wroth Memorial Symposium, Oxford, 1992 5 J.B. Burland et al., Assessing the risk of building damage due to tunnelling lessons from the Jubilee Line Extension, London. In: Proceed. 2nd Int. Conf. on Soil Structure Interaction in Urban Civil Engineering, Z¨ urich 2002, ETH Z¨ urich, ISBN 3-00-009169-6, Vol. 1, 11 -38.

19.1 Estimation of settlement

343

Fig. 19.2. Estimation of A by Peck

Soil a/H granular 0.2 - 0.3 stiff clay 0.4 - 0.5 soft silty clay 0.7 Table 19.1. Estimation of a

The horizontal displacements uh of the ground-surface follow from the observation that the resultant displacement vectors are directed towards the tunnel axis (as shown in Fig. 19.1) i.e. uh =

x uv H

The distribution of the settlements in longitudinal direction of a tunnel under construction is represented in Fig. 19.3. The volume of the settlement trough (per current tunnel meter) results from the Gauss-distribution to √ Vu = 2π · a · uv,max (19.4) and is usually designated as volume loss6 (ground loss). The volume loss amounts to some percent of the tunnel cross-section area per current meter. If 6 This designation is based on the conception that the soil volume Vu is dug additionally to the theoretical tunnel volume

344

19 Settlement of the surface

Fig. 19.3. Settlement trough over a tunnel (left); Approximate distribution of the surface settlements in tunnel longitudinal direction. Z x The shown curve coincides rea2 1 e−y /2 dy (right). sonably with the function y = erf x = √ 2π 0

this ratio is known by experience for a given soil type, then the maximum settlement uv,max can be estimated with (19.3) and (19.4). Mair and Taylor7 give the following estimated values for Vu /A: Unsupported excavation face in stiff clay: . . . . . . . . . . . . . . . . . . . . . . . . . 1-2% Supported excavation face (slurry or earth mash), sand: . . . . . . . . . . . . 0.5% Supported excavation face (slurry or earth mash), soft clay: . . . . . . . . . 1-2% Conventional excavation with sprayed concrete in London clay: . . . 0.5-1.5% The volume loss depends on the skill of tunnelling. Due to improved technology the volume loss has been halved over the last years. The evaluation of numerous field surveys and lab tests with centrifuge leads to an empirical relationship8 between the volume loss Vu related to the area A of the tunnel cross section and the stability number N := (σv −σt )/cu . Herein, σv is the vertical stress at depth of the tunnel axis, σt is the supporting pressure (if any) at the excavation face, and cu is the undrained cohesion. If NL is the value of N at collapse, then: Vu /A ≈ 0.23 e4.4N/NL

.

The estimations represented here refer to the so-called greenfield. If the surface is covered by a stiff building, then the settlements are smaller9 . 7

R.J. Mair and R.N. Taylor, Bored tunnelling in the urban environment. 14th Int. Conf. SMFE, Hamburg 1997 8 S.R. Macklin, The prediction of volume loss due to tunnelling in overconsolidated clay based on heading geometry and stability number. Ground Engineering, April 1999 9 ’Recent advances into the modelling of ground movements due to tunnelling’, Ground Engineering, September 1995, 40-43

19.1 Estimation of settlement

345

The maximum settlement uv,max can also be roughly estimated by the following consideration: Let εr0 and εv0 be the radial strain and the volume strain at the crown, respectively. We can determine these values by a triaxial or biaxial extension test in the laboratory. Then we have εϑ0 = εv0 − εr0 = u0 /r0 , whereby u0 is the displacement (settlement) of the crown and r0 is the radius of the tunnel. We now assume  r d 0 (19.5) u = u0 r for the distribution of the displacement above the crown10 (Fig. 19.4). With du dr |r0 = εr0 it follows from Equ. 19.5 εr0 = −d

u0 r0

.

With u0 = εϑ0 r0 = (εv0 − εr0 )r0 it follows d=−

εr0 εv0 − εr0

.

Fig. 19.4. Distribution of the vertical displacement u above the crown

The settlement of the surface (r = r0 + h) results then via #  r d−1 r ## d du ## 0 0# = −u d = −u0 = −d εϑ0 εr0 = 0 dr #r0 r r2 #r=r0 r0 to 10

cf. C. Sagaseta: Analysis of undrained soil deformation due to ground loss. G´eotechnique 37 , No. 3 (1987), 301-320; R. Kerry Rowe and K.M. Lee: Subsidence owing to tunnelling. II. Evaluation of a prediction technique. Can. Geotech. J. Vol. 29, 1992, 941-954

346

19 Settlement of the surface

 u1 = (εv0 − εr0 )r0

r0 r0 + h

d .

The surface settlement is therefore smaller, the larger h is and the smaller the crown displacement u0 is. One can keep the surface settlement small, if one keeps the strain εr0 (and, consequently εv0 ) at the crown small. This can be ¨ller-Salzburg reported that he could obtained by rapid ring closure. Mu always keep the crown displacement u0 between 3 and 5 cm.11

19.2 Reversal of settlements with grouting With shield driving the surface settlements result mainly from the tail gap, if the excavation face is suitably supported (e.g. by pressurised slurry). Grouting of the tail gap is expected to reverse the surface settlement. However, it is observed that even if the grouted mass exceeds the theoretical gap volume, the surface settlement is not reversed.12 This fact can be explained in terms of soil mechanics: A cycle of loading and unloading leaves behind a net volume change, usually a compaction (Fig. 19.5). The effect of soil compaction due to a loading-unloading cycle in shield tunnelling is shown in Fig. 19.6 which represents the surface settlement due to closure of a 7 cm thick tail gap (curve a) and the one obtained after the grouting of the gap (i.e. reversing of the convergence of 7 cm). This result is obtained with the FEM programme ABAQUS and use of the hypoplastic constitutive equation calibrated for medium dense sand.13

19.3 Risk of building damage due to tunnelling For rough assessments of damage risk it is assumed that surface buildings are completely flexible, i.e. they have no stiffness and undergo the same deformation as the ground surface of the ’greenfield’. This is a conservative assumption, because the real deformation will be reduced due to the stiffness of the building as compared to the one of the greenfield.14 Evaluating the predicted 11

L. M¨ uller-Salzburg und E. Fecker: Grundgedanken und Grunds¨ atze der ¨ ’Neuen Osterreichischen Tunnelbauweise’. In: Grundlagen und Anwendungen der Felsmechanik. Felsmechanik Kolloquium Karlsruhe 1978, Trans Tech Publications, Clausthal 1978, 247-262 12 S. Jancsecz et al., Minimierung von Senkungen beim Schildvortrieb am Beispiel der U-Bahn D¨ usseldorf. Tunnelbau 2001, VGE Essen, 165-214 13 M. M¨ ahr, Settlements from tail gap grouting due to contractancy of soil, Felsbau, in print, 2004 14 This section is based mainly on the book ”Building Response to Tunnelling. Case Studies from Construction of the Jubilee Line Extension, London”, Vol. 1, edited by J. B. Burland et al, Telford, London, 2001

19.3 Risk of building damage due to tunnelling

347

σ −σ 1

2

ε

εv

1

ε1 Fig. 19.5. A loading-unloading cycle (here shown for the example of triaxial test) leaves behind a permanent densification 1 settlement [cm]

0 -1 -2 -3 -4 -5 40

35

30

25

20

15

10

5

0

distance from axis [m]

Fig. 19.6. Surface settlement due to gap closure (full line) and after grouting of the gap (dashed). Numerically obtained results.

settlements of the greenfield, we can assess that buildings with a maximum tilt of 1/500 and a settlement of less than 10 mm have negligible risk of damage. For the remaining buildings, a risk assessment must be undertaken which is still based on the greenfield deformation and, therefore, is quite conservative (because settlements are over-estimated). Damage of buildings is assessed in terms of tensile strain ε according to Table 19.2. The strain of the building

348

19 Settlement of the surface

is to be inferred from the settlement trough. Burland and his co-authors consider a building as Timoshenko beam15 and derive its strains from the deflection Δ (Fig. 19.7). Possible cracks (due to shear and due to bending, as shown in Fig. 19.8) are perpendicular to maximum tensile strains.

Fig. 19.7. Deflections Δ in sagging and hogging zones.

Fig. 19.8. Deformation and cracks due to pure shear (a, b) and pure bending (c, d).

However, the estimation of the strain in the building, assuming that it behaves like a beam is more or less academic, because (i) it contradicts the starting assumption that the building is infinitely flexible, and (ii) the shear and bending stiffnesses of this beam can hardly be assessed, especially for old masonry buildings with vaults, timbering etc. For a rough estimation it appears reasonable to use table 19.2 with the assumption that the maximum tensile strain in a building situated over the inflexion point has the order of magnitude of uv,max /a. For more elaborate estimations, a method is used in the cited book that attempts to take the stiffness of the building into account. This method 15

Contrary to the ’classical’ or Euler-Bernoulli beam, where shear forces are recovered from equilibrium but their effect on beam deformation is neglected, in the Timoshenko beam cross sections remain plane but do not remain normal to the deformed longitudinal axis. The deviation from normality is produced by transverse shear.

19.3 Risk of building damage due to tunnelling

349

is based on the results of FEM computations. It should be added that timedependent settlements may be observed several years after the damage of the tunnel. Thereby, the settlement through expands laterally. Degree of severity Negligible Very slight

Description of typical damage

Hairline cracks less than about 0.1 mm. Damage generally restricted to internal wall finishes. Close inspection may reveal some cracks in external brickwork or masonry. Cracks up to 1 mm. Easily treated during normal decoration. Slight Cracks may be visible externally and some repointing may be required to ensure weather-tightness. Doors and windows may stick slightly. Cracks up to 5 mm. Moderate Doors and windows sticking. Service pipes may fracture. Weather-tightness often impaired. Cracks from 5 to 15 mm. Severe Windows and door frames distorted, floor sloping noticeably. Walls leaning or bulging noticeably, some loss of bearing in beams. Service pipes disrupted. Cracks 15. . . 25 mm. Extensive repair work involving breaking-out and replacing sections of walls, especially over doors and windows. Very Beams lose bearing, walls lean badly and require severe shoring. Windows broken with distortion. Danger of instability. Cracks > 25 mm. Major repair is required involving partial or complete rebuilding.

Tensile strain ε (%) 0 - 0.05 0.05 - 0.075

0.075 - 0.15

0.15 - 0.30

> 0.30

Table 19.2. Relation between damage and tensile strain (according to Burland et al.)