casestudy cemented

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The 12th

International Conference of

International Association for Computer Methods and Advances in Geomechanics (IACMAG)1-6 October, 2008Goa, India

Using Particle Elements to Model the Torino Subsoil MechanicalBehaviour to Improve the Applicability of Microtunnelling Technique

M. Barla, M. CamussoDept. of Structural and Geotechnical Engineering, Politecnico di Torino, Italy

Keywords: microtunnelling, particle modelling, jacking forces, conglomerate

ABSTRACT: This paper describes a research project being carried out at the Politecnico di Torino with the mainpurpose of improving the applicability of microtunnelling in the metropolitan area of Torino by producing usefultools for the estimation of the jacking forces required by the microtunneller and the pipeline to advance into theground. The subsoil conditions in the city are characterised by a sand and gravel deposit, locally cemented, dueto calcareous deposition processes. Undisturbed sampling is difficult if not impossible to undertake thereforeinvestigations on the subsoil conditions for geotechnical characterisation and evaluation of design parametersneed to rely on indirect methods. With the intent to seek for a relationship between jacking forces and the degreeof cementation in the ground, a discrete numerical code, able to simulate the granular nature of the soil, wasused. The paper will show results on the calibration process of the numerical model. Based on these results, thepaper will describe a number of numerical simulations of microtunnel installations through several models of theground, each of them characterised by a different randomly distributed cementation degree. This will allow one togain insights into the applicability of microtunnelling in the Torino subsoil.

1 Introduction

In order to study the applicability of microtunnelling technology in the metropolitan area of Torino (Italy), a

research project is being carried out at the Politecnico di Torino with the main purpose of producing useful toolsfor the estimation of the jacking forces required by the microtunneller and the pipeline to advance into the ground.This objective, besides the obvious need of choosing the correct MTBM and its set-up, is important for improvingthe reliability of the design of pipelines carried out with this technology, making it more competitive with respect totrench excavation which, up to now, represents the most common method of installation of pipelines in Torino.

As well known (Chapman & Ichioka, 1999; Milligan & Norris, 1996; Pellet-Beacour & Kastner, 2002), themagnitude of the jacking forces is related mainly to the characteristics of the soil being excavated. In the case ofthe Torino subsoil the key issue for a detailed analysis of the ground response to tunnelling is related to thedegree of cementation in the ground as will be described in the following. Available empirical correlations tocompute the friction forces acting at the pipe-soil contact, in this case, are not able to capture the real nature ofthe soil, therefore do not allow for sensible predictions.

With the intent to seek for a relationship between jacking forces and the degree of cementation in the ground, itwas decided to use the discrete numerical code PFC

2D(Itasca, 2005), which is able to simulate the granular

nature of the soil. By modelling the excavation process it will be possible to analyse the stability conditions at the

microtunnel contour. Unstable ground will overload the pipe causing the friction forces arising on the pipe lateralsurface to increase.

The use of the PFC2D

code requires as input data the definition of the micro-mechanical properties at the level ofthe numerical elements (particles) constituting the soil model. These properties can be calibrated by simulatinglaboratory biaxial compression tests as will be shown in the following.

2 Subsoil conditions in Torino

Geotechnical characterization of the Torino subsoil, as carried out during relevant underground infrastructuresconstruction that took place in the city in the last few years, such as the New Underground Railway Link and theMetro Line 1 (Barla & Vai, 1999; Geodata, 2000), revealed detailed information on the subsoil conditions in thecity. These are characterised by a sand and gravel deposit, ranging from medium to highly dense, down to adepth of 8 to 10 m; below this depth, cemented soil (in cases a conglomerate), due to calcareous depositionprocesses, is often present. Direct observation in the field has indeed shown that cemented areas of ground are

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generally randomly distributed along horizontal layers, with thickness varying between a few centimetres to a fewmetres. This can be clearly evidenced in Figure 1 where the geological map and a photograph of a tunnel facealong the Underground Railway Link project are compared.

Grain size distributions of samples taken from boreholes as well as from shafts have shown that both thecemented and the loose soil are mainly characterised by the same grain size (Figure 2).

(a) (b)

Figure 1. Geological map (a) and photograph (b) at the Railway Link tunnel face (C = cobbles, G = gravel, S =sand, L = silt, A = clay, X = cementation).

0

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0.010.11101001000

Grain size [mm]

Perc

entfinerbyweight[%]

Figure 2. Grain size distributions from soil samples, the average distribution is shown in bold (Geodata, 2000).

Undisturbed sampling is difficult if not impossible to undertake mainly due to the presence of cobbles larger than100 mm in diameter. Investigations on the subsoil conditions for geotechnical characterisation and evaluation ofdesign parameters need to rely on indirect methods such as recording of boring parameters, in situ testing indeep test pits (plate loading tests), and geophysical investigations (Barla, 1997). Large size cubic samples ofconglomerate (50 cm side) were also retrieved from the site and subjected to unconfined compression tests in thelaboratory.

The degree of cementation (C%) is a key issue for a detailed analysis of the ground response to tunnelling. Thegeotechnical model of the Torino subsoil comprises four Geotechnical Units (GU), which are characterised by thesame grain size and different degree of cementation. Depth and thickness of the Geotechnical Units depend onthe location within the city. Deformability (Ed = deformation modulus) and strength parameters (c = unconfinedcompressive strength; m = Hoek & Brown constant) of the different units clearly depend on the degree ofcementation. The following correlations were determined (Barla & Barla, 2005):

53100%C

12

100%C

c108

100%C

d e20m;e4.3;e364E V (1)

which allow one to asses the GU parameters as a function of the degree of cementation. The above correlationswere obtained on the basis of plate loading tests, in the case of deformability, and on the basis of thePapantonopoulos & Atmatzidis (1993) yield criterion, in the case of strength. This yield criterion assumes that fora loose soil the behaviour is Mohr-Coulomb like, while for a cemented one the behaviour is Hoek-Brown like. ThePapantonopoulos & Atmatzidis (1993) criterion may be expressed as:

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k1c3kc

k131 m

VVVVV (2)

where kis a coefficient which governs the transition from the Mohr-Coulomb (k = 0) to the Hoek-Brown criterion (k= 1), m and care given by the equations (1) above, 1 and 3 are the principal stresses.

Deformability and strength parameters for the loose (C% = 0) and the fully cemented soil (C% = 100%) wereassumed as given in Table 1.

Table 1. Geotechnical parameters for the loose and the fully cemented soil.

Parameter Loose Soil Cemented Soil

Lab Tests Esec,50% [MPa] - 480Deformation modulus

In Situ Tests Ed [MPa] 55 255 -

Unconfined compressive strength c [MPa] - 3.79

Hoek & Brown constant m [-] - 20

Friction angle M [] 36 38 -

Cohesion c [kPa] 0 -

3 Modelling the volume element

The magnitude of the jacking forces required by the microtunneller and the pipeline to advance into the ground isstrongly related to the geotechnical properties of the soil. In the case of the excavation in the Torino subsoil, therandomly distributed presence of cementation heavily influences the behaviour at the tunnel surround implyingvariability of the jacking forces, which depend on where the excavation is taking place. In the present study, inorder to improve design methods presently available, it was decided to use the discrete element numerical codePFC

2Dthat, allowing for finite displacements and detachment of discrete elements, is able to simulate the

granular nature of the soil.

In order to simulate the mechanical behaviour of the ground, the use of the PFC2D

code requires as input data thedefinition of the micro-mechanical parameters. These parameters control the interaction between the differentparticles in the model, and should be determined both for the loose and for the fully cemented soil. Although it isrelatively easy to assign chosen properties to a PFC

2Dmodel, it is often difficult to choose such properties so that

the behaviour of the resulting synthetic material resembles that of an intended physical material. For codes such

as PFC2D that synthesize macro-scale material behaviour from the interactions of micro-scale components, theinput properties of the microscopic constituents are usually not known. The appropriate micro-properties can bechosen by means of a calibration process in which the behaviour of the synthetic material is compared directlywith the relevant measured responses of the intended physical material.

In order to limit the calculation time it was decided to limit the widespread grain size distribution of the realmaterial by simulating a synthetic material with a restrained grain size distribution (from 10 to 100 mm), ruling outthe finer and the coarser fractions. To account for the two dimensional conditions, the porosity assigned to it hasto be computed in 2D. This value is equal to 15.65% and was obtained on the basis of the Torino soil relativedensity (known by SPT tests) and from the maximum and minimum 2D porosity of the synthetic material, derivedby means of appropriate numerical simulations.

3.1 Mechanical behaviour of loose soil (C% = 0)

The numerical micro-parameters required to simulate the loose soil behaviour are the particle stiffness

parameters (kn and ks) and the particle friction coefficient (P). Although the geotechnical properties of the loosesoil were obtained on the basis of in situ test results, it was decided to carry out the micro-parameter calibrationprocess by simulating biaxial tests. This choice is supported by the fact that, for a loose soil, the scale effects onthe mechanical properties are supposed to be negligible. Numerical analyses were performed on square samples(1 m size), consisting of about 2000 infinite stiffness cylindrical particles, whose contacts are treated as elasticsprings with stiffness dependent on kn and ks (Figure 3a). During the biaxial tests the confining stress was keptconstant by means of a servo-mechanism that rearranges the velocity of the lateral walls, while the horizontalwalls were assigned a constant displacement velocity.

Calibration of the particle stiffness parameters was performed by comparing the Youngs modulus resulting fromthe numerical tests to the deformation modulus obtained from in situ plate loading tests while calibration of theinterparticle friction coefficient was carried out by determining the Mohr-Coulomb failure envelope for the soil.

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(a)

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0.01 0.1 1 10

Global axial strain [%]

Eloc

[MPa]

= 100 kPa

= 150 kPa

= 200 kPa

= 250 kPa

= 300 kPa

V'3

V'3

V'3

V'3

V'3

(b)

Figure 3. Specimen for the loose soil with clumps (red) (a) and Youngs modulus obtained from biaxial tests (b).

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800

1000

0.0 1.0 2.0 3.0 4.0 5.0 6.0


q[kPa]

= 100 kPa

= 150 kPa

= 200 kPa

= 250 kPa

= 300 kPa

V'3

V'3

V'3

V'3

V'3

(a)

M' = 37.60

100

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400

500

600

0 200 400 600 800 1000

s' [kPa]

t[kPa]

(b)

Figure 4. Stress strain curves for biaxial tests on the loose soil (a) and failure envelope (b).

Only by introducing clumps in the model it was possible to obtain a satisfactory mechanical behaviour in termsof strength. To this extent, a selected number of particles were substituted with three rigidly connected particles(a clump) equivalent in terms of area and mass to the substituted ones, so not to alter the original porosity andinertial properties of the specimen (Figure 3a). As a matter of fact, an assembly of cylindrical particles does notallow to account for the shape and asperities typical of true material, which play a major role in defining themechanical behaviour, while the response is much better if clumps are included in the assembly.

The calibrated normal stiffness was set to 1 x 109

N/m, while the ratio ks/kn was taken equal to 0.20. These highvalues reduce the analysis time-step increasing dramatically the computational time. To overcome this aspect,the platens velocity was set to 5 mm/s and the simulation was carried out in 20 different stages. After each stagethe analysis was run to equilibrium. The stress-strain state obtained at the end of each stage, being independent

of the velocity, was considered to be representative of the mechanical behaviour of the synthetic material.

Figure 3b shows the result in terms of the Youngs modulus of the simulated tests. The modulus is computedbased on the axial strain measured at the centre of the specimen and for this reason named local. The syntheticmaterial modulus is in the range 55255 MPa for a strain level between 0.08% and 0.6% and for a mobilisedstrength of 0.32 to 0.97, when a confining pressure of 200 kPa is applied. These values satisfactorily match thosemeasured by plate loading tests at a depth of 10 m (i.e. approximately 200 kPa of vertical stress). Figure 3b alsodepicts an increase with the confining pressure of the strain range for which the modulus values are in therequired range. This result is even more convincing if one takes into account that field tests may have suffered bythe presence of levels of cemented ground and therefore appear slightly overestimated.

Figure 4 shows the stress strain curves and the failure envelope for the simulated tests. The friction angle isequal to 37.6, which was obtained by applying an interparticle friction coefficient equal to 2.10.

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3.2 Mechanical behaviour of cemented soil (C% = 100%)

As previously outlined, the cemented soil is characterised basically by the same grain size distribution of theloose soil. This allowed to simulate the mechanical behaviour of the cemented soil by adopting the samenumerical model previously described, accounting for the effect of cementation. This was done by introducing

parallel bonds between the different particles. This particular contact model in PFC2D is characterized by a finitevalue of stiffness and strength parameters. It acts in parallel with the stiffness and slip model at the contact pointand approximates the physical behaviour of a cement-like substance lying between and joining the bondedparticles. The total stiffness of the new contact is the sum of the contact stiffness parameters of the particles (knand ks, already calibrated for the loose soil) and the stiffness parameters of the parallel bonds installed ( k

nand

ks). This implies that any additional load applied to the two-particles system after the parallel bond is installed is

shared between the contact spring and the parallel bond spring. The parallel bond breaks when the stresses atthe contact are greater than the corresponding strength parameters (tensile strength cand shear strength c). Inthis case its effect is removed from the contact and the behaviour is governed by the slip model.

Laboratory unconfined compression tests results were available for the cemented ground. This allowed tocalibrate the new parameters to be introduced (parallel bond parameters k

n, k

s, c and c) by simulating

unconfined tests, removing the lateral walls of the sample (i.e. without applying any confinement stress) duringthe shearing phase. Calibration of stiffness parameters for the parallel bonds was performed comparing theYoungs modulus obtained from the synthetic material to that measured during laboratory tests (Table 1). The

procedure was not straight forward and required a complex parametric study. Figure 5 shows the Youngsmodulus obtained during unconfined and biaxial compression tests. In this case, the modulus is computed basedon the global axial strain of the specimen and for this reason is named global. This is justified by the intention toreproduce laboratory tests results where axial measurements were taken by means of external transducers. TheYoungs modulus is between 470 and 510 MPa for 50% of mobilised strength, in good agreement with the valuesmeasured in the laboratory.

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600

0.01 0.1 1 10


E

glob[MPa]

= 0 kPa

= 100 kPa

= 200 kPa

= 300 kPa

= 400 kPa

= 500 kPaV'3

V'3

V'3

V'3

V'3

V'3

Figure 5. Youngs modulus obtained for the cemented soil.

Calibration of strength parameters required to perform parametric analyses in order to define parallel bondstrength. Basically two factors influence the calibration process. First of all, the need to reproduce the appropriateunconfined compressive strength and, secondly, the need to reproduce the correct slope of the failure envelope(i.e. the increment in strength due to confining pressure). The first effect is directly dependent on the strength of

the parallel bonds (c and c), while the second effect was controlled by varying bond strength within thespecimen. A tentative value ofc and c, allowing for an acceptable simulation of the unconfined compressionstrength, was determined, then the effect of confining pressure was taken into account and the failure envelopecomputed. In order to match the desired behaviour, a higher strength was given to one parallel bond out of five.This procedure implies a complex failure path inside the sample and allows to increase the slope of the failureenvelope. It also required to slightly reduce the tentative value of c and c to a final value. Figure 6 shows thestress strain curves and the results in terms of state of stress at failure for the simulated tests, superimposed onthe Hoek & Brown criterion for the cemented soil (parameters from Table 1). The final strength parameters for theparallel bond are c equal to 3.1 MPa and c equal to 6.2 MPa while the stronger parallel bonds were given a tentimes higher strength.

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0

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0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0


q[kPa]

= 0 kPa

= 100 kPa

= 200 kPa

= 300 kPa

= 400 kPa

= 500 kPaV'3

V'3

V'3

V'3

V'3

V'3

(a)

0

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2000

3000

4000

0 1000 2000 3000 4000 5000

s' [kPa]

t[kPa]

Hoek & Brown Failure Envelope

PFC Synthetic Material

(b)

Figure 6. Stress strain curves for biaxial tests on the cemented soil (a) and failure envelope (b).

4 Modelling microtunnelling excavation

The attention is now moved to the site scale. The excavation of a 1 m diameter microtunnel, with a 50 mmovercut, is simulated in the Torino subsoil at a depth of 10 m below the surface. A discrete numerical model isbuilt up by assembling particles with the properties calibrated at the volume element scale.

4.1 Model set up

The model was intended to reproduce a cross section, perpendicular to the microtunnel axis, thus showing thesoil response radial to the microtunnel contour. The numerical model has a width of 10 m and a height of 7.75 mand was constructed by randomly combining together assemblies of cemented soil with assemblies of loose soil.A porosity of 15.65%, according to the value used during the calibration process, was considered during theparticles generation. To optimise the model in terms of PC memory requirements and calculation times, aconcentric upscale of the particles radius was used (Konietzky et al., 2001), starting from 1 in the vicinity of thetunnel contour (i.e. the grain size is the same of that used during the calibration process) to 2 in the outer area of

the model. The model consists of about 70,000 particles and is generated by using the same percentage ofparticles substitution with clumps as adopted at the volume element scale.

The tunnel centreline is located at a distance of 5 m from the upper boundary. Upper and lateral boundaries arecomposed by a series of 0.5 m long walls that allow to apply geostatic stresses to the model by means of anumerical servomechanism (similar to that described in Section 3.1) while the lower boundary is fixed. Anoverload of about 112 kPa, corresponding to 5 m of overburden, and a K0value of about 0.50.6 were consideredin order to apply the appropriate state of stress at the depth of the microtunnel.

With the aim to introduce the randomly distributed cementation within the ground, the model was subdivided insmall rectangular areas (width ranging from 0.4 to 2 m and height from 0.2 to 1 m). These assumptions reflect theresult of direct observation in the field as described in Section 2 (Figure 1). Using a random-number generator,randomly distributed rectangular areas were chosen as cemented material, until the desired degree ofcementation was reached within the model. The microparameters calibrated for the cemented soil were applied tothese areas while those pertaining to the loose soil were already applied to the remaining particles of the model. Itis to be mentioned though that cemented layers in the field may be distributed in a more complex way as afunction of the deposition process that leads to the calcareous concretion formation. The above distribution wasconsidered to be suitable given the aim of the present study.

Different models were constructed with a specific percentage of cemented layers. In order to avoid geometricaleffects on results, different cementation distributions were considered for each specific degree of cementation bychanging the seed of the random-number generator, hence the rectangular area chosen. Figure 7 shows, as anexample, two models for a 25% and 75% cementation respectively; they refer to the stage after generation andprior to excavation, when the particles within the tunnel area are removed and a number of rigidly connectedparticles are generated in order to simulate the pipe.

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(a) (b)

Figure 7. Discrete numerical model corresponding to a 25% cementation degree (a) and to a 75% cementationdegree (b). Loose soil areas are shown in orange while cemented soil ones in blue.

4.2 Results

The required jacking forces for the pipeline and the MTBM to advance into the ground are certainly influenced bythe friction forces that arise at the soil-pipe contact. For the geotechnical environment under consideration, in thecase of excavation taking place in the fully cemented soil, the microtunnel is shown to be stable and frictionforces, developed at the soil-pipe contact, will mainly be due to the weight of the pipeline and the MTBM. In thecase of excavation taking place in the loose soil, the microtunnel is not stable, unless appropriate lubricating fluidis applied, and pressures will arise at the soil-pipe contact increasing the jacking forces, if compared to theprevious case. In an intermediate case, when the ground is characterised by a certain degree of cementation,local failures and instabilities at the microtunnel contour will occur. In this case, the amount of normal stressloading the pipe will cause an increase of jacking forces, compared to the stable case.

The result of the work performed so far is shown in Figure 8, for the two selected models of Figure 7, whereparticles are plotted with different colours as a function of their total displacement. Models refer to the end ofnumerical excavation process, corresponding to when the relevant parameters (i.e. displacements, stresses,

mean unbalanced force) tend to a constant value.

(a) (b)

Figure 8. Total displacements throughout the model in the case of a 25% cementation degree (a) and of a 75%cementation degree (b).

During the excavation process, the development of contact forces between the particles representing the soil andthe pipe was monitored. This is shown in Figure 9a in terms of total normal stress built up at the soil-pipe contact,for the same two models. As it can be seen, the normal stress reaches a constant value at the end of theexcavation stage. Results from different analyses are shown in Figure 9b where the normal stress is shown as afunction of the degree of cementation. It is clear that, despite the preliminary status of the results, there is anexponential increase in normal stress with the reduction of the degree of cementation. This relationship may beused to estimate, at the design analysis stage, the jacking forces required by the pipe and the MTBM to advanceinto the ground as a function of the cementation degree determined by means of appropriate site investigation.

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0

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Cycles [x1000]

Normalstress[kPa]

Cementation = 25%

Cementation = 75%

(a)

0

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35

0 20 40 60 80 100

Degree of cementation [%]

Normalstress[kPa]

(b)

Figure 9. Normal stress built-up on the pipe during the excavation process for two different models (a) andrelationship between normal stress and cementation degree (b).

5 Conclusions

The calibration process of the discrete numerical model used to simulate the mechanical behaviour of the looseand the fully cemented soil, in the case of the Torino subsoil, was described in this paper. Thanks to the workperformed so far and described above, the mechanical behaviour of the ground can be reproduced satisfactorily.Preliminary results pertaining to the numerical modelling of the microtunnelling problem at the site scale werealso described and some remarks on the relationship between the normal stress developed at the soil-pipecontact and the degree of cementation were given.

In fact, the scope of the research undergoing at the Politecnico di Torino is to allow one to find a relationshipbetween jacking forces required by the pipeline to advance into the ground and the degree of cementation in theground itself. This would clearly improve the applicability of microtunnelling technique in the metropolitan area ofTorino. The required jacking forces can be computed as a function of the degree of cementation in the ground bytaking advantage from the results of the discrete numerical simulations performed.

6 References

Barla G. 1997. Tunnelling for Turin railway link. Proc. 14th

International Conference on Soil Mechanics and Foundation

Engineering, Hamburg (Germany), 4, 2387-2390.

Barla G., Vai L. 1999. Indagini geotecniche per la caratterizzazione del sottosuolo di Torino lungo il tracciato del passanteferroviario. Proc. XX Convegno Nazionale di Geotecnica, Parma (Italy), 335-342.

Barla M., Barla G. 2005. Assessing design parameters for tunnelling in a cemented granular soil by continuum and

discontinuum modelling. Proc. 11th

Iacmag Conference, Torino (Italy), 4, 475-484.

Chapman D.N., Ichioka Y. 1999. Prediction of jacking forces for microtunnelling operations, Trenchless Technology Research,

14 (1), 31-41.

Geodata 2000. Metropolitana Automatica di Torino Linea 1 - Tratta funzionale Collegno - Torino Porta Nuova - RelazioneGeotecnica, Report No. MTL1T1A0DGEOGENR002.

Itasca 2005. PFC2D

(Particle Flow Code in Two Dimensions), Version 3.10, Itasca Consulting Group, Minneapolis (U.S.A.).

Konietzky H., te Kamp L., Blmling P., Mayor J.C. 2001. Micro-mechanical analysis of excavation disturbed zones aroundtunnels. Proc. 10

thIacmag Conference, Tucson (U.S.A.), 543-546.

Milligan G.W.E., Norris P. 1996. Site-based research in pipe jacking-objectives, procedures and a case history, Trenchless

Technology Research, 11 (1), 3-24.

Papantonopoulos C.I., Atmatzidis D.K. 1993. A failure criterion for natural and artificial soft rocks. Proc. of the First InternationalSymposium on Geotechnical engineering of hard soils - soft rocks, Athens (Greece), 729-735.

Pellet-Beaucour A.-L., Kastner R. 2002. Experimental and analytical study of friction forces during microtunneling operations,

Tunnelling and Underground Space Technology, 17, 83-97.

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