1 INTRODUCTION

Twice a year the huge move-on-dollies (as shown in Fig. 1) will cross the desert and a new railway line. Thus, designers have to provide adequate ramps, in order to lift dollies over the railway embankment, and protect the railway structures.

We analyze two solutions: a permanent reinforced slab railway crossing and a temporary ballast filling over the railway. For the permanent solution (see Fig. 2), full geotechnical 3D analysis is mostly useful to evaluate rails displacement, because we could also design the concrete slab through a simple plane FEM analysis.

As for the temporary solution, ramps leave a gap over the railway, which workers will fill with temporary ballast when the crossing occurs. In this second 3D model, steel plates lying on the temporary ballast, help pressures spread below, while steel rails have a secondary function to share these extra-pressures among several concrete sleepers. The design issue is then to set the proper thickness of the temporary ballast (0.50 m average), to verify acceptable displacements of the railway and stress level of the concrete sleepers. A FLAC

3D (Itasca 2012) full interaction

model is necessary to investigate stress distribution over many soil and structural elements. Figure 3 shows a typical section of the Rig Crossing design.

Evaluation of railway grade crossing designs

L. Castellani, G. Furlani & A. Lucarelli Studio Sintesi, Rimini, Italy

ABSTRACT: Grade crossings by heavy equipment are a significant issue concerning new railway line designers, due to the weight of the equipment and of the move-on-dollies. Designers can choose two ways to address this issue: a permanent railway crossing made of a reinforced concrete slab, or temporary ballast filling that covers the railway when the crossing takes place. Both options are studied here using FLAC

3D. Due to considerable maintenance

difficulties of the isolated desert spot, the temporary filling seems to be most convenient, but concrete sleepers are highly stressed by the exceptional loads. 3D models consider many positions for each dolly, looking for the most severe condition for structures. FLAC

3D’s Chsoil

constitutive model reproduces the soil hardening with depth, accurately given by in situ geophysical survey. Moreover, the adopted constitutive law, implements a modulus reduction with the accumulated plastic strain rate, reproducing realistically the soil deformability.

Figure 1. Rig move-on-dollies, (Courtesy of Eni-Saipem S.p.A.).

Figure 2. Permanent concrete slab solution. Cross section.

Figure 3. Typical section of temporary ballast fill solution.

Move on dolly n.1

Move on dolly n.2

Temporary ballast

Sleepers

Steel plates

Dolly wheels

Ramp

2 MODELS DESCRIPTION

We developed full 3D models for both options. For the permanent concrete rail crossing solution, a really wide geometry has been modeled, to compare it with the 3D model of the preliminary design phase, as requested by the client. In this analysis ramps were completely modeled. The only relevant structural element is the rail crossing reinforced concrete slab, which we modeled with liner structural elements that are shell-type structural elements with pre-configured soil interaction parameters on their surfaces. Hence, liner structural elements have mechanical proprieties of reinforced concrete, 640 mm thick in the central part, where the rails are located, and 850 mm thick in the side portions. As for surface interaction properties with liners we assumed no cohesion, 32° friction angle, 1·10

5 kPa shear modulus and 1·10

5 kPa

normal modulus. Figure 4 shows the FLAC3D

grid that models existing soil (ZGroups U1, U2 and U3), the new railway line, and the Rig Crossing ramps. A close-up view shows the liners, colored by thickness.

Figure 4. Permanent concrete slab solution. Global mesh and liner structural elements.

The temporary ballast filling solution 3D model has much smaller dimension, but much more

detailed structures. For this model a symmetry plane is assumed. The grid is approximately a cube of side 15 m, shown by following Figure 5, where part of the soil zones are made transpar-ent in order to see the structural elements.

Six steel plates lay upon the temporary ballast and partly on the ramps, and we have modeled three of them with liners. These steel plates are 40 mm thick and have steel mechanical proprieties. As for surface interaction properties with liners we assumed no cohesion, 32° friction angle, 1·10

5 kPa shear modulus and 1·10

5 kPa normal modulus. The three steel plates

are not linked each other in reality, so they are not linked in the numerical model. Focusing on the railway structural elements, highlighted by the zoomed view of Figure 5, we

modeled the 210 mm thick sleepers as shell structural elements, with concrete mechanical prop-erties, and without any interface with the soil elements. Rails are beam elements and they are rigidly connected to soil zones. Rails have orthotropic section properties, with the actual rail moments of inertia in the two principal directions. Links between rails and sleepers are also beam elements, with infinite axial stiffness and no flexional stiffness.

We implemented railway structures in FLAC3D

model with rigidly connected elements (beams and shells), without any interfaces, in order to have a model that could be used to compare results with other codes. Nevertheless, implementing soil interaction properties for the railway structures would bring only minor improvement for deformations and stresses.

Concrete slab:Liner SELs

Figure 5. Temporary ballast fill model showing global mesh and structural elements.

3 LOADS APPLICATION

As the big dolly wheels have fixed internal pneumatic pressure, the total vertical load of the single wheel results in a rectangular contact area. Thus, we had to model four loading areas for dolly n.1, and two loading areas for dolly n.2, in six different positions for each dolly, to determine the most critical condition for the railway structures.

Wheel pressure can be applied to the soil elements or directly to liner structural elements and we had to take into account all possible loading areas when we generated the grid. We performed, then, an automated procedure to apply loads, though Visual Basic and FISH routines. Figures 6 & 7 show some examples of loads application, for the permanent slab solution and for the temporary ballast filling solution.

Figure 6. Permanent slab solution. Some examples of load applications.

Steel plates:Liner SELs

Concrete sleepers:Shell SELsSteel rails:

Beam SELs

Rails feet:Beam SELs

Move on dolly n.1Load position n.1

Move on dolly n.1Load position n.1

Move on dolly n.2Load position n.6 Cooper load condition

Figure 7. Temporary ballast filling solution. Move-on-dollies load application. Liner pressures plot.

4 SOIL CHARACTERIZATION – CHSOIL CONSTITUTIVE MODEL

Subsurface soil characterization comes mainly from boreholes, Cone Penetration Tests (CPT) and one Down-Hole test (DH) at the site. Each CPT gives a profile with depth of the shear mod-ulus (G0) for very small strain rate, through an empirical correlation (Robertson 2009). The only DH test directly output the shear wave velocity (VS) profile, and subsequently G0: its result con-firms the several profiles drawn from the CPTs. In conclusion, CPTs and geophysical survey were sufficient to determine a design modulus profile with depth (see Fig. 8).

Figure 8. Survey results, stratigraphy and initial shear modulus profile (solid black line) with depth.

Move on dolly n.1. Load positions n.1 to n.6

Move on dolly n.2. Load positions n.1 to n.6

0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

8.0

9.0

10.0

0 50 100 150 200 250 300 350 400 450 500 550 600 650 700 750 800 850 900

Dep

th b

elo

w g

.l. [m

]

G0 [MPa]

RIG Crossing - Shear modulus at small strains from CPT and DH

CPT 52a

CPT 52b

CPT 52c

CPT 53a

CPT 53b

CPT 53c

CPT 54a

CPT 54b

CPT 54c

S1-DH-38A

Design Go

U_1

U_2

U_3

Soil at the site is mainly sand. Three main geotechnical layers were identified. Water is not

present. The best fit of the shear modulus design profile can be well obtained through Chsoil – Simplified Cap Yield – constitutive model of FLAC

3D v5, as shown in Figure 8.

Moreover, with the recent addition in Chsoil of the “fric0” parameter (ϕ0), we could initialize soil to the actual anisotropic condition, matching the plastic shear modulus (G

p) with the effec-

tive modulus profile got by the survey. As reported in the FLAC3D

constitutive model manual:

2m 00 m f

f 0

 : (1 )p e

f

sin sinG G R

sin sin

So we set ϕ0 equal to the mobilized friction ϕm evaluated after the initialization of the model.

The finite difference code evaluates the mobilized shear strain (γp) from this given initial state,

as:

0 m f

'0

0

0

sin sin 11

sin sin1

sin sin

 :fp m

emf

f

f

p

G RR

An accurate reduction law of shear modulus can be plotted then (see Fig. 9), at an average

depth for every geotechnical unit, where accumulated strain rate is correctly evaluated from the

given initial state that corresponds to the survey state. The Chsoil parameters for the modeled units are reported in Table 1.

Table 1. Geotechnical parameters. __________________________________________________________________________________________________________

Unit z γsat k0 c' φ' ν pref n m Gref Kref Rf [--] [m] [kN/m

3] [--] [kPa] [deg] [---] [kPa] [--] [--] [--] [--] [--]

__________________________________________________________________________________________________________

Ballast 2.2 18.0 0.269 0 40° 0.3 100 0 0 192 417 0.9 1.6 __________________________________________________________________________________________________________

Sub- 1.6 19.0 0.357 0 35° 0.3 100 0 0 385 833 0.9 ballast 1.3 __________________________________________________________________________________________________________

Subgrade 1.3 19.0 0.470 0 32° 0.3 100 0 0 231 500 0.9 1.0 __________________________________________________________________________________________________________

Embank- 1.0 18.0 0.470 0 32° 0.3 100 0 0 192 417 0.9 ment 0.0 __________________________________________________________________________________________________________

U_1 0.0 18.0 0.485 0 31° 0.3 100 0.94 0.99 2921 6328 0.9 -1.5 __________________________________________________________________________________________________________

U_2 -1.5 19.0 0.412 0 36° 0.3 100 0.97 1.00 3370 7301 0.9 -4.0 __________________________________________________________________________________________________________

U_3 -4.0 19.0 0.398 0 37° 0.3 100 0.51 0.56 3091 6698 0.9 -50.0 __________________________________________________________________________________________________________

N.B.: For Mohr-Coulomb constitutive model, we adopted the same strength parameters (c’, φ’) and Young’s modulus equal to E0/3.

Furthermore, we performed several sensitivity analyses in order to validate soil model behavior. In particular, we repeated the same geometry and load history with a Mohr-Coulomb constitutive law soil, and compared the results, as follows.

We adopted a standard procedure of three main steps to perform FLAC3D

initialization: at first we set a temporary material with Mohr-Coulomb constitutive law and specify high strength parameters, in order to generate initial stress in volume elements; then, maintaining the M-C law, we assign real strength parameters, in order to refine the horizontal stress state; finally, we

assign the Chsoil constitutive law, with the same strength parameters that were used in previous step, but with the calibrated modulus profile.

At the end of this procedure, we set ϕ0 equal to the mobilized friction ϕm, in order to reset γ

p=0 and match model initial state to the actual soil state, as previously mentioned (G

p=G

e=G0).

Then we could start simulating the embankment construction, the railway construction, the ramps construction, by subsequent calculation phases. Focusing on the temporary ballast filling solution, Figures 10 & 11 show for two construction phases the shear moduli contour plot diagrams and profiles with depth: G

p reduction is clearly relevant after railway construction and

grows after Rig crossing loads application.

Figure 9. Plastic shear modulus reduction law with accumulated shear strain.

Figure 10. Railway construction calculation phase. Contour plot and profiles with depth of shear moduli.

0

20

40

60

80

100

120

140

1.00E-07 1.00E-06 1.00E-05 1.00E-04 1.00E-03 1.00E-02

Mo

bili

zed

pla

stic

sh

ear

mo

du

lus

Gp

[MP

a]

Accumulated shear strain ϒp []

U_1U_2U_3

GeGp

Ge

Gp

Figure 11. Rig crossing calculation phase. Contour plot and profiles with depth of shear moduli.

5 MAIN RESULTS

For the permanent slab solution 3D model, we could describe with good precision the actual geometry of the Rig Crossing junction (ramps, railway embankment and concrete slab), estimating the service displacements due to the dollies, and moreover we could implement all the loading cases and design the steel reinforcement of the slab.

No displacement or stress problems were evident. Maximum vertical displacement due to move-on-dollies loadings is about 1.6 mm, certainly compatible with railway service state (see Fig. 12). Maximum bending moments are about 25 kNm/m in X direction and 39 kNm/m in Y direction, easily manageable with normal steel reinforcement (see Fig. 13). The thickness reduc-tion of the central part of the slab involves a notable discontinuity in My, while a very small dis-continuity in Mx.

As for the temporary ballast solution, higher displacements resulted for move-on-dolly n.2 at position n.5, which the following comments will focus on. Maximum displacement is about 3.2 mm, still admissible for the railway. The adopted constitutive model is very important, for the settlements evaluation analysis.

Figure 12. Permanent concrete slab solution. Settlement (in m) evaluation at several levels.

Ge

Gp

Ge

Gp

Settlementsat desert ground level

Settlementsof railway embankment

Settlementsof concrete slab

Figure 13. Permanent concrete slab solution. Bending moment stresses in both principal directions.

Figure 14 shows sleeper displacements for the two developed analyses, respectively with

Chsoil and Mohr-Coulomb (M-C) constitutive models for soil zones. These two constitutive models have the same effective stiffness profile with depth, but Chsoil has a modulus reduction law with plastic accumulated strain rate, as previously described, so that M-C analysis estimates rail displacements with differences of about 20% (depending on the adopted value for E’=E0/3).

Differences in soil zones constitutive model have resulted in only minor differences in sleeper stresses evaluation, as shown in Figure 15. M-C model estimates maximum bending moment with differences of just 6%. Sleeper bending moment verifying was the crucial issue of this analysis, and the resulting Mx = 56 kNm/m · 0.30 m = 17.1 kNm, at railseat, is still admissible (assuming the sleeper is 0.30 m wide).

Figure 16 shows principal stress vectors and strain increments contour plot, for the move-on-dolly n.2 at position n.5. The diagrams have been sectioned to show the diffusion of pressures in the temporary ballast and the involved soil volume.

Figure 14. Temporary ballast filling solution. Sleeper displacements for different constitutive models.

Figure 15. Temporary ballast filling solution. Sleepers Mx stresses for two different constitutive models.

Slab Mx Slab My

Thickness breaks

Thickness breaks

Sleepers displacementswith Chsoil constitutive model

Sleepers displacementswith Mohr-coulomb constitutive model

Sleepers Mx stresseswith Chsoil

constitutive model

Sleepers Mx stresseswith Mohr-coulomb constitutive model

Figure 16. Temporary ballast filling solution. Principal stresses and strain increment.

6 CONCLUSIONS

Both 3D models provided useful cases of study for FLAC3D

new Chsoil constitutive model, with an improved initializing procedure. The new ϕ0 parameter let us initialize the model at a given state, matching the geotechnical survey results using the soil hardening law with depth. At the same time, we could have a good shear modulus reduction law with the accumulated plastic strain rate that was evaluated starting from the given initial state.

The permanent slab solution allowed us to model with good precision the actual geometry of the Rig Crossing junction (ramps, railway embankment and concrete slab), estimating the ser-vice displacements due to the dollies, and implementing all the loading cases to design the steel reinforcement of the slab. This solution, as expected, is very rigid, with only 1.6 mm maximum displacement.

The temporary slab solution obviously is more deformable (maximum displacement of 3.2 mm) and was interesting for several reasons. First of all, the implementation of several structural elements, with complex geometry, fully integrated with the grid nodes, shows the modeling ca-pabilities of the FLAC

3D code. Furthermore, the model let us investigate the pressures path

among soils and structural elements: steel plates (liners) laying on the temporary ballast (zones), help pressures spread below, while steel rails (beams) have a secondary function to share these extra-pressures among several concrete sleepers (shells). Several questions could be answered only through this full 3D model: the pressures diffusion, the principal stresses directions, the in-volved soil volume, and the number of stressed sleepers by the single loading area. We could al-so verify the concrete sleepers adequacy for the Rig Crossing unconventional loads.

Finally, sensitivity and comparative analyses show the importance of the adopted Chsoil con-stitutive model for settlements evaluation. A parallel Mohr-Coulomb analysis, with the same ef-fective stiffness profile with depth, showed that in this particular case M-C model estimates rail displacements with differences of about 20% (and of about 6% for bending moment), depending on the adopted modulus and on its lack of a modulus reduction law with the accumulated plastic strain rate.

ACKNOWLEDGEMENT

We would like to thank Eni-Saipem S.p.A., for letting us write this paper.

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