Info

Figure 3. Full scale model of the barrel vaulted structure.

Figure 4. (a) Abutment brick arrangement; (b) change in the crown thickness; (c) specimen constraint at the base; (d) detail of the backfill; (e) Plexiglas plate constraint to the masonry.

Figure 5. Vertical load application system: (a) side view of the loading apparatus, (b) load distribution at the wall top edge, (c) cup-springs at the base reducing the vertical bar stiffness.

Figure 4. (a) Abutment brick arrangement; (b) change in the crown thickness; (c) specimen constraint at the base; (d) detail of the backfill; (e) Plexiglas plate constraint to the masonry.

reproducing the real structural constraints, but inhibiting any shearing sliding (Fig. 4c).

An intrados tie rod confines the arch horizontal thrust at the springing. The 12 mm tie rod, having an initial pretension of 7kN (equal to 75% of the vault lateral thrust) is anchored to the abutments using steel plates.

The backfill consists of fine sand, laterally contained by means of Plexiglas plates bolted to the masonry structure (Fig. 4d). Bolt-hole clearance avoids any participation of the Plexiglas to the resisting mechanism (Fig. 4e). Thin layers of chalk are

Figure 5. Vertical load application system: (a) side view of the loading apparatus, (b) load distribution at the wall top edge, (c) cup-springs at the base reducing the vertical bar stiffness.

inserted in the backfill to emphasise the vault crown deformation during loading and unloading cycles (Fig. 4d).

Four 7 kN point loads are applied at the top edges of the abutment to simulate the first floor masonry weight. Transverse steel profiles spread the load along the crown (fig. 5a,b). The load is applied trough vertical rebars tightened to the concrete supports. Four packs of cup-springs are interposed at the rebar bases, as shown in Figures 5a-c, to reduce the stiffness of the rebars. This was done to prevent an increase in vertical load due to rebar elongation induced by increasing the applied lateral displacement.

The total dead load of the specimen, including the additional load of the vertical rebars is W = 90.7 kN.

2.2 Testing bench and lateral load application system

The experimental test aims at investigating the behaviour of vaulted structures undergoing earthquake-induced rocking of the abutments. Further studies will focus on the bending moment induced in the vault crown by seismic action.

The seismic action is simulated by introducing horizontal loads at the vault springing. Horizontal point loads are applied by means of an electro-mechanicjack fixed to a steel frame, as shown in Figure 6. The horizontal loading system was designed in order to impose the same force (instead of the same displacement) to each abutment (Fig. 6). The load is equally divided between the abutments through the pulley and rope system shown in Figure 6. The point load is uniformly spread at the vault springings by means of transverse loading beams.

Figure 6. (a) Load application system; (b) perspective view of the testing bench and the pulley system.

Figure 7. and Ey.

(a) Instrument layout, (b) detail of LVDT Cy

Figure 7. and Ey.

(a) Instrument layout, (b) detail of LVDT Cy

Figure 8. Applied horizontal force versus abutment top horizontal displacement curve (LVDT Bx, Fx).

Figure 6. (a) Load application system; (b) perspective view of the testing bench and the pulley system.

2.3 Instrument set up

During the loading and unloading steps, vertical and horizontal displacement were recorded at some key points of the structure by means of linear variable displacement transducers (LVDT).

The drift of the abutments at different heights was monitored by LVDT Ax, Bx, Fx, Gx, whereas LVDT Cxy, Dy, Exy were located to detect any flexural displacement along the vault ring (see Fig. 7a).

The vertical component of the displacements at the vault springing and keystone were measured using LVDT Cy, Dy and Ey. These instruments were fixed to the vault intrados trough spherical hinges sliding on horizontal supports (Fig. 7b), in order to reduce interference with the global lateral displacement.

The applied load is measured by means of a load cell placed between the jack and the transverse beam.

Figure 8. Applied horizontal force versus abutment top horizontal displacement curve (LVDT Bx, Fx).

The tension in the vertical rebars and the tie rod were also monitored during the test.

2.4 Loading modalities

Load-controlled cyclic tests were carried out with a loading rate of 600 N/min. The specimen was initially subjected to loading and unloading cycles, in the same direction. The horizontal point load was increased by

2 kN (corresponding to 2.2% of the total vertical load) from cycle to cycle, until the vault developed a four hinge mechanism. Later, two fully reversed cycle were applied by repositioning the steel frame. The maximum applied load was equal to 11 kN (equal to 12% of the total vertical load W).

It is worth noting that as a result of the increase in the horizontal displacement, a small increase of the axial force in the rebars occurred, changing the vertical confinement of the specimen, despite the use of the cup-spring systems.

Details on the experimental study can be found in Giardina et al. (2007b).

3 EXPERIMENTAL RESULTS AND DISCUSSION

Figure 8 shows the structural response in terms of applied horizontal force versus abutment top horizontal displacement (LVDT Bx, Fx). Figure 9a and 9b show the detail of the curve for positive and negative applied horizontal loads. The structural response remains basically linear elastic until 6-7 kN (equal to 6.6% of the total vertical load) for both directions of applied displacement.

As for the cyclic behaviour, damage is accumulated after a few load cycles, and the global stiffness slightly decreases.

Figure 8 shows that the structure is relatively ductile with little dissipation capacity and a pronounced self-centering behaviour (see the flag-type curve). Inelastic deformations are almost negligible compared to the maximum experienced displacements.

Figure 10. Crack pattern for: (a) positive and (b) negative applied lateral loads; (c) detail of the cracks in crack pattern (b).

Figure 9. Details of the (a) positive and (b) negative applied horizontal force versus abutment top horizontal displacement curve (LVDT Bx, Fx).

Figure 10. Crack pattern for: (a) positive and (b) negative applied lateral loads; (c) detail of the cracks in crack pattern (b).

The test was interrupted during the negative load application (10 kN = 10%W, top displacement of 47 mm corresponding to a 1.5% drift) after a further vertical crack opened from excessive compressive strength on the four hinge mechanism.

For increasing applied lateral forces, cracks subsequently formed at the vault springing, where the vault crown thickness abruptly halves, and at the abutment bases. As a result, the global stiffness of the structure progressively decreases (Fig. 8) and the envelope curve shows a piecewise linear behaviour. Figure 10 shows the evolution of the structure toward the 4 hinge mechanism; numbers refer to the crack onset chronology, and to the value of the applied load triggering the crack. It is worth noting that the mechanisms change for different directions of the applied loads (Fig. 10a,b). This is evidenced by the higher position of the crack in the left abutment base (Fig. 10b), which results in a different rocking behaviour of the two abutments.

All cracks perfectly closed upon the first load reversals, whereas in the final stages, for increasing drifts, the non-cohesive backfill material poured into the larger crack at the vault crown extrados (n.2 in Fig.10b), thus preventing its closing.

Figure 11 shows the structural response in terms of applied horizontal force versus horizontal displacement at the vault springings (LVDT Ax, Gx). When positive horizontal forces are applied, a maximum positive differential displacement of 0.04 mm was recorded, which corresponds to the lengthening of the

Figure 11. Details of the (a) positive and (b) negative applied horizontal force versus abutment displacement at the vault springings (LVDT Ax, Gx).

vault span (Fig. 11a). Conversely, when negative horizontal displacement was applied, 4 mm of relative displacement was surveyed, resulting in the shortening of the vault span (Fig. 11b).

Figure 12. Vertical displacement at the vault intrados springing and key sections (LVDT Cy, Ey, and Dy) in case of positive applied lateral loads (see Fig. 9a).

Figure 13. force.

Sand backfill cracks due to internal tension

Figure 13. force.

Sand backfill cracks due to internal tension

The horizontal displacements of the abutments induced the bending of the vault crown. The vertical displacements at the intrados of the vault springing and key, recorded by transducers Cy, Ey and Dy are shown in Figure 12 for positive lateral load cycles. The maximum uplift displacement of the vault intrados is equal to 5.6 mm at the right springing, corresponding to 1/3 of the abutment top lateral displacement; whereas a 2.5 mm maximum downward displacement, equal to 1/8 of the abutment top displacement, was recorded at the left springing. The vault key also rose 1.9 mm. Vault flexural deformations were emphasized by the crack extending into backfill (Fig.13).

The tie tensile force significantly changed for increasing applied lateral loads (Fig. 14).

When positive maximum displacements were applied and the mechanism was that corresponding to the crack pattern of Figure 10a, the tie tensile force increased to 12% of its initial value (AF = 0.82 kN, Fig.14a). Note that the test was stopped in this direction well before the cracks had completely penetrated the element cross sections. Thus, for increasing lateral displacement, a further significant increment in the tie tension should be expected. Furthermore, the abutments underwent a positive relative displacement of AL = 0.04 mm (Fig. 11a) at the vault springings, which only partially explains the increment in the tie force. As a matter of fact, given

Figure 14. Tie traction force for a few cycles of: (a) positive and (b) negative applied horizontal forces.

the tie length L = 3260 mm, the axial strain is equal to s = AL/L = 1.23 x 10-5, thus the increment in the axial force is AF = sESAT = 0.29 kN (where ES = 210000MPa, AT = 113mm2). The further tie increment indicates that following the development of the crack pattern, the ideal arch increases its span and the buttress action significantly reduces (Giuriani E. et al. 2007).

When negative maximum displacements were applied, the mechanism changed, as shown in Figure 10b. The crack pattern showed two wide cracks at the abutment bases located at different heights, thus resulting in a negative relative displacement of the abutments at the vault impost. In this case, the tie tensile force reduced to approximately 50% of its initial value (Fig. 14b).

Finally, the vertical tension in the rebars increased during the test, as the lateral load and displacement increased, despite the positioning of the cup-spring packs at the bar bases. However, the maximum increment was at most equal to 15% of the initial value.

Was this article helpful?

0 0
Renewable Energy Eco Friendly

Renewable Energy Eco Friendly

Renewable energy is energy that is generated from sunlight, rain, tides, geothermal heat and wind. These sources are naturally and constantly replenished, which is why they are deemed as renewable.

Get My Free Ebook


Post a comment