Designed for seismic survival

	September 2009 meeting
	Designed for seismic survival

At the first meeting of the 2009/10 season in September, Gary Kramer of Hatch Mott MacDonald delivered a presentation on the seismic response of segmental tunnel linings.

The presentation started with how the research into the seismic response came out of design work for the Silicon Valley Rapid Transit Project (SVRT) an extension of the Bay Area Rapid Transit (BART) out of San Francisco in California, to San Jose. The extension is being designed by the Valley Transit Authority and will ultimately be operated by BART. Though the project is in final design, the project is suffering from a lack of political will as are major projects in the USA with respect to funding for construction.

The underground section of the extension will be in 8.2km of twin tunnel with three cut-and-cover stations, two portals and two vent structures. The TBMs and linings will be owner procured.⁽¹⁾

Typical cover will be 12m with 25m in some sections to avoid obstructions. The geology is deltaic alluvial deposits lightly over-consolidated with stiff silty clays and interbedded sand layers. The groundwater table varies from 3m to 5m below grade.

Being one of the most famous seismic regions in the world, the San Andreas Fault runs roughly north-south to the west of San Jose and has a potential for a magnitude 8.0 seismic event; the Heyward Fault to the north has a potential for a magnitude 7.3; and the Calaveras has a potential for a magnitude 7.0 quake (Fig 1). The Lower Silver Creek fault has negligible offset potential so no special provisions were required.

Fig 1. Locations of major faults in Northern California

The lining will be owner designed and will be 5.44m i.d., 1.5m long, 254mm thick with a double taper. The ring will have a universal trapezoidal arrangement. All the joints will have packers with traditional reinforcement. The use of a hybrid fibre reinforcement design had been looked at although it is likely that it will stay as normal rebar cage reinforcing. Dowels will be used on the circumferential joint with bolts on the radial joints and each segment will have a single EPDM gasket.

The project was to be designed to the BART Facilities Standard (BFS). The existing tunnels for BART have used steel linings, which are rigidly connected and performed well during the 1989 Loma Prieta earthquake. The cost of using such a lining for the SVRT project however would be prohibitive.

The BFS had a number of provisos for segmental linings but tended to be appropriate for steel linings only. Though BART staff were receptive to the use of segmental concrete linings they had little experience of these and had a concern over stability during seismic events. Their concerns included:

• where they had been used before in seismic zones.
• how do they behave in a seismic event?

It was explained to BART staff that concrete linings were now used virtually everywhere but being surface seismic engineers, they were unaware of this therefore research was carried out where the use of precast tunnel linings of a similar size to those envisaged to SVRT, was coincident with known seismic events.⁽²⁾

The thousands of systems with concrete linings were cross-referenced with those in seismic locations. This reduced the list to the hundreds with most of those in Japan. This was compared against seismic events and this produced a list of 12 schemes. With inspections of structures after significant seismic events generally only covering damaged sections, facilities where no damage occurred generally go unreported.

The most significant was Michoacan in Mexico, which underwent an 8.1 quake and the Loma Prieta quake in 1989. Actual documented performance of the tunnels themselves reduced the list to four (Table 1). A high level structural analysis was therefore required to justify the use of concrete linings to BART.

Table 1. List of tunnels where the effect of seismic events has been documented

Tunnel	Earthquake	Earthquake Date	Surface Horizontal Acceleration Near Tunnel(g)	Post Event Tunnel Condition	Source(s)
LA Metro	Northridge	1/17/94	0.4	No Damage	Monsees and Elioff, 1999 and EERI, 1995
Isobe Dori Shield Tunnel	Kobe	1/17/95	0.5	Some Spalling at Segment Joints	JSCE, 1995
Athens Metro	Athens	9/7/99	0.25	No Damage	EERI, 1999
Taipei Metro	Hualien	3/31/02	0.20	No Damage	Taipei Times,2002

The concern of BART in particular was whether the segment joints would pull apart causing a collapse of the lining system. Acknowledging the help and expertise of SC Solutions Ltd in Sunnyvale, California, Kramer explained that a paper produced for RETC in 2007 documented the detailed analysis undertaken to show that a segmental lining would not separate.⁽³⁾

Explaining P(compression/extension), S(shear) and L (love/Rayleigh) waves in seismic events, Kramer described how it is the L waves which are those affecting shallow tunnels in seismic zones.

Three types of seismic events occur that can affect tunnels:

1. The potential for fault rupture if the tunnel crosses the fault. This was not part of the research presented here, although the solution where this occurs is generally to construct an oversized tunnel allowing for quick repair in the event of a rupture.
2. The potential for liquefaction. The potential on the SVRT project for this was low. This occurs in saturated loose soil. The seismic event increases the porewater pressure, resulting in a complete loss of shear strength.
3. Ground shaking which can cause compression/extension of the lining and longitudinal bending of the tunnel.⁽⁴⁾ Of most concern is the shear wave propagation from the bedrock below causing an effect called ovalling or racking.

To analyse this, a programme called SHAKE is often used to model a vertically propagating wave from the underlying rock formation. For each soil the shear modulus is inputted, with a strain and damping factor added for each soil layer. Also added would be the outcrop acceleration of the rock (assuming it was exposed at surface). The shear strain and displacement versus depth/time are obtained for the entire soil column. The model does not take into account the presence of the tunnel or any surface structures.

A Type C soil was used for SVRT, which is a soil dense enough that it is effectively bedrock. The departure from square is the shearing strain (Fig 2). There are very small strains at depth but these increase towards the surface as the rayleigh and love waves become more prevalent.

Fig 2. Free field shear distortion of ground (after Wang 1993)

Fundamental to understanding underground seismic design are the ground mass deformations and their interaction with the tunnel excavation and structure itself. The tunnel must accommodate the ground movements without excessive damage itself. The tunnel will never stop the ground movement.

The modelling was to look at overall shear strains of 0.2% to 0.4%. The shear strain being the 'out of square' that the hypothetical ground mass would go through in a seismic event. There are various methods for dealing with the seismic response of tunnels. Common behaviour assumptions to virtually all of them assume linear elasticity of the ground mass and lining:

• Idealized ground/lining interaction considers full slip or no slip,
• Separate analysis of the static and seismic effects, and
• Continuity of the tunnel lining is generally assumed i.e. no joints.

A segmental lining system does have joints however, allowing flexibility and can thus respond better in a seismic event.

The various methods over-estimate the internal lining loads but do underestimate displacements. Both of these need to be as accurate as possible because seemingly conservative on strength is actually non-conservative in a seismic event as it is a displacement controlled event, not a strength controlled event. Making the lining material stronger doesn't necessarily mean that you have a stronger lining.

The linear elastic closed from solutions developed by a number of researchers predict under seismic loading that tensile stresses will develop in the lining system what would be problematic in a jointed tunnel. The stability of a lining system depends on maintaining the continuous joint contact between the segments and between the rings so the methods that have to be used have to predict the forces and displacements as accurately as possible so that there are two demands on the tunnel lining system itself; a displacement demand and a more traditional strength demand. The lining system must deal with both.

SC Solutions brought their expertise in dealing with seismic connections and structural analysis so were able to 3D model the effects on the lining using ADINA software to look at the stability of the lining and modelled the joints as a no-tension, friction-only connection with compression. They did soil structure interaction, and finite element modelling to predict ovalling response so shear strains of 0.2% and 0.5% were used to envelope the conditions to a maximum credible earthquake to assess if any instability occurs with excessive birdsmouthing, slipping or separation by joint rotation between segments. The need for inter segment connecting devices such as dowels and bolts was evaluated, the reason being that the dowels and bolts were just alignment devices, not intended as structural devices. Internal loads also needed to be provided for the structural design of the segments.

Construction loading was put into the 3D model as well as seismic ovalling. It was important to follow the stress path history in the ground during construction as well as subsequent to construction and the dissipation of pore pressures as well as the seismic event itself. To do this, a non-linear soil behaviour would be required. The Mohr Coulomb (M-C) approach was adopted here. Other systems such as Duncan-Chang have since been used to compare. Partial slip was allowed for rather than no-slip between the lining and ground. No tension frictional behaviour was allowed between the radial and circumferential joints. Circumferential dowels were modelled as non-linear springs. The radial joints (bolts) were deliberately not modelled so the joints would not be restrained from opening and then see what the opening demand on the bolts would be.

The 3D model was placed inside a soil medium with a trapezoidal lining. A rectangular lining was also tried as, at the time of the analysis, a decision on lining types had not been reached. There was a concern about additional torque and shear angles of a rectangular lining but these turned out to be a non-issue.

Table 2. Ground parameters used for modelling

Soil Behaviour Parameter	Mohr Coulomb Sand	Mohr Coulomb Clay-1	Mohr Coulomb Clay-2
Total unit weight, Υ	19.7kN/m³	19.7kN/m³	19.7kN/m³
In-situ Horizontal Pressure Coefficient (K0)	0.65	0.65	0.60
Effective Friction Angle, (Φ')	37.5 degrees	Not used	Not used
Effective Cohesion, (c')	0	Not used	Not used
Undrained Shear Strength (Su)	0	100 kPa (at tunnel depth)	100 kPa
Effective tensile strength, T'	0.5kPa	Not used	Not used
Poisson's ratio, n	0.35	10.49	0.49
Elastic modulus, ES	335 MPa	270 MPa	40 MPa

The Sand and Clay 1 was generally stiffer materials but the Clay 2 was an extreme case of very soft clay to check the sensitivity. Cracked and uncracked properties were used. The concrete strength was 41 MPa (6000 psi). Modulus of elasticity was 38,500 MPa, poisson ratio of 0.15.

It is important in seismic design to use what are termed expected properties, not necessarily the specified properties (e.g. 46 MPa actual for concrete strength).

The lining analysis results were then presented:

• The diametric displacements,
• The internal force,
• Rotational gapping, and
• Demand on connecting devices.

There was a very good comparison between the free field perforated ground and the linear elastic predicted for full slip. So full slip linear elastic analysis does provide a good comparison.

Interestingly as the model went to the higher strains for the 0.5% strain, the non-linear finite element modelling showed less displacement occurring than the free field perforated ground or the elastic full slip solution. This is significant because a flexible system was being modelled and also allowing the soil to develop plasticity around it which also acts as a structural fuse reducing the displacements and hence the demand on the lining system.

At 0.2% strain the model deformations were very close to the elastic continuous lining solution. At the higher strains the model deformations were significantly less. This was due to the relatively uniform compressive thrust that stiffened the lining and tended to prevent the tensile strains that would occur using a linear elastic model.

Fig 3. 3D model used for seismic modelling

The axial forces were generally compressive throughout a uniform thrust for the full range of strains that occur. Two rings were modelled beside each other with two exterior rings to act as a buffer for boundary conditions. The uniform distribution of the axial forces is very similar to the elastic model for a full slip case and higher thrusts do occur in stiffer soils and lower thrusts in softer soils (Fig 3).

The graph in Fig 4 gives a comparison between the bending movements using the linear elastic solution developed by Joe Wang in 1993. A full slip was then used with a modified version of Joe Wang in 1993 and Joe Penzien's paper in 2000 at 0.2% and 0.5%. The solution modelled by SC Solutions significantly reduced bending moments in the segmental lining by taking into account the inelastic behaviour of the ground.

Fig 4. Comparison of analysis results using different solutions

Of key importance to the study was the segment rotation and gapping. The model had to be tested for its ability to predict the joint separation at high strains. It is pointless to model an effect if the model can't predict it. By taking the model to extreme strains of 1.2%, this did develop a gapping and rotation that could lead to instability of the segments (Fig 5).

The maximum predicted rotation angles and joint widths at the modelled strains showed that birdsmouthing did not occur over the range of expected credible earthquakes. The 1.2% referred to above is about double what would ever be expected in any seismic analysis. There was no total loss of contract with joint separation when the non-linear soil M-C effect was used. The linear thrust was always compressive even at 0.5% shear soil strain.

Fig 5. The ability of the model to predict joint separation was confirmed

The key conclusion is that the joints themselves collect strain without generating load which is one of the inherent benefits of a flexible segmental lining system. That is their inherent advantage. The circumferential joint friction is not overcome when the connecting devices were looked at and the dowels did not contribute to joint sliding resistance. The presence of dowels in reality would cause damage to the concrete. The connecting devices were modelled as flexible elements abut the joints remained in contact. Ovalling did not impose a significant force or displacement demand on the devices. The connecting devices are therefore not required for stability which is typical for static conditions. Small keys (< 20 degrees) could be problematic at high strain levels from a joint separation perspective.

Some additional analysis was done outside of SC Solutions work which looked at longitudinal bending where the strains could be quite high. The concern was whether the joints would open up in the lining and uncompress the gasket. The results of that analysis obtained using the linear elastic analysis was to avoid the use of axially stiff connecting devices e.g. curved steel bolts. Gary stated that any bolts across the circumferential joint in high seismic zones are to be avoided to prevent damage from the bolt being pulled. This occurred in a tunnel at Kobe in Japan along some of the bolts. The Kobe structure performed well but there was some cracking around some of the bolt pockets and minor spalling from this effect. Therefore a maximum force for the expected displacement should be specified for those devices.

In conclusion, the analyses were undertaken successfully. They evaluated the state of stresses in the ground around the lining and in the lining itself during construction and seismic ovalling. Due to joint friction, construction loads and the inclusion of a non-linear behaviour no gapping occurred demonstrating the stability of the segmental lining system for the range of ovalling strains. BART's consultants looked at the results and accepted them and approved the lining system. Bending moment comparisons were undertaken showing that the benefit of including the inelastic effects versus using the more simplified methods, were that the bending moments were significantly less. That resulted in little, if any, changes in reinforcing for the SVRT conditions although there have been other lining designs undertaken where a modest adjustment in the reinforcement was needed, generally going one wire size higher. Seismic ovalling places negligible demand on the connecting devices, which are not required for seismic stability. The devices themselves should be detailed to have compatible force displacement characteristics and flexibility.

Fig 6. 3D modelling of station/tunnel interface

A 2D analysis using FLAC was undertaken using a pseudo-static analysis where the ground is subjected to a maximum shear strain similar to a pushover analysis. A full, dynamic analysis was also undertaken giving similar results. For static loads the bending moments generally increase to around 50-100% for high seismic event like a 0.4% strain.

A 3D pseudo-static analysis was done with and without the invert concrete to see whether or not the presence of this would act as stiffening to the tunnel lining but again, no significant effect was found to occur. A 3D pseudo-static analysis was also carried out of single and twin tunnels to see whether the pillar between may be at risk.

There was a 25% increase in loading which warranted a change to the strength design.A pseudo-static analysis of tunnels with a cross passage to see whether a risky event may make the cross passage lining punch holes in the segmental lining was carried out. Again there was no impact except possibly minor repairs.

A full 3D dynamic was done on the station tunnel interface which would pull the station away from the tunnel (Fig 6). A gap of about 25mm would occur so the connection between the tunnel and the station had a gap to allow movement to occur but retain watertightness using an omega ring concept.

References

1. Owner Procured Tunnel Machines - A discussion; RETC Proceedings 2005; A.R. Biggart, G.J.E. Kramer, A.R. Walters
2. Use & Performance of Precast Concrete Tunnel Linings in Seismic Areas; IAEG 2006; A.Dean, D.Young, G.J.E. Kramer
3. Seismic Response of Tunnel Linings; RETC Proceedings 2007; G.J.E. Kramer, H.Sedarat, A.Kozak, A.Liu, J.Chai
4. Seismic Design and Analysis of Underground Structures; Tunneling and Underground Space Technology, 2001; Hashash, Y.M.A., Hook, J.J., Schmidt, B., and Yao, J.I.-C.

Audience Discussion
Sigmund Lopkavski (Arup) asked what displacement on a fault would be considered negligible and what performance criteria were BART hoping to achieve in a seismic event. Kramer stated that as BART used a normal distribution curve for probabilities it was difficult to convince them that there would be virtually no chance of a significant fault rupture along the alignment. Eventually they were happy with the phrase 'so low as to be practically negligible'. For performance criteria, BART require all systems operational within 3 working days. For the station tunnel interface the analysis showed a movement of about 25mm. Their criteria was to allow for 100mm of movement.
John Jau (Skanska) asked if any physical modelling such as a centrifuge had been used to back up the analysis. No, it had not been done, was the reply.
Milutin Srbulov (Mott MacDonald) asked how much the analysis cost. This was about $US200,000 and took eight months
David Court (BAM-Nuttall) pointed out that on a tunnel in Cairo in 1995 with a six-segment trapezoidal lining there had been an earthquake where an operative had seen the tunnel 'whip'. Upon inspection there was no observable damage. He wondered whether more lining plates per ring could be considered in larger tunnels to allow more movement. More segments had been considered said Kramer, but these would have required fibre reinforcement. These could not be for the prevailing conditions. In Japan hybrid designs with fibre reinforcing and normal reinforcement at critical locations were being developed.
Peter South (Laing O'Rourke) asked if liquefaction was a concern particularly under the Bay in San Francisco and, what were the safety considerations if a moving train was in a tunnel in a seismic event. Kramer pointed out that the BART tunnel under the Bay is an immersed tube so not comparable with a bored tunnel. This had been recently seismically retrofitted by BART. Also, there are seismic triggers for the trains and stations that will cause the trains to shut down in the event of an earthquake.
Shani Wallis (TunnelTalk) asked of the consequences of seismic events during actual construction. This was considered but as the tunnel would be in a near completed state during construction then the effects would be similar to the permanent situation.
Bob Ibell (London Bridge Associates) asked if any particular requirements for bolting and grouting were necessary to ensure the lining performed as required. An analysis of this was said to have been done but no special requirements were needed. The modelling was done on the basis of normal construction quality with tailskin volume and pressure grouting specified for the SVRT project.
Rapporteur: Andrew Hindmarch

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At the first meeting of the 2009/10 season in September, Gary Kramer of Hatch Mott MacDonald delivered a presentation on the seismic response of segmental tunnel linings.

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