Tunnel Design Methods
Design Overview
Tunnel designs are very specific designs that we may design once or two three times in our life. Generally, reservoirs or under ground roads are not constructed every day like other structures. So may designers are not getting the opportunity to engage with such designs.
Mainly tunnels are designs for internal loads or external loads or both the loads. For example, tunnel constructed for a highway is design for external loads which is applied from the rock cover or any other overburden material. However, tunnels carry water are design for both external and eternal loads. When tunnel carry water with a large head, it exert water head on the surrounding area. Specially when a rock cover is smaller we have to check the whether the overburden is sufficient to take that load when tunnel is unlined. When tunnel is line we have to consider the loads on the tunnel and it should be design considering those factors. In addition, area around the tunnel can be collapse in the the tunnel. Depending on the type of surrounding material, a design can be carried out.
Generally, tunnels with having good quality rock cover are not lined by reinforced concrete in addition to the shotcreating. However, at the outlet, tunnel has to be lined by steel liner or concrete liner if there is no adequate rock cover. Most of the tunnels designers come across with this situation. They normally find the distance that unlined section can be continued and rest of the length is lined.
Design of a Section with adequate rock cover
When a adequate rock cover is presents, we can do the design the tunnel with lining or without lining. If we have good quality rock, we can have unlined tunnel. But if the rock is weak we have to consider the rock quality for the design.
Design for External Loads
When adequate rock cover is present, we need not to worry about the total collapse of the tunnel. However, it can be fail locally. If the rock is not fairly good or it can not be stabilized with shotcreeting(reinforced or un-reinforced), we have to have a lining that can bear the external loads.
Lining design is done considering the type of the rock. Rock quality and the type of rock shall be inspected at the site and then the design should be carried out. In tunnel designing books or design standards, it can be found the load that need to be considered for the lining design depending on the rock type.
"EM 1110-2-2901 Tunnels and Shafts in Rock" on of most commonly used standard that can be reffed for our designs. If provides a guide line to design a tunnels depending on different ground conditions.
Above figure is extracted form EM 1110-2-2901. Depending on the rock condition, fracture spacing and RQD value, rock load can be selected. For example, consider massive moderately jointed rock, rock load is 0.5B.
Hp = 0.5 B x (density of rock)
Assume tunnel diameter(B) as 2.5 m
Rock density 25 kN/m3
Hp = 0.5 x 2.5 x 25
= 31.25 kN/m2
This load can be applied on tunnel as a gravely load. Finite element analysis or equations given in codes for different shapes of tunnels, can be used to find the stresses of the tunnel.
Loads should be factored when analyzing the tunnel. EM 1110-2-2901 provides a table that can be used to create load combinations.
Load combinations can be created by considering the factors given in the above table.
If there is a lateral deformation, it increases the bending and shear forces of the tunnel. When large rock cover is exist, tunnel can not deform laterally. This can be considered in the analysis and rock can be considered as a support to the tunnel.
Rock support can be model depending on the type of the rock. Sub grade reaction of the rock can be calculated for the equations given in the EM 1110-2-2901.
Depending on the arc angle, element size, position reaction and modulus of rock, sub grade reaction can be calculated in radial and tangential directions.
Above figure shows the graphical representation of subgrade reaction. We should apply the subgrade reaction as show in the figure. Depending on the design requirements, we may omitted the tangential subgrade reaction. In addition, if we model the tunnel with a software, springs should not allowed to take any tension. Compression only condition should be considered as rock can not take any tension load.
Design for Internal Loads
When there is a adequate rock cover, internal load generated from the water head can be bared by the surrounding rock. Also when a large rock cover is exist, it does not allowed the tunnel to deform. Therefore, stresses are not generated due to the internal water load.
Design of a Section with inadequate rock cover
Good quality rock can be fond in the areas where the tunnels are constructed. However, there are instances we meet with poor quality rock or soils on the top of the tunnel. Even if we have the quality rock, it should be adequate to take the internal load exerted by the water head on the surrounding rock.
Design for external loads
When the rock cover is not adequate, we have to have a either steel lining or concrete lining to carry the internal loads. When the tunnel is not carry any water, it does not have internal pressure on the surrounding rock. External loads applied on the tunnel lining should be considered when designing it.
Technical paper "Big Tunnels in Bad Rock 2000 Terzaghi Lecture by Evert Hoek" can be refer for the design. It is very good guide to design such cases. However, there are different techniques that have been proposed by researches/books for calculating rock load.
EM 1110-2-2901 provides a guide line to find position that required line section. Beyond this position, section can be constructed as a unlined section if required. Following figure extracted from EM 1110-2-2901 can be referred to find the distance that lined section is required.
Figure 9-2 shows the requirement of rock cover for unlined pressurized waterway. It is the Norwegian criterion for confinement of rock. This concept is commonly used method by the design engineers. This is a very simple technique and tool to find the minimum rock cover for a unlined tunnel. Weight of the rock mass or the overburden material is balanced by the internal head of the tunnel. Attention should be paid to the surface condition when find the rock cover(hs). For example, if the top cover is soil or weathered rock, these type of material can be washout when water is flowing along the surface. In addition the safety factor should be considered adequately. It may vary 1.05 - 3 and may be referred from the design intent.
Figure 9.1 shown bellow, also can be used for designing the tunnels. We can select a method, and then design can be started. Most commonly used method and simplest method is Norwegian criterion for confinement.
Once we select a criteria, we can calculated the section that required the lining from the equation given in the guide line.
External load need to consider for the design is weight of rock cover or weight of overburden material. We can apply that weight as a gravity load for the analysis. If there is large rock cover in lateral direction, we can consider rock as support against the lateral deformation. However, if there is no sufficient rock cover in lateral direction, it is advisable to not to consider it as a support.
Design for Internal Loads
When sufficient rock cover is not present, tunnels should be lined as discussed above. Water head can be considered as the internal load while the weight of the overburden material can be considered as load applied from the top of the structure as gravity load. It should be very careful with the weight of the overburden material depending on the value of the load and the deformation of the tunnel. Some times it may acts as beneficial but it could be a adverse load as well. For example, if we apply a factor when creating a load combination, it generate a weight that is more than that of existing weight of overburden material. If may increase hogging moment and may reduce sagging moments. Actually this purely depends on the analysis we do. So it is better to be very careful with weight of the overburden material if we intend to apply to the model.
Design Overview
Tunnel designs are very specific designs that we may design once or two three times in our life. Generally, reservoirs or under ground roads are not constructed every day like other structures. So may designers are not getting the opportunity to engage with such designs.
Mainly tunnels are designs for internal loads or external loads or both the loads. For example, tunnel constructed for a highway is design for external loads which is applied from the rock cover or any other overburden material. However, tunnels carry water are design for both external and eternal loads. When tunnel carry water with a large head, it exert water head on the surrounding area. Specially when a rock cover is smaller we have to check the whether the overburden is sufficient to take that load when tunnel is unlined. When tunnel is line we have to consider the loads on the tunnel and it should be design considering those factors. In addition, area around the tunnel can be collapse in the the tunnel. Depending on the type of surrounding material, a design can be carried out.
Generally, tunnels with having good quality rock cover are not lined by reinforced concrete in addition to the shotcreating. However, at the outlet, tunnel has to be lined by steel liner or concrete liner if there is no adequate rock cover. Most of the tunnels designers come across with this situation. They normally find the distance that unlined section can be continued and rest of the length is lined.
Design of a Section with adequate rock cover
When a adequate rock cover is presents, we can do the design the tunnel with lining or without lining. If we have good quality rock, we can have unlined tunnel. But if the rock is weak we have to consider the rock quality for the design.
Design for External Loads
When adequate rock cover is present, we need not to worry about the total collapse of the tunnel. However, it can be fail locally. If the rock is not fairly good or it can not be stabilized with shotcreeting(reinforced or un-reinforced), we have to have a lining that can bear the external loads.
Lining design is done considering the type of the rock. Rock quality and the type of rock shall be inspected at the site and then the design should be carried out. In tunnel designing books or design standards, it can be found the load that need to be considered for the lining design depending on the rock type.
"EM 1110-2-2901 Tunnels and Shafts in Rock" on of most commonly used standard that can be reffed for our designs. If provides a guide line to design a tunnels depending on different ground conditions.
Above figure is extracted form EM 1110-2-2901. Depending on the rock condition, fracture spacing and RQD value, rock load can be selected. For example, consider massive moderately jointed rock, rock load is 0.5B.
Hp = 0.5 B x (density of rock)
Assume tunnel diameter(B) as 2.5 m
Rock density 25 kN/m3
Hp = 0.5 x 2.5 x 25
= 31.25 kN/m2
This load can be applied on tunnel as a gravely load. Finite element analysis or equations given in codes for different shapes of tunnels, can be used to find the stresses of the tunnel.
In addition to the rock loads, external water pressure should be considered for the design. If proper drainage system is not provided, water head or part of the head should be considered for the design. When proper drainage system is provided, external pour water pressure can be reduced or nearly eliminate for the design. However, design water pressure may be taken as the lesser of 25 percent of the full pressure and a pressure equivalent to a column of water three tunnel diameter high.
Loads should be factored when analyzing the tunnel. EM 1110-2-2901 provides a table that can be used to create load combinations.
Load combinations can be created by considering the factors given in the above table.
If there is a lateral deformation, it increases the bending and shear forces of the tunnel. When large rock cover is exist, tunnel can not deform laterally. This can be considered in the analysis and rock can be considered as a support to the tunnel.
Rock support can be model depending on the type of the rock. Sub grade reaction of the rock can be calculated for the equations given in the EM 1110-2-2901.
Depending on the arc angle, element size, position reaction and modulus of rock, sub grade reaction can be calculated in radial and tangential directions.
Design for Internal Loads
When there is a adequate rock cover, internal load generated from the water head can be bared by the surrounding rock. Also when a large rock cover is exist, it does not allowed the tunnel to deform. Therefore, stresses are not generated due to the internal water load.
Design of a Section with inadequate rock cover
Good quality rock can be fond in the areas where the tunnels are constructed. However, there are instances we meet with poor quality rock or soils on the top of the tunnel. Even if we have the quality rock, it should be adequate to take the internal load exerted by the water head on the surrounding rock.
Design for external loads
When the rock cover is not adequate, we have to have a either steel lining or concrete lining to carry the internal loads. When the tunnel is not carry any water, it does not have internal pressure on the surrounding rock. External loads applied on the tunnel lining should be considered when designing it.
Technical paper "Big Tunnels in Bad Rock 2000 Terzaghi Lecture by Evert Hoek" can be refer for the design. It is very good guide to design such cases. However, there are different techniques that have been proposed by researches/books for calculating rock load.
EM 1110-2-2901 provides a guide line to find position that required line section. Beyond this position, section can be constructed as a unlined section if required. Following figure extracted from EM 1110-2-2901 can be referred to find the distance that lined section is required.
Figure 9-2 shows the requirement of rock cover for unlined pressurized waterway. It is the Norwegian criterion for confinement of rock. This concept is commonly used method by the design engineers. This is a very simple technique and tool to find the minimum rock cover for a unlined tunnel. Weight of the rock mass or the overburden material is balanced by the internal head of the tunnel. Attention should be paid to the surface condition when find the rock cover(hs). For example, if the top cover is soil or weathered rock, these type of material can be washout when water is flowing along the surface. In addition the safety factor should be considered adequately. It may vary 1.05 - 3 and may be referred from the design intent.
Figure 9.1 shown bellow, also can be used for designing the tunnels. We can select a method, and then design can be started. Most commonly used method and simplest method is Norwegian criterion for confinement.
Once we select a criteria, we can calculated the section that required the lining from the equation given in the guide line.
External load need to consider for the design is weight of rock cover or weight of overburden material. We can apply that weight as a gravity load for the analysis. If there is large rock cover in lateral direction, we can consider rock as support against the lateral deformation. However, if there is no sufficient rock cover in lateral direction, it is advisable to not to consider it as a support.
Design for Internal Loads
When sufficient rock cover is not present, tunnels should be lined as discussed above. Water head can be considered as the internal load while the weight of the overburden material can be considered as load applied from the top of the structure as gravity load. It should be very careful with the weight of the overburden material depending on the value of the load and the deformation of the tunnel. Some times it may acts as beneficial but it could be a adverse load as well. For example, if we apply a factor when creating a load combination, it generate a weight that is more than that of existing weight of overburden material. If may increase hogging moment and may reduce sagging moments. Actually this purely depends on the analysis we do. So it is better to be very careful with weight of the overburden material if we intend to apply to the model.
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