Stress models are developed similar to the displacements models. But after the interpretation we select the mean stress from the tool bar instead of total displacement. Then the model with stress contours are displayed. We capture the required stress values at surface and around tunnel and are tabulated. Comparison of stresses with different conditions is figuratively represented.
8.1 No Loading Condition
8.1.1 Lime Stone
In no loading condition, the overburden is considered to be 20 meters in both the circular and semicircular tunnel with lime stone as the litho. The stresses developed around the tunnel in both the circular and semicircular tunnels are as follows:
The stress from Fig. 35 is about 1.05 MPa and from Fig. 36, it is 1.59 Mpa. From the figures, circular results in lesser stress around the tunnel than semi circular in lime stone litho with no loading condition.
8.1.2 Sand Stone
In no loading condition, the overburden is considered to be 20 meters in both the circular and semi circular tunnel with sand stone as the litho. The stresses generated around the tunnel in both circular and semi circular tunnels are as follows:
The stress from Fig. 37 is about 1.07 MPa and from Fig. 38, it is 1.64 MPa. From the figures, circular results in lesser stress than semi circular in sand stone litho with no loading condition.
The stresses which are calculated for circular and semi circular tunnels with different materials in no loading condition are tabulated below.
Table 12 Mean stress in no loading condition
Materials
|
No Loading
|
Mean Stress in Mpa
|
Circular
|
Semi Circular
|
Sandy Gravel
|
0.820
|
1.170
|
Lime Stone
|
1.050
|
1.590
|
Sand Stone
|
1.070
|
1.640
|
Shale
|
1.070
|
1.640
|
Marble
|
1.070
|
1.780
|
Granite
|
1.050
|
1.420
|
Basalt
|
1.100
|
1.440
|
Quartzite
|
1.040
|
1.450
|
8.2 Residential structure away from top of the tunnel
8.2.1 Lime Stone
In residential away loading condition, the overburden is considered to be 20 meters in both the circular and semi circular tunnel with lime stone as the litho. The stresses developed around the tunnel in both the circular and semi circular tunnels are as follows:
The stress from Fig. 39 is about 1.08 MPa and from Fig. 40, it is 1.71 MPa. From the figures, circular results in lesser stress around the tunnel than semi circular in lime stone litho with residential away loading condition.
8.2.2 Sand Stone
In residential away condition, the overburden is considered to be 20 meters in both the circular and semi circular tunnel with sand stone as the litho. The stresses generated around the tunnel in both circular and semi circular tunnels are as follows:
The stress from Fig 41 is about 1.1 MPa and from Fig. 42, it is 1.76 MPa. From the figures, circular results in lesser stress than semi circular in sand stone litho with residential away condition.
The stresses which are calculated for circular and semi circular tunnels with different materials in residential away condition are tabulated below.
Table 13 Mean stress in residential away loading condition
Materials
|
Residential Away
|
Mean Stress in MPa
|
Circular
|
Semi Circular
|
Sandy Gravel
|
0.850
|
1.320
|
Lime Stone
|
1.080
|
1.710
|
Sand Stone
|
1.100
|
1.760
|
Shale
|
1.100
|
1.760
|
Marble
|
1.110
|
1.870
|
Granite
|
1.070
|
1.550
|
Basalt
|
1.120
|
1.570
|
Quartzite
|
1.060
|
1.580
|
8.3 Residential structure on top of the tunnel
8.3.1 Lime Stone
In residential top condition, the overburden is considered to be 20 meters in both the circular and semi circular tunnel with lime stone as the litho. The stresses developed around the tunnel in both the circular and semi circular tunnels are as follows:
The stress from Fig. 43 is about 1.07 MPa and from Fig. 44, it is 1.66 MPa. From the figures, circular results in lesser stress around the tunnel than semi circular in lime stone litho with residential top loading condition.
8.3.2 Sand Stone
In residential top loading condition, the overburden is considered to be 20 meters in both the circular and semicircular tunnel with sand stone as the litho. The stresses generated around the tunnel in both circular and semicircular tunnels are as follows:
The stress from Fig. 45 is about 1.09 MPa and from Fig. 46, it is 1.71 MPa. From the figures, circular results in lesser stress than semi circular in sand stone litho with residential top condition.
The stresses which are calculated for circular and semi circular tunnels with different materials in residential top condition are tabulated below.
Table 14 Mean stress in residential top loading condition
Materials
|
Residential Top
|
Mean Stress in Mpa
|
Circular
|
Semi Circular
|
Sandy Gravel
|
0.840
|
1.280
|
Lime Stone
|
1.070
|
1.660
|
Sand Stone
|
1.090
|
1.710
|
Shale
|
1.090
|
1.710
|
Marble
|
1.100
|
1.810
|
Granite
|
1.070
|
1.510
|
Basalt
|
1.120
|
1.530
|
Quartzite
|
1.050
|
1.540
|
8.4 Commercial structure away from top of the tunnel
8.4.1 Lime Stone
In commercial away condition, the overburden is considered to be 20 meters in both the circular and semi circular tunnel with lime stone as the litho. The stresses developed around the tunnel in both the circular and semi circular tunnels are as follows:
The stress from Fig. 47 is about 4.21 MPa and from Fig. 48, it is 5.48 MPa. From the figures, circular results in lesser stress around the tunnel than semicircular in lime stone litho with commercial away loading condition.
8.4.2 Sand Stone
In commercial away loading condition, the overburden is considered to be 20 meters in both the circular and semicircular tunnel with sand stone as the litho. The stresses generated around the tunnel in both circular and semicircular tunnels are as follows:
The stress from Fig. 49 is about 4.24 MPa and from Fig. 50, it is 5.59 MPa. From the figures, circular results in lesser stress than semicircular in sand stone litho with commercial away condition.
The stresses which are calculated for circular and semi circular tunnels with different materials in commercial away condition are tabulated below.
Table 15 Mean stress in commercial away loading condition
Materials
|
Commercial Away
|
Mean Stress in Mpa
|
Circular
|
Semi Circular
|
Sandy Gravel
|
4.050
|
4.860
|
Lime Stone
|
4.210
|
5.480
|
Sand Stone
|
4.240
|
5.590
|
Shale
|
4.240
|
5.590
|
Marble
|
4.420
|
6.030
|
Granite
|
3.870
|
4.810
|
Basalt
|
3.760
|
4.680
|
Quartzite
|
3.980
|
5.000
|
8.5 Commercial structure on top of the tunnel
8.5.1 Lime Stone
In commercial top loading condition, the overburden is considered to be 20 meters in both the circular and semi circular tunnel with lime stone as the litho. The stresses developed around the tunnel in both the circular and semi circular tunnels are as follows:
The stress from Fig. 51 is about 3.99 MPa and from Fig. 52, it is 4.97 MPa. From the figures, circular results in lesser stress around the tunnel than semi circular in lime stone litho with commercial top loading condition.
8.5.2 Sand Stone
In commercial top condition, the overburden is considered to be 20 meters in both the circular and semi circular tunnel with sand stone as the litho. The stresses generated around the tunnel in both circular and semi circular tunnels are as follows:
The stress from Fig. 53 is about 4.03 MPa and from Fig. 54, it is 5.07 MPa. From the figures, circular results in lesser stress than semi circular in sand stone litho with commercial top condition.
The stresses which are calculated for circular and semi circular tunnels with different materials in commercial top loading condition are tabulated below.
Table 16 Mean stress in commercial top loading condition
Materials
|
Commercial Top
|
Mean Stress in Mpa
|
Circular
|
Semi Circular
|
Sandy Gravel
|
3.810
|
4.390
|
Lime Stone
|
3.990
|
4.970
|
Sand Stone
|
4.030
|
5.070
|
Shale
|
3.950
|
4.270
|
Marble
|
4.250
|
5.490
|
Granite
|
3.620
|
4.370
|
Basalt
|
3.500
|
4.260
|
Quartzite
|
3.740
|
4.540
|
8.6 Commercial structure on top of the tunnel with lining
8.6.1 Lime Stone
In commercial top with lining condition, the overburden is considered to be 20 meters in both the circular and semi circular tunnel with lime stone as the litho. The stresses developed around the tunnel in both the circular and semi circular tunnels are as follows:
The stress from Fig. 55 is about 3.97 MPa and from Fig. 56, it is 4.73 MPa. From the figures, circular results in lesser stress around the tunnel than semi circular in lime stone litho with commercial top with lining condition.
8.6.2 Sand Stone
In commercial top with lining condition, the overburden is considered to be 20 meters in both the circular and semi circular tunnel with sand stone as the litho. The stresses generated around the tunnel in both circular and semi circular tunnels are as follows:
The stress from Fig. 57 is about 3.79 MPa and from Fig. 58, it is 6.45 MPa. From the figures, circular results in lesser stress than semi circular in sand stone litho with commercial top with lining condition.
The stresses which are calculated for circular and semi circular tunnels with different materials in commercial top with lining condition are tabulated below.
Table 17 Mean stress in commercial top with lining loading condition
Materials
|
Commercial Top with Lining
|
Mean Stress in Mpa
|
Circular
|
Semi Circular
|
Sandy Gravel
|
3.570
|
4.810
|
Lime Stone
|
3.970
|
4.730
|
Sand Stone
|
3.790
|
6.450
|
Shale
|
3.760
|
5.180
|
Marble
|
4.240
|
5.230
|
Granite
|
3.610
|
3.940
|
Basalt
|
3.490
|
3.830
|
Quartzite
|
3.730
|
4.120
|