CHAPTER FOUR

RESULTS AND DISCUSSION

4.1 RESULTS

4.1.1 Satellite geographical survey of the area

This was performed using Google Earth application. The distance, overburden, map, latitude and longitude of the project area were obtained from this application as follows;

The distance between Unilorin and Ilorin federal railway station is 11.8km, latitude 28’57.52’’N, longitude 37’2.32’’E and the overburden of section x-x to be considered is 40.3ft (Google earth). The Satellite image of the project area is shown in figure 4.1 below; section x-x is shown with red circle in this figure.Figure 4.1- Map and topography of the project area (Google earth)

Figure 4.2 Section X-X of the project area

4.1.2 DESIGN CALCULATION

Function of Tunnel

The planned tunnel is to be used as a subway tunnel.

Figure 4.3 Section X-X. Load condition for design

REFERENCE / CALCULATION / OUTPUT
JSCE,1996 / Design Condition
Dimensions of Segment
Type of segment: RC, Flat type
Diameter of segmental lining: = 9500 mm
Radius of centroid of segmental lining: = 4550 mm
Width of segment: b = 1200 mm
Thickness of segment: t = 400 mm
Ground Condition
Overburden: H = 40.3ft =12.3 m
Groundwater table: G.L. + 0.6 m =12.3+0.6=12.9 m
N Value: N = 50
Unit weight of soil: = 18 kN/
Submerged unit weight of soil: ' =8 kN/
Angle of internal friction of soil: = 30 °
Cohesion of soil: C = 0 kN/
Coefficient of reaction: k = 50 MN/
Coefficient of lateral earth pressure: k = 0.4
Surcharge: = 39.7 kN/
Soil condition: Sandy
Allowable stresses of materials:
Concrete: Nominal strength =48 MN/
Allowable compressive strength =17 MN/
Allowable shear strength =0.55 MN/
Reinforcement (SD35):
Allowable strength: = 200 MN/
Bolt (Material 8.8):
Allowable tensile strength = 240 MN/
Load condition
Dead load:
g =B = 1.2 @ 26.5 @ 0.4=12.72 kN/
where,
= unit weight of RC segment
= 26.5 kN/
:Reaction of dead load at bottom:
= g=39.96 kN/ / =39.96 kN/
REFERENCE / CALCULATION / OUTPUT
JSCE,1996 / Vertical pressure at tunnel crown:
Earth pressure: = B(+' H)
= 1.2@ 138.1 =165.7 kN/
Water pressure:
= B= 1.2 @ 129.0
= 154.8 kN/
= + = 320.5 kN/
Vertical pressure at tunnel bottom:
= + =320.5 + 39.96
=360.46 kN/
Lateral pressure at tunnel crown:
Earth pressure: =B{ + (H+t/2)}
= 1.2 @ 55.88 = 67,1 kN/
Water pressure: = B ( + t/2)
= 1.2 @ 131.0 = 157.2 kN/
= + =224.3 kN/
Lateral pressure at tunnel bottom:
Earth pressure:
= B{+ (H+ - t/2)}
= 1.2 @ 85.00 = 102.0 kN/
Water pressure:
= B ( + - t/2)
= 1.2@ 222.0 = 266.4 kN/m
= + = 368.4 kN/ / = 320.5 kN/
=360.46 kN/
=224.3 kN/
= 368.4 kN/

Computation of Member Forces

The member forces are computed with the bedded frame model

Figure 4.4 Bedded frame model to compute member forces

Figure 4.5 Model of rotation spring

Model for Computation of Member Forces

A 58-regular polygon having 60 nodes is used to compute the member forces.

Node 16 is the middle point between Node 15 and 17, and Node 46 is the middle point between Node 45 and 47. Nodes 6, 8, 17, 25, 33, 41, 50 and 58 are located at the joints of the segmental lining. The joint is simulated as rotation spring, and it is assumed that moment (M) is in proportion to the angle of rotation(e), as follows (see Fig. 5).

Table 4.1 Member forces of segmental lining

Critical Condition / Node / M (kNm) / N (kN)
Segment / Max / 3 / +205.83 / 1178.09
Min / 11 / -169.05 / 1675.45
Joint / Max / 58
3 (@0.6) / +20.10
+123.50 / 1578.24
1178.09
Min / 50
11 (@0.6) / -22.70
-101.43 / 1448.58
1675.45
31 = 178.70 kN
REFERENCE / CALCULATION / OUTPUT
BS 8110 Chart No. 44
BS 8110 Chart No. 44 / Area of Reinforcement
,



where , ,


Since the grade of steel in the chart used is approximately 60% higher, 60% of the area obtained must be subtracted.




Since inner section of the segment will experience more tension due sagging as a result of the external loading, a factor of 1.2 will be multiply with the outside reinforcement.
/

Figure 4.6 Section of segment

Figure 4.7 Section of segment and arrangement of bars and joint

Figure 4.8 Distribution of stress of critical sections at Node 3 and Node 11

Table 4.2 Computation result of check of safety of segment

Node / 3 / 11
M (kNm/m)
N (kN/m)
(MN/) (Compressive)
(MN/) Tensile)
(MN/) (Compressive) / +205.83
1178.09
7.1
43.2
84.5 / -169.05
1675.45
3.4
3.6
82.4

Table 4.3 Computation result of check of safety of joint

Node / 58 / 3 / 50 / 11
M (kNm/m)
N (kN/m)
()
()
d (cm)
d (cm)
X (cm)
(MN/m2)(Compressive)
(MN/m 2) (Tensile)
(MN/m 2) (Compressive) / +20.1
1578.2
11.45
32.00
34
1
Full section compressive
3.3
49.8
- / +123.5
1178.1
11.45
32.00
34
1
31.00
5.1
7.40
74.1 / -22.7
1448.6
11.45
120.00
25
7
31.00
3.4
46.6
- / -101.4
1675.5
11.45
120.00
25
7
35.10
5.8
25.0
69.5

4.2 Result of Computation

Result of Computation

Table 1 shows the result of computation of member forces of segmental lining. In case the safety of the joint is checked, the bigger moment of the maximum moment of the joint and 60% of the maximum moment of the segment is adopted. Figure 6,7 shows the arrangement of bars in the segment and the bolted joint.

Check of Safety of segmental Lining

The safety of the segment shall be checked at Node 3 and 11. The safety of the joint shall be checked at Node 58 and 50, and at Node 3 and 11 by using 60% of the moment of each node and the capacity of the joint.

REFERENCE / CALCULATION / OUTPUT
JSCE, 1996 / Check against shear force
=
= 0.486 MN/< 1.1 MN/
where
S = 178.7 kN, B = 120 cm, j = 0.875, d = 35 cm
Check of Joint
Table III-5 shows the computation result of the safety
check of the joint. The steel plate of the bolt box is evaluated
as a compressive bar.
Check of Bolt
Bolt (M27) and bolt (M30) are used between the segment
pieces and between the segmental rings, respectively.
Check of bolt between A-type segments and
between A-type segment and B-type segment
= () = 54.8 MN/< 150 MN/
where
S =Maximum shear force among joints
= shear force at Node 6 =125.5 k
= Number of bolts = 4,
= Area of one bolt (M27) = 5.726 c
Check of bolt between B-type segment and K-type
segment
S = Nsin + ScosN = 45.5 kN
where
S = Shear force between B-type segment and K-type
segment in consideration of angle of joint and
friction between both segments
N = Axial force at Node 6 = 1612.7 kN,
S = Shear force at Node 6 = 125.5 kN
= Angle of joint between B-type segment and K-type
segment = 6.7 degree
= Coefficient of kinetic energy = 0.2
= S/() = 19.9 MN/< 150 MN/
REFERENCE / CALCULATION / OUTPUT
JSCE,1996 / Check of fall of K-type segment (Fig. II1-11)
= Max(, /B) = =333.3 kN/
where
= Pressure of backfill grouting/1.5 = 333.3 kN/
= 2 × Wx B × (8/360) = 394.92 kN
= /(+ ) = 65.8 MN/< 150 MN/ OK
where = Number of bolts = 8, = Number of bolts=2,
=Area of one bolt (M30) = 7.069 c

Figure 4.9 Check of fall of K-segment
Check of fall of segmental ring (Fig. 111-12)
W= × 2 x ×B + 2 ×x × g = 3799.62 + 363.65
= 4163.27 kN
where
x 2 x x B = Force acting one segmental ring
by pressure of backfill grouting
2 xx x g = Weight of one segmental ring
=W/(2) = 101.5 MN/ < 150 MN/ OK

Figure 4.10 Check of fall of segmental ring

Table 4.4 Comparison of Midas Software with Bedded frame model

Critical condition / Node / Member forces / Bedded frame model / Midas Software / Difference / % variance
Segment / +Max / 3 / M(kNm) / 205.83 / 135.62 / 70.21 / 51.76
Segment / -Max / 11 / M(kNm) / -169.05 / -118.37 / -50.68 / 42.81
Segment / +Max / 3 / N(kN) / -1178.09 / -1130.76 / 47.32 / 4.184
Segment / -Max / 11 / N(kN) / -1675.45 / -1650.71 / 115.26 / 6.44
Segment / Max / 31 / S(kN) / 178.70 / 172.65 / 6.05 / 3.50

Figure 4.11 Bar Chart of maximum moments on the lining segment

Figure 4.12 Bar Chart of maximum axial forces on the lining segment

Figure 4.13 Bar Chart maximum shear forces on the lining segment

4.2 DISCUSSION OF RESULTS

From the analysis, it was observed that there is an average reduction in the member forces of FEM (Midas Software) when compared to Bedded frame model. These reductions are due to the Bedded frame model, which is a structural model subjected mainly to vertical and horizontal loads. Thus, there is no structure to soil interaction but FEM is able to model construction sequences and soil to structure interaction was taken into account. This soil-structure interaction capability in the FEM analysis caused the results to be smaller than analytical method due to soil arcing effect. The soil will transfer part of active pressure by arcing and the tunnel lining gets relative smaller pressure, this arcing effect will be

larger if the soil surround the tunnel is stiffer according to Vermeer (2001).

The average percentage variance betweenMidas Software and Bedded frame model is 24.33. Thus, Midas GTS is more conservative to use than Bedded frame model.