1 INTRODUCTION

It is well known that the segments production cost accounts for a large part of the total shield tunnel construction cost and one of the effective methods to reduce the shield tunnel construction cost is to de-sign the segments more efficiently. The common de-sign method for shield segments is to determine the load acting on the tunnel lining first, then determine the material and the cross sectional dimensions of the segments by structural calculations. It is, there-fore, very important to evaluate the load accurately. Up to now, overburden earth pressure or loosening earth pressure calculated by Terzaghi’s formula has generally been adopted as the vertical load acting on the tunnel lining for the segment design on the basis of previous field measurement data. But some of the field measurement results have recently shown that the load acting on the tunnel lining adopted in the design might be greater than the actual load, particu-larly in case of good ground conditions (Koyama et al. 1995). Also the effect of the ground reaction, es-pecially to the self-weight of the segments has not been fully resolved (JSCE 1996). Therefore, it is necessary to carry out measurements and analyses of the earth pressure acting on the shield tunnel lining in order to establish a rational design method for shield tunnel lining.

In this study, field measurements of earth pres-sure, water pressure and strain in the reinforcing steel bars of the segments were carried out at two shield tunnel construction sites in gravel. The meas-

ured earth pressure and water pressure were com-pared with the value adopted in the segment design. The measured bending moment occurring in the segments was also compared with the calculated re-sults using frame analysis to evaluate the load acting on the shield tunnel lining, and to determine the in-fluence of ground reaction on the bending moment in the segments due to their self-weight.

2 OUTLINE OF FIELD MEASUREMENT

Field measurements were conducted at two shield tunnel construction sites as shown in Figure 1. The overburden height H at the measurement section of Tunnel A with a diameter D of 6.2m is 9.6m, giving an overburden height to diameter ratio of approxi-mately 1.5. The overburden height at the measure-ment section of Tunnel B with a diameter of 4.75m is 12.1m, giving an overburden height to diameter ratio of approximately 2.5. The ring of both tunnels was composed of six reinforced concrete segments, with a thickness of 27.5cm and a width of 100cm at Tunnel A, and a thickness of 22.5cm and a width of 100cm at Tunnel B. The ground at the tunnel site and its vicinity, where the measurements were car-ried out, appeared to be composed of permeable gravels with the standard penetration test value (N value) greater than 50. Both tunnels were excavated by the Earth Pressure Balanced Shield method.

Table 1 shows the items of measurements carried out at Tunnel A and Tunnel B.

Evaluation of the load on a shield tunnel lining in gravel

H.Mashimo & T.Ishimura Public Works Research Institute, Independent Administrative Institution, Tsukuba, Japan

ABSTRACT: It is important to accurately evaluate the load acting on a shield tunnel lining for the economi-cal and rational design of shield tunnel lining. In Japan, the load calculated by Terzaghi’s formula or overbur-den load is generally adopted for the design of tunnel segments. But some previous field measurements have shown that the actual load acting on the shield tunnel lining could be much smaller than that adopted for the design in the case of good ground conditions.

In this study, field measurements at two shield tunnel construction sites in gravel were carried out, and the load acting on the shield tunnel lining was evaluated by analyzing the field data to establish the rational de-sign of the shield tunnel segments. The way of treating the self-weight of segments in the design was also in-vestigated.

Figure 1. Description of the measured tunnels. Earth pressure and water pressure acting on the

tunnel lining were measured at one ring, as well as the strains in the reinforcing steel bars of the seg-ments at two rings of each tunnel. The measured earth pressure is considered to be the total ground earth pressure, including pore water pressure. In or-der to measure the earth pressure and the strains in the reinforcing steel bars, earth pressure cells of 16cm in diameter at Tunnel A, and of 65cm x 32cm in length and breadth at Tunnel B, and strain gauges, were installed in the segments as shown in Figures 2 and 3 at the time of fabrication. Pore water pressure gauges were mounted in grouting holes, drilled through the segments as shown in Figure 4 after the backfill grouting materials were injected.

Table 1. Items of measurements.

Figure 2. Detail of the earth pressure cell(Tunnel B).

Figure 3. Detail of the strain gauge attached to rein-forcing steel bar (Tunnel A).

Figure 4. Detail of the pore water pressure gauge.

3 MEASUREMENT RESULTS BY EARTH PRESSURE CELLS AND PORE WATER PRESSURE GAUGES

The earth pressure measured by the earth pressure cells and the water pressure measured by the pore water pressure gauges are shown in Figures 5 and 6. The earth pressure and water pressure shown in the figures are those measured at the stable state about three months after a segment ring was assembled, and the measured earth pressure includes the water pressure.

It can be seen that the earth pressure acting on the segment reaches approximately 70kN/m2 at the tunnel crown at Tunnel A. The ground water level around the tunnel is estimated to be at the tunnel crown level according to the ground water level in a borehole in the vicinity of the tunnel, and the meas-ured water pressure corresponds to the theoretical hydrostatic pressure. Consequently the effective overburden earth pressure Pv=γH (γ:submerged unit weight) adopted as the design load reaches about 170kN/m2 and the water pressure is nearly zero at the tunnel crown level. The measurement data, therefore, indicate that the load acting on the tunnel lining at the tunnel crown accounts for approxi-mately 40 to 50% of the total amount of the effective

Figure 5. Earth pressure and water pressure distribu-tion (Tunnel A).

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(kN/m2)

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Measured earth pressureMeasured water pressureTheoretical hydrostatic pressure

(a) Tunnel A (b)Tunnel B

(D5)

3.2m

6.

4m

7.6m

6.

5m

surface

gravel(Dg1)

sand(Ds1)

N value 1020304050

1.8m

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2m

8.8m

12.1

m

soil(Fs)

gravel

gravel with cobble stone

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N value 1020304050

clay(Dc1)

clay(Dmc)

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(D3ug) grand water level

grand water

level

ItemsTunnel A Tunnel B

pore water pressure 4／RING×1RING 4／RING×1RINGearth pressure 8／RING×1RING 8／RING×1RINGstrains in reinforcingsteel bars 11／RING×2RING 11／RING×2RING

Number of Instrument

backfill grouting materials

pore water pressure gauge valve

segment

grouting hole

groundwater

Figure 6. Earth pressure and water pressure distribu-tion (Tunnel B). overburden earth pressure and water pressure.

Also it can be seen that the earth pressure meas-ured by the earth pressure cell reaches about 80 to 170kN/m2 and is almost equal to the measured water pressure at Tunnel B. The ground water level around the tunnel estimated from the ground water level in the borehole is about 9m higher than the tunnel crown, and the measured water pressure corresponds to the theoretical hydrostatic pressure. Therefore it is presumed that only the hydrostatic pressure acts on the tunnel lining.

4 EVALUATION OF LOAD ON LINING FROM MEASURED BENDING MOMENTS

Frame analyses using the beam-spring model were carried out to estimate the earth pressure acting on the shield tunnel lining by comparing the calculated bending moments in the segments with measured ones.

4.1 Calculation Method The beam-spring model adopted for the calculation is shown in Figure 7. Two parallel segment rings are modelled, where each ring consists of beam ele-ments representing the segments. Rotational spring elements with a rotational stiffness coefficient kθrepresent the segment joints which connect the segments in the circumferential direction, and shearing spring elements with a shearing stiffness coefficient ks represent the ring joints which connect the segment ring. The support of the ground that sur-rounds the tunnel is modelled by a continuous spring support with a coefficient of ground reaction kr in a normal direction, which has no stiffness on the ten-sion side. The ground conditions at the calculated section are shown in Figure 8.

Table 2 shows the values of the parameters used in the calculation. In the calculation, the effective

earth pressure and hydrostatic pressure, the models of which are shown in Figures 9 and 10, were adopted as vertical loads acting on the tunnel lining. To estimate the actual vertical load acting on the lin-ing, calculations were carried out using three kinds of combination of vertical load, i.e. effective over-burden earth pressure together with hydrostatic pres-sure, effective loosening earth pressure obtained from the following Terzaghi’s formula (1) together with hydrostatic pressure, and only hydrostatic pres-sure.

B1(γ-c/B1) Pv = ･(1-exp(-K0tanφ･H/B1)) (1)

K0tanφ B1=Rc･cot((π/4+φ/2)/2)

where Pv= Terzaghi’s effective loosing earth pres-sure ; K0= lateral earth pressure coefficient ; c,φ=cohesion and angle of internal friction of soil ; γ= submerged unit weight ; and Rc= tunnel radius.

The self-weight of the segments was not taken into account in the calculation at Tunnel A, as the data collection of strain in the reinforcing steel bars started after the assembly of a tunnel ring, while the self-weight was taken into account at Tunnel B. The stiffness coefficients of segment joints and ring joints were determined by laboratory tests using the actual joints or theoretical calculations, and the lat-eral earth pressure coefficient and the coefficient of ground reaction were determined from previous case studies in similar ground conditions.

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(kN/m2)

-100-50050100150200Measured earth pressureMeasured water pressureTheoretical hydrostatic pressure Figure 7. Beam-spring model.

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Table 2. Parameters for calculation. Figure 9. Earth pressure model. Figure 10. Ground water pressure model.

4.2 Calculation results and consideration

4.2.1 Evaluation of load acting on tunnel lining Figure 11 shows the comparison between the meas-ured bending moments and the calculated bending moment at Tunnel A. The measured bending mo-ments were obtained by using the measured strains in the reinforcing steel bars of the segments three months after assembly of a tunnel ring. To calculate the bending moments, it is assumed that the elastic modulus of reinforcing steel bars and concrete are Es=206kN/mm2 and Ec=31kN/mm2 respectively, ig-noring the effects of the stress of the concrete on the tension side. The calculated results show the value for different value of vertical load. It can be seen that the calculated results using the effective loosing earth pressure give the closest agreement with the measured values. The effective loosing earth pres-sure based on the bending moments accounts for ap-proximately 60% of the effective overburden earth pressure at the tunnel crown. This result is compati-ble with the effective earth pressure obtained from the earth pressure cell measurements which was ap-proximately 40% to 50% of the effective overburden earth pressure.

Figure 12 shows the comparison between the measured bending moments and the calculated bend-ing moments at Tunnel B. The measured bending moments were obtained in the same way as Tunnel A, assuming an elastic modulus of concrete Ec of 32kN/mm2 and an elastic modulus of reinforcing steel bars Es of 206kN/mm2. The calculated results show the value for different values of vertical load. It can be seen that the calculated results using the theoretical hydrostatic pressure give the closest agreement with the measured values. Therefore it is

Tunnel A Tunnel BTunnel radius Rc (m) 5.925 4.525

Thickness of segment h (m) 0.275 0.225Width of segment w (m) 1.000 1.200Moment of inertia of segment I (m4) 0.001733 0.001139Elastic modulus of segment Ec (KN/mm2) 31.44 32.36

Rotational stiffness coefficient ofsegment joint kθ (MN･m/rad) 32.8～65.7 36.3～127.5

Shearing stiffness coefficient ofring joint ks (MN/m) 1.96 1.96

Load

－ self-weight of segmentsLateral earth pressure coefficient λ 0.45 0.45

50(After tail leaving)Coefficient of ground reaction kr (MN/m3) 50(After tail leaving) 1,10,100(Before tail leaving)

Effective overburden earth pressure and hydrostatic pressureEffective Tergaghi's loosening earth pressure and hydrostatic pressureHydrostatic pressure

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presumed that only the hydrostatic pressure acts on the tunnel lining. This result is also compatible with the measurements obtained from the earth pressure cells and pore pressure gauges.

4.2.2 Influence of ground reaction model In the calculation as above mentioned, ground reac-tion was basically modelled by the no-tension springs which do not resist on the tension side. But it is thought that the evaluation of ground reaction plays a very important role in the segment design. Figure 13 shows the influence of the ground reaction model on the calculated bending moments when the ground reaction was modelled by linear elastic springs. It can be seen that the maximum bending moments at both the positive and negative side ob-tained from the calculation using linear elastic springs account for approximately 60% of those us-ing no-tension springs. This indicates that the calcu-lated results using the linear elastic springs tend to give lower bending moments than those calculated using no-tension springs. Therefore more attention should be paid to determining the value of the lateral earth pressure coefficient and coefficient of ground reaction if the ground reaction is modelled by linear elastic springs.

4.2.3 Evaluation of ground reaction to self-weight of segments

Up to the present, it has been thought that there was no support around a shield tunnel at the stage of as-sembly of a tunnel ring in the shield machine, and that the stress occurring in the segments during as-sembly of a ring remained. Therefore in the conven-tional design method of shield segments, the bend-ing moments occurring due to the self-weight have been calculated without taking account of the ground reaction. However, the bending moments due to the earth and hydrostatic pressure have been calculated taking account of the ground reaction. The sum of these calculated bending moments has been used to determine the material and the cross sectional di-mensions of the segments. But according to recent experiences, it appears that little bending moment due to the self-weight of the segments occurred at the stage of assembling a tunnel ring, because of the improvements of backfill grouting technology, em-ployment of the circle retainer and correct control of the jack thrust.

The measured bending moments that occurred due to the self-weight of segments before the tunnel ring left the tail of shield machine at Tunnel B is shown in Figure 14. To study the influence of the ground reaction, the calculated bending moments due to the self-weight of the segments with various coefficients of ground reaction kr of 1, 10, 100MN/m3 are also plotted in the figure. It can be seen that the bending moments that occurred due to the self-weight before the tunnel ring left the tail of shield machine are very small and the calculated bending moments taking account of the ground reac-tion with the coefficient kr of more than 100 MN/m3

are compatible with the measured values. Furthermore, to investigate the influence of the

ground reaction due to the self-weight of the seg-ments after a ring leaves the tail of shield machine and is loaded by the soil, two kinds of ground reac-tion model were adopted in the calculation (see Fig-ure 15). The standard model was the same model

(a) Section Ⅰ(kN･m)

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250-12.5

-25-12.5-250

(b) Section Ⅱ(kN･m)

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12.525-25

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Measured

no-tension spring

linear elastic spring

Figure 11. Bending moments distribution (TunnelA).

Figure 12. Bending moments distribution(Tunnel B).

Figure 13. Influence of the ground reaction model.

(a) Section Ⅰ(kN･m)

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(b) Section Ⅱ

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(a) Section Ⅰ

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(kN・m)(b) Section Ⅱ

(kN・m)

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Measuredloosening earth pressure+hydrostatic pressureoverburden earth pressure+hydrostatic pressurehydrostatic pressure

Figure 16. Influence of the ground reaction tothe self-weight of segments. mentioned in section 4.1, where the ground reaction to the self-weight of segments was taken into ac-count as the reaction of spring support. In model Ⅰ, the ground reaction to the self-weight of segments was taken into account as the fixed ground reaction acting on the invert equal to the weight of segments.

In model Ⅱ, the bending moment that occurred due to self-weight was calculated without ground reac-tion. The calculation results for Tunnel B are shown in Figure 16. It can be seen that the value of the cal-culated bending moments using model Ⅰ is ap-proximately two to three times larger than those measured. The calculated bending moments using model Ⅱ are approximately three to four times lar-ger than those measured. From these results, it will be desirable to take account of the ground reaction to the self-weight of the segments based on the reac-tion of a spring support.

5 CONCLUSION

In this study, field measurements and frame analysis were carried out to evaluate the load acting on shield tunnel in gavel. The main results obtained from the study are as follows.

1) The water pressure acting on the shield tunnel lining is almost equivalent to the theoretical hydro-static pressure.

2) In the case of an overburden height H to the tunnel diameter D ratio of nearly 1.5, the vertical earth pressure acting on the shield lining is equiva-lent to the effective earth pressure calculated by Terzaghi’s formula, and in case of an overburden height to the tunnel diameter ratio of 2.5, only the hydrostatic pressure acts on the shield tunnel lining based on the field measurements conducted by the authors.

3) At the stage of assembling shield segments in the shield machine, small bending moments in the shield segments occurred due to their self-weight. The ground reaction to the self-weight of the seg-ments could be taken into account by considering the reaction of a spring support.

REFERENCES

Koyama,Y. et al. 1995. In-situ measurement and consideration on shield tunnel in diluvium de-posit. Proceedings of tunnel Engineering, JSCE, Vol.7: 385-390. (in Japanese)

Japanese Society of Civil Engineers (JSCE) 1996. Japanese standard for shield tunneling, The third edition.

(a) Section Ⅰ

0 -10 -20102010 20-10-20

(kN･m)

0

(b) Section Ⅱ (kN・m)

-20-20 -10-10 00 10 20 20 10

Measuredkr= 1MN/m3

kr= 10MN/m3

kr= 100MN/m3

Figure 14. Bending moments distribution due tothe self-weight of segments.

Figure 15. Model of the ground reaction to theself-weight of segments.

(a) Section Ⅰ（kN・ｍ）

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