Prediction of Ground Settlement Induced by Slurry Shield Tunnelling in Granular Soils

Underground structures play an important role in achieving the requirements of rapid urban development such as tunnels, parking garages, facilities, etc. To achieve what is needed, new transportation methods have been proposed to solve traffic congestion problems by using of high-speed railway and subway tunnels. One of the issues in urban spaces due to tunnel excavation is considerable surface settlements that also induce problems for surface structures. There are a variety of published relationships concerned with field measurements and theoretical approaches to evaluating the amount of the maximum surface settlement value due to tunneling. This paper studies the ground surface settlement caused by the Greater Cairo Metro – Line 3 Phase-1. This project was constructed by a slurry shield Tunnel Boring Machine (TBM). Therefore, this work consists of two parts. The first part presents the details of the project and monitoring results field and laboratory geotechnical investigations in order to determine the soil properties. The second part is to the comparison between the field measurements and theoretical approaches for surface settlement due to tunneling construction. At the end of the works, the results show that the more convenient methods which approach the field measurements, and the major transverse settlement occurs within the area about 2.6 times the diameter of the tunnel excavation.


Introduction
Underground structures play an important role in achieving the requirements of rapid urban development such as tunnels, parking garages, facilities, etc. To achieve what is needed, new transportation methods have been proposed to solve traffic congestion problems by using of high-speed railway and subway tunnels [1]. For instance, Line 3 of Cairo metro meets huge transportation demands along the route, and reduces the traffic density at the other means of transportation with a rate equivalent to 2 million trips/daily. However, the construction of tunnel induces ground movements, both vertical and lateral, causing surface subsidence, curvature change, inclination, and discontinuous deformation, which in turn affect the safety and stability of adjacent existing buildings within the settlement range of strata, thus bringing potential safety obstacles to the building structures [2][3][4][5][6][7][8][9].
It is well-acknowledged that the soil movement occurring during deep excavation process plays a significant role in this regard. Excessive soil movement causes excessive settlements of nearby buildings and may cause different damages [10]. However, in reality, ground movements depend on a number of factors such as: behavior of the soil around tunnel, geometry of tunnel and depth, tunnel construction method, the quality of the workmanship and management [11,12]. This emphasize that the ground movements and the depth of tunnel is neither simple nor nonlinear relationship [13].
Several approaches, such as the empirical method, centrifugal method, numerical simulation method, and field monitoring, have been used to predict the surface settlement during the shield tunneling. Peck (1969) [14] used the results of monitoring program to predict the deformations and stresses related with construction of tunnel and deep excavation. Since then, ground movements have been determined by investigations of many empirical and semiempirical methods. These methods do not take into account the building effects and therefore they measure only the greenfield deformations. However, the empirical and semi-empirical methods considered the initial important phase in predicting the excavations effect on close buildings.
The increase of the surface settlement may cause more buildings to be damaged or influence the serviceability of the buildings [15][16][17]. Therefore, to control tunneling induced deformation on the buildings in the nearby area within the allowable limit is an important task for engineers involved in a tunneling project. The damage to an existing building can be caused by excessive settlement [16]. To date, in spite of the recent advances made in assessing the stability and effects of excavations on nearby properties, structures failures or adjacent roadway, the serviceability problems such as cracking of structural or architectural elements, uneven flooring, or inoperable windows and doors due to the vertical settlement and lateral deformations caused by deep excavations are much more common than failures [18]. Recently on July 2020, one of the most examples of such damage to corners of building number 17 on Brazil Street in Zamalek as well as at the front yard and fence of the adjacent Bahraini embassy caused by the slight ground subsidence that occurred. The subsidence was due to the result of ongoing excavation works in the line 3 -phase 3 of the metro undergoing in Zamalek district.
The Greater Cairo Metro, Line 3, Phase-1 starts from El-Attaba Station to El-Abbasia Station and crosses very close to a multi-story carparking building founded on piles namely, El-Attaba Garage. Considering that the underground construction might cause damages to the building, the survey before the construction and prevention and monitoring measures during and after the construction were carried out. This work consists of two parts. The first part presents the details of the project and monitoring results field and laboratory geotechnical investigations in order to determine the physical soil properties of the site which helps in predicting the behavior of the soil and the settlement that occurring on adjacent El-Attaba Garage building due to construction of tunneling. The second part is to comparison between the field measurements and theoretical approaches for surface settlement.
The remainder of this paper is organized as follows. Section 2 presents the details of the case study. In Section 3, the site investigations are explained. The stages of construction are demonstrated in Section 4. Section 5 presents the theoretical methods of ground surface settlement. The computational results are presented and analyzed in Section 6. Finally, Section 7 presents conclusions and suggestions for future research. The research flowchart is shown in Figure  1.

Case Study
One of the Egyptian mega projects established to solve many traffic problems that have been recently raised is the Greater Cairo Underground Metro project. The Greater Cairo Metro-Line 3 was constructed by a slurry shield Tunnel Boring Machine (TBM), with 9.55 m a diameter. The tunnel has an external and internal diameter with 9.15 m and 8.35 m respectively. The precast segmental lining thickness of 0.4 m. This line is 47.87 km length starts from Imbaba to Cairo airport; also, as planned, it is going to be constructed in four phases. In this study, The Greater Cairo Metro -Line 3 -Phase-1 moves underground from El-Attaba to El-Abbasia stations was considered to understand performance of tunnel system and the expected ground movement during tunneling construction that passes through soil layers. This Phase is 4.3 km length and consists of 5 underground stations and 4 annexed structures, as shown in Figure 2.
El-Attaba Garage building is 77.04 m-length and 45.55 m-width. It is founded near the greater Cairo metro-line 3phase-1, constructed with 8 stories as shown in Figure 3. This building is 6.45 meters from the center of the tunnel and making an angle of about 42 ᵒ from the tunnel as shown in Figure 4. The building was supported by 245 non-displacement concrete piles arranged in pile caps group. The pile dimensions are 0.6m in diameter and 20m length and passes through layered soil.
As reported in National Authority for Tunneling (NAT), several instrumentations were used to monitor the predicted ground movements of the soil during tunnel progress. The five measured vertical Surface Settlement Points (SSP.b, SSP.c, SSP.d, SSP.e and SSP.f) were installed around the Garage El-Attaba building as shown in Figure 3. Through the tunnel advancement from July 2010 to August 2010, the building was monitored at the location of surface settlement points and an Elevation Reference Point (ERP.a).

Site Investigations
Referring to geotechnical investigation of the Greater Cairo Metro -Line 3-Phase-1, thirteen boreholes and standard penetration tests [20], were carried out with a vary depths from (24 to 70) m and different locations along the phase-1 as indicated in Figure 5. The thirteen boreholes were performed using mechanical rotary drilling fluid (using bentonite) techniques. This research focused on the boreholes that located at the first station (from El-Attaba to Bab-El-Shaaria) near the El-Attaba Garage building. After review these boreholes, it's found there is consistent with soil description but difference with the level of depth. As shown in Figure 3. borehole No. 2A is nearest to Garage El-Attaba building, thus the soil cross section at this borehole was taken as representative to soil profile in this study:

Standard Penetration Test (SPT)
In this study and according to the Egyptian code of practice [21], there are many required corrections such as: (overburden effect, underground water table and the borehole diameter effect) were taken into account to measure the N-corrected value in order to classify the soil and determine the friction angle as listed in Table 1. In the same line, the friction angle, ø are estimated by Peck et al. (1953), Guiliani and Nicoll (1982) and Wolff (1989) [22][23][24] for cohesionless soil layers as shown in Figure 9. As shown in the summary at the end of this section, and based on SPT-N value, the Young's modulus, for sandy soil layers are estimated using theoretical equations by Webb (1969); Bowles (1982) and Denver (1982) [25][26][27]. In addition, The Young's modulus for coarse soil layers, are obtained using the SPT original N-values according to the following recommended correlations by ECP 202/3 (2005) [28]; For silty sand soil, For medium to fine sand soil, For dense sand soil, For gravelly sand and gravel soil,

Grain-Size Distribution
To classify the soil properly, the grain-size distribution of coarse-grained soil is generally determined by means of sieve analysis. Table 2 shows the sieve analysis test results. The soil stratification at location of BHD. 2A can be summarized as follows: Layer (1) starts at level (+19.40) and extends to level (+15.40), and it is a made ground layer consisting of 30% stone pieces and red bricks, and 70% clay. Layer (2) begins from level (+15.40) to level (+10.40), and it consists of firm to stiff brown micaceous clay. Layer (3) is a thick segment of silty poorly graded sand that starts from level (+10.40) to level (-00.60) with a thickness of 11.0 m. Layer (4) starts from level (-00.60) to level (-2.10), and it consists of yallowish brown slightly sand poorly graded gravel. Layer (5) starts from level (-2.10) to level (-3.60), and it consists of dense yallowish brown micaceous slightly gravelly silty poorly graded sand with little calcareous materials. Layer (6) starts from level (-3.60) to level (-10.10), and it contains of hard formation consist of cobbles and boulders. The last layer is very dense yallowish brown calcareous slightly silty poorly graded sand extended to the end of boring. The permeability coefficient of sand soil layers was estimated from sieve analysis test results using (Equation 4) [29]: Where, per = Coefficient of permeability (cm/sec) = Constant, typically assumed to be 100. 10 = Grain size corresponding to 10% by weight passing, also referred to as the effective size (mm). = Diameter corresponding to 60% by weight passing, indicated by the gradation curve at the 60% passing level (mm), 30 = Grain size, indicated by the gradation curve at the 30% passing level (mm), U = Uniformity coefficient ( 60/ 10), and = Curvature coefficient of the gradation curve ( 30 2 / 60 * 10).

Water Content and Atterberg Limits
There are three clay samples were taken from BHD. 2A at vary depths of 4.0, 5.0 and 7.50 m underground surface to estimate the Atterberg limits and water content that is necessary to classify the cohesive soil. Also, the relative consistency ( ) was estimated by using the following equation (Equation 6) [30], and based on the relative consistency values, the soil classified and the undrained cohesion for each clay sample were determined and given in Table 3.

Consolidation Test
Consolidation test was conducted on clay soil samples taken from site at depth of (8.00-8.30) m underground surface. Figure 7 shows the e-Log curve for consolidation test. Three pressure increments (56.81-111.80, 111.80-166.78, and 166.78-221.77) kN/m 2 were applied on this sample. Based on test results, the average soil volume compressibility coefficient, mv was determined with value of (9.29 -05) m 2 /kN. Then, clay soil constrained modulus, was estimated to be 1.10 +04 kN\m 2 using (Equation 7): Figure 7. The relationship between the pressure and voids ratio in consolidation test (e-Log P curve)

Unconfined Compression Test
The unconfined compression test is a special type of unconsolidated undrained triaxial test, UUT. The soil undrained shear strength, was estimated. Also, the undrained shear strength ( or ) and the undrained Young's modulus ( ) of the cohesive soil layer are calculated using (Equations 8 and 9), respectively. Table 4, display measured values of ( ) for clay samples at variable depths using the unconfined compression test.

Direct Shear Test
A direct shear device is used to determine the shear strength indicated by Cohesion ( ) and Angle of Internal Friction (ø) of any soils. Many calculations depend on these two parameters such as; bearing capacity measurements at any depths, slopes design, and to calculate the consolidation parameters and in many other analyses. Figure 8 shows the shear stress and shear displacement for 12 m and 35 m depth, respectively.
The Figures 9 to 11 show the summery of values of the soil's physical properties such as friction angle, young's modulus, and cohesion at different depth of BHD.2A, which were calculated in this study from laboratory, field tests and theoretical equations of previous studies as mentioned above. Also, it must be mentioned that, in this case study, the Young's modulus and the friction angle for (sand, gravel, and boulders) layers are taken based on ECP code measurements. On the other hand, the clay soil properties (un-drained shear strength, and undrained young's modulus, are taken from unconfined compression test. Table 5 shows the soil parameters that are used in this study to measure the ground surface settlement.

Stages of Construction
In the construction of the Greater Cairo Metro, line-3, slurry shield was used to execute utilizing of 9.55 m external diameter. The length of TBM is 9 m with a tail piece thickness 5 cm. According to NAT., the rate of TBM advance is ranging from (6 to 13) m/day. Figure 12 describes the sequence followed in the construction of the tunnel. Six stages of construction were adopted as follows: The objective function of the model is given as follows: a) 1 st Stage: Starts with boring a vertical pit. b) 2 nd Stage: A cylindrical excavator called a "tunnelling shield" is brought in through the vertical pit and assembled.

c) 3 rd Stage:
The machine starts excavation toward the adjacent vertical pit. The tunnelling shield presses and rotates its cutting wheel at the front against soil to excavate.

d) 4 th Stage:
The machine excavates and moves forward as hydraulic jacks at the back stabilized it. Once a certain distance is excavated the machine folds the jacks in and install a ring-shaped concrete wall called a segment.

e) 5 th Stage:
The grouting is acted on the perimeter of the segments toward the soil.

f) 6 th Stage:
The machine builds the tunnel by repeating the process of precasting the segment extending the jacks, then folding the jacks in and precasting the segment. When the machine reaches the next vertical pit, it is removed to complete the underground tunnel.

Theoretical Calculation of Surface Settlement
The ground movements estimation is the first step to proceed a reliable risk-assessment of the potency effects on buildings and underground structure, which is necessary for the tunneling design of in urban regions. There are many research examples clarifying the characteristics of ground movement when a tunnel is excavated. The maximum settlement amount ( ) and the position of the inflection point ( ) are indicated by a normal distribution curve (Gaussian distribution curve) on the form of subsidence on the cross-section of the tunnel, as shown in Figure 13. For the case of a single tunnel, the development of the surface settlement trough is estimated by various methods as follows: 1. Peck (1969) [14], summarized a large number of measured data to describe the surface settlement caused by construction of a shield tunneling and expressed that surface settlement approximate normal distribution and proposed the Peck formula as follows: Where ( ) = the surface settlement, = the horizontal distance from tunnel centreline, = the maximum settlement on the tunnel centreline, and = the inflection point position.
Settlement due to tunnelling is usually realize by a dimensionless parameter that is called Ground Loss or Volume Loss. Volume loss is defined as the proportion of excavation area volume to initial volume of the tunnel per unit length of excavation [32], modified the Gaussian distribution based on many in-situ measurements and centrifuge test. By integrating Peck's Gaussian relationship, the volume of settlement trough, can be estimated.
Mair et al. (1982) [32], suggested the following equation to measure the maximum surface settlement: Where; = 2 = the radius of tunnel This formula is needed to determine two parameters for the prediction of settlement: the volume loss ( ) and the inflection point position ( ). The volume loss ( ) depends on tunneling techniques and the soil behaviors, and it is almost obtained through measurements or local experiences and it ranges between (0.5-1%) for shield tunnel boring machine. The technical data of the employed TBM recommended the total volume loss as 0.5%. The inflection point position ( ) determines the influence domain of settlement and plays a main role in the settlement amount when the volume loss is constant, the value of the inflection point position ( ) is related to the nature soil formation, the tunnel depth, and the tunnel radius.
O'Reilly and New (1982) [33] were presented more generalized empirical equations of the profile settlement depends on the Peck's research. They developed the general trough width equation for all soil types for multi-layered strata (N layers) as the following equation: Where; is the width of the settlement trough; is a parameter depending only on the nature of soil. Field data during tunnelling collected all over the world indicate that varies between 0.4 and 0.6 for stiff clays, between 0.6 and 0.75 for soft clays, and between 0.2 and 0.45 for sands and gravels, Mair and Taylor 1997 [34], regardless the size and method of the tunnel.

The Oteo Method
This semi-empirical method is based on Oteo's works over the last 30 years Oteo and Moya (1979) [35] and Sagaseta et al. (1980) [36], which allows estimating the settlement along the perpendicular to the axis of the tunnel. In general, this method is a modification of the Peck method, in which more parameters of the tunnel and the mass containing it are used: Where, 3. Limaniv's Method Limaniv (1957) [37] has presented the theoretical methods proceed from the assumption of elastic behavior of the soil surrounding the tunnel to calculate the surface settlement resulting from the construction of tunnels or mine excavations. The Limaniv's relationship for computing the maximum settlement is as follows: Where; = Poisson's ratio, = Young's modulus, 0 = Tunnel radius, ℎ 0 = Tunnel depth, and = Radial load that can be expressed as; Where, = The vertical stress in tunnel centreline and = Lateral earth pressure.

The Sagaseta Method
The equation of the maximum surface settlement is calculated based on the analytical solution given by Sagaseta 1987 [38] and later modified by Sagaseta 1988 [39] and Uriel and Sagaseta 1989 [40], and expressed as: Where, = Tunnel axis depth, = Distance to the centre line, and = Volume of settlement trough.

The Ecrelebi Method
Ecrelebi (2005) [41], presented the following relationship for estimating the maximum surface settlement over the tunnel axis: Where, ℎ 0 = Tunnel axis depth = Tunnel radius = Unit weight (ton/m 3 ), and = Elasticity modulus (ton/m 2 ), which is the weighted average for layers in this study.

Results and Discussion
In this section, the ground surface settlement due to tunneling was calculated with the theoretical methods and compared with field data measurements. Figure 14 shows the transverse settlement trough of the ground surface. The results indicate that the settlement obtained by Oeto and Mair methods and the monitoring results match well with the Gauss distribution. From the Oeto and Mair methods, it can be found that the maximum surface settlement, Smax, occurs at the tunnel axis x, and the final values of Smax are 10.55 mm and 11.95 mm, respectively. These methods are more appropriate than that of Limanov's method (Smax=16.78 mm). While the maximum surface settlement in the monitoring of the field data measurements is 8 mm. On the other hand, the Ecrelebi method overestimates the settlements up to Smax=26.23 mm. This causes to an uneconomic estimation and over design. In contrast, the Sagaseta method underestimates the settlement with the maximum of Smax=4.40 mm. The reason for the variation between the results of the different theoretical methods mentioned above is due to the assumptions and simplifications used in these relationships that neglect the influence of some factors, so that some cases give good results and disparate results in others. In spite of the theoretical methods have several advantages in the prediction of ground settlements induced by tunneling, there are major constraints in their practical application because the large number of influential factors involved makes tunnel-ground interaction complicated, it is difficult to say whether these methods can be used in confidence. In fact, there are some factors that are effect on the ground surface settlement which among; the geometry of tunnel (depth and diameter of the tunnel), tunnel construction method including; types of excavation and construction stages, and soil properties such as; poisson's ratio, friction angle, lateral earth pressure and ground water conditions. Therefore, most of empirical methods didn't take into consideration the effect of these parameters that play an important role in decision making for the proper selection of calculate the surface settlement.

Figure 14. Transverse settlement trough of the ground surface
In the area close to the tunnel axis (−25 < x < 25 m), about 2.6 times of the excavation diameter, the theoretical results for Sagaseta, Oeto and Mair methods are larger than the measured result with an average value of about 3.00 mm, which means the theoretical prediction slightly overvalue the eventual surface settlement. The overvalues of theoretical results could be treated as the safety margin in a sensible way. In the area far away from the tunnel axis (x < −25 m and x > 25 m), the theoretical result is almost equal the measured result, which means the theoretical prediction slightly underestimates the eventual surface settlement. As all the measured results are smaller than 3.00 mm, the influence of the underestimation could be well accepted in the tunneling construction.

Conclusions
During the design and construction of the tunnels in urban areas, it is very necessary to predict the surface settlement to control the tunneling construction on an adjacent structure. Despite of unsuitability of the empirical methods for all different soil conditions and all variable site circumstances to calculate the ground surface displacements due to tunneling. However, it is preferable to using these methods for estimation of ground surface settlement due to tunnel construction are relatively simple procedures that are very often used in practice. They provide very good results when tunneling conditions are well known, i.e. when design parameters and soil calculation parameters are adequately calibrated. Main conclusions which could be deduced from the study performed, are listed below:  The main advantage of using the theoretical methods that it can be used easily for different soil, where it just needs to substitute directly in the equation instead of using any charts.
 Good convergence in results for Oteo and Mair methods comparing with the field measurements where the maximum surface settlement ranges from 10.55-11.95 mm, respectively.
 A marginal agreement in results for Limanov's method comparing with the field measurements where the maximum surface settlement is 16.78 mm. Finally, there are many factors that influence on the results accuracy such as; soil parameters and construction stages especially the loading and unloading behavior of soil that must be taken into account to measure the surface settlement. This paper presents the details of the project and monitoring results field and laboratory geotechnical investigations in order to determine the soil properties, which play a critical key role in the accuracy of results. Consequently, by numerical simulation the effects of tunneling construction on surface settlement and piles foundation are the scope of interest for future research.

Funding
The publishing of this paper is financially supported by the National Natural Science Foundation of China (No. 11672215).

Conflicts of Interest
The authors declare no conflict of interest.