The prediction of settlements induced by conventional tunnel excavation on the Üsküdar – Ümraniye – Çekmeköy (UUC) metro project in Istanbul was a great challenge from the start of works.

In any urban tunnelling process, surface settlement estimation becomes a crucial part of the project for assessing the risk of damage to the existing buildings and proposing, whether it is required, specific ground treatments or protective measures to avoid or minimise them, as well application of proper excavation methods.

Due to the number of buildings along the UUC alignment, a systematic and practical approach to estimate the ground movements induced by conventional tunneling in weak rock was adopted.

Project description
The UUC metro line is an underground link running beneath a very dense urban area at the Asian side of Istanbul beginning at Üsküdar Station, which connects to the recently opened Marmaray submerged railway link, and ends at Çekmeköy Station. The line is approximately 17km long, and includes the construction of running twin tunnels, cross passages every 250m, several crossovers along the alignment and 16 underground stations.

The twin running tunnels are excavated with two EPBMs in some stretches and with conventional methods used for crossovers. A mixture of mining and cut and cover methods are used for the construction of the 16 stations, cross passages and crossovers are excavated with conventional methods as well, the latter with large tunnel sections with an excavation area of approximately 120m2.

The overburden along the alignment ranges between 20 to 40m, with minimum at the beginning of the line, at Üsküdar station, with 13m, and maximum of 80m, where the tunnels underpass a hill relief, whose peak reaches the +189.0 elevation.

The prevalent geology along the UUC line is formed by weak to medium strong sedimentary rocks belonging to the Paleozoic and Cenozoic era (i.e. limestone, claystone, sandstone).

At specific areas the excavation is performed within weathered terms, at fault zones or in sandy-clayey alluvial quaternary deposits.

Along the initial sector of the alignment the tunnels are excavated through claystone-sandstone formations (3.5km). A second stretch is basically formed by limestone and conglomerate (4km) and then by intercalation of mudstone-claystone and Arkosic sandstone (5.7km). In the last kilometers, the tunnels are excavated within sandyclayey soil and limestone (3.7km). Along the alignment several faults are being intercepted as were identified in the geotechnical campaign.

The rock mass quality, defined in the GBR, varies basically from poor to good rock mass, with RMR from 30 to 70, although lower values are expected at the faults zones.

In terms of hydrogeology, the investigations indicated that the encountered geological formations show low to very low permeability (from 10-6 to 10-8m/s). Despite that, it is noticeable that the lithologies are also characterised by secondary permeability because of the high rate of weathering and fracturing, and low water inflows are actually occurring (recorded water inflows < 5 l/s through tunnel face).

Sections types
Eleven different mining sections were designed for the UUC project for running, platform and crossovers tunnels. The geometry of the mining sections was defined with an optimal polycentric section in regards of the required tunnel clearance (see Figure 1).

The main tunnels sections along the alignment are the platform tunnels excavated at the stations (75.6m2 excavation area), the running tunnels excavated for the main line (36.8m2) and the crossover tunnels which are enlarged sections (119.6m2).

Five classes of support were designed for each section type according to the geomechanical conditions in terms of RMR. On site, depending on the encountered rock mass condition the adequate support type is installed. The difference between the classes of support remains on the shotcrete thickness, lattice girder dimension and spacing, number and length of crown bolts and spilling or pipe umbrella installation.

Final lining
A cast in situ lining is always applied at mining sections after the installation of a waterproofing system consisting in a geotextile and a PVC membrane. The thickness of the final lining was determined according to the section area. Three types of final lining reinforcement were designed according to the rock mass quality.

Settlements prediction
The tunnels of the UUC are excavated underneath a very populated area of the Üsküdar municipality, at the Asian side of Istanbul. More than 3000 buildings were surveyed before commencing the works, located within 50m at both sides of tunnel axis. Actually, the tunnelling influence zone was defined in the UUC Technical Specifications as the zone where the settlements are expected to be greater than 10mm. After the first prediction of the tunnelling settlements, the maximum influence zone width was 80m, which is lower than the 100m of the initial surveyed area.

The prediction of induced movements is a very crucial process of the project since it enables the identification of the stretches where the maximum settlements are expected, and consequently analyse the possible damage to the existing buildings and structures.

Due to the extension of the project, the variability of tunnels size, and the different geotechnical conditions, a systematic analysis approach was conceived at the beginning of the works to habilitate the settlements prediction task.

The procedure consists of the definition of a formula and the estimation of the input parameters to compute the settlement basin. The adopted expression for the calculation of vertical ground movement was the semi empirical normal distribution curve, and its input parameters were defined according to the available geometrical and geotechnical information, general references and complementary computations (e.g. the convergence-confinement method).

Peck curve adoption

The semi empirical method to estimate the surface settlements in the UUC project was based on the Peck approach that assumes a Gaussian curve for vertical ground movements in soft ground.

This method for calculating transversal settlements was firstly described by Peck in 1969, who proposed that the shape of the settlement through could be well represented by a normal distribution curve.

Later on, a Gaussian model was developed considering that the ground loss could be represented by a radial flow of material to the tunnel and the trough could be related to the ground conditions through an empirical width parameter (BTS/ ICE, 2004).

Therefore, several semi empirical equations were developed based on soil excavation case studies giving a suitable procedure of the surface settlements behavior.

The vertical settlement formula adopted in the UUC project is a Gauss distribution in accordance to the equation (1):

equation (1)

S(x) is the settlement at x distance from the tunnel axis; Smax is the maximum settlement at tunnel axis, expressed as:

equation (2):

Vs is the volume of the settlement trough per unit length of tunnel and VL is the ground loss, which is the volume of soil excavated in excess of the theoretical volume of the tunnel (see Figure 2). These two volumes are considered equal for shallow tunnels in cohesive and incompressible ground formations, as in the UUC project (ITA/AITES, 2006).

i is the distance of the inflexion point to the tunnel axis. It can be calculated as i = Z0K. With Z0 being the depth of the tunnel axis and K the trough width parameter.

The use of semi empirical methods, such as the Gaussian curve, based on soil settlements was considered applicable in this project although the tunnels were excavated through weak to medium strong rock. Nevertheless, in the ‘Back Analysis’ part of this paper, the applicability of the Gaussian curve in the UUC weak rock is validated.

Trough width K parameter
The empirical K parameter describes the settlement basin width and depends on the geotechnical characteristics of the ground, the tunnel depth and, in some cases, excavation method. Following the research from O’Reilly and New (Aoyagi, 1995) the K parameter can be estimated depending on the tunnel depth (Z0) and the cohesion of the soil as:

equation (3-4)

Similarly, other studies reveal that the K parameter varies from 0.2 to 0.3 in granular soils and from 0.4 to 0.5 in stiff clayey soils and even reach 0.7 for very soft silty clays (Burland, 2008).

Taking into account the rocky nature and frictional behavior of the excavated geological formations along the UUC tunnels, the adopted K parameter was calculated from the tunnel depth using equation (4), which corresponds to the cohesive soils formula. Taking into account the minimum and maximum overburden of the UUC alignment, 13m and 80m respectively, the estimated K parameter varies from 0.495 to 0.443.

Volume loss estimation
The cause of the settlement is the volume loss generated due to excavation, which mainly depends on the geological formations and their stress state, excavation rates, tunnel size and installed support type. Hence, the adopted conventional construction methods were designed to minimise the volume loss during excavation.

The volume loss, VL is commonly defined as the percentage of the volume of ground excavated in excess to the theoretical tunnel volume divided by the theoretical tunnel volume, as per equation (5):

equation (5)

In the UUC project the expected volume loss for the settlement curves computation was systematically and quickly estimated with the convergence-confinement method. The result of the convergence-confinement method is the radial tunnel deformation which easily allows the computation of the volume loss.

The convergence-confinement method, also known as the stress-deformation curve, considers the weak rock mass deformability and strength and the installed support capacity and characteristics (AFTES, 2002). An equivalent radius was considered for the mining sections according to their excavation areas.

For each geological stretch of the alignment, two sets of parameters were identified corresponding to the maximum and minimum expected RMR. Thus, two stress-deformation curves could be computed to obtain the tunnel deformation in a favourable and unfavourable scenario at each section.

Consequently, the settlement curve could be defined under favourable and unfavourable conditions, expecting the actual ground movements to fall into these two scenarios.

Settlements curve
In order to describe the applied method for settlement prediction on the UUC project, the computation of the settlement curve at chainage 7+640 is presented, with the corresponding parameters assumptions and estimations.

The section at chainage 7+640 corresponds to two platform tunnels with an equivalent radius of 4.91m each located at Ümraniye station. The average overburden is 22m, identified in the available alignment profile.

Two platform sections with axial distance of 29.1m are excavated and the corresponding settlement curves are summed up. Moreover, from the authors’ experience, twin tunnel reciprocal interference is to be considered in the calculations where the distance between tunnel axes is less than three diameters.

Hence, an increase of 10 per cent to the second tunnel volume loss is considered due to the previous ground relaxation induced by the first tunnel, resulting in an asymmetrical settlement trough.

The adopted K parameter is in this section 0.471, considering equation (4), for 27m of tunnel depth.

The stress-relaxation curve is computed for the geotechnical parameters indicated in the GBR for claystone-mudstone rock mass present at Ümraniye station. The relevant geotechnical properties are summarised in Table 2.

The result of the stress-deformation curves is a radial displacement of 6.4mm and 17.5mm in the favourable and unfavourable scenarios respectively, which brings equivalent volume losses of 0.18 per cent and 0.68 per cent.

Therefore, two different settlements curves can be computed for each rock class, as shown in Figure 3.

The process of volume loss estimation is repeated for every homogeneous stretch of the tunnel with similar geometric and geological conditions, enabling the systematic computation of the settlement curve.

Back analysis
Back analysis is performed on the settlements analysis prediction to refine the K and volume loss parameters and verify the applicability of the Gaussian curve for the overall conditions of UUC project. The back analysis is based on the available monitoring data from the installed transversal section leveling pins along the alignment.

The computed back analysis at four settlement stations with varying geological conditions is presented from here on. The selected stations, together with their geology and actual RMR values are summarised in Table 3.

The computed back analysis at four settlement stations with varying geological conditions is presented from here on.

The platforms are excavated as two tunnel sections (75.6m2 of excavation area) and separated 29.1m. The average tunnel depth along each station has been also considered in the analysis (specifically: 27.7m at Bulgurlu station, 25.6m at Çarsi station, 37.1m at Kisikli station and 26.9m at Ümraniye station). The K parameter has been estimated with the cohesive ground formula (4).

The expected settlement basins computed with the volume losses for the favourable and unfavourable scenarios are plotted together with the recorded ground movements. A Gaussian curve has been fitted to the actual ground movements, which has been compared in shape and depth to the previous estimated settlement troughs (see Figures 4 to 7).

Analysis of the back analysis results
The first conclusion of the back analysis is that the measured ground movements for the four stations follow a settlement shape consistent with a Gaussian distribution. It is noticed that for lower RMR values (worse rock mass condition) this is even more evident, as in Figure 7, where the registered ground movements follow quite precisely a Gaussian curve.

On the other hand, according to the results of the back analysis, the K width parameters calibrated from the monitoring data fitted curve is equivalent to the K parameter estimated with the cohesive soils formula as per equation (4). Hence, the approximation on the K parameter calibration with the cohesive soil expression can be considered fairly successful.

Regarding the calibrated Gauss curve for the four stations, the estimated volume loss using the convergence confinement method gives matching results because the back computed volume loss falls, for all the cases, between the expected limits of the favorable and unfavourable scenario.

At Çarsi station (Figure 6) the excavated volume loss is close to the unfavourable scenario. This might have an explanation, since this station was the first one to be excavated and a learning period could partly be responsible for it.

The calibrated volume loss from the four analysed stations has been plotted together with the recorded RMR values on site from Table 2. From the Figure 8 it can be inferred that the volume loss decreases approximately linearly while the RMR values increase. It is noted that this assumption of linearity is only based on four stations and that further sections should be studied to verify the lineal equation. However, as an estimation method, it can be used for the prediction of the volume loss depending on the RMR values when platform sections are excavated. It could be also interesting to perform the same back analysis with a large tunnel size, for which excavation is not yet completed.

FEM analysis verification
During the systematic prediction approach, for crossover sections (excavation area larger than 100m2) the expected settlements computed using semi empirical methods were verified with 2D FEM analysis.

The tunnel excavation FEM analysis with Plaxis 2D v8 enables the simulation of actual geotechnical conditions, the section geometry, and reproduces the excavation method with the designed tunnel support system.

The results of the analysis carried out simulating the excavation of two crossover sections under fair to poor rock conditions (30<RMR<50) are presented from here on.

The model considers the construction of two crossover sections separated 24.2m, which are excavated in multiple drifts at the top heading and then the benching. The model takes into account the corresponding tunnel support, and the crown and lateral rock bolts installation.

The vertical displacements computed in the FEM analysis can be then compared with the predicted semi empirical settlements and the surface settlements registered from the monitoring. In Figure 9 the vertical displacements basin from the FEM analysis is plotted together with the curve fitted to the monitoring data and the curves from the semi empirical analysis under the favourable and the unfavourable scenario.

The predicted volume loss using the convergence-confinement method and the Peck formula is 0.10 per cent and 0.47 per cent for the favourable and unfavourable scenarios. The K parameter has been calculated with equation (4) for cohesive ground giving a value of 0.468. A Gaussian curve is fitted to the monitoring data with a volume loss of 0.19 per cent and a K=0.468. Thus, the prediction of the settlements induced by the crossover mining sections with semi empirical methods is considered applicable for large sections too.

The FEM analysis confirms the normal distribution of the vertical movements for large mining sections under fair to poor rock conditions. The FEM analysis curve is slightly wider, which means a higher related K value. Thus, to sum up the back analysis and the FEM analysis reveals the good approximation of the settlements predictions with a Gaussian curve in weak to medium rock.

Building damage assessment
The systematic settlements prediction approach is completed in the UUC project with a building risk assessment that analyses the impact of the predicted settlements to the existing buildings and structures.

Basically, three types of damages can occur to buildings, which are defined as: aesthetics, functional or stability. According to these types of damage and its ease of repair, six categories of damages are defined in order to classify the buildings into them. The adopted building risk assessment follows the three stage assessment recommended by Mair (1996). The stage one assessment is based on the predicted settlements curve and the corresponding angular distortion. The computed surface settlements are plotted along the alignment in a plan drawing including the buildings location as in Figure 10. Hence, the predicted settlements for each building are identified.

The stage two assessment is carried out for all the buildings that are in the slight to very severe category of damage in the previous stage one according to the admissible limits from Table 4.

The stage two analysis is based on the calculated maximum tensile strain. The methodology to compute the tensile strain in the buildings follows the commonly implemented equivalent beam analysis (ITA/AITES, 2006) and follows the expression of Burland (Burland et al., 2004). This model represents the building by means of a simple rectangular beam, undergoing sagging and hogging modes of deformation.

This approach easily gives an idea for the mechanisms of cracking and enables the calculation of the critical tensile strain, which is the maximum between the tensile strain due to bending ( b) and the tensile strain due to shear ( d). Figure 11 exemplifies the second stage assessment of the building with reference number S-176 identified with settlements greater than 10mm in Figure 10. The maximum computed tensile strain in hogging is 0.055 (very slight damage) and in sagging is 0.032 (negligible damage) according to the admissible limits of Table 5.

The stage three assessment is carried out for those buildings where the category of damage is expected to range from moderate to very severe in stage two. The use of FEM analysis is considered to simulate the effects of tunnelling to the existing buildings. The accuracy of the calculations gives more precise and reliable settlement and strain predictions. If the results of stage three assessment indicates that the category of damage for the buildings is moderate or higher, protective measures need to be considered.

The defined systematic approach evaluating ground movements has given successful results in the settlement prediction of excavation on UUC. The estimated settlement trough using the semi empirical method has been compared with ground movements from the installed leveling pins, with a back analysis showing fine similarities in shape, width and maximum settlement basin. Hence, although the semi empirical Gaussian theory was conceived for settlement estimation in a continuous and homogeneous soil, its application in weak rock excavation proved to be successful, as in UUC project, with a significant gain in prediction speed and accuracy.

Regarding the systematic approach described in this article, the attempt to narrow down the volume loss with the convergence-confinement method under the favourable and unfavourable geotechnical scenario gives well approximated thresholds since the actual volume loss falls for all the studied sections within these limits. Moreover, the calibrated volume loss from the monitoring data has shown a linear relation with the recorded RMR. Thus, a linear relation from the RMR and the excavated volume loss under the same section geometry has been found out.

This regression can be then used in the systematic approach for the volume loss estimation in other stretches with the same tunnel section according to the expected rock mass conditions.

Finally, the empirical K parameter formula for cohesive soils has been verified and resulted applicable for the weak rock classes encountered along the 17km of the UUC project.