ORIGINAL PAPER

Subsidence Due to Groundwater Leakage into Tunnels

Vikas Thakur

Received: 18 June 2011 / Accepted: 7 January 2012 / Published online: 5 April 2012

� Indian Geotechnical Society 2012

Abstract When rock tunnels are constructed under pop-

ulated areas, additional geotechnical challenges that could

often be met are ground subsidence due to groundwater

leakage into the tunnels. The effect of such subsidence is a

serious issue with regard to the infrastructures built around

the tunnel areas. Subsidence analysis as adopted, today, for

various transportation projects is based on classical con-

solidation theory. The increase in effective stress, which

comes from groundwater-lowering, is assumed to induce

an equivalent excess pore pressure that results in consoli-

dation settlement. The settlements are then computed based

on the classical theory of one-dimensional consolidation.

However, in the particular type of problem, the total

stresses in soil remains practically unchanged throughout

the subsidence process. Therefore, excess pore pressure is

not expected to be generated. In other words, the classical

theory of primary consolidation alone under-predicts the

subsidence. A real case example, the Hommelvik tunnel,

from Norway is considered in this study to elaborate this.

The paper presents subsidence data gathered during the

past 20 years from representative locations at the tunnel

site. The results show that the area has been subjected to

larger subsidence than expected. This paper emphasizes the

importance of prediction and instrumentations to under-

stand resulting subsidence over a large area due to tunnel

construction. The results obtained from the finite element

(FE) analyses are discussed in light of these measured data

and background assumptions. FE analysis using a soft soil

creep model is seen to give a very promising framework to

analyse such problems. This particular study calls for a

better subsidence prediction procedure using a framework

that also considers the effect of creep.

Keywords Groundwater leakage �Subsidence measurement � Tunnels � Creep �Finite element modelling

Introduction

When rock tunnels are constructed under populated areas,

additional geotechnical challenges that could often be met

are ground subsidence due to groundwater (GW) leakage

into the tunnels. When GW leaks into a rock tunnel overlain

by marine clay deposits or compressible sediments, it can

cause a significant reduction in the pore pressure and induced

settlements in the sediments. The subsidence associated with

such pore pressure reduction could be significant especially

in areas where there are reasonably thick layers of soft

compressible clays overlaying the tunnels. The immediate

effect of such subsidence is a serious issue with regard to

houses situated around the tunnel areas. These subsidences

are mainly results of an increase in effective stress, due to

reduction of excess pore pressure, over a certain period of

time. In addition, due to change in effective stress, the soil

exhibits higher tendency to undergo time-dependent subsi-

dence. Hence, stress and time-dependent settlements are

expected to be induced due to the associated changes.

The Norwegian Public Roads Administration (NPRA)

report 103 published in 2003 suggests two alternative

mechanisms associated with GW leakage into tunnels.

Accordingly, a change in the pore pressure profile over a

certain period may occur in two different ways as shown in

Fig. 1a and b. Figure 1a shows a hypothetical situation

where the GW level has reduced hydrostatically. This also

V. Thakur (&)

Geotechnical and Landslide Division, Norwegian Directorate of

Roads, Trondheim, Norway

e-mail: vikas.thakur@vegvesen.no

123

Indian Geotech J (January–March 2012) 42(1):37–48

DOI 10.1007/s40098-012-0001-y

implies that changes in the effective stresses are uniform

along with depth. Another way is a gradual reduction of pore

pressure at the bottom of a soil layer due to drainage towards

the tunnel. This drainage is possible through open fractures

created by the tunnel construction. This process is illustrated

in Fig. 1b. In this particular type of pore pressure reduction,

the GW level at the top remains unchanged whereas the pore

pressure lowers at the bottom of the layer. Experiences from

various tunnels in Norway suggest a combination of alter-

native 1 and 2 as the more likely scenario.

The NPRA report also presents some data, from different

tunnels constructed in Norway, regarding pore pressure

reduction over and around the tunnels, see Fig. 1c. Measure-

ments shown in the figure suggests that there is a correlation

between the groundwater-lowering (GWL) and the distance

from the tunnel. Hence, large GWL results in large influence

area. For instance, NSB Abelhaugen had a maximum GWL of

13 m, and this resulted in 4 m GWL in about 450 m away

from the tunnel. Additional factors which influence GWL are

the natural GW flow patterns, local topography, soil perme-

ability in horizontal and vertical directions, the rock fractures

and thickness of overlying clay layers.

In this work, GW leakage induced subsidence is studied

using a real case example, the Hommelvik tunnel, from

Norway. The paper is divided into two parts; the first part

of the study, presents detailed engineering characterization

of the areas surrounding the Hommelvik tunnel. It also

presents subsidence data gathered during the past 20 years

from several locations at the tunnel site. This second part of

the paper focuses on numerical analyses of measured

subsidence and future predictions according to a guideline

by NPRA and using a FE tool.

Part I: Case Description of the Hommelvik Tunnel

Case Description

The Hommelvik tunnel is located about 30 km east of

Trondheim, Norway. The tunnel was constructed in 1989.

The Hommelvik tunnel is a rock tunnel which was con-

structed under 10–12 m thick marine clay deposits. Today

this tunnel constitutes one of the most important elements

of the surface transportation between Trondheim city and

the Vaernes international airport. The Hommelvik tunnel is

located under an urban area. Around 48 houses exist in the

vicinity of the tunnel, of which 15 are constructed on clay

deposits, 21 on rocks and the remaining 12 houses on

combined ground conditions. Figure 2 shows an overview

of the location of the tunnel and its surroundings.

Prior to the construction, settlement gauges were

installed under several houses to monitor possible subsi-

dence effects. To assess differential settlements several

settlement gauges were installed on each house. Figure 2

shows some of the houses where subsidence have been

monitored. The locations for pore pressure measurements,

Fig. 1 a GW lowering (GWL)

and pore pressure reduction due

to leakage (Alternative 1).

b Pore pressure reduction due to

leakage without GWL

(Alternative 2). c GWL with

respect to the distance from a

tunnel

38 V. Thakur

123

Hull 13 and Hull 16, are also shown in the same figure.

Subsidence measurements gathered since 1989 shows that

subsidence are in between 35 and 150 mm. Some parts of

the area are still under continuous subsidence. The mea-

surements show that the houses founded on clay deposits

experienced the largest subsidence; whereas, the houses

partly founded on the clay deposit and partly on the rock

surface have suffered severe differential settlements. The

Hommelvik tunnel resulted in about 5 m of GWL.

According to Fig. 1c, this may induce subsidence between

200 and 450 m away from the tunnel.

Site Characterization

An extensive ground investigation around the tunnel areas

was carried out by NPRA in 1988 [8]. The investigation

consisted of 23 soundings, total 21 54-mm diameter sam-

ples from the different locations, and pore pressure mea-

surement at the locations shown in Fig. 2. A typical

laboratory results for Hull 13 is presented in Fig. 3. The

Hommelvik tunnel is located under 10–15 m thick marine

clay deposit. Table 1 shows representative soil properties

taken from the tunnel area.

Predicted Subsidence

Subsidence induced due to the tunnel construction was

predicted a priori. Figure 4 shows that the predicted sub-

sidence is directly dependent on the thickness of com-

pressible layers (H) as well as the GWL. The worst case

scenario occurs if the GW table is lowered to the bottom of

the draining clay layer. In such a scenario the subsidence

that may occur due to GWL, i.e. due to increase in effective

stress, are presented in Fig. 3. This was calculated, using

the equation proposed by Janbu [6].

d ¼ZH

0

1

M� ln p0o þ Dp

p0cdH ð1Þ

M ¼ m � pap0

pa

� �1�n

ð2Þ

where M is the deformation modulus; m is Janbu’s modulus

number; po0 is the initial vertical effective stress; Dp is the

additional stress due to GWL; pc0 is the preconsolidation

pressure; pa is reference pressure (100 kPa); p0 is vertical

effective stress and n = 1 for clays.

Fig. 2 Overview of the

Hommelvik tunnel

Subsidence Due to Groundwater Leakage into Tunnels 39

123

From experience on such clays, the creep rate was

assumed to be 10–20 mm/year for first two years and

5 mm/year for next ten years. The total creep induced

subsidence in the first ten years was expected to be as much

as the consolidation induced subsidence in first two years.

Predictions given in Table 2 were made with respect to

creep subsidence on the area during the first ten years.

Based on the subsidence evaluation it was concluded

that total 23 houses are expected to get high subsidence risk

Fig. 3 Results from a typical routine tests [Hull 13], FCR Fall cone test in remoulded soil, FCI Fall cone test in intact soil and UU unconfined

compression test

Table 1 Soil properties around the Hommelvik tunnel

Depth

H (m)

Water

content

w (%)

Undrained

shear

strength

Cu (kPa)

Coefficient

of consoli-

dation

Cv (m2/year)

Odometer

modulus

M (MPa)

Over

consolidation

ratio

OCR

0–2 0–20 80–100 20–50 10–20 [2

2–15 30–40 20–30 10–30 3.5–5.0 1.8

Fig. 4 (Left) Predicted subsidence under the full drainage condition

related to the thickness of the compressible layer. Original GW level

is assumed to be at 1 m. (Right). Predicted Subsidence due to the GW

lowering in a 10 m thick marine deposit having original GW level at

1 m below the terrain level. Here M is the odometer modulus, Alt. 1

refers to the hydrostatic pore pressure reduction, and Alt. 2 refers to a

full drainage condition at the bottom of the clay layer

40 V. Thakur

123

whereas the remaining 25 houses will either have low or no

subsidence risk.

Measured Subsidence and Discussion

Immediately after construction of the Hommelvik tunnel,

significant pore pressure reductions as well as subsidence

were recorded. The maximum pore pressure reduction, was

up to 60 kPa at Hull 16, which is on average equivalent to a

3 m GWL with hydrostatic conditions. The immediate

subsidence recorded on the area was around 50 mm, see

Fig. 5. The figure shows pore pressure readings for Hull 16

(depth 15.2 m) and Hull 13 (depth 4.3 m and 7.6 m) along

with the observed subsidence from 1988 to 1992. An effort

was made to stop the subsidence process using a water

infiltration technique. From Fig. 5, it can be observed that

the water infiltration technique was implied twice, first

time for 6 months somewhere at a depth of 10–15 m,

whereas the second time the water infiltration was made at

a depth of 5 m from the surface. The pore pressure increase

due to the infiltration was in the range of 50–70 kPa. Lower

part of Fig. 5 also shows that the water infiltration has very

little impact on stopping the undergoing subsidence.

This may be due to the fact that the pore pressure

increase over the area was unfavourable. For example, after

the first water injection the recorded pore pressure was 80

to 100 kPa at Hull 13 at depth 7.6 m, this is significantly

higher compared to the original pore pressure of 50 kPa at

similar depth. This also implies that clay at this depth was

60–100% above the hydrostatic pressure and effective

stress is reduced by the same proportion. The same has

been observed at 4.6 m depth for Hull 13 after the second

infiltration. Such a high reduction in the effective stresses

might have aggravated the subsidence process once the

water injection is stopped.

At present, subsidence measurements are being moni-

tored at 28 locations over the Hommelvik tunnel area. In this

paper, some representative results are presented. Some of the

locations were instrumented with more than one settlement

gauge to observe the differential settlement. Subsidence

measurements for four house locations shown in Fig. 6 are

presented in Table 3. The magnitudes of the normalized

measured subsidence (ratio of measured subsidence to clay

layer thickness) for locations A, B and C seem to be inversely

proportional to the distance from the tunnel. This response is

according to the Fig. 1. However, locations D does not show

similar trend. This is mainly believed to be because of the

fact that house D is located in a different topography than

other houses A, B and C. In addition to the complex topog-

raphy, the amount of GWL and variation in the soil proper-

ties could affect subsidence measurements at house D.

The influence zone where the subsidence is observed is

up to 400 m from the tunnel, this is in accordance to Fig. 1.

Table 2 Expected creep subsidence

Creep subsidence (mm) GWL (m)

\50 3–4

50–100 5–6

Up to 20 6

Fig. 5 Pore pressure and the

subsidence reading for house B

Subsidence Due to Groundwater Leakage into Tunnels 41

123

However, only a few millimeters of subsidence are noticed

on the houses which are located more than 250 m away

from the tunnel. The pore pressure data showed that the

equivalent GWL due to the tunnel construction was around

3.0 m at a distance of 50 m from the tunnel. For such case,

the preliminary investigation report [9] predicted a

subsidence of around 60 mm (Fig. 4). However, the mea-

surements (Fig. 6) are seen to be significantly higher than

the predictions. In addition, the subsidence measurements

indicate no sign of slowing down. The differential settle-

ments on the houses are also significant and tend to

increase with time. New sets of pore pressure and

Fig. 6 Measured subsidence at location B (ref. Fig. 2)

42 V. Thakur

123

subsidence readings will be made in 2011. As per now the

data is not received by the authors of the paper. This par-

ticular case lacked an in-depth investigation of GWL

induced creep subsidence analysis. A better prediction and

corresponding mitigation would have helped in minimizing

damages on the surrounding houses. In fact, guideline 103

by NPRA [9] mainly focuses on prediction of subsidence

due to the consolidation process, but the creep induced

subsidence is not discussed. Perhaps, the Hommelvik tun-

nel may serve as a reference case for further modifications

in the practice.

Part II: Numerical Modelling

This part of the paper aims to numerically analyse mea-

sured subsidence, in Hommelvik area, using two approa-

ches. The first approach is taken from the guidelines by the

NPRA. This approach is also adopted by the practitioners

all over the globe. In the second approach, the subsidence

is analysed using a simplified procedure in an FE tool by

taking into account creep effects. The two ways of analyses

are discussed in light of measured data and their back-

ground assumptions. Subsidence prediction and sensitivity

analyses are also presented in this section.

Idealization of GWL

An FE code Plaxis 2D version 9.0 was used to analyse

subsidence in Hommelvik tunnel area. Ideally such prob-

lem should have been modelled by taking into account

several effects such as 3D geometry with a fully coupled

flow deformation analysis. However, the aim of this anal-

ysis is to provide an insight towards modelling of such

problems with reasonable simplifications.

The idealization of the FE model and the mechanisms

are assumed to be in accordance to the NPRA guideline

[9]. In the NPRA guideline, it is indicated that tunnel

construction could induce subsidence as a result of pore

pressure reduction. For FE analysis, this case is idealized as

shown in Fig. 7. Measurements showed that, the tunnel

construction resulted in pore pressure being under-hydro-

static condition. However, this condition is assumed to

come to equilibrium condition over time and result in a

hydrostatic condition with lowered groundwater table

(GWT). In Fig. 7, the dotted lines are the measured pore

pressure profiles while the solid lines represent the initial

and final pore pressure profiles. The effect of groundwater

lowering (GWL) will introduce an increase in effective

stress increment which will induce subsidence. The pore

pressure profile measured in Day 707 is converted into an

equivalent pore pressure profile with a hydrostatic distri-

bution. This gave an equivalent GWL of 3.0 m. During the

Hommelvik tunnel construction, a water injection proce-

dure was attempted in order to increase the pore pressure to

reduce subsidence. However, it was seen that the effect of

water injection on subsidence was minor [14]. In addition,

after water injection was ceased the pore pressure profile

was seen to come to its initial state, i.e. before the water

injection procedure was applied. Hence, this effect is not

considered in this analysis. The pore pressure profile

reduction before water injection is assumed to be repre-

sented by an equivalent GWT as shown in Fig. 7.

The initial GWT was located round a depth of 2.2 m and

the pore pressure measurement was conducted at a hori-

zontal distance of 52 m from the tunnel. From visual

observations it was seen that there were some leakages

toward the tunnel and this was assumed to be counter

balanced by infiltrations. It must be noted that if the GWT

is raised then the soil will be unloaded and this will result

in low subsidence rate and heaving. In this study, only the

case of GWL is considered as this would represent the

worst case scenario in predicting subsidence. In addition,

subsidence measurements indicated that this could be the

case.

Table 3 Measured subsidence as a function of the thickness of clay

layer and the distance from the tunnel

Location Clay

layer

(m)

Distance

from the

tunnel (m)

Measured

maximum

subsidence

(mm)

Normalized

subsidence (910-3)

[subsidence/

clay layer]

A 11.8 80 80 6.7

B 15.3 50 150 9.8

C 13 125 31 2.5

D 7.6 40 33 4.3

0

2

4

6

8

10

12

14

0 50 100 150

Dep

th [m

]

Pore pressure [kPa]

Original GWT

Assumed f inal GWT

Fig. 7 Idealization of GWL for FE analyses

Subsidence Due to Groundwater Leakage into Tunnels 43

123

Approach One: Subsidence Analysis According

to the Current Practice

The main assumptions adopted in NPRA [9], to analyse

subsidence, are briefly presented. The increase in effective

stress due to groundwater leakage is assumed to induce an

equivalent excess pore pressure increase that results in a

consolidation settlement. The settlements are then com-

puted based on the classical one-dimensional consolidation

theory. Accordingly, a complete subsidence shall occur

over a time period, tp, defined by H2/Cv. The amount of

subsidence is then assumed to directly depend on the

amount of GWL. The NPRA procedure is illustrated by

analyzing a 15 m thick normally consolidated clay layer

having Cv = 25 m2/year and m = 20. Here, m is the

modulus number as defined by Janbu [6]. Calculated sub-

sidence histories, due to equivalent pore pressure reduction

of 10, 20 and 30 kPa, are shown in Fig. 8. It can be seen

that the amount of subsidence is proportional to the

reduction of pore pressure. However, the calculated sub-

sidence occurs only within the first 6 years regardless of

the magnitude of pore pressure reduction. This also means

that, the subsidence shall remain constant after 6 years.

Accordingly, the maximum final subsidence predicted for

pore pressure reduction of 10, 20 and 30 kPa are 33, 64 and

94 mm, respectively.

A comparison between the predicted subsidence (for an

equivalent pore pressure reduction of 30 kPa) and mea-

surement is presented in Fig. 9. Further discussion on the

approach and its background assumptions are presented

later in this paper.

Approach 2: FE Modelling

Geometry and the Soil Model Adopted for the Analysis

The study is made with respect to measurement discussed

in earlier. A one dimensional oedometer condition is con-

sidered. The thickness of the clay layer considered for the

analysis is 15.30 m. An axisymmetric model with very fine

mesh, consisting of 15 node triangular elements, is

adopted.

Measurements showed that subsidence continue even in

the locations where the GWL is expected to be minimal.

This is considered to be effect of creep. Besides, the soil in

the tunnel area is characterized by its strong tendency to

undergo deformation due to change of effective stress as

well as time. Hence, the soil model selected for analysis is

the soft soil creep (SSC) model [1, 10, 11]. The SSC model

is implemented, as a standard model, in Plaxis. The SSC is

formulated based on early works by researchers working on

creep [2, 5, 12, 13]. Accordingly, the SSC model assumes a

creep rate to be given by the current effective stress and the

current void ratio (strain). In other words, any combination

of void ratio (strain), effective stress and rate of change of

void ratio (strain rate) is considered to be unique

throughout primary and secondary consolidation phases.

Such formulation is refereed as isotache concept. An iso-

tache is a line defining a constant creep rate.

All stress states are expressed by an equivalent isotropic

(mean) stress measure, peq. The SSC model assumes that

strains come either from change in stress (elastic strains) or

from time effects (creep strains). The mechanism of sub-

sidence in light of isotache concept is illustrated in with the

help of Fig. 10. In the figure, s refers to intrinsic time

corresponding to a specific isotache, _ecv ¼ l�=s.

In Fig. 10, consider an initial soil state of a soil given by

point A. Assuming a pore pressure reduction to result in an

incremental mean effective stress of Dpeq, as shown in

Fig. 8 Calculated subsidence due to equivalent pore pressure reduc-

tion of 10, 20 or 30 kPa

Fig. 9 Measured subsidence as compared to subsidence predicted

according to NPRA guidelines

44 V. Thakur

123

Fig. 10, the resulting subsidence involves two strain com-

ponents. The first part of strain comes from change in

effective stress, eev, and the second one comes from creep

ecv: From the figure it can be noted that an effective stress

increment, Dpeq, results in subsidence to continue at higher

creep rate, _ecv (i.e. corresponding to s3) than when the soil

state was at point A which corresponds to s4.

Model Parameters

Based on the soil parameters presented in Table 4, the soil

can be characterized with two layers. The top 2 m is a dry

crust. The GWT is located at 2.2 m and the soil layer which

is subjected to effective stress change is the layer from 2.2

to 15.3 m. Two incremental oedometer tests have been

conducted within this depth, i.e. 3.7 m and 7.45 m. The

tests indicate that the soil to be characterized by

l*/k* = 0.04. This ratio of l*/k* lies within the range for

soft clays which is 0.03–0.06 [7]. In this study, a uniform

soil layer is considered since the dry crust is not subjected

to a change in effective stress resulting from GWL. The

input parameters adopted for SSC model are given in

Table 4.

The symbols in Table 4 represent the following SSC

parameters. kv is the vertical permeability of the soil; OCR

(over consolidation ratio) is defined as the ratio of pre-

consolidation stress to initial effective stress; j* (the

modified swelling index), k* (the modified compression

index) and l* (the modified creep index) are defined in

Fig. 10.

Calculation Procedures

Settlement gages were installed on foundation of 27

houses, in 25 August 1988, before construction of the

tunnel. To be able to compare simulation results with

measurements, three calculation phases are considered.

The first phase is to simulate the condition before the

construction of the tunnel, i.e. from 25/08/88 to 01/11/89.

In this calculation phase, the soil creeps at its initial creep

rate. The second calculation phase is to simulate the GWL

as per the idealization of NPRA guidelines discussed ear-

lier. The GWT was lowered by 3.0 m within 345 days, i.e.

from 01/11/89 to 15/07/90. The third calculation phase is a

pure creep phase where the soil creeps at a relatively higher

creep rate due to the effective stress change. This phase

runs from 15/07/90 when the lowered GWT was assumed

to stabilize till the end of measurement, i.e. 30/06/06.

Another set of analyses were also carried out. In this

analysis, one calculation phase is defined that simulate only

a creep phase from 25/08/88 to 30/06/06 without change in

pore pressure profiles. This analysis is done, in order to

separate the effect of subsidence that is solely due to GWL.

FE Results

The analysis result is presented along with subsidence

measurements which were considered to be critical. The

starting time in Fig. 11 corresponds to a date of 25/08/88.

In accordance, to Fig. 10, construction of house could have

affected the initial creep rate of the soil beneath the houses.

In the analysis, this effect is considered to be negligible. In

addition, water injection effects shall result in decrease in

effective stress leading to possible unloading and creep at

reduced rate. The effect of water injection is not also

considered. Due to such simplifications, analysis results

should not be compared directly with measurements.

Hence, the predictions are separately presented (Fig. 11b)

along with subsidence measurements (Fig. 11a).

As shown in Fig. 11, the analysis result is in fairly good

agreement with the measured subsidence despite the sim-

plifications adopted in the analysis. It is seen that with only

creep effect, the subsidence is insignificant. However,

when GWL along with creep effect is taken into account,

the resulting subsidence becomes significant and the creep

deformation with a creep rate that gradually decreases with

Fig. 10 Illustration of subsidence with the isotache concept as

implemented in SSC model

Table 4 SSC model input parameters

c (kN/m3) kv (m/day) j* k* l* OCR

20 2.4e-4 0.009 0.083 0.0033 1.70

Subsidence Due to Groundwater Leakage into Tunnels 45

123

progress of time. Hence, the overall predicted subsidence is

in accordance to the measurements.

Prediction of Further Subsidence

Assuming that the calculated subsidence is representative of

the measured subsidence history and the current conditions

to remain unchanged, the next interesting step would be

predict future subsidence. The analysis and measurements in

Fig. 11, are shown for the first 18 years. This simulation is

continued for another 32 years, giving the settlement history

of 50 years, Fig. 12. Accordingly, the expected subsidence,

within the next 32 years, is 50 mm. The settlement rate at the

end of simulation is given by approximately 1.5 mm/year.

This is lower than the creep rate predicted in 30/06/06 which

was approximately 5.4 mm/year.

Variations in GWL

The measurements shown in Fig. 11a are taken close to the

borehole where the pore pressure profile was monitored, as

shown in Fig. 2 and 7. However, this GWL may not be

representative of the whole area since the GWL is expected

to vary with distance from the leakage area in the tunnel

[4, 14].

In order to provide an insight to subsidence in areas

where GWL is less pronounced, sensitivity analysis is

performed. As in the previous analysis, the same set of

input parameters, FE geometry and analysis procedure is

adopted. However, the GWL is varied from 0 to 3.5 m. The

result of this sensitivity analysis is presented in Fig. 13.

Discussion and Closing Remarks

Subsidence analysis as adopted by NPRA [9] is based on

classical consolidation theory. However, in the particular

case studied in this paper, the total stresses (Dr) in soil

remains practically unchanged throughout the subsidence

Fig. 11 a Subsidence measurements versus b simulation

Fig. 12 Analysis for 50 years of subsidence history

Fig. 13 Sensitivity/parametric study of variations in GWL (The

numbers represent the GWL)

46 V. Thakur

123

process. Therefore, excess pore pressure (Du) is not

expected to be generated. In other words, subsidence cal-

culation based on the consolidation theory, as in approach

one, is not applicable for such type of problem. A simpli-

fied conceptual model on this is show in Fig. 14. Accord-

ingly, the total subsidence shall be due to the increase in

effective stress and due to creep settlement.

In the problem considered in this study, the changing GWT

is fully coupled process along with the resulting time- and

stress-dependent deformations. This demands a finite element

code that can handle full coupling of flow and deformations.

To simulate a condition where the flow and deformations are

fully coupled, then the consolidation has to be formulated

based on total pore pressures. In the current Plaxis version,

deformation is coupled with excess pore pressure and for cases

where flow problems needs to be studied, the standard Plaxis

program is used along with another program PlaxFlow.

However, this is also subjected to some limitations and does

not provide a true coupling between flow and deformation.

Hence, ideal way would have been to use such analysis pro-

cedure. However, Plaxis is yet to release a new version where

full coupling between flow and deformation is possible [3]. In

this study, in order to get rough estimates the current Plaxis

version is used by manually changing the pore pressure pro-

files. Such procedure is shown to give reasonable predictions

as compared to measurements.

The subsidence calculation using the SSC model con-

siders two subsidence components, i.e. due to increase in

effective stress as well as due to creep at higher creep rate.

Several simplifications, discussed in the paper, are adopted

in the analyses that could influence the results. Still, the FE

analysis is seen to give a very promising framework to

analyse such problems. Better problem definition and

considerations would further improve accuracy of subsi-

dence analysis. This particular study calls for a better

subsidence prediction procedure using a framework that

also considers effect of creep.

Closing Remarks

This paper presents a lesson about how severe subsidence

may occur due to pore pressure lowering induced subsi-

dence. The paper emphasized the importance of prediction

and instrumentation to understand resulting subsidence over

a large area due to tunnel construction. Predictions made

prior to the construction of the tunnel were seen to under-

estimate measured subsidence. Moreover, subsidence are

seen to continue with time and this calls for a better pre-

diction tool that considers time effects as well as modifi-

cations on the current code of practice in Norway. The

subsidence calculation using the SSC model in Plaxis

considers two subsidence components, i.e. due to increase

in effective stress as well as due to creep at higher creep

rate. Several simplifications, discussed in the paper, are

adopted in the analyses that could influence the results. Still,

the FE analysis is seen to give a very promising framework

to analyse such problems. Better problem definition and

considerations would further improve accuracy of subsi-

dence analysis. This particular study calls for a better sub-

sidence prediction procedure using a framework that also

considers effect of creep. This study is in on-going.

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Fig. 14 Conceptual model on mechanism of subsidence

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