PROBABILISTIC ANALYSIS OF SOIL - DIAPHRAGM WALL FRICTION

USED FOR VALUE ENGINEERING OF DEEP EXCAVATION,

NORTH/SOUTH METRO AMSTERDAM

Stefan M. Buykx1, Steven Delfgaauw

2, Johan W. Bosch

3

1, 2

North/Southline Consultants, Witteveen+Bos, P.O. Box 12205, 1100 AE Amsterdam,

The Netherlands 3

Delft University of Technology, P.O. Box 5048, 2600 GS Delft, The Netherlands

Keywords: diaphragm wall friction, vertical stability of deep excavation, probabilistic analysis

INTRODUCTION

The excavation of deep building pits often requires a check against failure by uplift of low

permeability ground layers below excavation level. Whenever the weight of these soil layers is less

than the pore-water pressure underneath, measures to resist buoyancy are to be considered. The

measures most commonly adopted include: decreasing the water pressure by drainage, anchoring an

underwater concrete slab in the underlying strata or executing the excavation in a pressurised

working chamber.

This paper discusses a case study in which it was shown successfully that side wall friction too can

contribute significantly to the vertical stability of a diaphragm walled deep excavation. The safety

against failure by uplift is demonstrated through probabilistic analysis of all relevant parameters.

The project presented is the top-down constructed, up to 31 m deep building pit of Ceintuurbaan

Station, Amsterdam, The Netherlands. In the deepest excavation stage of this pit the soil weight and

uplift force would not balance. As dewatering or other measures were deemed not feasible, the

deepest part of the excavation and the construction of the bottom slab were initially designed to take

place under compressed-air. However, a considerable reduction of cost and construction time was

achieved after extensive analysis of the friction between soil and diaphragm walls proved that the

pressurised excavation could be limited.

Air

G

P

FGround+Air

≥≥≥≥Pore-pressure

G

P

Ground+Friction

≥≥≥≥Pore-pressure

Value engineering

Figure 1 - Compressed-air or D-wall friction to secure vertical equilibrium

1

Scope

Following an introduction to the project and case study, this paper will comprise in subsequent

sections:

• verification of failure by uplift for a deep excavation

• analysis of diaphragm wall friction, focusing on the calculation of horizontal stresses after

excavation

• value engineering: assessment of the probability of failure by means of Monte Carlo analysis

• observational method: verification of design assumptions through field and laboratory tests

• conclusion.

CEINTUURBAAN STATION - DESIGN AND BOUNDARY CONDITIONS The construction of the Ceintuurbaan Station is part of the new metro project North/South line,

situated in the historic centre of Amsterdam. Due to the limited width available in the street, the

station has been designed for two tunnel boring machines to drive through the station above each

other. Thus yielding a relatively narrow and deep building pit. The station will be 11 m wide, 230 m

long and will have single track platforms at NAP -16.5 m and NAP -26.5m depth. Local street level

is at approximately NAP, which is the Dutch reference level.

This section addresses key aspects of the design and boundary conditions of Ceintuurbaan station.

Figure 2 - North/South line in Amsterdam and artist’s impression of Ceintuurbaan Station

Construction method

To minimize the duration of impact on city and infrastructure, the top-down method was selected

for construction. The construction phases as adopted in the design can be summarised as follows:

• installation of diaphragm walls

• installation of jet grout strut below deepest excavation level

• construction of roof and restoration of street level

• sub-roof, multiple stage, excavation and installation of pre-stressed struts

• construction of intermediate floor

• sub-floor excavation, installation of pre-stressed struts and construction of base slab working

under up to +1.6 bar compressed-air

• TBM passage

• final construction

2

Geometry

The geometry of the building pit in the deepest excavation phase is depicted in figure 3.

At first, an assessment into the settlement risk of adjacent historic buildings resulted in strict

requirements regarding deformations of the building pit. Typically, the historic buildings in

Amsterdam are founded on wooden piles driven into the so-called 1st sand layer. It is not

uncommon for these pile foundations to have barely sufficient bearing capacity, if verified along

modern-day standards. Hence, the retaining walls, roof and floor slabs, several layers of pre-

stressed struts and a jet grout strut have been designed to resist all actions and forces, and to limit

differential settlements of adjacent foundations.

Secondly, the verification of the vertical stability of the building pit resulted in the requirement to

extend the diaphragm walls below the so-called intermediate sand layer. This layer at NAP -37 m is

water bearing with a piezometric head of approximately NAP -3 m. Practically speaking, lowering

this head to a secure level to avoid instability of the remaining Eem clay layer during excavation

could only be achieved by confining the intermediate sand layer. The D-walls have therefore been

designed to function as cut-off walls too, resulting in lengths of up to 45 m.

Geotechnical conditions

The geology, depicted in figure 3, is characteristic for the centre of Amsterdam (Wit, 1999). The

stratigraphy is formed by a glacial basin filled with sediments. The 3rd sand layer, relevant as

highly permeable aquifer, is at its base. For this paper’s case study, especially the Eem and Drenthe

clay layers and the intermediate sand layer are of interest. The latter are a glacial clay and

fluvioglacial sand deposited in the Saalian period. These glacial deposits are overlain by marine

clays of Eemian age. Above, the 1st and 2nd sand layer, often separated by the more silty Allerød

layer, have been combined into one layer here. These two medium to dense, aeolian (1st) and

fluvial (2nd) sand layers are of Weichselian origin. On top, the Holocene deposits have been

condensed into one layer too. This unit consists of a tidal sand and mainly of soft clay and peat

layers.

The sand layers are permeable, water bearing strata. For this case study it is assumed that all have a

head of circa NAP -3 m. The freatic level in the Holocene layers differs, and is circa NAP -0.5 m.

A summary of geotechnical parameters for all layers is included in figure 3. For further reference,

table 1 comprises additional data on the marine Eem clay and glacial Drenthe clay.

Table 1 - Geotechnical parameters Eem and Drenthe clay, mean values

Parameter Eem clay Drenthe clay

water content w [%] 36 23

liquid limit wL [%] 42 28

plastic limit wP [%] 23 18

liquidity index IP [%] 19 10

undrained shear strength cu [kPa] 150 180

compression index Cc [-] 0.358 0.143

secondary compression Cα [-] 0.0044 0.0018

swelling index Csw [-] 0.033 0.014

consolidation coefficient cv [m2/s] 1*10-6 2*10-6

permeability k [m/s] 2*10-9

1*10-9

3

Description γsat ϕ' c' E'50;ref OCR

[kN/m3] [

o] [kPa] [kPa] [-]

0m width = 11m 0m Roof, t = 0.9m

-3m

-5m Struts, pre-stressed

-10m Struts, pre-stressed

-12m

-15m Struts, pre-stressed(temporary)

-19m Floor, t = 0.9m

-25m -25m Struts, pre-stressed(temporary)

-31m Max. excavation level

-33m Jetgrout strut, t = 1.5m

-37m

-40m

-45m -45m D-wall, t = 1.2m

Drente layer, overcons.

glacial firm CLAY19.3 33 11

Holocene layers, soft

PEAT / CLAY / SAND

1st & 2nd sand layer,

(medium) dense SAND

Eem layer, overconsol.

marine firm CLAY

Intermediate layer,

medium SAND

3rd sand layer,

dense SAND

15 28 3

18 32 15

8000 n/a

19 34 0 34000 n/a

13000 2,0

19.5 33 0 25000 n/a

19.5 35 0 35000 n/a

15000 1,5

Figure 3 - Soil parameters and geometry (modified for the purpose of the paper)

VERTICAL STABILITY OF DEEP EXCAVATION Hydraulic failure by uplift, as mentioned before, is critical to the design of the deep excavation of

Ceintuurbaan Station. A simple analysis in terms of total stresses yields that the mean overburden

pressure in the pit at NAP -45 m becomes less than the pore-pressure under the glacial clay once the

excavation works have reached a level of NAP -22.5 m in depth. That is, presuming a confined and

adequately drained intermediate sand layer. Taking a safety margin into account, this would

conclude in a maximum allowable excavation level of approximately NAP -20 m. Some 11 m short

of the design level.

Reference design approach

To reach the targeted level of NAP -31 m, it was decided initially to excavate the deepest section

under compressed-air. The D-walls and intermediate floor were constructed as to function as a safe

pressurised working chamber. Two schemes to secure the vertical stability of the bottom of the

excavation were anticipated:

• +0.8 bar for the excavation down to NAP -25 m (i.e. 0.8 bar above atmospheric pressure)

• +1.6 bar for the excavation down to NAP -30 m and subsequent construction of the floor slab

Note: the air pressure increases the pore-pressures and total stresses in the building pit.

4

Value engineering approach

Since above method is obviously costly, time consuming and not without health & safety risks, a

more detailed analysis of the deep excavation phase seemed valuable. In the narrow pit of

Ceintuurbaan the stability against buoyancy of the clay layers below excavation level is

significantly influenced by the friction between soil and diaphragm wall. After a first appraisal of

this possible stabilising effect showed promising results, the client initiated a value engineering

study. The results of this study, which aimed at an integral assessment of the safety of the

excavation, including wall friction, are outlined below.

Verification of uplift limit state

The basic equation for the verification of failure by uplift of the building pit is:

Gd + Ad + Fd ≥ Pd (1)

where Gd = design value of total weight of Ground (excavation level - bottom of clay layer)

Fd = design value of total side wall Friction

Ad = design Air pressure above atmospheric pressure

Pd = design value of total Pore-pressure (in 3rd sand layer applied under clay layer)

In the remainder of this paper the excess air pressure is presumed to be zero (i.e. atmospheric), the

excavation level is taken at NAP -26 m (i.e. just below the lowest temporary strut level) and the

weight density of water is 10 kN/m3.

The total weight of the soil and sum of the water pressures seem well defined parameters. Both can

be deduced from sampling and piezometer readings respectively. In this example:

Gd = 353 kN/m2 * W / γm

Pd = 420 kN/m2 * W

W = 11 m width

γm = 1.1 according to Dutch code NEN6740:1997

Clearly, without air-pressure or wall friction equation (1) would not be met.

The friction Fd between soil and diaphragm wall requires closer attention. The wall friction cannot

be tested or monitored in-situ directly. The next section therefore deals with the question how to

predict the maximum side wall friction.

It should be noted that the strength of the jet grout strut in the Eem layer is being neglected in the

analysis. Yet, its stiffness is taken into account implicitly. This approach has been chosen to design

on the safe side. Cause, despite of a perhaps vertically stabilising effect of the grout strut, its

primary function has been determined to reduce deformations. It has not been designed to take

lateral load. On the other hand, its presence reduces a (favourable) horizontal ‘pre-stressing’ of the

soil. This effect is similarly being neglected in the analytical analysis below.

ANALYSIS OF DIAPHRAGM WALL FRICTION The maximum shear between soil and diaphragm wall primarily depends on normal effective stress

and (reduced) interface friction:

τmax = R * ( c’ + σ’N * tanϕ’ ) or τmax = R*c’ + σ’N * tanδ’ (2)

5

The total side wall friction follows by integration:

Fd = 2 * z∫ τmax dz (3)

Below, first the distribution of normal stresses will be evaluated, and next the interface friction.

Normal stress distribution

Several methods are available for the estimation of effective stress normal to a retaining wall.

Essential in this case is the notion that the deep clay layers are in a state of over consolidation after

excavation. The ratio between horizontal and vertical stress changes during excavation and might

differ considerably from K0;nc. For comparison, the finite element code Plaxis and an analytical

model have been applied. In both the decrease in horizontal effective stress is deduced from the

reduction in vertical effective stress.

As illustrated in figure 4, the stress path for elastic unloading in Plaxis’ Hardening-Soil model can

be described with:

∆σ’h = ∆σ’v * νur / ( 1 - νur ) (4)

Though, the ratio of horizontal and vertical stress is limited by the Mohr-Coulomb failure criterion.

Plastic failure would occur if:

σ’h;excavated = σ’v;excavated * Kp + 2 c’ √Kp (5)

in which, for simplicity, a Rankine passive pressure coefficient can be adopted:

Kp = ( 1 + sinϕ’ ) / ( 1 - sinϕ’ ) (6)

0

100

200

300

0 100 200 300 σσσσ'v [kPa]

σσ σσ' h

[kP

a]

K_0;nc

v_ur / (1-v_ur)

s'v*Kp + 2c'sqrt(Kp)

Hardening-Soil

K0 - OCR (Mayne)

Figure 4 - Stress paths over consolidated Eem clay, unloading from σ’v;initial = 255 kPa

Alternatively, application of the well known K0 - OCR relationship (Schmidt, 1966) suggests a

somewhat different stress path during unloading:

σ’h = σ’v * K0;nc * OCRsinϕ’

= σ’v * ( 1 - sinϕ’ ) * OCRsinϕ’

(7)

where

OCR = σ’v;max / σ’v = OCRinitial * σ’v;initial / σ’v;excavated (8)

6

The difference between the Hardening-Soil model and the K0 - OCR relationship becomes apparent

for small vertical stresses. Equations (4) and (5) show that the minimum value found for the

horizontal stress σ’h when using the Hardening-Soil model for unloading would still equal 2c’√Kp,

even for zero vertical stress. On the contrary, the K0 - OCR relationship results in zero horizontal

stress for zero vertical stress. The relationship (7) finds sound support in the statistical analysis of

ample laboratory test results on clay and sand samples (Mayne, 1982).

Concluding, the analysis of normal stresses after unloading by means of the K0 - OCR relationship

will result in a lower design value of total side wall friction. The latter is therefore regarded a safer

design approach and has been adopted in this case study.

Interface friction

The friction capacity of the soil - diaphragm wall interface might in two ways be affected by the

construction method itself. First, the slurry trench phase is likely to result in an alteration of initial

lateral stresses. Second, the bentonite support slurry is known to plaster the trench wall, forming a

filter cake, which might not be expelled during concreting of the panel. Especially in granular soils,

such cake of soft clay has been observed to decrease the shaft friction capacity.

To take the latter effect into account, a range of δ/ϕ-ratios can be found in literature. The possible

reduction of lateral stress has been expressed in a Ks/K0-ratio. With reference made to research data

on slurry supported bored piles (Kulhawy, 1991), the following values were initially recommended

for use within the framework of this case study:

δ/ϕ = 0.8 - 1.0

Ks/K0 = 0.6 - 0.7

or combined into a Plaxis-type interface strength reduction factor R:

R = 0.5 (lower boundary value)

R = 0.7 (mean value)

Main considerations in selecting these values were: the sedimentation and presence of a bentonite

cake was regarded less likely at the low permeability marine and glacial clay layers. Besides,

former research had shown incremental outward horizontal displacements in the deeper layers

during concreting of a panel (Wit, 2002). Nonetheless, being a key parameter, it was determined

that validation of the interface friction by testing prior to the critical excavation stage would be

decisive. The results of these tests are summarised at the end of this paper.

Vertical eff. stress [kN/m2]

-45

-40

-35

-30

-25

-100 0 100 200 300 400

initial

excav.

Pore pressure [kN/m2]

-45

-40

-35

-30

-25

-100 0 100 200 300 400

initial

excav.

Horizontal eff.stress [kN/m2]

-45

-40

-35

-30

-25

-100 0 100 200 300 400

initialexcav. HS-modelexcav. K0-OCR

Figure 5 - Interface stresses prior to and after excavation down to NAP -26m (mean values, 1D-analytical)

7

MONTE CARLO ANALYSIS The basic question to be answered at last is whether the analysis of the vertical stability including

diaphragm wall friction leads to a safe design of the deep excavation. The applicable Dutch code for

geotechnical design at the time did not contain a suitable definition for this safety. Hence, the safety

of the deep excavation was defined in connection with higher order code NEN6700:1997 (compare

Eurocode 0) and in terms of the probability of failure. This section comprises the assessment of the

probability of failure by means of probabilistic analysis.

Deterministic approach

For comparison, a summary of characteristic results is provided first. Substituting aforementioned

mean values subsequently into equations (7), (2) and (3) would lead to the conclusion that equation

(1) for the verification of failure by uplift can be satisfied even without additional air pressure

support. Here:

Gk + 2 * z∫ τmax;k dz > Pk

353 kN/m2 * 11 m + 2 * 702 kN/m

2 = 5287 kN/m’ > 420 kN/m

2 * 11 m = 4620 kN/m’

If expressed in an overall factor of safety, this results in: safety = 1.14.

Probabilistic approach

As can be examined from above discussion, the important parameters in the vertical stability check

are: the initial stress situation, over consolidation ratio, decrease of overburden pressure, pore

pressure distribution, interface reduction factor and the soil parameters: weight density, angle of

shearing resistance and cohesion.

Since these parameters all vary by nature, it was decided to assess the risk of failure by uplift

through a Monte Carlo analysis. All relevant soil, groundwater and geometrical parameters were

implemented as stochastic variables into a 2D analytical spreadsheet model. This was used to

calculate the reliability function Z up to 100,000 times per cross section. The probability of failure

can then be found as:

Pf = P(Z<0) (9)

where

Z = Resistance - Sollicitation = (Gk + Fk) - Pk (10)

Table 2 - Stochastic variables in Monte Carlo analysis (refer to figure 3 for mean values)

Parameter Distribution Stand. deviation

weight density γsat [kN/m3] standard normal 0.4 to 1.5

angle of shearing resistance ϕ’ [°] standard normal 2 to 4

cohesion intercept c’ [kPa] n/a 0

interface reduction factor R [-] uniform 0.2

over consolidation ratio OCR [-] standard normal 0.25

length of D-wall L [m] standard normal 0.1

piezometric level

- at excavation level

- at intermediate sand layer

- at 3rd sand layer

hexcav.

hint.sand

h3rd sand

[m]

[m]

[m]

uniform

standard normal

standard normal

0.2

0.5

0.05

8

Results

The Monte Carlo analyses provided clear and quantitative data on the probability of failure by

uplift, and on how this failure probability relates to the contributive factors: soil weight, wall

friction and uplift. Their probability density functions are shown in figure 6, together with a

histogram of the reliability function Z.

Reliability function; failure = Z<0

0

1000

2000

3000

4000

5000

-100 200 500 800 1100 1400

0

25

50

75

100

-100 -50 0 50 100

Probability density function

1000 2000 3000 4000 5000[kN/m']

F (1358) G (3923) P (4620)

Figure 6 - Results of Monte Carlo analysis of deep excavation Ceintuurbaan Station

For the case study presented, the following results have been computed:

total number of calculations = 50,000

number of calculations with Z<0 = 8

probability of failure Pf = 8 / 50,000 = 1.6 * 10-4

result → reliability index β = 3.6 (assuming a normal distribution for reliability function Z)

required reliability index β ≥ 3.6 ���� (NEN6700:1997)

Concluding, the vertical stability of the deep excavation down to NAP -26 m meets the

requirements regarding reliability, also without pressurising the working chamber. The remainder of

the section shall be excavated under compressed-air. Although the friction’s relatively wide

probability density function could be said to increase the uncertainty (the ‘tail’) of the reliability

function, its contribution to the safety is significant.

SITE INVESTIGATION INTO DIAPHRAGM WALL INTERFACE The interface friction delta is assumed to depend largely on the possible presence of any bentonite

cake on the diaphragm slurry walls. As excavation works progressed, the opportunity was seized to

assess the bentonite cake visually. By means of sampling and direct shear testing the earlier

assumptions regarding δ/ϕ-ratios were verified. The limited number of samples did not allow for

full statistical analysis. Still, the qualitative observations below are deemed illustrative.

Visual inspection

In line with expectations, a bentonite cake could be observed in sand layers, however, it was

virtually absent in layers with low permeability. At the soil - diaphragm wall interface a filter cake

of approximately 5 to 20 mm was found in the 1st and 2nd sand layer, a cake of approximately

1 mm in a Holocene peat layer, and no bentonite cake in the Eem clay layer nor in a Holocene clay

layer. Where present, the sand next to the bentonite cake showed some discolourisation in a zone of

10 to 40 mm.

9

The presence or absence of a bentonite filter cake can, presumably, be explained by the difference

in permeability of the ground layers. It seems that where (nearly) no bleeding or consolidation of

the bentonite slurry could take place, such as in the low permeability clay layers, the slurry has been

effectively expelled during concreting of the D-wall panel. In contrast, the thickness of bentonite

cake in the sand layers exceeded the specific roughness of the diaphragm wall in several cases

observed. A possible correlation between cake thickness and duration of the slurry trench phase

could not be investigated.

Direct shear tests

To verify previously assumed values for shearing resistance direct shear tests on samples including

and excluding bentonite cake have been performed. For reference, also laboratory-made samples

with and without filter cake were tested. For the bentonite-cake-in-sand samples only those results

were considered where the shear plane clearly cut the filter cake (sand - sand shear disregarded).

The test results confirmed a δ/ϕ-ratio of 0.5 (lower boundary) to 0.7 (mean value) for diaphragm

wall friction in sand. In Eem clay it was suggested to calculate the maximum shear in connection

with the test results as:

τmax = σ’N * tanδ’shear test (note: c’=0), with

δ’mean = 35°

δ’st.dev. = 4.9°

δ/ϕ ≤ 1.

Since the possible decrease of horizontal stress due to installation effects could not be deduced from

the tests, it was recommended to apply the aforementioned Ks/K0-ratio of circa 0.7 undiminished.

Design verification

A re-run of the Monte Carlo analysis, implementing the direct shear test parameters, proved a

minimal difference with earlier calculations. Hence, the design parameters could be confirmed.

Note: the results depicted in figure 6 are based on the latter analysis.

CONCLUSION Side wall friction can contribute significantly to the vertical stability of a diaphragm walled deep

excavation. In the case study presented, the safety against failure by uplift was demonstrated

through probabilistic analysis of all relevant parameters.

The approach to calculate the horizontal stress distribution after excavation by implementation of

the K0 - OCR relationship leads to a safer design than the application of the Hardening-Soil model.

In contrast to some literature, a bentonite cake on the diaphragm wall could be observed in sand

layers, but was virtually absent in low permeability clay layers.

Furthermore, the results lead to practical recommendations regarding groundwater management,

monitoring and lower acceptable levels for pressurised air during the deepest excavation stage than

earlier anticipated. Based on the analysis, the client was able to significantly reduce the application

of compressed air, without bearing higher risk.

10

REFERENCES Kulhawy, F.H. (1991), “Drilled shaft foundations”, in Fang, H.Y. (Ed.), Foundation Engineering Handbook, Van

Nostrand Reinhold, pp.537-552

Mayne, P.W. and Kulhawy, F.H. (1982), “K0-OCR Relationships in soil”, Journal of the Geotechnical Engineering

Division, Proceedings of the American Society of Civil Engineers, Vol.108, No.GT6, pp.851-872

Schmidt, B. (1966), “Earth pressures at rest related to stress history”, Canadian Geotechnical Journal, National

Research Council, Ottawa, Vol.3, No.4, pp.239-242

Wit, J.C.W.M. de and Lengkeek, H.J. (2002), “Full scale test on environmental impact of diaphragm wall trench

installation in Amsterdam”, Proceedings of International Symposium on Geotechnical Aspects of Underground

Construction in Soft Ground, Toulouse

Wit, J.C.W.M. de, Roelands, J.C.S. and Schiphouwer, R.A. (1999), “Geotechnical design aspects of the deep

underground stations in the North/South Line in Amsterdam”, in Barends, F.B.J. et al. (Ed.), Geotechnical engineering

for transportation infrastructure, Taylor&Francis, pp.211-220

http://www.northsouthline.com/ (2009)

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