The foundation of a 40-storey tower in jointed basalt - UGRhera.ugr.es/doi/16521663.pdf · The...

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International Journal of Rock Mechanics & Mining Sciences 43 (2006) 267–281

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The foundation of a 40-storey tower in jointed basalt

J.L. Justoa,�, E. Justoa, P. Duranda, J.M. Azanonb

aDepartment of Continuum Mechanics, University of Seville, Spain [E.T.S. Arquitectura, Avenida Reina Mercedes 2, 41012 Seville, Spain]bDepartment of Geodynamics, University of Granada, Spain

Accepted 28 July 2005

Available online 18 October 2005

Abstract

A 132.70-m-high tower (above foundation) has been successfully completed at Tenerife Island. The foundation of the tower, a 2-m-

thick reinforced concrete slab, is supported by jointed, vesicular and weathered basalt, and scoria. A three-dimensional, elastic finite

element program has permitted to calculate the displacements of the tower and the stresses in the slab. The installation of rod

extensometers at different depths below the slab and clinometers at the lower basement has provided comparison between measured and

calculated displacements, and the estimation of in situ deformation moduli. A first stage prediction (before construction) has allowed

establishment of an upper limit, based upon pressuremeter modulus, and a lower limit, based upon Bieniawski’s equation [The

geomechanics classification in rock engineering applications. In: Proceedings of the fourth cong. ISRM congress, Montreux, vol. 2. 1979.

p. 41–48], of the settlements of the tower slab. The geometric mean of these values comes close to the measured settlement. The moduli

deduced from the simple empirical equation proposed by Gokceoglu et al. [Predicting the deformation modulus of rock masses: a

comparative study. Int J Rock Mech Min Sci 2003;40:701–10], and Hoek and Brown [Practical estimates of rock mass strength. Int J

Rock Mech Min Sci 1997;40:701–10] as a function of GSI provide a good fit with the measured settlements in this type of rock. A good

correlation is also obtained with the empirical equation presented by Verman et al. [Effect of tunnel depth on modulus of deformation of

rock mass. Rock Mech Rock Eng 1997;30(3):121–7] that incorporates the influence of the confining stress in the deformation modulus.

r 2005 Elsevier Ltd. All rights reserved.

Keywords: Modulus of deformation; Jointed rock; Basalt; Finite elements; In situ measurements; RMR; GSI; Q; RQD

1. Introduction

Twin towers are integrated in a privileged expansionzone of Santa Cruz (Tenerife Island) at the seaside, in theland reclaimed from a refinery, near outstanding structuressuch as the Auditorium and the Congress Palace bothdesigned by the well-known Spanish Architect SantiagoCalatrava.

The first tower, with a height of 132.70m (abovefoundation), has been recently completed (Fig. 1). Thebuilding, 40 storeys high, with 35 storeys above groundlevel and 5 basements, is the highest apartment building inSpain; an attached building, only 2 storeys above groundlevel and with four underground levels, is placed at theside.

e front matter r 2005 Elsevier Ltd. All rights reserved.

mms.2005.07.007

ing author. Tel.: +34954556588; fax: +34954556965.

ess: [email protected] (J.L. Justo).

Several authors, starting with Habib and Puyo [1], havetreated the problem of towers with shallow foundations.When the tower reaches a critical height, dependent uponthe geometrical dimensions and foundation modulus, itmay lean due to an instability phenomenon similar tobuckling.This paper expounds the geological and geotechnical

conditions at the site. Finite element (FE) calculations ofthe foundation were carried out and will be detailed below.The installation of rod extensometers at different depthsunder the ground and clinometers at the lower cellar, at thebeginning of construction, has provided comparisonbetween measured and calculated displacements, and theestimate of the in situ modulus. These moduli will becompared with predictions based on some indices such asrock mass rating (RMR), geological strength index (GSI),Q or RQD. Most of the direct measurements of in situdeformation modulus of rock are based upon tests that

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Fig. 1. Section of tower and attached building.

J.L. Justo et al. / International Journal of Rock Mechanics & Mining Sciences 43 (2006) 267–281268

only affect a small volume of rock. When made at depth,they are affected by the introduction of the loading deviceinto the ground. In the case presented in this paper, theinstrumentation has allowed testing of a large volume ofintact rock below the foundation of the tower.

2. Rock conditions and study site

2.1. General geological conditions

Tenerife (Fig. 2) is the largest (2058 km2) and highest(3718m above sea level) island in the Canaries and has a

complex volcanic history. The oldest visible materials (theOld Basaltic Series) are preserved in three isolated anddeeply eroded massifs: Anaga (NE), Teno (NW) andRoque del Conde (SW). They were formed in late Mioceneand early Pliocene times [2].After the Old Basaltic Series, the volcanic activity

became concentrated within two large volcanic edifices:the central volcano of Las Canadas and the Dorsal Ridge, aSW-NE volcanic ridge linking Las Canadas and the Anagamassif. On each side of the Dorsal Ridge, two largedepressions were formed, the so-called ‘‘valleys’’ of Guimarand La Orotava. Subsidence at the end of this stage formed

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Fig. 2. Volcanic structures in Tenerife Island.

J.L. Justo et al. / International Journal of Rock Mechanics & Mining Sciences 43 (2006) 267–281 269

one of the most impressive calderas of the world: the Circo

de las Canadas. The eruptive and most recent history ofTenerife is characterized by at least three long-term cyclesof basaltic-to-phonolitic explosive volcanism between 1.6and 0.17Ma [3,4]. There were medium-term periods ofnon-explosive activity separating the explosive cycles,which correspond to major erosive unconformities inthe extra-caldera stratigraphy, and episodes of effusivevolcanism.

Santa Cruz de Tenerife is located in the NE of the islandbetween the Anaga massif and the Guimar Valley.Quaternary basaltic lava flows, sourced from the so-called‘‘Dorsal Ridge’’, are the main constituents of the substrateof this town. They are interbedded with thin pumice layersthat had been carried to the site by westerly winds. Thestratification is sub-horizontal. The thickness of the lavaflows rarely exceeds 1m, and usually ranges from 40 to80 cm, alternating with scoriaceous levels (Fig. 3). Nofaults are encountered. Lava flows are typical fresh alkalinebasalts with olivine included in a fine-grained plagioclaseand pyroxene matrix (Fig. 4). Alkaline basalts have acharacteristic porphyritic texture with a very low propor-tion of olivine phenocrysts. The porphyritic texture,especially common in extrusive rocks, indicates twoseparate stages of solidification. In the first phase, thephenocrysts form in the molten mass; in the second, themolten mass itself crystallizes into a solid. Titano-augite, as

pyroxene, and alkaline plagioclase constitute the matrix ofthe basalt. A low quantity of olivine and volcanic glass arealso included in the matrix of the rock. In both the alkalinebasalts and scoriaceous levels, a characteristic vesiculartexture, with millimetre cavities can be appreciated. Thethickness of the pumice layers never exceeds 2m. The sealevel and tides control the water level, although perchedwater tables may exist in paleosols. The volcanic materialsconstitute a very pervious mass, which cannot take anypressure during Lugeon tests.The sea level and tides control the water level, although

perched water tables may exist in paleosols.

2.2. Study site

Fig. 5 shows the construction plan, the boreholeslocation and their depth. Seven boreholes (S1–S7) weredrilled from the ground surface. At the tower site, the finalmaximum height of the vertical excavation was 18.6m. Allrocks were excavated with mechanical means, withoutblasting. Three new boreholes (SR1–SR3) were drilledfrom 1m above the bottom of the excavation using double-tube core barrel and diamond bits. The cores were carefullyplaced in boxes with dividers indicating the depth of theground changes (Fig. 6). The lithological properties of thecores, core recovery, RQD, hammer resistance, spacingbetween joints and weathering degree (WD) were recorded.

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Fig. 3. Excavation front, 17.46m deep, showing the excavating machine. The volcanic tuff level shows oil seepage from the old refinery.

Fig. 4. Olivine phenocrysts in a matrix of titano-augite, plagioclase and olivine in a thin-section of alkaline vesicular basalt.


Fig. 3 shows the front of the excavation. The followinglayers appear from top to bottom in the geological profile(Fig. 7) with respect to the sea level:

(a)
Fill and volcanic tuff from +15 to +19m. (b) Upper basalt from +7 to +15m. There are small
cavities at +7.5 and +11.0m, and oil infiltrations fromthe old refinery. Fig. 8 shows jointing and small cavitiesin the upper basalt.

(c)
Red volcanic tuff and whitish pumice from +0.6 to+7m.
(d)
Jointed lower basalt below level +0.6m. Small cavitiesappear at �11.5, �2 and 0m. Within this stratum, theone situated below the foundation of the tower, thereare scoriaceous, vesicular and massive levels. Fig. 9shows sketches of the logs of boreholes SR1 and SR2.The two boreholes, spaced only 24m apart, show largedifferences in their lithological characteristics, due to

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Fig. 5. Location and depth (m) of boreholes and rod extensometers.

Fig. 6. Cores obtained from rotary drilling, prepared for logging.


the presence of pyroclastic breccia in SR2 below adepth of 18m.

The tower was founded on a 2m thick, reinforced concreteslab resting on 10 cm of plain concrete at level +0.6. Theauthors decided to include a fifth level below the tower toplace its foundation on the lower basalt, because thevolcanic tuff is much softer.

Twenty-nine uniaxial compression strength tests wereperformed on the samples following the NLT-250/91Spanish standard [5]. In 10 additional tests, carried out

on massive and vesicular basalt according to the UNE22950-3:1990 Spanish standard [6], the vertical andhorizontal strains were measured with strain gauges (Fig.10). The behaviour of the samples under stress was almostelastic for vertical stresses up to 52.5MPa, with smallplastic strains. The dependence of the modulus upon basalttype or stress level is small for stresses up to 15MPa.Sixpressuremeter tests were carried out on the boreholes. Thetests results are tabulated in Table 1.The difference between the average moduli in uniaxial

compression for loading (61MPa) and reloading (71MPa)

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(11)

(11)

(1)

(10)

(10)

(9)

(3)

(3)

(1)

(11) (4

)

(4)

(8)

(8)

(7)

(7)

(6)

(6)

(5)

(5)

(2)

(2)

b f

b f

b f

best fit (bf)

LAYER 4

-50

LOWERBASALT (d)

LOWERBASALT (d)

-5.4

+0.6

-29.4

-11.65LOWERBASALT (d)

(9)

(2)

(5)

201816141210

EM (GPa)

(6)

(7)

(8)

(1)

(4)

(3)

(9)

(10)

8642DE

PT

H (

m)

belo

w s

lab

botto

m

+2.60

+7

+15

+19

(3) modulus obtained from equation (3) in Table 8

END OF DISCRETIZATION

EV3EV4EV5EV6

EV2EV1

50.6

30

12.25

6

0SLAB

SLAB

LOWERBASALT (d)

LAYER 3

LAYER 2

LAYER 1

VOLCANICTUFF (c)

UPPERBASALT (b)

FILL (a)

STRUCTURAL FLOOR

TOWERATTACHEDBUILDING

Fig. 7. Section of tower and attached building, showing the geological profile, vertical position of rod extensometers, layers for FE calculation in lower

basalt and moduli obtained from the equations in Table 8.

Fig. 8. Jointing and small cavities detected in the upper basalt level.


may be ascribed to some strain hardening (Fig. 10). Thecorresponding Poisson’s ratio values were 0.33 and 0.37,respectively.

For the ratio Ei /sc the statistical median obtained (880)has been chosen instead of the mean so as to betterapproach a normal distribution.

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d2

d3

d3

d3

d1

d1

d1

d1

d1

d1

d1

SB= scoriaceous basalt

SC= scoria

VB= vesicular basalt

G = gravel

MB= massive basalt

PB= pyroclastic breccia

Dep

th

(m)

5

10

15

20

25

30

0

Description

Ro

ck

typ

e

Co

re

rec

ov

ery

RQ

D

Jo

ints

sp

ac

ing

(m

)

VB 0.45

0 100

0 100

G

SC

d3

d1d3

0.17

VB & MB

SC

VB & MB

PB

Fractured PB

0.28

0.20

0.12

VB SC

VB & SC

SC

SR2SR1

0.45

0.20

0.20

0.75

SBVB

SB

MB

d2

d3

MB & VB

SC

VB 0.55d1

d3

d3

d1

d2

SC

SB

100

0100

0

0.4VB with SC

Jo

ints

sp

ac

ing

(m

)

RQ

D

Co

re

rec

overy

Ro

ck

typ

e

Description

Fig. 9. Sketches of the logs of boreholes SR1 and SR2.

0

2

4

6

8

10

12

14

16

-150 -100 -50 0 50 100 150 200 250 300 350 400

STRAIN (10-6)

ST

RE

SS

ES

(Mp

a)

1st cycle

2nd cycle

horizontal vertical

Fig. 10. Stress–strain graphs obtained from the uniaxial loading performed on massive basalt.


The pressuremeter modulus is 40 times lower than theuniaxial compression one.

2.3. In situ measurements

Rod extensometers were placed below the tower slab, asindicated in Figs. 5 and 7, at depths corresponding

approximately to changes in ground conditions. Clin-ometers were installed in one cellar’s walls. Fig. 11 showsthe measured settlements and the evolution of constructionas a function of time. Both manual and automaticmeasurements were taken, and they are close, except inextensometer EV-6 placed at the centre of the tower slab ata depth of 29.1m below the slab bottom. In this case, the

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Table 1

Values obtained in laboratory and in situ tests

Rock description Uniaxial compression Pressuremeter

sc (MPa) Ei (GPa) Er (GPa) Unit weight (kN/m3) Ep (GPa)

Whitish pumice (c) Minimum 0.50

Average 0.82

Maximum 1.13

n 7

Red volcanic tuff (c) Minimum 1.71

Average 3.29

Maximum 4.89

n 5

Vesicular & massive basalt (b & d1) Minimum 20.3 44.1 49.9 27.4 0.797

Average 69.0 60.9 70.5 1.67

Maximum 150 80.1 86.1 2.57

n 16 10 5 5

Weathered basalt (b & d2) Average 15.1 22.8

n 1

Pyroclastic breccia (d2) Average 0.422

n 1

sc ¼ uniaxial compressive strength; Ei & Er ¼ uniaxial compression moduli for loading & reloading, respectively; Ep ¼ pressuremeter modulus.

-0.50

0.000.50

1.001.50

2.002.50

3.003.50

4.0015/12/2001 25/3/2002 3/7/2002 11/10/2002 19/1/2003 29/4/2003 7/8/2003 15/11/2003

Dates

Se

ttle

me

nts

(m

m)

-5

0

5

10

15

20

25

30

35

Sto

reys

EV-1 EV-2 EV-3 EV-4 EV-5 EV-6 Work advance (storeys)

Fig. 11. Settlements at rod extensometers (Fig. 5 shows the position and depth of the extensometers).


manual measurements are somewhat larger. The clin-ometers showed rotations smaller than 0.11 duringconstruction (Fig. 12).

2.4. Simplified rock types and plate loading tests

The great difference between borings SR1 and SR2(Fig. 9) is not reflected in the extensometer measurements(Fig. 11). For this reason, the different rock types thatappear in the lower basalt (layer d in Section 2.2) werecollected, then divided into three types:

(d1)
Massive or vesicular basalt, with thin scoriaceouslevels. Normalized WD 0.36 [17]. Relative thickness68%.
(d2)
Weathered, scoriaceous basalt and pyroclastic breccia.Normalized WD 0.58 [17]. Relative thickness 14%.
(d3)
Scoria and fractured pyroclastic breccia. NormalizedWD 0.62 [17]. Relative thickness 18%.
The three ground types are interbedded in the geologicalprofile. Their average properties and rock mass classifica-tions are included in Tables 1–5.Plate loading tests were carried out near the foundation

level of the second tower with the results indicated in Table2. The values correspond to volcanic tuff or scoriaceouslevels and are very low.

3. Calculation of deformation modulus of rock masses

3.1. Rock mass classifications

Justo et al. [7] carefully applied Bieniawski’s [8] RMR tothe strata of the site. Importance ratings were allocated to

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Fig. 12. Discretized volume of ground.

Table 2

Mean deformation modulus values, E, obtained from plate loading tests

Ground type 1st cycle p(kPa) 2nd cycle p(kPa)

0-196 196-0 0-588 588-0

E (GPa) E (GPa) E (GPa) E (GPa)

Volcanic tuff (c) 0.029 0.082 0.055 0.105

d2–d3 0.064 0.213 0.204 0.308

d2 0.088 0.173 0.168 0.247

p ¼ pressure range.

Table 3

RMR for the site

Ground typea sc (MPa) R RQD (%) R Discontinuities Water R Strike & dip R RMR

Spacing (m) R Condition R

d1 69 7 77 17 0.5 10 SR SW so1mm 25 wet 7 fair �7 59

d2 15 2 42.5 8 0.125 8 SR HW so1mm 20 wet 7 fair �7 38

d3 13b 2 0 3 0.05 5 15 wet 7 fair �7 25

aSee Section 2.4.bfrom correlations with hammer strike. R ¼ rating, SR ¼ slightly rough, SW ¼ slightly weathered, s ¼ separation.


each of the six parameters: the uniaxial compressivestrength of the rock material, drill core quality RQD,spacing, orientation and condition of discontinuities andground water conditions. The total RMR was alsodetermined (Table 3).

Hoek [9] and Hoek et al. [10] proposed the GSI basedupon visual impression on the rock mass structure. This

index has been modified by Sonmez and Ulusay [11]. Cai etal. [12] and Sonmez et al. [13] proposed EM equationsdepending on GSI.

Table 4 shows how this index is obtained for the stratad1, d2 and d3 defined in Section 2.4.According to Hoek and Brown [14] when the new

version of Bieniawski’s classification [8] is used, then

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Table 5

Q index for layers d1, d2, and d3 [12]

Ground

type

RQD

(%)

Joint set

number

Jn Joint roughness

number

Jr Joint alteration

number

Ja Jw SRF Q (%) Qc (MPa)

d1 77 G–H 14 E 1.5 B 1 1 1.25 6.6 4.6

d2 42.5 H 15 E 1.5 B 1 1 1.25 3.4 0.51

d3 0 H–J 18 B 3 F 4 1 1.25 0 0

Table 4

Geological strength index (GSI) for the ground below the tower foundation according to Sonmez and Ulusay [11]

Rock

type

Description Size of

blocks

Volumetric

joint count, Jv(joint/m3)

Structure

rating, SR

(%)

Surface condition rating, SCR GSI

Rr Rw Rf SCR

d1 Very blocky—interlocked

partially disturbed rock mass

with multifaceted angular

blocks formed by four or more

discontinuity sets

Medium 6 62 3 5 4 12 52

d2 Disintegrated—poorly

interlocked, heavily broken

rock mass with a mixture of

angular and rounded rock

pieces

Small–very

small

30 25 4 3 4 11 39

d3 Disintegrated—poorly

interlocked, heavily broken

rock mass with a mixture of

angular and rounded rock

pieces

Shattered 460 5 3 3 2 8 28


GSI ¼ RMR�5. This relationship holds approximately forrock type d1. Table 5 presents the Q index.

3.2. Deformation modulus values

One fundamental piece of input to the FEs calculation isthe rock mass deformation modulus. McMahon andMcMahon [15] present the case of a 68 storey, 246-m-hightower (MLC Centre Tower) in Sidney with five parkinglevels. In 1980, this building was the highest building inAustralia and the highest office building in the world. It isfounded on footings, and rod extensometers were placedbelow the footings up to a depth of 12.2m. The foundationrock was quartz sandstone with clayey cement. The authorsfound a good fit with the extensometer settlements using adeformation modulus equal to the median of the modulifrom the cores. However, in the case of Tenerife, the rock isheavily jointed and it would not be reasonable to use themodulus obtained from uniaxial compressive tests on thecores (Table 1) to obtain the deformations of the rockmass.

Several authors present correlations between RMR, GSI,Q or RQD and the modulus from in situ tests[12–14,16–24]. Table 6 shows the mass moduli obtainedaccording to correlations given by different authors. Theempirical equations proposed for the prediction of the

deformation modulus have serious limitations. It is verydifficult to find out the frequency and state of the joints inthe mass of rock examining the cores obtained from theboreholes. Fortunately, in this case it was possible toexamine the front of the excavation as well. In addition,most of the correlations are based on tests carried out onrocks of better quality than the strata d2 and d3 of this site.

4. Finite element calculations

A linear elastic FE calculation was carried out includingthe foundation of both the tower and the attachedbuilding, using the ANSYS program. The pressure of theexcavated soil was 417 kPa. The average pressure at thebottom of the plain concrete at the end of construction wasnearly the same (427 kPa). Therefore, until this stage, it wasa compensated foundation and the stress follows areloading path permitting elastic calculation. With thesurcharge, the average pressure will increase up to 558 kPa.The following elements were modelled (Fig. 7): the twoslabs, the cellar walls, the structural floors of bothbuildings, the concentrated column loads and moments,and the ground surrounding the building (down to a depthof 50m below the slab and at a distance of 30m around thebuildings.) The slabs, walls and structural floors weremodelled with shell elements, and the ground with solid

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Table 6

Rock mass deformation moduli (in GPa) according to different authors

Gokceoglu et al. [16]

Barton [23]

Groundtype

E(G

pa)=

0.14

51e

M Mi

M

M

M

Mi

Mi

M

M M

M

Mi

f Mi

M Mc

Mc

c

0.06

54G

SI

E(G

pa)=

10-3

[E/�

c(1+

RQ

D/1

00)/

WD

]1.55

28

E(G

pa)=

0.07

36e0.

0755

(R

MR

)

Hoe

k an

d B

row

n [1

4]

�<

100

MP

a

E

(Gpa

)=(�

c/1

00)1/

2 1

0 G

SI-

1040

Kay

abas

i et a

l. [1

7]

E(G

pa)=

4.32

-3.4

2WD

+0.

19E

(1+

RQ

D/1

00)

S

eraf

ím a

nd P

erei

ra [1

8]

30<

RM

R<

55

E(G

pa)=

10(R

MR

-10)

/40

M

itri e

t al.

[19]

E

=0.

5E[1

-cos

(�R

MR

/100

)]

P

alm

strö

m a

nd S

ing

[20]

E=

0.2�

B

oyd

[21]

p

=10

kP

a,

E(G

pa)=

RM

R4 /1

06

p=

1 M

Pa,

E(G

pa)=

RM

R3 /1

04

B

ieni

awsk

i [8]

R

MR

>50

,E

(G

Pa)

= 2

RM

R -

100

Son

mez

et a

l. [1

3]

d =

0.96

,

E

=E s

0.4a

Zha

ng a

nd E

inst

ein

[22]

E

=E0.

0186

RQ

D-1

.91

E(G

Pa)

= 2

5 lo

gQ

E(G

Pa)

= 10

(GP

a)10

Q

(MP

a) 1/

3

Ver

man

et a

l. [2

4]

E =

0.4

H� 1

0(RM

R-2

0)/3

8

�=

0.0

427+

0.0

0378

RM

RH

= h

eigh

t of t

he o

verb

urde

n (m

)

d1 4.4 36 6.3 9.3 27 45 13.8 19.0 (1) 19.6 (2) 20.5 (3)

18 19 24 21 17 5.7 (1)7.7 (2)9.6 (3)

d2 1.9 12.4 1.3 2.1 5.9(4) 5 4.2 3.0 4.7 (1) 5.0 (2)5.4 (3)

2.4 1.0 13 8 1.5 (1)1.8 (2)2.1 (3)

d3 0.91 6.4 0.49 1.1 4.4(4) 1.7 2.6 1.3 (1) 1.4 (2) 1.5 (3)

0.21 0.14 0.63 (1) 0.73 (2) 0.82 (3)

(1) 0−6 m below the slab; (2) 6−12.25 m below the slab; (3) 12.25−30 m below the slab; (4) E obtained from i i cE / � = 880.


elements. The model had 39,998 elements and 42,810nodes. A dilation joint was simulated between bothbuildings. Fig. 11 shows the discretized volume of theground. Poisson’s ratio value (0.35) was determined fromunconfined compression tests with strain measurements(Section 2.2).

4.1. Preliminary calculations

In the study carried out before construction, in situmoduli were assigned to eight different strata. Thedeformation moduli obtained from the pressuremeter(Table 1) were used in the calculations as a lower limitand those obtained from Bieniawski’s equation [8], whenthe average RMR of the stratum was above 50, as theupper limit. Justo et al. [7,27] have presented the details ofthis preliminary calculation.

Both short-term calculations (with a concrete modulus30 of GPa) and long-term calculations (with a concretemodulus of 12.8GPa) were carried out. The influence ofthe concrete modulus on the settlements was very small,but the slab moment at the centre of the slab was largerwith the upper modulus. The maximum settlement valuescalculated at the end of construction were 13mm using thepressuremeter modulus and 0.8mm employing Bieniaws-

ki’s moduli. They are first stage predictions, because theywere made in April 2001 [7] and construction started at theend of 2001. As will be shown in Table 7, measuredsettlements at the extensometers when the construction wascompleted might correspond to a maximum settlement atthe centre of the slab of 3.8mm.This value is included inthe range between the minimum and maximum assump-tions made before construction, and is a little larger thantheir geometric mean (3.2mm).

4.2. New calculations using correlations with rock indices

Fig. 7 shows the rock layers considered in the new FEcalculations. The foundation rocks of the tower have beendivided into depth increments corresponding to thepositions of the extensometers and the end of discretization(layers 1–4).

5. Comparisons

The FEs calculation was repeated using the moduli thatbest fit the settlements measured at the extensometers asinput, using the least squares criterion. Table 7 shows theresults obtained. The increase of the moduli in the vertical

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Table 7

Moduli that fit the measured settlements using the ANSYS program

Extensometer Depth (m) Settlement (mm) Depths of layers

(m)

Deformation

modulus (GPa)

Calculated

settlement at

surface (mm)Measured Calculated

1 0–12.2 1.95 1.78 0–6.00 1.47 2.15

2 0–31.2 2.13 2.06 6.00–12.25 1.961 2.20

3 0–12.2 0.68 1.51 12.25–30.0 18.44 1.70

4 0–12.7 0.49 1.48 30.00–50.6 30.59 1.66

5 0–6.0 1.97 1.61 3.82

6 0–29.2 3.32 3.49 3.63

Sum of the squares of the errors ¼ 1.86mm2.

Table 8

Rock mass deformation moduli (in GPa) for the foundation rock according to different authors

Gokceoglu et al. [16]

Layer (Fig. 7)

Depth (m)

E(G

M

iM M c

c

M

Mi

Mi

M

M M Mf

i

iM M

pa)=

0.14

51e0.

0654

GS

I

(

1)

E(G

pa)=

10-3

[E/�

c(1+

RQ

D/1

00)/

WD

]1.55

28

(2)

E(G

pa)=

0.07

36e0.

0755

(R

MR

)

(3)

Hoe

k an

d B

row

n [1

4]

�<

100

MP

a,

E

(Gpa

)=(�

c/1

00)½

10

G

SI-

10

(4)

40

Kay

abas

i et a

l. [1

7]

E(G

pa)=

4.32

-3.4

2WD

+0.

19 E

(1+

RQ

D/1

00)

(

5)

M

itri e

t al.

[19]

E

=0.

5E[1

-cos

(�R

MR

/100

)]

(6

)

P

alm

strö

m a

nd S

ing

[20]

E

=0.

2�(7

)

B

oyd

[21]

(8)

p=

10 k

Pa,

E(G

pa)=

RM

R4 /1

06

p=

1 M

Pa,

E

(Gpa

)=R

MR

3 /104

S

onm

ez e

t al.

[13]

d

=0.

96,

E

=E s

0.4a

(9

)

Zha

ng a

nd E

inst

ein

[22]

E

=E (

GP

a)10

0.01

86R

QD

-1.

91

(

10)

Ver

man

et a

l. [2

4]

(1

1)

E =

0.4

H� 1

0(RM

R-2

0)/3

8

1 0−6 2.08 15.2 1.44 2.87 10.0 5.4 5.53 4.05 0.80 0.53 1.72

2 6−12.25 2.35 17.6 1.73 3.43 12.0 6.7 6.65 5.13 0.96 0.65 2.46

3 12.25−30 2.38 17.5 1.78 3.35 11.1 6.7 5.96 5.91 1.18 0.76 2.91


direction is larger than suggested by the pressuremeter andRMR values.

The dependence of the modulus with depth shown inTable 7 indicates an increase with stress level, especiallyfrom 12.25 to 30m. Among criteria included in Table 6,Boyd’s [21] reflects an increase of the modulus withconfining pressure, but their moduli are too high. Thismatter has been treated by Asef and Redish [25] andRamamurthy [26] for anisotropic rocks. The empiricalequation obtained by Verman et al. [24] has been includedin Tables 6 and 8.

Most of the correlations of the so-called mass moduluswith indices actually correspond to in situ tests and not tomeasurements taken at the actual works. In one excep-

tional case, Chryssanthakis and Barton [28] comparemeasured and calculated stresses in a cavern spanning62m; to obtain a good fit the modulus derived fromcorrelations with Q must be corrected for depth.Research has been undertaken to find the moduli,

obtained from correlations with rock indices that best fitthe measured settlements. The corresponding moduli havebeen calculated as the weighted harmonic mean withrespect to the thicknesses of each ground type (d1–d3). Themoduli obtained for layers 1, 2 and 3 are collected in Table8 and drawn in Fig. 7. The lower values correspond toZhang and Einstein [22] correlations, and the upper onesto Eq. (2) given by Gokceoglu et al. [16]. The bestagreement with the settlements measured at extensometers

ARTICLE IN PRESS

Table 9

Comparison between measured settlements and those calculated using the FE program at the end of construction. Moduli obtained Eq. (1) of Table 8


(m)

Deformation

modulus (GPa)

Calculated

settlement at


1 0–12.25 1.95 1.22 0–6.00 2.08 2.79

2 0–31.20 2.13 2.30 6.00–12.25 2.35 2.82

3 0–12.2 0.68 1.18 12.25–30.0 2.38 2.50

4 0–12.7 0.49 1.18 30.00–50.6 3.52 2.48

5 0–6.00 1.97 1.08 5.43

6 0–29.2 3.32 4.32 5.27


Table 10

Comparison between measured settlements and those calculated using the FE program at the end of construction. Moduli obtained from Eq. (3) of Table 8


(m)

Deformation

modulus (GPa)

Calculated

settlement at


1 0–12.25 1.95 1.66 0–6.00 1.44 3.07

2 0–31.20 2.13 3.04 6.00–12.25 1.73 3.12

3 0–12.2 0.68 1.64 12.25–30.0 1.78 2.82

4 0–12.7 0.49 1.60 30.00–50.6 30.59 2.79

5 0–6.00 1.97 1.73 6.68

6 0–29.2 3.32 6.39 6.51


Table 11

Comparison between measured settlements and those calculated using the FE program at the end of construction. Moduli obtained from Eq. (4) of Table 8


(m)

Deformation

modulus (GPa)

Calculated

settlement at


1 0–12.25 1.95 0.90 0–6.00 2.87 1.69

2 0–31.20 2.13 1.64 6.00–12.25 3.43 1.71

3 0–12.2 0.68 0.86 12.25–30.0 3.35 1.52

4 0–12.7 0.49 0.84 30.00–50.6 30.59 1.50

5 0–6.00 1.97 0.72 3.38

6 0–29.2 3.32 3.12 3.24



corresponds to Eq. (1) given also by Gokceoglu et al. andrelating the modulus with GSI; Table 9 compares measuredand calculated results. Tables 10–12 compare the resultsobtained with Eqs. (3), (4) and (11) of Table 8, respectively.The sum of the squares of the errors (indicated at the footof the Tables) is lesser in Table 7, followed by Tables 9 and11, and larger in Table 10. The remainder correlationsindicated in Table 8 give poorer fits.

6. Results and conclusions

6.1. Results

A comparison of the moduli that best fit the extens-ometer measurements (Table 7), and those obtained from

different tests and regressions with indices, deserves thefollowing comments (restricted to jointed and weatheredbasalt):

(1)
Moduli obtained from uniaxial compression tests aretoo high (Table 1).
(2)
The settlements calculated with pressuremeter modulusare 3.5 times larger than the settlements measured atextensometers.
(3)
Moduli obtained from surface plate loading tests(Table 2) are too low. Perhaps they would be allowableat the surface when a variation of the modulus withdepth is considered. McMahon and McMahon [15]found settlements more than twice those measured,using the modulus obtained from plate loading tests.

ARTICLE IN PRESS

Table 12

Comparison between measured settlements and those calculated using the FE program at the end of construction. Moduli obtained from Eq. (11) of

Table 8


(m)

Deformation

modulus (GPa)

Calculated

settlement at


1 0–12.25 1.95 0.91 0–6.00 1.72 2.25

2 0–31.20 2.13 2.21 6.00–12.25 2.46 2.28

3 0–12.2 0.68 1.32 12.25–30.0 2.91 2.06

4 0–12.7 0.49 1.29 30.00–50.6 30.59 2.04

5 0–6.00 1.97 1.41 4.72

6 0–29.2 3.32 4.42 4.54



(4)
Moduli obtained from correlations with the Q or Qc
(Table 6) are too great. Barton [23] has alreadyindicated that this reletionship is generally applicableto hard rocks, which is not the case in fractured orweathered basalt. Notwithstanding, these moduliwould be applicable to greater depths (12.25–30m).

(5)
Some correlations [29] have not been included in Table6 because they give modulus values, which are too high.
(6)
Some of the equations that relate the moduli with rockmass classifications indices give calculated settlementsthat fit well the settlements measured at extensometers.
6.2. Conclusions

1.
The construction of the tower on fractured and weatheredvesicular basalt and scoria has been successfully com-pleted with negligible settlements and rotations. A firststage (before construction) prediction has allowed estab-lishment of an upper limit, based upon pressuremetermodulus, and a lower limit, based upon Bieniawski’sequation [8] of the settlements of the tower slab. Themeasured settlement is near the geometric mean of thesevalues (Section 4.1).
2.
The settlements measured with rod extensometers haveallowed an estimate of the in situ modulus and itsvariation with depth (Table 7).
3.
The estimate of the modulus of jointed vesicular andweathered basalt is a difficult task. The pressuremetermodulus overestimates the settlements.
4.
Correlations with different geomechanical indices maygive an acceptable fit between measured and calculatedsettlements (Tables 9–12 ). Nearly the same fit is reachedwith the simple statistical relationships given by Gokceo-glu et al. [17], and Hoek and Brown [14] that relate themodulus with GSI:
EMðGPaÞ ¼ 0:145e0:0654GSI : ðEq: 1; Table 8Þ

For sco100MPa

EMðGPaÞ ¼ ðsc=100Þ1=210ðGSI-10Þ=40: ðEq: 4; Table 8Þ

A good correlation is also obtained with the empiricalequation given by Verman et al. [24] that takes intoaccount the influence of depth:

EMðGPaÞ ¼ 0:4Ha10 RMR�20ð Þ=38; ðEq: 11; Table 8Þ

where H ¼ height of the overburden (m), a ¼ 0.0427+0.00378RMR.

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