5.4 preliminary stability assessemnt - 17 june 2008

8/12/2019 5.4 Preliminary Stability Assessemnt - 17 June 2008

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Mokihinui DamPreliminary Stability Analysis for

Conceptual Design

June 2008

Prepared for Anderson Lloyd

On behalf of Meridian Energy Ltd.

Issue 1


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Approved for issue: ...........................................................................................Peter Amos Date: 18 June 2008

Mokihinui DamPreliminary Stability Analysis

for Conceptual Design

June 2008

Prepared for Anderson Lloyd

On behalf of Meridian Energy Ltd.

Issue 1


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Meridian Energy Ltd

Mokihinui Preliminary Stability Analysis for Conceptual Design Jun-08

EXECUTIVE SUMMARY

The proposal to develop a hydro power project on the Mokihinui River includes a concretegravity dam located approximately 11km from the coast. The preliminary layout of the dam is

shown on Drawing MLD461/20/5. The dam is proposed to be constructed from RCC (roller

compacted concrete). Approximately two-thirds of the dam would be founded on granite rock

along the valley bottom and up the steep right abutment, with the remaining one-third founded

on greywacke rock on the left abutment.

A conceptual design has been developed with spillway crest level at RL100m. For the

purposes of developing the concept a dam cross section is shown based on a vertical upstream

face, downstream face of 0.8:1 and crest width of approximately 3m. These are dimensions

typically used for preliminary design of a concrete dam. Dams with these sectional properties

have typically been found to be well proportioned for most design loading conditions.

The Dam Safety Guidelines produced by the New Zealand Society of Large Dams (NZSOLD1)

and Bulletin 72 of the International Commission on Large Dams (ICOLD2) give the following

performance criteria under earthquake loading:

Following the 150-year Operating Basis Earthquake (the earthquake having a 50%

probability of occurring over a period of 100 years), there should either be no damage or

minor repairable damage.

During and after the Maximum Design Earthquake (the maximum level of ground motion

for which the dam is designed), some damage is allowable but it must not lead to

catastrophic failure or uncontrolled release of the reservoir. For a concrete dam, the

main shaking may lead to cracking and reduced strength.

A concrete dam can actually be designed to retain the reservoir contents following any seismic

event, provided that sufficient funds for construction are available. The art of dam engineering

is to provide an optimised solution which will meet acceptable design standards for all load

conditions, but also satisfy economic criteria. Typical practice is to produce a partially optimised


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The purpose of this report is to provide a preliminary check that the concept dam section is in

the right order to meet dam stability criteria considered acceptable in the industry. Dam stabilitycriteria are represented by the Dam Safety Guidelines published by the New Zealand Society of

Large Dams (NZSOLD). A well proportioned concrete dam section would be expected to easily

meet stability criteria for normal service loads and floods, but can be expected to be well tested

by an extreme earthquake. Usual practice for a straight concrete gravity dam at this early stage

of the project is to initially analyse the structure as two-dimensional slices for simplicity.

However this is often grossly conservative as three dimensional aspects that contribute to

safety are not considered. Where the concept design section is close to minimum safety limits

under two dimensional analysis, there is scope to assess the three dimensional contributions to

safety or enhance the dam section during detailed design. Irrespective, a concrete dam will be

designed at Mokihinui to safely retain the reservoir contents following the Maximum Design

Earthquake.

This report is therefore a preliminary assessment of:

The two-dimensional stability of three sections of the dam that are founded on both

granite and greywacke rock to determine if the dam meets New Zealand dam safety

guidelines for usual, flood, and seismic loads;

The likely extent of possible damage to the dam under earthquake loading; and

The post-earthquake stability of the dam, taking into account the extent of likely damageto the dam.

The analyses carried out include normal (or usual) loading conditions, an extreme flood, and a

range of earthquake loads. The extreme flood load is the Probable Maximum Flood (PMF). A

range of earthquake loads with peak ground accelerations up to 0.91g have been considered.

These are intended to represent the range of earthquake loads anticipated as requiring

consideration in the final design, with the 0.91g representing fault rupture of the nearby

Glasgow Fault (assuming it is an active fault, a detail yet to be determined).

The study uses the site geotechnical information obtained to date, and assumes typical

properties of RCC concrete From these preliminary estimates of the shear strength of the


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The results of static and dynamic two-dimensional analyses for the typical dam sections shown

in Drawing MLD461/20/5 show that:

The dam meets the NZSOLD sliding stability criteria for usual and extreme flood load

cases.

The dynamic analyses show the dam should not be damaged, or have only minor

repairable damage, if it were subject to 150-year earthquake shaking.

For earthquake loading up to and including the 2,500-year event, the analysed sections

meet the sliding stability criteria in the NZSOLD Dam Safety Guidelines. For 10,000-year earthquake loading, the dam meets the 1.3 minimum FOS except at the

greywacke foundation of the powerhouse section where the calculated factor is 1.20. If

specific tests were performed on the greywacke rock to confirm the shear strength

parameters assumed for this study, the powerhouse section would meet the reduced

minimum NZSOLD with-test FOS of 1.1.

For the Glasgow Fault rupture earthquake, the FOS against sliding on the granitefoundation is also less than the minimum value of 1.3. The calculated value is 1.23.

Again, if testing of the granite confirms its assumed properties, the spillway section

would meet the with-test minimum value of 1.1.

If rock tests indicates peak shear strengths less than assumed, widening of the dam

footprint by about 15% in the least stable areas would ensure the NZSOLD criteria are

met (assuming conservative two-dimensional analysis methods only are used in finaldesign). Alternatively 3-dimensional analyses may prove the existing section

proportions satisfactory.

For post-MDE loading, when the foundation rock is assumed to be cracked across the

entire dam footprint, the granite spillway foundation and the greywacke powerhouse

foundation are less than the minimum NZSOLD requirement of FOS of 1.1. The

calculated sliding FOS values at these locations are 0.95 and 1.05 respectively. Modestincreases in the assumed residual friction angles of the rock would result in compliance,

and specific further testing may confirm this. If not, slight widening of the dams footprint

in these areas could be employed to improve the post-earthquake stability.


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TABLE OF CONTENTS

EXECUTIVE SUMMARY...............................................................................................ii1.0 Introduction.............................................................................................................12.0 Performance Criteria ..............................................................................................3

3.0 Sections Analysed and Foundation Type...............................................................44.0 Loading...................................................................................................................5

4.1 Usual Loads ........................................................................................................54.2 Flood Loading .....................................................................................................54.3 Earthquake Loading............................................................................................54.4 Post-Earthquake Uplift........................................................................................6

5.0 Shear Strength of Rock and Concrete ...................................................................75.1 Rock....................................................................................................................7

5.2 Concrete..............................................................................................................86.0 Methods Of Analysis...............................................................................................97.0 Acceptable Sliding Factors for Stability................................................................108.0 Analysis Results ...................................................................................................11

8.1 Sliding Stability for Usual Loading....................................................................118.2 Sliding Stability for Flood Loading ....................................................................128.3 Assessment of Seismic Stresses from Modal Response Spectrum Analysis..128.4 Sliding Stability for Earthquake Loading...........................................................138.5 Post-Earthquake Stability .................................................................................16

9.0 Three-Dimensional Effects on Dam Stability........................................................1810.0 Conclusions ..........................................................................................................20

Appendices

Appendix A Drawing of Proposed Mokihinui Dam

Appendix B Rock Strength Analyses

Appendix C Finite Element Analysis Report

Appendix D Sliding Stability at Base of Dam - Calculations


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1.0 Introduction

The proposal to develop a hydro power project on the Mokihinui River includes a concretegravity dam located approximately 11km from the coast. The preliminary layout of the dam is

shown on Drawing MLD461/20/5 (refer Appendix A). The dam is proposed to be constructed

from RCC (roller compacted concrete). Approximately two-thirds of the dam would be founded

on granite rock along the valley bottom and up the steep right abutment, with the remaining

one-third founded on greywacke rock on the left abutment.

A conceptual design has been developed with spillway crest level at RL100m. For the

purposes of developing the concept a dam cross section is shown based on a vertical upstream

face, downstream face of 0.8:1 and crest width of approximately 3m. These are dimensions

typically used for preliminary design of a concrete dam. Dams with these sectional properties

have typically been found to be well proportioned for most design loading conditions.

A concrete dam can actually be designed to retain the reservoir contents following any seismic

event, provided that sufficient funds for construction are available. The art of dam engineering

is to provide an optimised solution which will meet acceptable design standards for all load

conditions, but also satisfy economic criteria. Typical practice is to produce a partially optimised

design at the feasibility level, the design then being a broad approximation to constraints in

project information known at that stage. Further optimisation can be expected at the later detail

design level.

The purpose of this report is to provide a preliminary check that the concept dam section is in

the right order to meet dam stability criteria considered acceptable in the industry. Dam stability

criteria are represented by the Dam Safety Guidelines published by the New Zealand Society of

Large Dams (NZSOLD). A well proportioned concrete dam section would be expected to easily

meet stability criteria for normal service loads and floods, but can be expected to be well tested

by an extreme earthquake. Usual practice for a straight concrete gravity dam at this early stage

of the project is to initially analyse the structure as two-dimensional slices for simplicity.

However this is often grossly conservative as three dimensional aspects that contribute to


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The two-dimensional stability of three sections of the dam that are founded on both

granite and greywacke rock to determine if the dam meets New Zealand dam safety

guidelines for usual, flood, and seismic loads;

The likely extent of possible damage to the dam under earthquake loading; and

The post-earthquake stability of the dam, taking into account the extent of likely damage

to the dam.

The study uses the geotechnical information obtained to date (as outlined above), and assumestypical properties of RCC concrete.

Geotechnical investigations undertaken to date indicate:

There are no major faults in the foundation requiring significant treatment

The contact between the greywacke and granite does not have significant flaws

The rock jointing is relatively tight There is no evidence of persistent near-horizontal weak seams in the rock that may form

potential critical sliding planes in the foundation

There is an apparent fault scarp associated with the Glasgow Fault located

approximately 1km from the site, but it is not yet known if the fault is active in

engineering terms.

No known fault crosses the dam site, so this report does not need to consider direct

displacement within the dam foundation.

The sliding stability at the base of the three dam sections is determined. The probable

maximum flood (PMF) loading condition is included in the analyses. The earthquake loadings

considered are events with return periods of 150, 475, 2,500 and 10,000 years, together with0.91g PGA (peak ground acceleration) loading associated with possible rupture of the nearby

Glasgow Fault.

In addition, finite element analyses of the highest section are undertaken to establish the


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2.0 Performance Criteria

The Dam Safety Guidelines produced by the New Zealand Society of Large Dams (NZSOLD3)

and Bulletin 72 of the International Commission on Large Dams (ICOLD4) give the following

performance criteria under earthquake loading:

Following the 150-year Operating Basis Earthquake (the earthquake having a 50%

probability of occurring over a period of 100 years), there should either be no damage orminor repairable damage.

During and after the Maximum Design Earthquake (the maximum level of ground motion

for which the dam is designed), some damage is allowable but it must not lead to

catastrophic failure or uncontrolled release of the reservoir. For a concrete dam, the

main shaking may lead to cracking and reduced strength.

In order to meet the above performance criteria, the dam is analysed to determine whether

there are adequate factors of safety present to prevent the relevant modes of failure from

occurring. Failure modes considered in this assessment relate to the dam sliding on horizontal

planes of weakness in the dam foundation or on cracks in the rock or the dam concrete.


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3.0 Sections Analysed and Foundation TypeTo provide a reasonable overall assessment of the dams stability, three sections of the dam as

follows are analysed:

The maximum 92m high section through the overflow spillway founded on granite,

A 67m high powerhouse section on the left abutment founded on both granite and

greywacke, and

A 40m high section on the left abutment founded on greywacke.

The spillway section will most likely have the greatest seismic demand of the dam and be

subject to the highest stresses. It is located within the existing river channel. Under usual river

flow conditions the downstream toe of the dam will be submerged under tailwater about 15m

deep.

The nominal 67m high powerhouse section (the height excludes the 8.5m high flood surcharge

wall at the top of the dam) will be about 60m long. At its left side extremity is the contact zone

between the granite and greywacke rocks at the site. Hence this will be the highest section of

the dam founded on greywacke rock. Investigations to date show that the greywacke will most

likely have a lower shear strength than the granite rock.

A 40m high left abutment section was analysed on the basis that this would provide a more

typical assessment of the stability of the 100m long abutment. The abutment is founded entirely

on greywacke rock.


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4.0 Loading

4.1 Usual Loads

The usual load conditions assumed for the analyses are:

Self-weight of the dam corresponding to a concrete density of 2.5tonnes/m3.

Hydrostatic reservoir load with lake level at spillway crest.

Uplift at the base of the dam assuming foundation drain efficiency of 67% (the usual

assumption for the preliminary design of a concrete gravity dam). Silt loading, assuming that silt may eventually reach a mid-height level on the upstream

face of the dam. The silt is assumed to be a fluid with a density of 1.36 tonnes/m3.

4.2 Flood Loading

The dam is required to pass safely the probable maximum flood (PMF) at the site. The flood

surcharge level above the spillway crest for the estimated PMF of 7,200m

3

/s is 8.5m. This willincrease the hydrostatic loading on the dam by about 20%. The sliding stability of the three dam

sections has been assessed for this maximum flood condition.

4.3 Earthquake Loading

The five levels of earthquake loading used in the analyses are based on a preliminary

assessment of available information on the seismic hazards in the Mokihinui River

5

. Fourloadings are probabilistically derived, ranging from an estimated 150-year return period

earthquake (the Operating Basis Earthquake) up to a 10,000-year event, and one is

deterministically derived assuming rupture of the Glasgow Fault located 1km from the site. Little

is currently known about the activity of the Glasgow Fault. The Maximum Design Earthquake

(MDE) for the dam is likely to be either the 10,000-year event or the Glasgow Fault rupture

scenario if further investigations indicate the fault can be classified as being active. At thisstage, therefore, Glasgow Fault rupture may be regarded as the Maximum Credible Earthquake

(MCE) for the site.

The peak ground accelerations for the selected loadings are shown in Table 1.


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Table 1 Peak Ground Accelerations

Earthquake Event Peak Ground Acceleration(g)

150-year 0.28

475-year 0.40

2,500-year 0.62

10,000-year 0.81

Glasgow Fault rupture 0.91

The assumed response spectra for the four probabilistically-derived earthquakes are shown in

Figure 4 of Appendix C.

4.4 Post-Earthquake Uplift

In keeping with international dam engineering practice, it is assumed that following a largeearthquake there will be higher uplift pressures in the dam. This may be the result of increased

foundation seepage and the inability of the drains to cope, or because the drains have become

blocked from the effects of the ground shaking. For the post-earthquake condition, the uplift is

assumed to vary linearly from full reservoir pressure at the upstream heel to tailwater pressure

at the downstream toe (for the spillway section) or to zero pressure (for the abutment section).


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5.0 Shear Strength of Rock and Concrete

5.1 Rock

There are no known persistent sub-horizontal weak seams in the granite and greywacke

foundation. Therefore it is assumed that the critical potential foundation failure plane would be

through intact rock located at or close to the base of the dam.

The assumed Hoek-Brown strength parameters for the granite and greywacke rock, based on

information obtained to date6, are shown in Table 2.

Table 2: Hoek-Brown Strength Parameters for Granite and Greywacke Rock

Property Granite Greywacke

Intact Uniaxial Compressive Strength 110MPa 80MPa

Geological Strength Index (GSI) 45 35

mi(material constant for intact rock) 20 11

Disturbance Factor 0 0

The Hoek-Brown parameters were used as input for analysis using the ROCLAB7program to

determine estimated cohesion and friction angle values for the foundation rock. The results of

the analyses are shown in Appendix B.

When the normal stress is relatively low (less than about 5MPa), the Hoek-Brown method for

determining equivalent shear strength parameters can sometimes over-estimate the cohesive

strength of the rock. To account for this, the cohesion values obtained from the ROCLAB

program and shown in Appendix B have been conservatively reduced by 25%.

The peak shear strength parameters for the rock foundation (from Roclab) assumed for this

study are shown in Table 3.


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Table 3: Peak Shear Strength Parameters for Rock

Location Normal Stress

(KPa)

Rock Type Friction Angle

()

Cohesion

(KPa)

Spillway section 1100 granite 60 650

Powerhouse section 750 granite 62 550

Powerhouse section 750 greywacke 53 350

Left abutment section 500 greywacke 56 280

Where cracking of the rock may occur as a result of earthquake shaking, it is assumed (on

advice from GNS) that the residual friction angle (R) of the rock reduces to:

R= 400 for granite, and

R= 350 for greywacke.

These are conservative preliminary values that are considered appropriate at this stage.

5.2 Concrete

It is probable that the dam will be constructed using RCC with a high cementitious content. This

concrete will have a relatively high strength, with properties similar to conventional mass

concrete. To establish appropriate shear strength parameters, the published results of the

testing of cores extracted from a number of RCC dams have been used

8

. The critical locationsin the dam are at the lift joints between RCC layers. The measured mean cohesion at the lift

joints in eight dams constructed from RCC with a high cementitious content is 1.9MPa, with a

range from 1MPa to 4MPa.

As typically used for preliminary design, the friction angle () of the concrete is assumed to be

45

0

In summary, the assumed shear strength parameters of the concrete are:

c = 1500KPa, and

= 450.


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6.0 Methods Of Analysis

The sliding stability of the dam on horizontal planes immediately above and below the

concrete/rock interface at the three sections is determined. Horizontal planes within the RCC

and within the foundation rock are considered.

The safety factor against sliding is defined by the following equation:

H

cAUW

FS

+

=

tan)(

Where: W = self weight of dam

U = uplift

= friction angle

c = cohesion

A = area of sliding plane

H= sum of horizontal forces (hydrostatic + silt + seismic inertia + hydrodynamic)

The Seismic Coefficient Method9is used to determine the earthquake sliding stability of the

three selected dam sections. Hence, the earthquake forces are treated simply as static forces

equal to the dam weight plus hydrodynamic weight multiplied by a seismic coefficient. As

accepted in international dam engineering practice, the seismic coefficient is assumed to be a

fraction of the peak ground acceleration. For this study a seismic coefficient of 2/3 times the

peak ground acceleration is used.

A modal response spectrum analysis has also been performed to determine the likely seismic

stresses in the spillway section. Hydrodynamic effects are modelled as an added mass of water

moving with the dam. A finite element model is used, with the base rock extending for 100m

upstream, downstream and beneath the dam. Details of the model geometry and of the

assumed rock and concrete elastic modulus values are provided in Section 3 of Appendix C.

Compusoft Engineering has used the SAP2000 finite element package for undertaking the


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7.0 Acceptable Sliding Factors for Stability

The NZSOLD guidelines10have been used to establish acceptable limits on the sliding stability

of the dam. The New Zealand guidelines are based on internationally-accepted dam safely

criteria.

The minimum factors of safety used for sliding in this preliminary study are shown in Table 4.

Table 4: NZSOLD Minimum Factors of Safety for Sliding Stability

Load Case Peak Sliding

FOS

(no tests)

Peak Sliding

FOS

(with tests)

Residual

Sliding

FOS

Usual 3.0 2.0 -

PMF 2.0 1.5 -

Maximum Earthquake* 1.3 1.1 -

Post-Earthquake - - 1.1

* As determined by the seismic coefficient (pseudostatic) method of analysis

The no-test factors are used for assessing the results in this study, but with acknowledgementthat for final design the with-test factors would be used.

The residual post-earthquake factor of safety assumes cracked rock or concrete that has no

cohesive strength. Therefore, only the friction force associated with the materials residual

friction angle is assumed to resist horizontal forces acting on the dam after an earthquake.


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8.0 Analysis Results

The results of the calculations performed to determine the sliding factors of safety at the base of

the three dam sections are provided in Appendix D. The results are summarised in Sections 8.1

to 8.5 below.

8.1 Sliding Stability for Usual Loading

The usual load case considers the self weight of the dam, hydrostatic loading, and the uplift at

the dam/foundation contact.

The results of the usual load analyses are summarised in Table 4.

Table 4 : Sliding Factors of Safety for Usual Loading

Location of base sliding plane Material Usual

Loading FOSSpillway section (92m high) granite rock 3.54

Spillway section (92m high) concrete 3.97

Powerhouse section (67m high) granite rock 4.98

Powerhouse section (67m high) greywacke rock 3.41

Powerhouse section (67m high) concrete 5.68

Abutment section (40m high) greywacke rock 4.99Abutment section (40m high) concrete 9.76

The factors meet the recommended minimum NZSOLD value of 3.0 for rock and concrete

material that have not been specifically tested to determine their shear strengths. The factors

are well above the minimum value of 2.0 for materials that have been tested.

The results show that for usual loads:

The granite rock at the base of the spillway and the greywacke rock at the base of the

67m high abutment section may have the equally lowest peak sliding factors (about 3.5)

for the dam structure


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8.2 Sliding Stability for Flood Loading

The sliding stability at the base of the dam has been checked for PMF flood conditions (an 8.5m

increase in the normal lake level). The tailwater under the PMF flow of 7,200m3/s is estimated to

rise to RL 38m, which is 14.5m above normal tailwater level and 30m above bed level. It is

conservatively assumed that all foundation drainage is overwhelmed during the PMF and that a

full uplift condition, linearly varying from reservoir flood level at the upstream toe to tailwater

flood level at the downstream toe, develops during the event.

The calculated sliding factors of safety are shown in Table 5.

Table 5: Sliding Factors of Safety for PMF Loading

Location of basesliding plane

Material Flood LoadingFOS

Spillway section granite rock 2.39

Spillway section concrete 3.05

Powerhouse section granite rock 3.15

Powerhouse section greywacke rock 2.14

Powerhouse section concrete 4.11

Left abutment section greywacke rock 2.88

Left abutment section concrete 6.28

The factors meet the recommended minimum NZSOLD values of 2.0 (without tests) and 1.5

(with tests).

As for usual loading, for a given material the factors improve as the dam section height

decreases.

8.3 Assessment of Seismic Stresses from Modal Response Spectrum Analysis

The peak vertical and horizontal (shear) seismic stresses in the 91m high spillway section for

four levels of earthquake loading up to 0.81g PGA are shown in Figures 13 to 20 of Appendix C.

These stresses are for seismic loading only. To obtain the total stress distribution, the stresses


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Comments on the results shown in Figure 25 of Appendix C are as follows:

Under usual load conditions, the foundation is subject to a relatively uniform

compressive stress of about 1MPa;

Under 150-year earthquake loading (the operating basis earthquake), there should

not be any cracking in the concrete dam but the rock near the dams foundation level

may crack up to a horizontal depth of about 10m under the dam at the upstream face;

Under the 475-year earthquake, there may be limited concrete cracking that

penetrates about 3m into the upstream face of the dam. The foundation rock may be

cracked to a depth of about 15m at both the upstream and downstream face as the

dam responds to the cyclic earthquake loading;

Under the 2,500-year and 10,000-year earthquakes, cracks in the conrete may

penetrate about 5m into the upstream face of the dam. Within the foundation rock,

only about a 10m long central core of rock may remain uncracked.

The results show that the dam will significantly exceed a linear-elastic range of behaviour for

earthquakes greater than about the 2,500-year event. To estimate the extent of cracking and

other damage for these higher levels of earthquake, a 3-D non-linear time-history analysis of the

dam would be required (discussed further in Section 9).

8.4 Sliding Stability for Earthquake Loading

For determining the horizontal seismic forces acting on the three dam sections, the self weight

and hydrodynamic masses shown in Table 6 are used.

Table 6: Self-Weight and Hydrodynamic Masses (per metre length of dam)

Dam section Self- weight

mass (tonnes)

Hydrodynamic

mass (tonnes)

Total mass

(tonnes)

Spillway 8,950 4,570 13,520

Powerhouse 5,420 2,420 7,840

Left abutment 2,320 860 3,180


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The results of the seismic coefficient analysis results for the three sections are shown in Tables

7, 8, and 9.

Table 7: Earthquake Sliding Stability at Base of Spillway SectionSeismic Coefficient Analysis Results

EarthquakeEvent

Peak GroundAcceleration

SeismicCoefficient

Peak slidingfactor of safety in

concrete

Peak slidingfactor of safety in

granite rock

150-year 0.28g 0.19 2.51 2.24

475-year 0.40g 0.27 2.17 1.942,500-year 0.62g 0.41 1.76 1.57

10,000-year 0.81g 0.54 1.50 1.34

Glasgow Fault

Rupture

0.91g 0.61 1.38 1.23

Table 8: Earthquake Sliding Stability at Base of Powerhouse SectionSeismic Coefficient Analysis Results

EarthquakeEvent

PeakGround

Acceleration

SeismicCoefficient

Peak slidingfactor ofsafety inconcrete

Peak slidingfactor ofsafety ingranite

Peak slidingfactor ofsafety in

greywacke

150-year 0.28g 0.19 3.45 3.03 2.08

475-year 0.40g 0.27 2.95 2.59 1.78

2,500-year 0.62g 0.41 2.37 2.07 1.42

10,000-year 0.81g 0.54 2.00 1.75 1.20

Glasgow Fault

Rupture

0.91g 0.61 1.84 1.62 1.11

Table 9: Earthquake Sliding Stability at Base of Left Abutment Section

Seismic Coefficient Analysis ResultsEarthquakeEvent

PeakGround

Acceleration

SeismicCoefficient

Peak slidingfactor ofsafety inconcrete

Peak slidingfactor ofsafety in

greywacke

150-year 0.28g 0.19 5.55 2.84


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For pseudostatic earthquake loading, the NZSOLD minimum recommended sliding factors are

1.3 (without tests) and 1.1 (with tests). The results show that the dam meets the minimum 1.3

requirement, except for 10,000-year or Glasgow Fault generated earthquakes at the following

locations:

The granite rock at the base of the spillway section for 0.91g Glasgow Fault shaking (FOS

= 1.23), and

The greywacke rock at the base of the powerhouse section for 0.81g 10,000-year shaking

(FOS = 1.20) and for 0.91g Glasgow Fault shaking (FOS = 1.11)

During detailed design, measures that could be adopted if necessary to improve the seismic

sliding stability would include flattening of the upstream and/or downstream faces of the dam.

For example,

changing the vertical upstream face of the dam to a 0.1:1 slope, or

changing the downstream face from 0.8:1 to 0.9:1

would improve the spillway sliding factor from 1.23 to 1.32 and the powerhouse greywacke

sliding factor for 10,000-year loading from 1.20 to 1.32.

Also, if testing of the foundation rock materials during the final design process should indicate

that they meet or exceed the shear strength parameters assumed for this study, then the

minimum 1.1 (with tests) FOS value would be met. Changes to the preliminary dam geometry

may not then be required.

In addition, as noted in Section 1, the two-dimensional analysis results are conservative. The

three-dimensional characteristics of the dam should appreciably improve its seismic

performance. This also suggests that the current assumed dam section (vertical upstream face

and 0.8:1 downstream face) may have acceptable resistance to seismic loading. The dams

probable three-dimensional performance is discussed further in Section 9.

The results in Tables 7, 8, and 9 also show that (as for usual and flood loading conditions) the

seismic sliding stability of the dam:


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8.5 Post-Earthquake Stability

For assessing the post-earthquake stability of the dam, the extent of damage and cracking to

the dam needs to be estimated. The modal spectral analysis results, as discussed in Section

8.2, provide guidance in this regard. These show that the foundation of the spillway section may

be fully cracked if the dam is subject to MDE earthquake loading (the 10,000-year event).

Following such an earthquake, when the dam is again subject to usual self-weight and

hydrostatic loads, there would be uniform compressive stress of about 1.2MPa on the cracked

spillway foundation. The maximum uplift pressure from 92m head of water will be 0.9MPa.

Therefore foundation cracks, even if penetrated at the upstream face of the dam by water at full

lake head pressure, should still remain in compression after the earthquake.

The foundation of the higher left abutment sections may also be fully cracked in a large

earthquake. But following such an event, as for the spillway section, there will be compressive

stress on the cracks.

Because of the compressive stress on the cracks, the assumption of a linear variation of post-

earthquake uplift from full reservoir pressure at the upstream heel to tailwater pressure (or zero

pressure in the case of the abutment sections) at the downstream toe is considered appropriate

(refer Section 4.4).

The rock would have no cohesive strength because of the cracking. As outlined in Section 5.1,

the peak friction angles of 62/60 for granite and 56/53 for greywacke are assumed to reduce

to estimated residual values of 40 and 35 respectively.

If cracking should occur in the concrete, the post-earthquake sliding resistance would be higher

than in the rock (the assumed residual friction angle for concrete is 45).

The calculated factors of safety for the post-earthquake scenario (that is, following an extreme

earthquake greater than the 2,500-year event) are summarised in Table 10 below.


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Meridian Energy Ltd


Table 10: Sliding Factors of Safety for Post-MDE Condition

Location of base slidingplane

Material Post-MDEFOS

Spillway section granite rock 0.95

Spillway section concrete 1.13

Powerhouse section granite rock 1.26

Powerhouse section greywacke rock 1.05

Powerhouse section concrete 1.50

Left abutment section greywacke rock 1.36

Left abutment section concrete 1.95

Both the 0.95 factor for the granite spillway foundation and 1.05 for the greywacke powerhouse

foundation are less than the recommended NZSOLD minimum value of 1.1.

The calculated factors are entirely dependent on the assumed residual friction angles Rof 40

for granite and 35 for greywacke. At this preliminary stage, these values are considered to be

conservative (particularly if it is demonstrated that no permanent sliding displacement will occur

on the cracked foundation in the course of the earthquake).

If the residual angles remain unchanged for the final design, the post-MDE stability could be

improved by (for example) flattening either the vertical upstream face of the dam to a slope of

about 0.1:1 or the downstream face form 0.8:1 to 0.9:1. In this case the 0.95 factor for the

spillway foundation would improve to 1.09, and the 1.05 factor for the greywacke powerhouse

foundation would improve to 1.22.

The three-dimensional behaviour of the dam could also possibly be relied on to provide the

required post-earthquake stability of the spillway section. This is discussed further in Section 9.


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Meridian Energy Ltd


9.0 Three-Dimensional Effects on Dam Stability

The analyses show that the dam should meet sliding stability requirements for usual and flood

loading conditions. The dam also demonstrates acceptable performance for earthquake

loadings up to and including the 2,500-year return period event.

The preliminary two-dimensional pseudostatic analyses for MDE 10,000-year or Glasgow Fault

rupture earthquake loading indicate sliding factors of safety below the recommended minimum

no-test value of 1.3. These occur in the granite foundation of the spillway section and the

greywacke foundation of the powerhouse section. Also, the factors of safety for post-MDE

sliding in these two areas of the foundation are less than the recommended 1.1 minimum value.

The above analysis results do not take into account the three-dimensional behaviour of the

dam. The dam is located in a relatively narrow valley, with a particularly steep right abutment

(refer dam elevation on Drawing MLD461/20/5, Appendix A).

The dam will also be constructed from RCC and will most likely not have fully-formed transverse

contraction joints. Considerable side shear from concrete aggregate interlock could be

developed on such joint planes through the dam under extreme earthquake loading. Loads on

the dam could therefore be distributed laterally over large areas of the foundation.

For the narrow less-stable powerhouse section of the dam on greywacke, the peak MDE (0.81g

or 0.91g) loading and the post-MDE loading on the foundation could be distributed:

To the more stable and broader section to the right founded on granite rock, and

To the lesser height and more stable abutment section to the left founded on greywacke.

Table 11 shows how the peak MDE and post-MDE factors vary in the foundation.

Table 11: Variation of MDE and Post-MDE Factors of Safety in Foundation

Load Case Powerhouse Powerhouse Abutment NZSOLD NZSOLD

M idi E Ltd


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Meridian Energy Ltd


Assuming that the greywacke powerhouse section is likely to be only about 10m long out of a

total left abutment/powerhouse length of about 160m, Table 11 indicates that:

The overall peak MDEfactor of safety for the powerhouse section foundation is likely to

be in the range of 1.5 to 1.6.

The overall peak MDEfactor of safety for the left abutment foundation is likely to be in

the range of 1.4 to1.5.

The overall post-MDEfactor of safety for the powerhouse section foundation is likely to

be about 1.2.

The overall post-MDEfactor of safety for the left abutment foundation is likely to be

about 1.25.

In this case, the dam would meet the NZSOLD minimum requirements for earthquake sliding

stability.

Similarly, the post-MDE sliding stability of the spillway foundation (indicated to have a FOS of

0.95) should attain the minimum requirement of 1.1 when support from the following is taken

into account:

the more stable dam section to the left (where the FOS is 1.26), and

the side shear from the right abutment contact zone to the right.

A three-dimensional nonlinear time history analysis of the complete dam would be required to

more accurately determine its stability under dynamic earthquake loading. This would determine

whether any permanent displacement of the dam may occur during the course of a large

earthquake. If this is indicated in the 3-D analyses, refinements to the final design of the dam

and defensive design measures could be employed. These could include such measures as the

keying-in of the right abutment contact, and/or providing local thickening at the base of the dam

(as discussed in Section 7.4). Such measures would also improve the post-earthquake sliding

stability of the dam.

Meridian Energy Ltd


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Meridian Energy Ltd


10.0 Conclusions

Preliminary estimates of the shear strength for the foundation rock and the dam concrete have

been used for assessing the two-dimensional sliding stability of the dam under usual, flood, and

earthquake loads. The seismic analyses have used earthquake loads up to a MCE peak ground

acceleration of 0.91g.

The results of static and dynamic two-dimensional analyses for the typical dam sections shown

in Drawing MLD461/20/5 show that:

The dam meets the NZSOLD sliding stability criteria for usual and extreme flood load

cases.

The dynamic analyses show the dam should not be damaged, or have only minor

repairable damage, if it were subject to 150-year earthquake shaking.

For earthquake loading up to and including the 2,500-year event, the analysed sections

meet the sliding stability criteria in the NZSOLD Dam Safety Guidelines.

For 10,000-year earthquake loading, the dam meets the 1.3 minimum FOS except at the

greywacke foundation of the powerhouse section where the calculated factor is 1.20. If

specific tests were performed on the greywacke rock to confirm the shear strength

parameters assumed for this study, the powerhouse section would meet the reduced

minimum NZSOLD with-test FOS of 1.1.

For the Glasgow Fault rupture earthquake, the FOS against sliding on the granite

foundation is also less than the minimum value of 1.3. The calculated value is 1.23.

Again, if testing of the granite confirms its assumed properties, the spillway section

would meet the with-test minimum value of 1.1.

If rock tests indicates peak shear strengths less than assumed, widening of the dam

footprint by about 15% in the least stable areas would ensure the NZSOLD criteria are

met (assuming conservative two-dimensional analysis methods only are used in final

design). Alternatively 3-dimensional analyses may prove the existing section

proportions satisfactory.

For post-MDE loading, when the foundation rock is assumed to be cracked across the

Meridian Energy Ltd


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Meridian Energy Ltd


The two-dimensional analyses provide conservative results for dam stability calculations. If the

three-dimensional effects that will be present for the Mokihinui proposal (lack of smooth

transverse joints and rough foundation shape) are taken into account, the overall earthquake

and post-earthquake sliding stability is likely to meet acceptable criteria. Significant changes in

the current assumed dam geometry would not then be necessary.

Meridian Energy Ltd


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Meridian Energy Ltd


APPENDIX A

Drawing of Proposed Mokihinui Dam


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APPENDIX B

Rock Strength Analyses


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Figure 1: Granite at Spillway Foundation 1.1MPa Normal Stress


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Figure 2: Granite at Powerhouse Section Foundation 0.75MPa Normal Stress


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Figure 3: Greywacke at Powerhouse Section Foundation 0.75MPa Normal Stress


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Figure 4: Greywacke at Abutment Foundation 0.5MPa Normal Stress

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Mokihinui Preliminary Stability Analysis for Conceptual Design Jun 08

APPENDIX C

Finite Element Analysis Report

CCCCOMPUSOFTOMPUSOFTOMPUSOFTOMPUSOFT


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CCCCOMPUSOFTOMPUSOFTOMPUSOFTOMPUSOFT E N G I N E E R I N GE N G I N E E R I N GE N G I N E E R I N GE N G I N E E R I N G

106B C arl ton Gore Road. P O Box 9493, Newmarket , Auckland, New Zealand.Telephone: +64 9 5 22 145 6 Facs imi le : +64 9 5 22 3366

Mokihinui Dam

Seismic Analysis

Ref: 07052-01

Prepared by: Compusoft Engineering Limited

For: Damwatch

P O Box 1549


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CCCCOMPUSOFTOMPUSOFTOMPUSOFTOMPUSOFT E N G I N E E R I N GE N G I N E E R I N GE N G I N E E R I N GE N G I N E E R I N G

106B C arl ton Gore Road. P O Box 9493, Newmarket , Auckland, New Zealand.Telephone: +64 9 5 22 145 6 Facs imi le : +64 9 5 22 3366

Table of Contents

Page no.

1.0 Introduction 1

2.0 Structure Description 1

3.0 Analysis Model 1

4.0 Loadings 4

4.1 Reservoir & Uplift Loading 4

4.2 Seismic Loading 4

5.0 Results 6

5.1 Static Analysis 6

5.2 Modal Analysis 12

5.3 Response Spectrum Analysis 13

6.0 Conclusions 25


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1.0 Introduction

A 2-D finite element analysis of the spillway section of the Mokihinui Dam has been undertaken.

The purpose of the analysis is to establish the likely stresses within the dam and to assess what

possible damage to the dam would be caused due to seismic loading.

2.0 Structure Description

At the maximum spillway section the dam is 92m high and tapers from 77.2m thick at its base to

3.6m thick at the apex. Foundation drains are assumed to be located 18m from the upstream face.

The tail water depth is taken to be 15.5m deep. The dam is constructed of RCC concrete and at the

spillway section considered in this report is founded on granite rock.

3.0 Analysis Model

An analysis model was formed in the finite element package SAP2000 (Version 11). The model

considers a typical two dimensional cross section of the dam with geometry as specified by

Damwatch. Modelling of the base rock material extends for a distance of 100m upstream and

downstream and 100m below the dam. Plain strain elements 1.0m thick were used with meshingundertaken such that the maximum edge dimension of any element was five (5) meters. Material

properties were applied per Damwatch instruction and are outlined in Table 1 below. Link (Gap

type) elements were modelled at the dam-rock interface to allow for the application of uplift

pressures to the base of the dam. The boundaries of the model are considered to be restrained

against both horizontal and vertical translation at the base and restrained against horizontal

translation only at the upstream & downstream edges. Figure 1 below presents a graphical

representation of the analysis model. The hydrodynamic effects of the retained upstream water

have been included following the Westergaard method whereby a series of discrete added masses

have been applied to the upstream face of the dam. The total hydrodynamic mass added to the

upstream face of the dam has been evaluated as 4 589 tonnes with the distribution presented in


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Table 1 Material Properties

Parameter Dam Rock

Density, 2.5 t/m3 0 t/m

3

Youngs Modulus Static, Es(1)

20 GPa 10 GPa

Youngs Modulus Dynamic, Ed 30 GPa 20 GPa

Poissons Ratio, 0.25 0.25

Notes:

1. The Youngs modulus values appropriate for static loading have not been used in the model

and have been included in the table for completeness only.


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Hydrodynamic Mass

0

10

20

30

40

50

60

70

80

90

100

0 20 40 60 80 100 120 140

Hydrodynamic Mass, mh(tonnes)

HeightUpDam,z(m)

Figure 2 Hydrodynamic Mass


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4.0 Loadings

4.1 Reservoir & Uplift Loading

Reservoir & Uplift loading has been applied to the model per the information supplied by

Damwatch. The reservoir loading assumes the lake is at spillway crest level. The uplift loading

assumes 67% efficiency of the foundation drains. Figure 3 below presents the loads applied to the

analysis model.

Figure 3 Applied Reservoir & Uplift Loads (kN/m2)

4.2 Seismic Loading

Response spectrum analyses of the dam were undertaken for four (4) design level seismic events.


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Mokihinui Dam Site Spectral Acceleration

0.28

0.65

0.78 0.80 0.84

0.63

0.51

0.420.36

0.30

0.190.14

0.40

0.92

1.12 1.16

1.20

0.90

0.75

0.600.52

0.44

0.280.20

0.62

1.74

2.11

1.98

2.11

1.43

1.12

0.87

0.74

0.62

0.430.37

0.81

2.26

2.73

2.57

2.75

1.88

1.42

1.13

0.94

0.84

0.57

0.46

0.0

0.5

1.0

1.5

2.0

2.5

3.0

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Period, T (sec)

SpectralAcceleration,Sa(g)

150yrs 475yrs 2,500yrs 10,000yrs

Figure 4 Elastic Site Spectra


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5.0 Analysis Results

5.1 Static Analysis

Linear static analyses were undertaken for the usual loading conditions (self weight and reservoir

& uplift loading). Figures 5 & 6 below present horizontal and vertical stress contour plots and

Figures 7 & 8 present max/min principal stress contour plots


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Page 7

Figure 5 Usual Loading Condition: S11 (Horizontal Stress) Contours

S11min= -2875 kPa, S11max= 932 kPa


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Page 8

Figure 6 Usual Loading Condition: S22 (Vertical Stress) Contours

S22min= -2155 kPa, S22max= 72 kPa


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Page 9

Figure 7 Usual Loading Condition: SMAX (Max Principal Stress) Contours

SMAXmin= -695 kPa, SMAXmax= 935 kPa


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Page 10

Figure 8 Usual Loading Condition: SMIN (Min Principal Stress) Contours

SMINmin= -4489 kPa, SMINmax= 70 kPa


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Section cuts have been established whereby the internal stresses within the dam structure are

integrated across the section to obtain resultant section forces horizontal shear (FX), vertical load

(FZ), and section moment (MY). The resulting section cut forces plotted over the height of the

dam are presented in Figures 9 & 10 below.

Dam Section Cut Actions(REPORTED @ "X" FROM DAM FACE)

Analysis Case: Self Weight of Dam Only

0.0

10.0

20.0

30.0

40.0

50.0

60.0

70.0

80.0

90.0

100.0

-100 -90 -80 -70 -60 -50 -40 -30 -20 -10 0

Thousands

Section Horizontal Shear, FX & Vertical Load, FZ (kN)

HeightUpDam,z

(m)

-1,200 -1,000 -800 -600 -400 -200 0 200

Thousands

Section Moment, MY (kNm)

FX

FZ

MY

X=2.6m

X=6.4m

X=14.2m

X=17.9m

X=22.5m

X=26.3m

X=30.2m

X=34.0m

X=37.8m

X=10.2m

SECTION LOCATION

Figure 9 Section Cut Forces: Self Weight of Dam Only


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Dam Section Cut Actions

(REPORTED @ "X" FROM DAM FACE)

Analysis Case: Usual Loading

0.0

10.0

20.0

30.0

40.0

50.0

60.0

70.0

80.0

90.0

100.0

-100 -80 -60 -40 -20 0 20 40 60

Thousands


HeightUpDam,z(m)

-20 0 20 40 60 80 100

Thousands


FX

FZ

MY

X=2.6m

X=6.4m

X=14.2m

X=17.9m

X=22.5m

X=26.3m

X=30.2m

X=34.0m

X=37.8m

X=10.2m

SECTION LOCATION

Figure 10 Section Cut Actions: Usual Loading

5.2 Modal AnalysisModal analyses were undertaken to assess the vibration characteristics of the dam and for use in the

response spectrum analyses. The modal analyses were undertaken using the stiffness state during

the usual loading, i.e. considering self weight of the dam and the reservoir and uplift loading.

Modal participating mass data for all modes with greater than 1% participating mass in any

direction is presented in Table 2 below. Figures 11 & 12 below present graphically mode shapes 1

& 2.

Table 2 Modal Participating Mass Ratios

Mode Period UX UZ (UX) (UZ)1 0 36 0 69 0 02 0 69 0 02


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Figure 11 Mode 1: UX=69% Figure 12 Mode 2: UX=24%

5.3 Response Spectrum Analysis

Response spectrum analyses have been undertaken for the prescribed levels of earthquakeexcitation as outlined in Sec 4.2.

Presented in Figures 13 - 20 below are horizontal and vertical stress contour plots for each of the

four response spectrum analysis cases.


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Page 14

Figure 13 RS-150yr: S11 (Horizontal Stress) Contours

S11max= 3575 kPa


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Page 15

Figure 14 RS-150yr: S22 (Vertical Stress) Contours

S22max= 6386 kPa


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Page 16


S11max= 5120 kPa


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Page 17


S22max= 9140 kPa


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Page 18


S11max= 7520 kPa


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Page 19


S22max= 13257 kPa


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Page 20


S11max= 9735 kPa


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Page 21


S22max= 17159 kPa


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Analysis Case: RS-2,500yr

0.0

10.0

20.0

30.0

40.0

50.0

60.0

70.0

80.0

90.0

100.0

0 20 40 60 80 100 120

Thousands


HeightUpDam,z(m)

0 500 1,000 1,500 2,000 2,500 3,000 3,500 4,000 4,500

Thousands


FX

FZ

MY

X=2.6m

X=6.4m

X=14.2m

X=17.9m

X=22.5m

X=26.3m

X=30.2m

X=34.0m

X=37.8m

X=10.2m

SECTION LOCATION

Figure 23 Section Cut Actions: RS-2,500yr



Analysis Case: RS-10,000yr

30.0

40.0

50.0

60.0

70.0

80.0

90.0

100.0

HeightUpDam,z

(m)

0 1,000 2,000 3,000 4,000 5,000 6,000

Thousands


FX

FZ

MY

X=2.6m

X=6.4m

X=14.2m

X=17.9m

X=22.5m

X=26.3m

X=10.2m

SECTION LOCATION


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reservoir & uplift loading). It should be noted that the values presented represent the stress averageover the link spacing (in this case 4.825m).

Dam Section Cut Vertical Stresses(REPORTED @ Z=0m, i.e. @ DAM-ROCK INTERFACE)

-20,000

-15,000

-10,000

-5,000

0

5,000

10,000

15,000

0 10 20 30 40 50 60 70

Distance from Upstream Face of Dam, X (m)

VerticalStress,v

(kPa)

Hyrdrostatic RS-150yr RS-475yr RS-2500yr RS-10000yr

Figure 25 Dam Section Cut Vertical Stresses: Z=0m (Dam-Rock Interface)


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5.0 Conclusions

With the assumption of a linear response as adopted for this analysis the dam would be required to

resist maximum (averaged) tensile stresses of approximately 13MPa at the dam-rock interface

when subjected to the levels of ground motion considered. From this it is likely that there will be

cracking along the dam-rock interface giving rise to non-linear behaviour. As a result of this the

stress plots presented in this document should be considered to be indicative only.

In order to get an accurate assessment of the dams behaviour and stress distribution due to seismic

loading a time history analysis that considers the effects of this non-linearity is recommended.

Meridian Energy Ltd



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APPENDIX D

Sliding Stability at Base of Dam - Calculations


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5.4 preliminary stability assessemnt - 17 june 2008

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