Numerical analyses of concrete buttress dams to design dam monitoring

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IN

DEGREE PROJECT CIVIL ENGINEERING AND URBAN MANAGEMENT,

SECOND CYCLE, 30 CREDITS STOCKHOLM SWEDEN 2016,

Numerical analyses of concrete buttress dams to design dam monitoring

DANIEL SVENSEN

KTH ROYAL INSTITUTE OF TECHNOLOGY

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Numerical analyses of concrete buttress dams to design dam monitoring

Daniel Svensen

June 2016

TRITA-BKN. Master Thesis 492, Concrete Structures 2016 ISSN 1103-4297,

ISRN KTH/BKN/EX–492–SE

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Daniel Svensen 2016c

Cover photo, Christer Vredin (Sweco) Royal Institute of Technology (KTH)

Department of Civil and Architectural Engineering Division of Concrete Structures

Stockholm, Sweden, 2016

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Abstract

Old concrete buttress dams are sensitive to cracking if exposed to large temperature variations. The cracks can make dams sensitive to failure, depending on the size and location of the cracks. These problems can be overcome by lowering the temperature variations and stabilizing the dams. Insulation walls can be built to lower the temperature variations, and the area inside the insulation wall can be climate con- trolled to ensure a constant temperature. Stabilizing measures could be installing tendons, anchoring monoliths to the foundation or to keep parts of the monolith together. However, the best way to make sure the dam is functioning as expected is to monitor the behavior of the dam through different sensors. The sensors should be connected to some kind of dam monitoring software, which can indicate whether the dam is going to fail in a near future. For this to work, some kind of alert and alarm values has to be determined.

The main purpose for this project is to develop a finite element model that could be used to simulate the real behavior of a concrete buttress dam and predict the future behavior of the dam. This makes it possible to determine alert and alarm values for monitoring equipment installed on the dam.

Some steps are necessary to be able to create a finite element model representing the real behavior and to predict the future behavior of a dam. A first step is calibration of the model against real measurements, and during the calibration process it is important to evaluate the predictions made. A second step is to determine the normal variation in the behavior of the dam. A last step is to define suitable alert and alarm values, where the alert values are based on the normal variation of the dam and the alarm values are based on failure analyses.

The results show that it is possible to calibrate a finite element model with sufficient accuracy in order for it to be used for predictions of the dams behavior. The results show two failure modes of the concrete buttress dam which deviate from previous research, where post-tensioned tendons were not included.

From the results, information is given about where to place sensors to be able to capture a failure, how well the finite element model is calibrated, and what the alarm values should be. Furthermore, the results show that the evaluation of predictions made in the calibration process is of utmost importance to achieve a model representing the real behavior.

Keywords: Concrete, buttress dams, thermal effects, finite element analysis, instrumentation, alarm values, alert values.

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Sammanfattning

Gamla betonglamelldammar är känsliga för sprickbildning om de utsätts för stora temperaturvariationer. Sprickor kan göra dammarna känsliga för brott, beroende på storlek och placering av sprickorna. Dessa problem kan övervinnas genom att sänka temperaturvariationerna och stabilisera dammarna. Isoleringsväggar kan byg- gas för att sänka temperaturvariationerna, och området innanför isoleringsväggen kan klimatkontrolleras för att säkerställa en konstant temperatur. Stabiliserande åtgärder skulle kunna vara att installera spännkablar, förankring av monoliten till berggrunden eller att hålla ihop delar av monoliten. Emellertid är det bästa sättet att se till dammen fungerar som förväntat för att övervaka beteendet hos dammen genom olika sensorer. Givarna borde anslutas till någon form av programvara för dammövervakning, som kan indikera om dammen kommer att gå till brott inom en snar framtid. För att detta ska fungera måste någon form av mjuka och hårda larmvärden bestämmas.

Huvudsyftet för detta projekt är att skapa en finit elementmodell som kan användas för att simulera det verkliga beteendet hos en betonglamelldamm och förutsäga framtida beteende av dammen för att kunna bestämma mjuka och hårda larmvärden för vald övervakningutrustning på dammen.

Några steg är nödvändiga för att kunna skapa en finit elementmodell som representerar det verkliga beteendet och göra det möjligt att förutsäga det framtida beteendet av en damm. Ett första steg är kalibrering av modellen mot riktiga mätningar och under kalibreringsprocessen är det viktigt att utvärdera predikterade värden.

Ett andra steg är att bestämma den normala variationen av dammens beteende.

Ett sista steg är att definiera lämpliga värden för mjuka och hårda larmvärden, där de mjuka värdena baseras på dammens normala variation och de hårda larmvärdena på brottsanalyser.

Resultaten visar att det är möjligt att kalibrera en finit elementmodell med tillräck- ligt god noggrannhet att den kan användas för prediktering av dammens beteende.

Resultaten visar två brottmoder av betonglamelldammen som skiljer sig från tidigare studier där spännkablar inte hade inkluderats.

Från resultaten ges information om var sensorer ska placeras för att kunna fånga ett brott, hur väl finita elementmodellen kalibrerats, och vilka de mjuka och hårda lar- mvärdena bör vara. Dessutom visar resultaten att utvärderingen av predikteringar som gjorts i kalibreringsprocessen är av yttersta vikt för att uppnå en modell som representerar det verkliga beteendet.

Nyckelord: Betong, lamelldammar, termiska effekter, finit element analys, intstru- mentering, larmvärden.

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Preface

This master thesis was carried out at Sweco Energuide AB, in collaboration with the department of Concrete Structures at the Royal Institute of Technology (KTH) and Uniper during the period January to June 2016. The project was initiated by Dr. Richard Malm, and supervised by MSc Rikard Hellgren, MSc Daniel Eriksson and Adj. Prof. Erik Nordström.

The research presented was carried out as a part of "Swedish Hydropower Centre - SVC". SVC has been established by the Swedish Energy Agency, Elforsk and Svenska Kraftnät together with Luleå University of Technology, KTH Royal In- stitute of Technology, Chalmers University of Technology and Uppsala University.

www.svc.nu.

I would like to thank all of my supervisors for supporting me and pushing me in the right direction during this project, also for their time reading, commenting and helping in the development of this project.

I would also like to thank Sweco Energuide AB and MSc Agnetha Bergström for giving me the opportunity to carry out my master thesis project at their office. Also a big thanks to all the people at Sweco who helped me with various problems during my time there.

I would also like to thank MSc Carl-Oscar Nilsson at Uniper for providing me with measurements and for arranging a site visit to Storfinnforsen and Ramsele hydropower plants.

Finally, I would also like to thank Scanscot for providing a software license for Brigade/Plus.

Stockholm, June 2016

Daniel Svensen

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Chapter 1 Introduction

1.1 Background

Concrete buttress dams in Sweden are subjected to considerable temperature variations over a year. The temperature difference, depending on location, can be in the magnitude of 70^◦C between summer and winter. In combination with different temperatures in the water, ground and air this leads to stresses in the concrete which in turn can lead to cracking of the concrete. Cracks in the structures can lead to numerous problems, for instance; leaching, reinforcement corrosion and weakened structural integrity. It is important to keep track of cracks and their propagation to be able to repair severe damages before these could lead to a structural failure.

Visual inspections of large structures like dams are not always enough since some parts of the dam can be hard to inspect. At these locations it would be good to install measuring equipment, that preferably could be monitored remotely. However, many old dams seldom have any measurement equipment installed.

The placement of the measuring equipment is important to be able to capture a possible failure. To determine the position of such equipment, it is important to analyse the structure and its failure modes. This can be done with the help of the Finite Element Method (FEM).

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CHAPTER 1. INTRODUCTION

1.2 Aim and scope

The main purpose of this thesis is to develop a finite element model (FE-model) that can be used to simulate realistic behavior of a concrete buttress dam. The model will be used for predictions of the dam behavior in order to define alert and alarm values for monitoring equipment on this dam.

The first step is to calibrate the model against available measurements. To get a well calibrated model, some changes may have to be made to the dam geometry or its material properties. Between these changes, evaluation of the predictions is important to see how well the model represent the real behavior. As a second step, the normal variation of the dam behavior must be established. Since the deformations mainly are affected by temperature variations; analyses of recorded temperature variations and previous simulations could be used to define its normal behavior. As the last step, failure analyses of the dam, based on the calibrated model, will be made in order to define suitable alarm values.

The research questions to be answered within this project are the following:

• Is it possible to define a calibrated finite element model that has sufficient accuracy in order to be used for predictions of alert and alarm values regarding dam failure?

• How should the evaluation of predictions in the calibration process be performed?

• What kind of monitoring equipment is needed to capture a failure of a concrete buttress dam?

1.3 Structure of the thesis

An introduction to concrete buttress dams is given in Chapter 2. Within this chapter, loads acting on concrete buttress dams are described, and potential failure modes are presented.

In Chapter 3, general information regarding monitoring of dams is presented. Be- havior models are introduced, and their application for defining alarm values are described. Furthermore, calibration and verification of numerical models is described, and statistical tools that could be used for these applications are presented.

A case study was made in this thesis, and it is presented in Chapter 4. Measurement data used in the analyses are presented, together with a description of the process of establishing the normal variation of the dam behavior, and which failure analyses were chosen for definition of alarm values.

A description of all the numerical models used for the analyses are presented in Chapter 5, together with descriptions of many aspects regarding numerical modelling. Mesh convergence and calibration of the models is also described in this chapter.

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1.3. STRUCTURE OF THE THESIS

The results from the calibration of the numerical models, expected future variation of the dam behavior and the results from the failure analyses are presented in Chapter 6.

Conclusions from this project is presented in Chapter 7, together with suggestions for future research.

Appendix A contains more measurement data for the case study.

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Chapter 2 Concrete buttress dams

A concrete buttress dam consists of monoliths, where each monolith acts independent from each other. A monolith consists of a front plate and a supporting buttress.

At the front plates the monoliths are connected with water-tight expansion joints.

Three monoliths of a concrete buttress dam is illustrated in Figure 2.1 and in Figure 2.2 the parts of a monolith are further explained.

Design of concrete buttress dams has been described in this chapter, and the information has been based on Ridas, which is a guideline for designing dams, created by a collaboration between Swedish power companies. (Ridas, 2012)

Figure 2.1: Overview of three monoliths of a concrete buttress dam.

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CHAPTER 2. CONCRETE BUTTRESS DAMS

a) b)

EXPLANATION

Expansion joints Bridge deck

Crest

Inspection Toe gangway Heel

Buttress wall Monolith Frontplate

H H

Figure 2.2: Overview of a monolith of a concrete buttress dam. a) Upstream view, b) Side view

2.1 Loads

According to Ridas (2012), concrete dams should be designed with regard to loads and load cases which can realistically act on a dam. The load cases are divided into three categories: ordinary, exceptional and accidental load cases. Loads that should be taken into account are: dead load, water pressure from reservoir- and tailwater, uplift pressure, ice loads, soil pressure, traffic loads, thermal effects, shrinkage and creep. There are, however, additional loads that could affect the dams, such as earthquakes. Some of the aforementioned loads are shown in Figure 2.3.

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2.1. LOADS

H

h

1

2

5

4

1 - Ice Load 2 - Water pressure 3 - Tail water pressure 4 - Uplift pressure 5 - Dead load

3

Figure 2.3: Typical loads acting on a dam.

The considered loads in this project are covered in more detail below.

2.1.1 Dead load

The dead load is caused by the structure itself. It is the weight of the structure that decides the magnitude. When analysing an existing structure, the best way of determining the density of the concrete is to analyse material from the structure itself, since this gives the most realistic value. Otherwise, it can be assumed to 2400 kg/m³ according to Eurocode 1 (2002).

The resulting dead load from the structure can be calculated with Equation (2.1).

Fg = ρc· g · Vc [N] (2.1)

where,

ρ_c is the concrete density [kg/m³]

g is the gravitational acceleration [m/s²] V_c is the volume of concrete [m³]

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2.1.2 Water pressure

The water pressure can be divided into three sub-categories, water pressure from reservoir- and tailwater as well as water pressure acting underneath the dam (uplift pressure).

Reservoir- and tailwater

Water pressure is the main load acting on concrete buttress dams. If there is water both on the upstream and downstream side, both should be taken into account in the calculations. Water pressure varies with distance below water level, and it is calculated using Equation (2.2). The equation describes the hydrostatic water pressure, which acts perpendicular to the surface, as shown in Figure 2.3.

p = ρw· g · h [Pa] (2.2)

where,

ρ_w is the water density [kg/m³]

g is the gravitational acceleration [m/s²] h is the water depth [m]

Uplift pressure

Uplift pressure comes from water underneath the dam, acting on the concrete in the connection between the monolith and the underlying foundation. If there is horizontal cracks in the foundation, the uplift pressure could increase, i.e. act on larger portion of the monolith.

(Ridas, 2012) divides the uplift pressure in two categories, one if the buttress is thicker than 2 m, and the second if the buttress is 2 m or thinner. In the second case, the uplift pressure can be assumed to act only on the frontplate. In the upstream end of the frontplate, the uplift pressure should be defined as the hydrostatic water pressure, and decreases toward the downstream end of the frontplate. An exception to this is if there is tailwater, uplift pressure should be included underneath the buttress as well, with the magnitude of the tailwater pressure, as shown in Figure 2.3.

If the connection between monolith and foundation is subjected to tensile stresses, this can be taken into account by modifying the uplift pressure to act on the entire area that is affected by tensile stresses. However, this is not considered in this thesis.

2.1.3 Ice load

The ice load varies depending on where the dam is situated, and it may even vary lo- cally. As guidance, Ridas (2012) has divided Sweden into three areas with different size of the ice load. For the southern part of Sweden, the ice load can be assumed

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2.2. FAILURE MODES

as 50 kN/m. In the middle part of Sweden it can be assumed as 100 kN/m. For the northern part it can be assumed as 200 kN/m.

The ice thickness also varies, south of Stockholm it can be assumed to 0.6 m, and north of Stockholm it can be assumed to 1.0 m. The ice load is a seasonally varying load. The ice load, obviously, has a seasonal variation with largest magnitude during winter.

2.1.4 Thermal loads

When heated or cooled, concrete will increase or decrease in volume. When there is different temperatures over a monolith, the concrete expand and shrink different amounts on different locations. If the monolith is restrained it will cause stresses in the concrete. If the tensile stresses become larger than the concrete tensile strength, cracks will occur. The stresses caused by thermal loads can be calculated according to Equation (2.3).

σ_T = ε_T · E = ∆L

L · E = α · ∆T · E [Pa] (2.3)

Where,

εT is the thermal strain [-]

E is the elastic modulus [Pa]

∆L is the change in length [m]

L is the original length [m]

α is the thermal expansion coefficient [1/^◦C]

∆T is the temperature difference [^◦C]

2.2 Failure modes

A failure mode is a way a structure goes to failure. Every structure usually have several different potential failure modes, where each failure mode is connected to different loads and load cases. When designing a structure, it is important to identify relevant potential failure modes to be able to prevent these from happening.

Concrete buttress dams utilizes the inclination of the frontplate in combination with the water pressure to stabilize the monolith. If the dam cracks, the stabilizing effect can decrease. (Bond et al., 2013)

In the following sections, potential failure modes for concrete buttress dams are described. Ridas gives guidelines for a few of these.

2.2.1 Overturning failure

When the overturning moment becomes larger than the stabilizing moment, the dam can start to rotate around the toe, as illustrated in Figure 2.4a). Reasons for

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this can be increased loads or a shortened lever arm for the stabilizing moments.

The safety factor for overturning can be calculated with Equation (2.4).

s = M_stab

M_over [−] (2.4)

where,

M_stab is the resultant of the stabilizing moments [Nm]

M_over is the resultant of the overturning moments [Nm]

The safety factor according to Ridas (2012) for overturning should be at least:

s =







1.5 Ordinary load cases 1.35 Exceptional load cases 1.10 Accidental load cases

2.2.2 Sliding failure

A sliding failure occur when the dam is separated from the foundation, and starts to slide away, as illustrated in Figure 2.4b). The sliding factor can be calculated with Equation (2.5). Rock bolts and reinforcement in the connection between the monolith and underlying rock mass are not allowed to take into account when designing dams for sliding according to Ridas (2012). The factor µ should not exceed µ_till. Table 2.1 contains values for s_g and u_till for rock foundation.

µ = R_H RV

≤ µ_till = tan(δ_g) sg

[−] (2.5)

where,

R_H is the resultant of forces parallell to the sliding plane R_V is the resultant of forces perpendicular to the sliding plane µ_till is a safety factor according Table 2.1

tan(δ_g) is the fracture value of the friction coefficient in the sliding surface and should be determined via investigations

s_g is a safety factor according Table 2.1

Table 2.1: Global safety factors according to Ridas (2012).

Variable Normal Exceptional Accidental

s_g 1.35 1.10 1.05

µ_till 0.75 0.90 0.95

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2.2. FAILURE MODES

2.2.3 Material failure

Cracks can divide a monolith into different parts, and in these cracks the water can come in and affect these areas with water pressure, which can lead to some parts of the dam overturning since the lever arm for the stabilizing forces on this part can greatly decrease. A failure of this type is illustrated in Figure 2.4c).

A breach in the frontplate can occur due to cracks or degradation, either near the buttress or near the expansion joint. The expansion joint is a weak zone, it can suffer from degradation by leaching and frost damage. A breach in the frontplate is illustrated in Figure 2.4d)

Cracks in the rock underneath the frontplate can lead to increased uplift pressure, and the stabilizing forces can get canceled out by this, increasing the risk for an overturning failure. (Nordström et al., 2016)

Figure 2.4: An illustration of different failure modes for a concrete buttress dam, a) Overturning failure, b) Sliding failure, c) Partial overturning failure due to cracks, d) Breach in the frontplate

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2.3 Cross-sectional analyses

When performing cross-sectional analyses, all sectional forces should be multiplied by a partial factor, called hydraulic factor, γ_h. By multiplying sectional forces with the hydraulic factor, a uniform system of handling loads and load cases between stability calculations and cross-sectional analyses is achieved. This makes it possible to compare cross-sectional analyses and stability calculations directly (Ridas, 2012).

In Table 2.2, the hydraulic factor is given for different forces and loadcases.

Table 2.2: Hydraulic coefficient, γ_h, for different forces and loadcases, Table from Ridas (2012)

γ_h γ_h

ordinary loadcases exceptional loadcases

Moment 1.50 1.25

Shear force 1.50 1.25

Normal force, tension 1.50 1.25

Normal force, compression 1.80 1.50

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Chapter 3 Monitoring of dams

3.1 Purpose

Dam incidents or failures can lead to large consequences, e.g. loss of income for the dam owner, flooding of downstream areas resulting in property damages and in worst case, loss of lives. Therefore, it is important to receive early indications of an upcoming dam failure, and this is where instrumentation and monitoring is of great importance.

Instrumentation and monitoring is a good way to keep track of the dam’s condition, but for this to work, both economically and practically, monitoring tools and sensor positions has to be chosen with care. The sensors chosen should be able to be read remotely, because they can be relatively hard to get access to depending on location.

Only having visual inspections is time consuming and it can be difficult to find all imperfections, such as cracks, leakage and displacements. If certain damages are missed, and not repaired in time, it could ultimately lead to a collapse of the dam.

In other words, sensors are great to monitor the behavior and to discover changes in the behavior of the dam. Monitoring also helps understanding the normal variations of a dam, especially if it’s an older dam with less documentation of the structure itself and the construction process.

3.2 Types of monitoring equipment

Today there are many different types of sensors, and many aspects of the dam can be monitored, e.g. as shown in Table 3.1. Some sensors can be said to be supporting sensors, as they measure the surrounding conditions, e.g. temperature and humidity, and not the behavior of the structure itself. The supporting sensors can give input data needed for numerical models. For information regarding different sensor types, see Table 3.1.

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CHAPTER 3. MONITORING OF DAMS

Table 3.1: Type of sensors typically used to monitor concrete dams.

Sensor type Used for measuring

Temperature Temperature in water, air, ground and concrete

Humidity Humidity in air and concrete

Linear variable differential transformer (LVDT)

Crack widths, relative displacements Pendulums, direct Crest displacements

Pendulums, inverted Monolith displacement, relative foundation

Piezometers Pore pressure

Weir Measure leakage

Load cells Load in tendons

Temperature sensors

Temperature sensors are used to measure the temperature in either water, air, ground or concrete. They could be used for e.g. verification of temperatures within an insulation wall, to see that it has the wanted effect. Temperature sensors also give valuable input for numerical models. An example of a temperature sensor is the PT100 from Pentronic (2016), seen in Figure 3.1. The sensor is waterproof and has a measuring range from -50^◦C to +105 ^◦C, which is suitable for measurements on dams.

Figure 3.1: A PT100 temperature sensor. Figure from Pentronic (2016)

Humidity sensors

Humidity sensors are used to measure the humidity in air and concrete, and they also could give information about any risk of condensation at chosen locations. The condensation could lead to frost damage in the concrete.

Direct and inverted pendulums

Direct and inverted pendulums are used to measure the relative displacement of the monolith. The direct pendulums measure the displacement of the crest relative the

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3.2. TYPES OF MONITORING EQUIPMENT

bedrock, which make them able to give indications of an overturning failure. Inverted pendulums are used for measuring the displacement of the buttress relative to the bedrock, which make them able to give indications of a sliding failure. (Nordström et al., 2016)

Direct pendulums consist of a long wire, a weight, a reading table and a damper tank. The wire is attached to the bridge deck and hangs down to the bedrock, where the weight is attached and submerged in a damper tank, see Figure 3.2.

The inverted pendulums consist of a long wire, a float, a reading table and a float tank. The lower end of the wire is grouted to the bedrock, and the wire goes up to a float tank, where the wire ends with a float. The float tensions the wire, to get the wire straight, see Figure 3.2. (Roctest Limited, 2005)

Damper tank

Reading table Wire

Float tank

Grouted

a) b)

Figure 3.2: Principal design of a) Direct pendulum, b) Inverted pendulum. Figure reproduced from Roctest Limited (2005).

Linear Variable Differential Transformers (LVDT)

LVDT’s can be used to measure crack widths in a concrete structure, see Figure 3.3, and thereby they give early indications of internal overturning or sliding. (Nordström et al., 2016)

A LVDT consist of a sensor and a rod. The sensor works like a transformer, consisting of a coil assembly and a core. LVDT’s convert physical movements to electrical signals. The sensors can measure movements down to a few millionths of a centime- ter and up to half a meter. (National Instruments, 2016)

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Figure 3.3: LVDT placed across a crack at Storfinnforsen dam. Photo: Daniel Svensen

Piezometers

Piezometers are used to measure pore pressure in either the connection between concrete and rock or in the connection rock and rock. They are used to detect any change in pressure, which may affect the stability of the dam or a material failure in the foundation, (Nordström et al., 2016). A piezometer can be installed in a borehole with filter sand surrounding the piezometer and should be grouted to seal the borehole. (Geosense, 2015). A piezometer from Geosense (2015) called VWP-3000 is shown in Figure 3.4.

Figure 3.4: Piezometers used for measuring pore pressure, Figure from Geosense (2015)

Weir

Weirs measure leaking water flows, and are used to detect increasing crack openings which may lead to leaching of the concrete, (Nordström et al., 2016). A weir usually

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3.2. TYPES OF MONITORING EQUIPMENT

consist of a tank that collect the leaking water, and over time one may see how fast the flow rate is by measuring the amount of water collected in the tank. There may also be an electronic weir monitor in this tank, which measures the water level in the tank, eliminating manual reading. An example of an electronic weir monitor is the VWM-2000 from Geosense (2016), shown in Figure 3.5. The weir monitor consist of PVC pipe with a suspended weight inside. The change in water level changes the tension in the wire suspending the weight.

Figure 3.5: A weir monitor, which is used in combination with a water collector to measure leakage water flows, Figure from Geosense (2016)

Load cells

Load cells are used to measure the force in the tendons, to verify the stabilizing effect in the tendons, (Nordström et al., 2016). The load cells are mounted beneath the tendon anchor to measure the applied load. An example of a load cell is the Geokon 4900, shown in Figure 3.6.

Figure 3.6: Load cell, model Geokon 4900, used for measuring load in tendons, Figure from Geokon (2016)

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3.3 Behavior models

Different methods for predicting the behavior of a dam exists, where some are simpler and faster constructed than others. However, there are more possibilities with some models than others. In the following sections, the models are described and evaluated briefly.

3.3.1 Deterministic model

A deterministic model strictly relies on physical laws, and applying these on a mathematical model of the physical structure; an example is a finite element model. In this type of model, no measurements of the behavior of the structure is used in the calibration. It is based on real material properties from testing, in the extent they are available. The advantage with this model is that it can be used for other analyses as well, for example failure mode analyses, which makes it easier to analyse different behaviors. (SCOD, 2003)

3.3.2 Statistical model

With a statistical model, a shape function for the behavior is chosen based on experience. Coefficients for the shape function are determined through calibration against available measurements of the structural behavior. The model is then pre- sumed to be able to predict future behavior. The upside with this model is that it is easier and faster to define than the other models. A downside with this model is if the structure is changed somehow the model has to be remade. Another downside is that the model requires a lot of measurement data to be able to predict usual variations. (SCOD, 2003)

Regression analysis

Regression analysis is a statistical method for describing the correlation between variables, to see how one variable varies with another. It is possible to create a function describing the relationship between the variables. Regression analysis is useful for analysing predictions.

Linear regression is the simplest form of regression analysis, and it gives a linear function describing the relationship between two variables. Multiple regression is when you want to make a prediction based on two or more variables. (Blom et al., 2005)

For n data points, a linear regression function can be expressed as Equation (3.1) and (3.2).

y_i = β₀+ β₁x_i+ e_i , i = 1, 2, ..., n (3.1)

e_i = y_i− p_i (3.2)

where,

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3.3. BEHAVIOR MODELS

y_i is the dependent variable x_i is the independent variable p_i is the predicted value β_i is the regression coefficient

The coefficients for the linear regression function can be calculated according to Equations (3.3) to (3.5).

¯ y = 1

n

X

i=1

y_i (3.3)

β₁ = (

n

X

i

(x_i− ¯x)(y_i− ¯y))/

n

X

i

(x_i− ¯x)² (3.4)

β₀ = ¯y − β₁· x (3.5)

However, there is a risk of overfitting the data when making the regression analysis more complicated. An overfit model means that it fits this sample very good, but when applying the model to another sample, it might be a poor assessment. One should always strive for a model that fits the entire population, not just a single sample. An overfit model can make the R² value meaningless. (Hastie et al., 2008) In Figure 3.7, an example of how overfitting works in a population is shown. When the model becomes more complex the sample error decreases, but the prediction error for the entire population increases. This implies that one must look at the entire population, and not only concentrate on a small sample during the calibration process.

Figure 3.7: Behavior of prediction models, specifically showing how overfitting may affect the prediction, picture reproduced from Hastie et al. (2008).

There are two statistical methods called Hydrostatic, Seasonal, Time (HST) and Hy- drostatic, Thermal, Time (HTT), which are based on the Statistical model. Both the HST and HTT model are multiple linear regression models describing the defor-

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effect by a seasonal function, and is widely used. The HTT model is based on temperature measurements and is considered to better represent the thermal effect, but more complicated to implement. (Mata et al., 2014; Léger and Leclerc, 2007)

The HST model

In the HST model, the thermal effect is based on a seasonal sinusoidal function that depend on the day of the year. The regression functions differ in composition, but a common composition of a HST regression function is shown in Equation (3.6).

(Chen, 2015)

d(h, S, t) = a0+

w

X

i=1

aihⁱ(t) + b0+

q

X

i=1

biSi(t) + c0+

p

X

i=0

ciIi(t) (3.6)

where,

a0, b0, c0 are regression constants a_i, b_i, c_i are regression coefficients h is the water level

Si is a seasonal temperature function

I_i is the irreversible time effects, such as creep

The HTT model

In the HTT model, the thermal effect is based on temperature measurements from sensors on the dam, and can be implemented in the dams monitoring system software. (Bühlmann et al., 2015)

The HTT models strength compared to the HST model is that it is based on measurements, and if the seasons are offset from year to year, the HTT model will give more accurate predictions.

An example of a HTT regression function is shown in Equation (3.7). (Chen, 2015)

d(h, T, t) = a₀+

w

X

i=1

a_ihⁱ(t) + b₀ +

q

X

i=1

b_iT_i(t) + c₀+

p

X

i=0

c_iI_i(t) (3.7) where,

Ti is the measurements from sensor i

3.3.3 Hybrid model

The hybrid model is a mix between a deterministic and a statistical model. The behavior is based on the mathematical model as described in the deterministic model, and then calibration is made with coefficients as described in the statistical model.

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3.4. METHODS TO DEFINE ALARM VALUES

The upside with this model, if correctly constructed, is that it describes the behavior of an existing structure the best. A downside is that it takes the longest time to construct. (SCOD, 2003)

3.4 Methods to define alarm values

The behavior models described in Section 3.3 may be used to decide the alarm values. The models may also be used define alert values. The alert values are used to find if measurements go outside the range of the structures normal variation. This can be due to a number of different reasons, e.g. faulty sensors or larger loads acting on the dam than usual. Alert values are, thus, a lower limit of the alarm values, they do not necessarily indicate that the dam is about to fail, but the reason for the alert should be investigated. Alarm values on the other hand are more serious, when measurements reach or go past this value, the dam is judged to fail in a near future if nothing is done. To prevent this, alarm values should be set on a level that allows prevention of an upcoming failure, or at the very least put an evacuation plan into action. Schematically, it can be interpreted as illustrated in Figure 3.8.

Normal variation

Alert value

Alarm value

Failure

Figure 3.8: Schematic boundaries for alert and alarm values

According to Malm and Tornberg (2013), crest displacements are a good indication of an upcoming failure. Therefore, it would be suitable to analyze the crest displacements for different failure modes and define alert and alarm values based on these displacements. However, redundancy is important and it would therefore be good to have several indicators of an upcoming failure.

3.4.1 Experience

For existing dams where monitoring equipment is installed and no changes have been made to the dam, there is a possibility to base the alarm values on past behavior.

Setting the alarm values with this method can be done on different levels, either a really simple method or a more complex.

The simplest method would be to set alert or alarm values based on the highest recorded displacements that the dam have been subjected to during the years of monitoring. A more complex method would be to further develop the simple method to also take degradation and cracks into account when setting the alarm values, i.e.

to take a more conservative approach.

If any changes are made to the dam, e.g. repair work, new cracks propagating or building a new insulation wall, the alarm values will be invalid. Then a new data collection period would start, until there is enough data to base new alarm values

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3.4.2 Numerical analyses

This method is based on the Hybrid model, Section 3.3.3.

The basis of this method is a FE-model. It relies on an accurate representation of the real structure. To get an accurate representation, the FE-model must be calibrated against the structure being investigated. For this, measuring data from the structure is needed. With more data, the FE-model has potential to become more accurate.

The next step in this procedure is to find potential failure modes of the structure.

This can be done by applying different loads and load combinations to the structure, and increasing these until failure is reached. The failure modes to check when designing a dam is overturning, sliding and material failures according to Ridas (2012), see Section 2.2.

When analysing the failure modes, one wants to find several indicators for an upcoming failure. Each of these indicators should be investigated, and individually evaluated to find a normal variation curve. The normal variation can e.g. be found by simulating different types of years. One type would be a year with high temperature variations, another type could be with low temperature variations. Those two years would together create limiting values for normal variation, and the limits themselves would be suitable to have as alert values. To set alarm values, the failure modes would have to be carefully analysed and defined with sufficient safety margin to make sure that an upcoming failure is captured with enough time to prevent the failure. In reality, material degradation is considered to be the primary driving force that could lead to a weakened structure, which in turn could lead to a potential failure. This is a slow process where there should be sufficient time to take measures against the failure, such as performing strengthening work, lowering the reservoir level or introducing ice prevention measures. Therefore, the alarm value could be defined relatively high, e.g. 90 % of the failure load, since it is deemed to be sufficient time for dam safety measures and maybe evacuation.

One alternative to define alarm values would be to look at a graph describing the failure, e.g. a graph showing the load increase versus the displacement of the crest, as shown in Figure 3.9. An alarm value could be set at a load 10% lower than for the failure load, but this number should be decided upon in collaboration with the dam owner.

There is a possibility to determine alarm values with a linear-elastic model. This would be a very conservative model, since the alarm values would be connected to when the tensile or compressive strength of the concrete is reached. A non-linear model can describe the failure process which would allow more detailed analyses.

The non-linearity of the model could come from geometric, material, boundary or interaction non-linearity.

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3.4. METHODS TO DEFINE ALARM VALUES

Figure 3.9: An example of setting alarm values for a failure

Non-Linear material properties of concrete

The non-linear compressive behavior of concrete can be described with the following equations, according to Eurocode 2 (2005).

σ_c

f_cm = kη − η²

1 + (k − 2)η , 0 < ε_c< ε_cu1 (3.8) η = ε_c

ε_c1 (3.9)

k = 1.05E_cmεc1

f_cm (3.10)

where,

σ_c is the mean concrete cylinder compressive strength [Pa]

f_cm is the compressive stress [Pa]

ε_c is the compressive strain [-]

ε_c1 is the strain at peak compressive stress f_c, [Pa]

ε_cu1 is the ultimate strain [-]

E_cm is the mean elastic modulus [Pa]

The tensile behavior of concrete can be described with crack opening laws. The crack opening laws describe the behavior after reaching the tensile strength. In Figure 3.10, three different crack opening laws are shown: linear, bilinear and exponential. The linear curve is the simplest, whereas the exponential is most realistic.

(Malm, 2015a) Equations (3.11) to (3.14) describe the crack opening width when the concretes tensile load capacity goes to zero for the different cases in Figure 3.10.

(Malm, 2015a)

w_cl = 2 · (G_F/f_t) [m] (3.11)

w₁ = 0.8 · (G_F/f_t) [m] (3.12)

w_cb = 3.6 · (G_F/f_t) [m] (3.13)

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Figure 3.10: Different types of tensile softening curves, a) Linear, b) Bilinear, c) Exponential, Figure reproduced from Malm (2015a).

Hordijk (1991) presents an equation describing the exponential crack opening law:

σ/f_t = (1 + (c₁· w/w_ce)³)e^−c²^·w/w^ce − w/w_ce · (1 + c³₁)e^−c² (3.15) where,

c₁ = 3 is a constant proposed by Hordijk (1991) c2 = 6.93 is a constant proposed by Hordijk (1991) w_ce = Equation (3.14)

Fracture energy is used to describe the concrete tensile behavior, it is the required amount of energy to open a unit area of a crack surface. The fracture energy of concrete should be investigated via material tests, but if this is not a possibilty, FIB (2013) has an equation for estimating this parameter, see Equation (3.16).

G_F = f_cm^0.18 [Nm/m²] (3.16)

where,

f_cm is the mean compressive strength in MPa

3.5 Calibration and verification of numerical mod- els

Calibration and verification of a numerical model goes hand in hand, meaning that the two must be done in connection with each other. When a calibration is performed, a verification of the results should be performed. The calibration and verification should be repeated until a satisfactory calibration has been reached.

3.5.1 Mesh convergence

Before commencing with the calibration process, a converging mesh size for the numerical model has to be found. It is important to achieve a realistic behavior of

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3.5. CALIBRATION AND VERIFICATION OF NUMERICAL MODELS

the model. The FE-model should also be compared with analytical calculations, or previous research.

According to Malm (2016), the crest displacements are to be analysed with different mesh discretizations, until the difference in displacement between a coarser and finer mesh is lower than 1%, then the coarser mesh could be used for the calculations.

For each mesh refinement, the mesh size should be half of the previous one.

3.5.2 Calibration

Calibration is performed to achieve behavior as similar to the real structure as possible. It can be done if a real structure with measurements exists.

The first step of the calibration process is to create a mathematical model that describes the physical structure. During the calibration process, the model is refined until sufficient calibration is achieved.

The first simulation starts of with a set of starting parameters. The results of this simulation should then be analyzed to find the differences between the model and the real structure. Sometimes several changes has to be done to the model, e.g.

changing some of the material parameters, change the geometry of the structure or change the geometry of possible cracks. This process should be repeated until wanted behavior of the model is achieved.

3.5.3 Verification of prediction

Verification of predictions is essential to achieve a model that accurately describes the structural response. There are several statistical tools for verificating predici- tions, and different authors use different statistical tools, but the standard deviation of the error σ_e, the coefficient of determination R² and the correlation coefficient r are the most common ones. (Mata et al., 2014; Bühlmann et al., 2015; Chen, 2015;

Léger and Leclerc, 2007)

Standard deviation of error

One way of describing the error in the predictions is through standard deviation. The error is the difference between measurements and predictions. Calculating the error gives information of the error magnitude. The variation in error can be described as e_var = µ_e± σ_e. Larger values of σ_e means there are much variation in the error, and vice versa. The standard deviation of the error can be illustrated with an error band, as seen in Figure 3.11, where the error band covers 2 · σe to each side of the predicted values. The error band shows the maximum allowable deviation, d, which is set to 2 · σ_e in this case, and it corresponds to a 95% confidence interval. If the measured values are inside this error band, it is considered an expected value.

e_i = m_i− p_i (3.17)

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µ_e = 1 n

n

X

i=1

e_i (3.18)

σ_e = v u u t

1 n − 1

n

X

i=1

(e_i− µ_e)² (3.19)

d = 2σe (3.20)

where,

e_i is the error

m_i is the measured value p_i is the predicted value

µ_e is the mean value of the error σ_e is standard deviation of the error n is the number of observations

d is the maximum allowable deviation

Coefficient of determination

One can look at the coefficient of determination, the R² value, to see how good a prediction was. R² varies between 0 and 1, where a value closer to one is a better prediction, and a value of 0 meaning there is no correlation. The coefficient of determination takes both the correlation and the error into account, which makes it a good tool to evaluate predictions. The R² value is calculated with Equations (3.21) to (3.23). (Mathworks, 2016)

SS_tot =

n

X

i

(m_i− ¯m)² (3.21)

SS_res =

n

X

i

(m_i− p_i)² =X

i

e²_i (3.22)

R² = 1 − SSres

SS_tot (3.23)

Correlation coefficient

The correlation coefficient is a value describing how two values correlate each other and varies between -1 and 1. If the coefficient is negative, it means that when one variable increase, the other decrease. If the coefficient is zero, then there is no statistical correlation. If the coefficient is positive, it means that when one variable increase, the other variable increase as well, see Figure 3.11. The correlation coefficient describes if an overall correlation is achieved or not, and this makes it a

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3.5. CALIBRATION AND VERIFICATION OF NUMERICAL MODELS

good indicator for evaluating if the calibration is on the right track. The correlation coefficient is calculated with Equation (3.24) and (3.25). (Blom et al., 2005)

r = c_pm/σ_pσ_m (3.24)

c_pm= 1 n − 1

n

X

i=1

(p_i− ¯p)(m_i− ¯m) (3.25) where,

¯

p is the mean of the predicted values

¯

m is the mean of the measured values

The difference between the coefficient of determination R² and the correlation coefficient r is illustrated in Figure 3.11.

Figure 3.11: An illustration of the difference between the correlation coefficient r and the coefficient of determination R². The standard deviation of the error between predictions and measurements is also shown

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Chapter 4 Case Study

This case study is about finding suitable alarm values for measuring equipment on a typically cracked monolith at Storfinnforsen hydropower dam, which is subject to an ongoing instrumentation program. The case study was made to study the application of the Finite element model method described in Section 3.4.2.

Storfinnforsen hydropower dam is about 1200 m long, where 800 m is a concrete buttress dam consisting of 81 monoliths, and 400 m is an embankment dam. The two types of dams are connected at monolith 1, which is the most northern part of the dam, as seen in Figure 4.1. The monoliths varies in height between 6 to 41 m.

Since the monoliths can be seen to act independently to each other, one monolith was chosen for the case study, and this was monolith 42. The placement of monolith 42 in relation to the dam can be seen in Figure 4.1 and 4.2. The selection of a monolith for the case study was based on previous research, described in Section 4.4.

N

Figure 4.1: Situation plan of Storfinnforsen dam, Figure from Sweco Energuide AB (2013b).

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CHAPTER 4. CASE STUDY

Figure 4.2: Downstream view of Storfinnforsen dam, Figure from Sweco Energuide AB (2013a).

4.1 Geometry

The geometry of the chosen monolith is shown in Figure 4.3. The buttress is 41 m high, 37 m wide and 2 m thick. The frontplate is embedded in the rock and is 8 m wide, and the thickness in the vertical part is constant at 1.2 m, whereas the inclined part of the frontplate varies in thickness between 1.2 at the top to 2.6 m at the heel.

The inclination of the frontplate is 125^◦ relative to the bottom of the reservoir. The bridge deck is 0.80 m thick, 8 m wide and spans 4 m in the upstream-downstream direction. There is also an inspection gangway located 8.7 m above the foundation.

The reinforcement of the monolith consists of reinforcement bars with three different diameters; 19, 25 and 31 mm. All vertical reinforcement bars are 19 mm in diameter. The horizontal reinforcement bars varies from 31 to 19 mm, where the largest diameter bars are in the bottom of the monolith, and decreasing in size further up. There are also diagonal reinforcement bars, with a diameter of 31 mm, connecting the buttress and the frontplate. The reinforcement has a minimum of 50 mm concrete cover. The reinforcement of the monolith is shown in Figure 4.4.

The water depth is 39 m and the head is 1.75 m below the crest of the monolith.

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4.1. GEOMETRY

H

37.04

106°

125°

41.53

29.95 8.25 1.750.80

4.00

8.65 2.10 1.20

2.62

22.10 10.00

0.80

8.00 H

2.00

a) b)

Figure 4.3: Geometry of the chosen monolith, a) Front view, b) Side view

22.16 6.40 3.75 10.00

Ø19c400 Ø19c400

Ø19c400 Ø19c400 Ø19c400

Ø19c400 Ø31c175

Ø31c175 Ø31c200 Ø31c200 Ø25c150 Ø25c150 Ø19c200 Ø19c200

Ø31c450 Ø31c450

a) b)

H H

; Figure 4.4: Reinforcement of the chosen monolith, a) Front view, b) Side view

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4.2 Existing cracks

Cracks exist on many of the monoliths at Storfinnforsen dam. The cracks are shown to be mainly caused by the seasonal temperature variations by Malm and Ansell (2011). The crack pattern is similar for several of the largest monoliths, this crack pattern was presented by Isander et al. (2013) and is shown in Figure 4.5.

Cracks of type 1) are horizontal cracks in the frontplate, and it has been shown that they propagated further through the buttress, going down toward the foundation, shown as type 2). Type 3) cracks are those who have propagated from the inspection gangway toward the frontplate. Type 4) are the cracks that has propagated from the foundation toward the inspection gangway. The cracks near the dam toe are type 5).

4 5 3

1 2

Figure 4.5: Typical crack pattern of the largest monoliths at Storfinnforsen hydropower dam. Figure reproduced from Isander et al. (2013)

4.3 Structural changes

Storfinnforsen has gone through quite a few changes since being completed in 1954.

These changes are taken into account when building and calibrating the numerical model.

• 1954 - Dam was built

• 1993 - Original insulation wall was completed

• 2006 - LVDT’s and temperature sensors were installed on monolith 42 & 43

• 2007 - Direct pendulum was installed on monolith 43

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4.4. PREVIOUS RESEARCH

• 2008/2009 - Ice prevention measures were taken until the tendons were installed

• 2012 - Vertical and horizontal tendons were installed

• 2015 - Original insulation wall was demolished

• 2016 - New insulation wall was completed

The original insulation wall was built to minimize the thermal movements of the dam, but research has shown that this led to more cracks propagating in the monoliths, (Ansell et al., 2010; Malm, 2009; Malm and Ansell, 2011). This led to the installation of the monitoring equipment in 2006-2007, and further research was made to develop a new insulation wall, (Malm, 2013).

The tendons were installed to increase the stability of the monoliths, since the stability in the cracked state was insufficient, (Bond et al., 2013).

When constructing the new insulation wall, it was thought that the air inside of the insulation wall will be kept at 2^◦C throughout the year.

4.4 Previous research

There has been a lot of research on Storfinnforsen hydropower dam, which has been the basis of this project. Many reports have been written for Elforsk, now called Energiforsk, which is a research and development company created by a collaboration between Swedish power companies. Examples of reports from Energiforsk contributing to the development to this project is Ansell et al. (2007) and Ansell et al. (2010) describing crack propagation in concrete buttress dams with focus on non-linear modelling.

Malm (2009) made a verification of an FE-model, which has been used for research showing that seasonal temperature variations has been an important cause for crack initiation and propagation at Storfinnforsen hydropower dam.

The master thesis by Chaoran and Hafliðason (2015) was a thesis about the influence of crack propagation on the structural dam safety, where they made progressive failure analyses of concrete buttress dams.

Prior to this project, a risk assessment of Storfinnforsen and Ramsele has been made, see Nordström et al. (2015a). In the risk assessment, risk and consequence for each monolith was analysed.

The classification of consequence was divided into three classes: High, higher and highest. High was for monoliths lower than 20 m. Higher was for monoliths between 20 and 30 m. Highest was for monoliths higher than 30 m or those monoliths adjacent to the embankment dam. The risk classification was also divided into three classes:

Low, Medium, and High, illustrated in Figure 4.6 with green, yellow and red color respectively. In the risk classification, monoliths were given a score for different deficiencies. Low corresponds to one to three points. Medium was four to six points.

High was seven to nine points. The risk and consequence classes were put into a

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risk matrix, see Figure 4.6. The deficiencies were cracks in the concrete, repaired cracks, amount of leakage and rock quality. (Nordström et al., 2015a)

Figure 4.6: Risk matrix, from Nordström et al. (2015a)

From the risk matrix, three monitoring levels were suggested: Basic, Medium and Extensive. Basic monitoring was suggested for the green risk level. Medium was suggested for the yellow and orange risk levels. Extensive was suggested for the red risk level. Within the monitoring levels, more monitoring levels were suggested, Basic only had one level called B1, Medium was divided into two levels, M1 and M2 and Extensive was divided into two levels, E1 and E2, see Table 4.1 for more information. This was done to make a cost effective instrumentation. (Nordström et al., 2015a)

The risk assessment was governing when a monolith was chosen for the case study, where a monolith from the high risk category was chosen. The chosen monolith was monolith 42, since it was in the high risk category and a lot of measurement data was available for this monolith.

Table 4.1: Monitoring levels and sensor types suggested for the monoliths at Storfinn- forsen hydropower dam, based on the recommendations from the risk assessment project

Monitoring level

Sensor type B1 M1 M2 E1 E2

Piezometer x x x x x

Direct pendulum x

Inverted pendulum x

Extensometer x x

Load cells x x x x x

Joint movement x x x x

Crack width sensors x x x

Temperature sensors x x x x

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4.5. MEASUREMENTS

4.5 Measurements

In 2006 some of the monoliths at Storfinnforsen were equipped with sensors, see Figure 4.7. There were a total of 14 temperature sensors, 10 crack width sensors and one direct pendulum. Measurement data from a total of seven sensors were chosen for calibration of the model, and the chosen sensors and their measurement periods are shown in Table 4.2.

Temperature sensor in concrete, 50 cm, right side Temperature sensor in concrete, 50 cm, left side

Temperature sensor in air, left side

Temperature sensor in air, right side

S2 S1 S8S3 S4 S7

S5 S6

S24S1_new LVDT-sensor

T15 T7T8

T12 T1 T3 T11

T10 T2 T6

T5

T4 T16T9

Direct pendulum

a) b)

Figure 4.7: Position of sensors on a monolith at Storfinnforsen hydropower dam

Table 4.2: Sensors and their data periods Sensor type and name Data period Cracks

S2 2006-03-03 to 2012-10-17 S4 2006-03-03 to 2012-10-17 S6 2006-03-03 to 2012-10-17

Temperature

T2 2006-03-03 to 2012-10-17 T8 2006-03-03 to 2012-10-17 T12 2007-01-16 to 2013-01-22 T16 2007-01-16 to 2013-01-22 Crest displacement DP 2007-10-10 to 2014-04-17

Data from these sensors were available, but there was data missing for a few periods, see Appendix A for more information. Temperature data was available from Smhi, and these measurements corresponded very well to the measurement data re-

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trieved from Storfinnforsen hydropower dam. In Figure 4.8, a comparison between measurements from Smhi and from Storfinnforsen hydropower dam is shown.

Figure 4.8: Comparison of temperature data from Smhi and Storfinnforsen, sensor T8

To extend the amount of data and complete the missing periods, temperature data from Smhi was collected and analysed. The temperature data from Smhi was collected from their station in Storfinnforsen and spanned from 1954 to 2015.

The completion of data was made by collecting corresponding inside and outside air temperatures, and performing regression analysis on the data to get an equation describing the inside temperature as a function of the outdoor temperature. Both linear and polynomial regression was performed. However, the linear regression achieved the best correlation with the data, and the linear regression function was therefore used to complete the temperature data, see Figure 4.9.

Figure 4.9: Regression analysis of temperature data

The variation in the temperature data is illustrated with boxplots in Figures 4.10 to 4.15. The boxplots are a compilation of the data from the measurement periods shown in Table 4.2. A boxplot is a way to illustrate several statistics in one plot and is used to see the variation of the data. The upper and lower lines of the boxes represent the 75th and 25th percentiles, respectively. The line inside the box is the median of the observed values. The whiskers show extreme values, where the extreme

Numerical analyses of concrete buttress dams to design dam monitoring

Numerical analyses of concrete buttress dams to design dam monitoring

DANIEL SVENSEN

Numerical analyses of concrete buttress dams to design dam monitoring

Daniel Svensen

June 2016

TRITA-BKN. Master Thesis 492, Concrete Structures 2016 ISSN 1103-4297,

ISRN KTH/BKN/EX–492–SE

Abstract

Sammanfattning

Preface

Contents

Chapter 1 Introduction

1.1 Background

1.2 Aim and scope

1.3 Structure of the thesis

Chapter 2

Concrete buttress dams

EXPLANATION

2.1 Loads

2.1.1 Dead load

2.1.2 Water pressure

2.1.3 Ice load

2.1.4 Thermal loads

2.2 Failure modes

2.2.1 Overturning failure

2.2.2 Sliding failure

2.2.3 Material failure

2.3 Cross-sectional analyses

Chapter 3

Monitoring of dams

3.1 Purpose

3.2 Types of monitoring equipment

3.3 Behavior models

3.3.1 Deterministic model

3.3.2 Statistical model

3.3.3 Hybrid model

3.4 Methods to define alarm values

3.4.1 Experience

3.4.2 Numerical analyses

3.5 Calibration and verification of numerical mod- els

3.5.1 Mesh convergence

3.5.2 Calibration

3.5.3 Verification of prediction

Chapter 4 Case Study

4.1 Geometry

4.2 Existing cracks

4.3 Structural changes

4.4 Previous research

4.5 Measurements