2014
Vazquez Borragan, Alejandro Master Thesis
10/4/2014
Modelling Internal Erosion
Within An Embankment Dam
Prior To Breaching
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Modelling Internal Erosion Within An Embankment Dam Prior To Breaching
M. A. Vazquez (avb@kth.se , 850323-3432)
KTH Royal Institute of Technology, Stockholm, SWEDEN.
October 2014
ABSTRACT
There are still uncertainties in the safety of existing embankment dams. For instance, the majority of embankment dams in Sweden were built between 1950s and 1970s, designed and constructedto standards that might be unacceptable nowadays. Particularly, Vattenfall’s records stated that 40% owned embankments dams developed sinkholes (Nilsson, 1999). Moreover, internal erosion and its failure mechanisms of initiation and development are still not fully understood (Bowles et al., 2013). Also, internal threats are difficult to detect and interpret even using new instrumentation techniques. The aim of this Master Thesis is to identify failure mechanisms of embankment dams prior to breaching and hence, verify the reliability of a risk analysis after the breaching of the dam. The methodology consisted of monitoring an embankment dam prone to fail by internal erosion mechanisms. Finally the results were modelled using FEM to identify the risk of internal erosion prior to breaching.
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“Sometimes…
Barriers are created with a retaining function. However, by nature some retained parts react, finding the mechanisms to get its freedom back. Meaning that, a wall can be defeated in its action.
…a failure can also be a Victory”.
-Alejandro Vazquez
“A veces…
Las barreras se crean con fines de retención.
Sin embargo, por naturaleza las partes contenidas reaccionan, Hallando los mecanismos que las liberan.
Significando que, se puede vencer al muro en su acción.
…un fallo también puede ser una Victoria”.
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ACKOWLEDGEMENT
First of all, I would like thank Johan Lagerlund, who has acted on behalf of Vattenfall Vattekraft and Vattenfall R&D to put his confidence on my skills and knowledge. I really appreciate the interest, time and effort he invested, which it has greatly helped to the success of this Master Thesis, and also to my professional development. I am also very pleased with all the members of the staff working at the Vattenfall R&D facilities in Älvkarleby, especially with Martin Rosenqvist, James Yang and Pelle Enegren(Master Thesis student), who showed a great interest and support during the performance of the experiments. Second of all, I would like to thank Stefan Larsson (KTH), especially, for all the advice provided to perform the academic writing and orientation to accomplish this Master Thesis, but also for being the link between Vattenfall and the university. Finally, and not for that the least importance, I wish to thank first my brother for his unconditional support; and to my friends for their support and motivation.
P.D: This work is dedicated to those who unfortunately I am not able to say thank you physically: {Maria Pilar Vazquez Borragan (Susana, mother) (1955-2008)}, {Eugenio Vazquez Añon (Abuelo, grandfather)(1912-2009}.
Alejandro Vazquez Borragan Stockholm, Sweden. 2014
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Contents
ABSTRACT ... 1
ACKOWLEDGEMENT ... 3
INTRODUCTION ... 7
State-of-art and limitations ... 7
Summary ... 9
METHODOLOGY ... 9
Dam design and materials properties ... 10
Building the dam ... 11
Instrumentation ... 14
Soil testing ... 14
Monitoring ... 14
Failure Mode Analysis ... 16
Dam Failure ... 20
RESULTS ... 22
Dam design ... 22
Slope stability analysis ... 22
Monitoring and modelling internal erosion ... 24
Seepage monitoring ... 24
Built model (SVFlux) ... 25
Deformation monitoring ... 27
Built model (SVSolid) ... 29
Internal erosion factors ... 30
Material susceptibility ... 30
Hydraulic load ... 33
Critical stress condition ... 36
Failure mode analysis (Critical zones) ... 40
Dam failure ... 41
DISCUSSION ... 46
Summary of the experimental results ... 46
Summary of the results from the analysis of the internal erosion factors ... 46
Failure Mode Analysis ... 47
Dam failure and event tree (Hypothesis verified) ... 48
5
REFERENCES ... 50
Figure 1. Dam, viewpoint from downstream side ... 10
Figure 2. Sequence of the experimentation ... 10
Figure 3. Design Model (GBE developed) ... 11
Figure 4. Layering sequences ... 12
Figure 5. Installation of piezometers in the core ... 13
Figure 6. Installation of piezometers top view ... 13
Figure 7. No filter at the crest ... 13
Figure 8. Vertical pipe ... 13
Figure 9. No erosion protection on top ... 13
Figure 10. Grain size distribution ... 14
Figure 11. Hydraulic conductivity test ... 14
Figure 12. Piezometers ... 15
Figure 13. Weir and pressure sensor inside the water tank ... 15
Figure 14. Turbidity meter ... 15
Figure 15. Laser scanner 3D ... 15
Figure 16. Venn Diagram, from (ICOLD, 2013). ... 16
Figure 17 Failure mode analysis ... 17
Figure 18. FOS Empty reservoir (upstream) ... 22
Figure 19. FOS empty reservoir (downstream) ... 22
Figure 20. FOS full reservoir (upstream) ... 23
Figure 21. Rapid drawdawn ... 23
Figure 22. Monitoring results (Core). ... 25
Figure 23. Monitoring results (Filter). ... 25
Figure 24. SVFlux results (Core). ... 26
Figure 25. SVFlux results (Filter). ... 26
Figure 26. Deformations monitored downstream (point of view from upstream) ... 28
Figure 27. Deformations monitored upstream (point of view from upstream) ... 28
Figure 28. Deformation monitored upstream and downstream (point of view from downstream). .. 29
Figure 29. BUILT MODEL-SVSolid deformation results ... 29
Figure 30. Comparison results SVSolid, DAM vs BUILT MODEL ... 30
Figure 31. Grain size distribution ... 31
Figure 32. Filter Internal stability ... 32
Figure 33. Core internal stability ... 32
Figure 34. Pipe internal stability ... 32
Figure 35. Pore-water pressure (kPa) ... 34
Figure 36. Hydraulic gradients ... 34
Figure 37. Water head (m) ... 35
Figure 38. Pressure head (m) ... 35
Figure 39. Seepage velocity (m/s) ... 36
Figure 40. Total stress Sy (kPa) ... 37
Figure 41. XY Displacements (m) ... 37
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Figure 43. XY Shear stresses (kPa) ... 38
Figure 44. X total stresses (kPa) ... 39
Figure 45. Y total stresses (kPa) ... 39
Figure 46. Total minimum principle stress (S3) (kPa) ... 40
Figure 47. Local Factor of Safety ... 40
Figure 48 Critical zones of failure mode analysis ... 41
Figure 49. Turbidity ... 42
Figure 50. Seepage flow, 10 days (Manual readings) ... 42
Figure 51. Seepage flow at day 10 (Thomson weir) ... 43
Figure 52. Pore-water pressure at day 10... 43
Figure 53. Acoustic emissions, day 10. ... 44
Figure 54. Dam Failure ... 45
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INTRODUCTION
In Sweden, there are two thousand damsproviding 65% of the energy demand, most of them are embankment dams. However, some of these 120 large embankment dams are classified as class 1, 2 and 3(Kraftnät, 2011) .This means that if a failure may occur, these dams would suppose a risk for people´s life and may cause severe economic damages. Even though, failures of embankment dams along the history of this country have not caused any exceptional consequences (Ekström, 2012), there are still uncertainties in the safety of these dams regarding to internal erosion. For instance, the majority of the dams were built between 1950s and 1970s, designed and constructed to standards that might be unacceptable nowadays. Particularly, Vattenfall’s records stated that 40% owned embankments dams developed sinkholes due to internal erosion (Nilsson, 1999) Furthermore, internal threats are difficult to detect and interpret even using new instrumentation techniques. Perhaps, due to the combination of these uncertainties and the state-of-art in the assessment of internal erosion, justify somehow, why approaches in the Swedish dam safety guidelines, RIDAS (2011), are considering conservative assumptions derived from the consequences of this phenomenon, e.g., extreme leakages, instead of assessing the factors of internal erosion within the dam. The results of the assessments with those assumptions usually imply costs of design and construction of new downstream berms, which may not protect the weakest part of the dam against internal erosion (the crest), and may cause associated risks from the new construction. However, why not facing internal erosion firstly, and see if there is any likelihood to occur?
In connection to the last question, the aim of this Master Thesis was to face internal erosion before the consequences. The approach was to identify failure mechanisms of embankment dams prior to breaching, and hence verify the reliability of a failure mode analysis after the breaching. Initially, after the literature review, a hypothesis was set as: “If there is internal erosion within the dam, it is possible to analyse the factors that initiate the failure mechanisms, and thus, assessing the safety of the dam prior to breaching”. Later on, in the experimentation phase, the methodology consisted of monitoring a small embankment dam prone to fail by internal erosion mechanisms, whereas, Finite element models (FEM) were implemented to analyse the likelihood of internal erosion prior to breaching. Finally, the hypothesis was verified when the failure mode analysis pointed out the same location where the dam failed in the experiment.
This project is the first research project of a program to study the safety of dams funded by Vattenfall Vattenkraft. It took place at Vattenfall Research and Development in Älvkarleby where a new infrastructure for the embankment dam was installed for this purpose.
State-of-art and limitations
Internal erosion, by definition, occurs when particles within an embankment or its foundation are carried downstream by seepage flow. It can initiate by concentrated leaks, backward erosion, contact erosion and suffusion (ICOLD, 2013). Even though the problem is known from times of the romans, it was not until the 1970s, when the famous Teton’s dam accident occurred (Solava, 2003), when actually internal erosion was considered a main dam safety issue. This phenomenon has been faced from different perspectives by many authors. Most of the approaches to assess internal erosion have been classified in this literature review in: 1) Hydraulic gradient and grain size of the soils; 2) Dam breach; 3) Surveillance 4) Failure mechanisms and internal erosion factors.
1) Hydraulic gradient and grain size of the soils
8 Terzaghi (1996) made extended experimentation. These investigations developed the filter criteria, which determine if the filters are capable to stop the transport of particles from the core. Meanwhile, experimentation of Skempton (1994) proofed that certain soils may develop internal erosion even at lower hydraulic gradients than Terzaghi critical gradient, gaining more importance the grain size distributions of the soils. Thus, other investigations combined internal stability analysis, such as Kenny and Lau (1985), and probabilistic methods from historical data of accidents. These assessments still were based on the grain size distribution of the core and filters, such as Rönnqvist (2007), Rönnqvist et al., (2014), Bridle, Delgado & Huber (2007), Foster (2001), Brown (2003). One of the problems of these methods in existing dams, older than the method itself, is that the finer part of the soils (sieve size <0,075 mm) may not be in the old particle size distributions analysis. Therefore, the evaluation with the methodology of Kenny and Lau is sometimes not possible. For instance, if a widely graded core has F(%)=35% at 0,075 mm, the H-F curves cannot evaluate the internal stability.
2) Dam breach
Another approach aimed to face the consequences of internal erosion (dam breaching procedure). These methods simulate the effects of a potential failure mechanism, which enables planners to set emergency plans. Some of these methods used parameters from historical accidents as well, such as Evans (1986) and Xu & Zhang (2009). Other authors such as Sellmeijer & Koenders (1991) or Bonelli (2006) used mathematical models to describe the phenomenon of “piping”. In spite of existence of advanced breaching simulation models such as Morris (2008). These methods will not provide realistic consequences unless an approach to assess the most likely failure mechanism is performed before.
3) Surveillance
Based on the observational method, attributed to Terzaghi by Peck (1969), surveillance was the other method to assess the behaviour of the dam for safety evaluation (Charles, 1996). Due to extended research in several surveillance methods, it was determined that internal erosion is influenced by other factors than the grain size and hydraulic gradients, for instance; the temperature and resistivity, as shown in research from Johansson (1997). Moreover, nowadays, numerical modelling allows modelling several parameters from monitoring data such as the experiment of Radzicki (2010). Therefore, it is possible to model different parameters for many case scenarios to analyse the failure modes, but in order to assess the safety of the dam, it is not possible to determine if these parameters can develop failure mechanisms. Basically, because of the fact that the only way to verify the assessment from the numerical modelling is to wait for the actual breach of the dams, or performing failure tests such as the experiments made by Sjödahl (2010).
4) Failure mechanisms and internal erosion factors
9 to the advanced research achieved in: seepage modelling, such as: Fredlund (1994) or Krahn (2004); and stress-strain soil models such as: Duncan & Chang (1970) or Schanz & Vermeer (1999), it is possible to analyse all the factors of internal erosion. Finally, recent laboratory experiments of Chang (2013), and Hunter & Fell (2012) have combined the analysis of the internal erosion factors using soil samples in their tests. However, no experiment modelling the combination of the three factors within dams was found out. This information was considered essential to assess internal erosion (ICOLD, 2013).
Summary
Nowadays, Failure mechanisms of internal erosion are still not fully understood and methods to estimate the probability of failure are under evaluation (Bowles et al., 2013) and (Fell et al., 2008). Therefore, it is necessary to analyse all the initiating factors of internal erosion (stress state, hydraulic conditions and material susceptibility). In addition to that, it is necessary to perform more laboratory tests of dams. For instance, dams developing vertical piping and Global Backward Erosion (GBE) in broadly graded cohesionless soils such as glacial tills (ICOLD, 2013). Moreover, duration of the experiments, dimensions of laboratories and characteristics of the test apparatuses cannot reproduce exactly what occurs within a large dam. Nonetheless, recently with the extended use of FEM is possible to reproduce stress states and seepage models in a simple fashion, allowing prediction of different case scenarios within the models. That is why an experiment breaching a small embankment was considered key to achieve reliable models. For the aim and time of the experiment 2D modelling was determined to be accurate enough.
METHODOLOGY
10 Figure 1. Dam, viewpoint from downstream side
Figure 2. Sequence of the experimentation
Dam design and materials properties
The geometric design was determined analysing the likelihood of slope instability for different dimensions. The design achieved was: 1½ meter height, 4(H):3(V) rock fill shoulders with sloped central core of glacial till (moraine) and a downstream gravel sandy filter. Furthermore, a vertical pipe was inserted in the dam. This defect can be seen in Figure 3. Moreover, it was included in the experiment to test if GBE could be developed during the test. Material properties (See Table 1) were determined using literature values of the soils and soil testing.
11 Figure 3. Design Model (GBE developed)
Table 1. Material properties
MATERIAL PROPERTIES MATERIAL HYD. COND. KSAT (m/s) POROSITY n UNIT WEIGHT γ (kN/m3) DRY DENSITY
ᵨ
d (kg/m3) GRAVI. WATER CONTENT W COHESION c’ (kPa) FRICTION ANGLE ф’ (˚) *YOUNG MODULUS, E (kPa) *POISSON RATIO μ ROCKFILL *1 x 10-3 *0.3 *21 *1855 *0.16 0 *40 1 x 107 0.4 GLACIAL TILL / PIPE 3.5 x 10 -9 0.2 23 2120 0.09 10.8 52 10000 0.3 FILTER *2 x 10-7 *0.35 *20 *1723 0.2 0 *33 20000 0.35*Geotechdata.info(2013), Bowles(1997), Stanford.edu (2014), Bergh (2014)
Building the dam
12 Figure 4. Layering sequences
There were two elements that needed to be placed carefully; piezometers pipelines and a vertical pipe through the core. Three piezometers at the core and three at the filter were used for the pore-water pressure monitoring. The piezometers pipelines were installed at the bottom of the core and inside the filter. The installation of piezometers pipelines was horizontal and perpendicular to the flow, wrapping them around with a geotextile to protect them from the soil, and connected with the piezometers outside through the right sidewall (See Figure 5 and 6).
An aluminium’s pipe , 10 cm diameter, was inserted at the central cross section of the dam. It was made from the glacial till (core), sieving grains of 0.8 cm and 0.1 cm to achieve a gap graded material i.e., internally unstable. The pipe was taken away from the embankment once it was finished (See Figure 8).
The top layer (120-150 cm) had no filter. Moreover, the crest was left unfinished, as it is in Figure 7 for one day. Later on, the acoustic emissions sensor was placed on the right abutment, that device had a weight of 2 kg inserted in the core with three steel rods of 2 cm diameter and 10 cm long at the top of the crest (See Figure 7 and 9). Finally, the crest was not protected with rock fill.
Day 6
Day 4
13 Figure 5. Installation of piezometers in the core
Figure 6. Installation of piezometers top view
Figure 7. No filter at the crest
Figure 8. Vertical pipe
Figure 9. No erosion protection on top
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Instrumentation
For the instrumentation, all stipulated equipment for a dam of consequence class 1 was used, following the RIDAS guidelines. The instrumentation to monitor the parameters of seepage, turbidity, deformations, pore-water-pressure and vibrations applied mainly indirect methods (except the water level) such as; a pressure sensor correlated to a Thomson’s weir downstream and manual readings filling a bucket to measure seepage; automated piezometers for the core and filter; acoustic emissions sensor over the crest to detect vibrations of piping; turbidity meter taking samples downstream; laser scanner of all surfaces of the dam .
Soil testing
Soil testing was carried out before and after the construction of the embankment. Some tests were performed in the laboratory such as the grain size distributions and gravimetric water content for filter and glacial till, and hydraulic conductivity tests for the core and the pipe (See Figure 10 and 11). Also, it was performed a proctor modified test to control the compaction of the core, and determine volume-mass parameters needed for the setup of the material properties in the FEM.
Figure 10. Grain size distribution
Figure 11. Hydraulic conductivity test
Monitoring
The dam was loaded for 10 days at different water levels. During that time, several methods were applied to monitor the following parameters, which are included in Table 2; Pore-water pressure (See Figure 12), flow (See Figure 13), turbidity (See Figure 14), deformations (See Figure 15) and the stored water level. Apart from these methods, video surveillance was installed downstream and upstream the dam, recording the full length of the experiment.
15 Table 2. Monitoring methods
MONITORING METHODS
METHOD PARAMETER FREQUENCY N˚ UNITS LOCATION
MANUAL PIEZOMETERS LOG
Pore-water pressure
continuous/each anomaly 6 cm Core/filter
AUTOMATED PIEZOMETERS LOG
Pore-water pressure
1 per minute 4 cm Core/filter
THOMSON WEIR Seepage 1 per minute 1 cl/min Downstream
FLOW MEASURE. Seepage continuous/each anomaly 1 cl/min Downstream
TURBIDIMETER Turbidity continuous/each anomaly 1 FNU Downstream
ACOUSTIC SENSOR Vibration 1 per 15 minutes/each anomaly
1 mm/s Crest
LASER SCANNER Deformations continuous 1 mm Downstream/upstream
RULER Water level continuous 2 cm Upstream
Figure 12. Piezometers
Figure 13. Weir and pressure sensor inside the water
tank Figure 14. Turbidity meter
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Failure Mode Analysis
As Garner and Fannin (2010) illustrated in a Venn diagram (Figure 16), internal erosion initiates when an unfavourable coincidence of material susceptibility, stress conditions and hydraulic load occurs (ICOLD, 2013). Based on that diagram, the method consisted of performing three analyses (hydraulic load, material susceptibility and stress state) within cross sections of the dam. Firstly, each analysis observed the location and magnitude of the factors of internal erosion. For instance, in the hydraulic load analysis, one of the factors was a maximum hydraulic gradient (magnitude of the factor) at the crest of the right abutment (location). After that step, critical zones at each cross section were identified as zones where combination of factors matched, e.g. maximum hydraulic gradient at the crest of the right abutment and low stresses at the crest. Finally, the combination of all the analysis pointed out the location of the most likely failure mechanism to breach the dam (Figure 17).
Numerical modelling was the key tool to analyse the stress state and hydraulic load factors within the cross sections. But firstly, in order to avoid other failure modes rather than internal erosion, the slope stability was assessed at design stage. Moreover, a spillway reduced the likelihood of overtopping. Thus, only internal erosion could occur. The package used for seepage analysis was SVFlux, for slope instability SVSlope and for stress analysis SVSolid. SoilVision (SV) utilized FlexPDE generic finite element solver to solve the partial differential equations (SoilVision, 2014). The FlexPDE for SVSlope and SVFlux solved linear and nonlinear PDE’s. The nonlinear behaviour was most commonly located in the unsaturated soil portion of the continuum. The solution utilized automatic mathematically designed mesh generation as well as automatic mesh refinement. The background theory applied by SoilVision can be obtained in the theory manual of the software or related literature, and therefore, only the methods and equations applied in the analysis will be mentioned from the manuals.
17 Figure 17 Failure mode analysis
Hydraulic load analysis
Two-Dimensional seepage analysis was applied for modelling cross-sections with and without the pipe at steady-state saturated/unsaturated seepage.
Considering the reference volume V0 constant and the water incompressible, the following partial
differential (PDE) equation was applied for saturated/unsaturated seepage:
𝝏 𝝏𝒙[(𝒌𝒙𝒘) 𝝏𝒉 𝝏𝒙] + 𝝏 𝝏𝒚[(𝒌𝒚𝒘) 𝝏𝒉 𝝏𝒚] = −𝜸𝒘𝒎𝟐 𝒘 𝝏𝒉 𝝏𝒕 Eq(1)
Considering saturated soil and neglecting the vapour flow, the PDE governing steady-state seepage reduces to: 𝝏 𝝏𝒙[(𝒌𝒙𝒘) 𝝏𝒉 𝝏𝒙] + 𝝏 𝝏𝒚[(𝒌𝒚𝒘) 𝝏𝒉 𝝏𝒚] = 𝟎 Eq(2)
Where kw, is the hydraulic conductivity in the x and y directions. These values are constant for saturated conditions. For unsaturated soil, it is the function of matric suction (difference of air and water pore pressures, ua-uw); m2w, represents the derivative with respect to matric suction from
the soil-water characteristic curve; γw, the unit weight of water; h, the hydraulic head; x and y are the horizontal and vertical coordinates in isotropic flow, respectively.
Failure mode analysis
Critical zones from analysis: -Suffusion -Hydraulic fracture -Soil distress -Cracking -Bridging -Piping
Hydraulic load analysis
Factors: -Gradients -Pore water pressure
-Seepage velocity
Material susceptibility analysis
Factors: -Internal Instability -Filter incompatibility -Void space -Free surface -Low plasticity
-Cracks Stress state analysis
Factors: -Low stress -Deformation
18 The software solved the PDE in seconds for different initial conditions. Solutions included in the results are; the pore-water pressure distribution, range of fluxes, water head distribution within the core and gradients and water heads. With these results, hydraulic load conditions were assessed.
Slope stability
SVSlope was utilized for limit equilibrium methods of slope stability analysis, and hence, to compute the factor of safety (FOS), ensuring the dam would not fail due to slope instability. The fully specified method was applied at different initial conditions for different critical slip surfaces: empty reservoir, maximum capacity and rapid drawdown transferring the seepage files from SVFlux (Design Model). The method of slices was assumed to be composite-circular. The shear force mobilized was obtained for each slice in the saturated soil as:
𝑺𝒎=𝑭𝜷 𝒔{𝒄
′+ (𝝈
𝒏− 𝒖𝒘) 𝐭𝐚𝐧 𝝋′} Eq (3)
And, for the unsaturated soil, the Phi-b method was applied using the following equation for the mobilized shear force.
𝑺𝒎=𝑭𝜷 𝒔{𝒄
′+ (𝝈
𝒏− 𝒖𝒂) 𝐭𝐚𝐧 𝝋′+ (𝒖𝒂− 𝒖𝒘) 𝐭𝐚𝐧 𝝋𝒃} Eq (4)
Where, Sm is the shear force mobilized on the base of the slice; 𝛽 is the length along the base of a
slice; Fs is the overall factor of safety; c’ is the effective cohesion; 𝜎𝑛 is the normal stress acting on
the base of a slice; 𝜑′ is the effective angle of internal friction; 𝑢𝑎 is the pore-air pressure at the base
of a slice; 𝑢𝑎− 𝑢𝑤 is the matric suction and 𝜑𝑏 is the angle defining the rate of increase of strength
due to an increase in the suction.
Stress state conditions
SVSolid modelled the stress-deformation state. The vibration was measured with an acoustic emission sensor; however results showed no effects to consider in the analysis. SVSolid is based on the theory of elasticity, a two-dimensional plane strain model was assumed to perform the stress analysis. These models were expressed in terms of partial differential equations, governing the static equilibrium of the forces acting on a representative elemental volume of material. The equilibrium equations were combined with constitutive models relationships, expressing changes in stresses in terms of strains. The strains were written in terms of the displacements, assuming small displacements (Lagrangian formulation). In order to express the PDE´s applied for the stress analysis, strain and displacement relationships, static equilibrium equations and generalized stress-strain relationship need to be defined firstly:
Relationships between the components of strain and displacements:
𝜺𝒙=𝝏𝒖𝝏𝒙, 𝜺𝒚=𝝏𝒚𝝏𝒗 , 𝜸𝒙𝒚=𝝏𝒗𝝏𝒙+𝝏𝒖𝝏𝒚 Eq (5)
Where u and v are displacements in the x- and y-directions, respectively.
19 𝝏𝝈𝒙 𝝏𝒙+ 𝝏𝝉𝒙𝒚 𝝏𝒚 + 𝒃𝒙= 𝟎 Eq (6) 𝝏𝝉𝒙𝒚 𝝏𝒙 + 𝝏𝝈𝒚 𝝏𝒚+ 𝒃𝒚= 𝟎 Eq (7)
Where 𝜎𝑖and𝜏𝑖𝑗are the total normal and shear stresses, respectively, and 𝑏𝑖 the body weight (i.e.,
unit weight).
SVSolid used the displacement components as the primary variables describing the stress-strain field model. Therefore, in order to obtain the PDE’s that govern the static equilibrium of forces throughout the continuum, the stresses present in the equilibrium equations must be replaced by the displacement components. Thus, from the following generalized stress-strain relationship:
𝒅𝜺 = 𝑫−𝟏𝒅𝝈 Eq (8) Where, in three-dimensions: 𝑫 = [ 𝑫𝟏𝟏 𝑫𝟏𝟐 𝑫𝟏𝟑 𝑫𝟐𝟏 𝑫𝟐𝟐 𝑫𝟐𝟑 𝑫𝟑𝟏 𝑫𝟑𝟐 𝑫𝟑𝟑 𝑫𝟏𝟒 𝑫𝟐𝟒 𝑫𝟑𝟒 𝑫𝟒𝟏 𝑫𝟒𝟐 𝑫𝟒𝟑 𝑫𝟒𝟒 𝟎 𝟎 𝟎 𝟎𝟎 𝟎 𝟎 𝟎 𝟎 𝟎 𝟎 𝟎 𝟎 𝟎 𝟎 𝟎 𝑫𝟓𝟓 𝟎 𝟎 𝑫𝟔𝟔] Eq (9) 𝝈𝑻= {𝝈 𝒙 𝝈𝒚 𝝈𝒛 𝝉𝒙𝒚 𝝉𝒙𝒛 𝝉𝒚𝒛 } Eq (10) And: 𝜺𝑻= {𝜺 𝒙 𝜺𝒚 𝜺𝒛 𝜸𝒙𝒚 𝜸𝒙𝒛 𝜸𝒚𝒛 } Eq (11)
Applying 2D plane-strain conditions; where: 𝜀𝑧 , 𝛾𝑥𝑧, 𝛾𝑦𝑧 , 𝜎𝑧, 𝜏𝑥𝑧 , 𝜏𝑦𝑧 , are zero. The PDE’s can be
reduced to: 𝝏 𝝏𝒙[𝑫𝟏𝟏 𝝏𝒖 𝝏𝒙+ 𝑫𝟏𝟐 𝝏𝒗 𝝏𝒚+ 𝑫𝟏𝟒( 𝒅𝒗 𝒅𝒙+ 𝒅𝒖 𝒅𝒚)] + 𝝏 𝝏𝒚[𝑫𝟒𝟏 𝝏𝒖 𝝏𝒙+ 𝑫𝟒𝟐 𝝏𝒗 𝝏𝒚+ 𝑫𝟒𝟒( 𝒅𝒗 𝒅𝒙+ 𝒅𝒖 𝒅𝒚)] + 𝒃𝒙= 𝟎 Eq (12) 𝝏 𝝏𝒙[𝑫𝟒𝟏 𝝏𝒖 𝝏𝒙+ 𝑫𝟒𝟐 𝝏𝒗 𝝏𝒚+ 𝑫𝟒𝟒( 𝒅𝒗 𝒅𝒙+ 𝒅𝒖 𝒅𝒚)] + 𝝏 𝝏𝒚[𝑫𝟐𝟏 𝝏𝒖 𝝏𝒙+ 𝑫𝟐𝟐 𝝏𝒗 𝝏𝒚+ 𝑫𝟐𝟒( 𝒅𝒗 𝒅𝒙+ 𝒅𝒖 𝒅𝒚)] + 𝒃𝒚= 𝟎 Eq (13)
Considering the hyperbolic model, the following constitutive relationships were applied in the Hook’s law (Eq 7).
𝑫𝟏𝟏= 𝑬(𝟏 − 𝝁)/[(𝟏 + 𝝁)(𝟏 − 𝟐𝝁)] Eq (14) 𝑫𝟏𝟐= 𝑬𝝁/[(𝟏 + 𝝁)(𝟏 − 𝟐𝝁)] Eq (15)
𝑫𝟒𝟒= 𝑬/[𝟐(𝟏 + 𝝁)] Eq (16)
Where, E is the Young Modulus and μ is the Poisson ratio. Assuming that, the Young’s modulus can be approximated as a tangent modulus. Then, the tangent modulus in the hyperbolic model is defined as a nonlinear function of the shear strength parameters.
20
𝑹𝒇= (𝝈𝟏 −𝝈𝟑)𝒇
(𝝈𝟏−𝝈𝟑)𝒖𝒍𝒕 Eq (18)
Where, 𝑅𝑓 is the failure ratio, equal to the ratio of the stress difference at failure (shear resistance)
and the actuating stress difference; 𝜎1 and 𝜎3 are the major and minor principal stresses,
respectively; K is a modulus of elasticity of reference; 𝑃𝑎𝑡𝑚 is the atmospheric pressure; and, n is an
experimental parameter that defines the ratio of increase of E with 𝜎3. The input values were
obtained from previous triaxial tests performed in similar materials (See Table 3) Table 3. Hyperbolic equation parameters
HYPERBOLIC EQUATION PARAMETERS*
MATERIAL FAILURE RATIO 𝑅𝑓 ELASTICITY MODULUS K (KPa) EXPERIMENTAL PARAMETER n ATMOSPHERIC PRESSURE 𝑃𝑎𝑡𝑚 (KPa) ROCKFILL 0.73 1450 0.30 101.15 GLACIAL TILL 0.77 520 0.42 101.15 FILTER 0.72 1141 0.20 101.15 *Dong et al., (2013)
Material susceptibility
Considering the factors of material susceptibility in Figure 17, the analysis was mainly focused on the grain size distributions, therefore performing soil testing. The factors analysed from these tests were the filter compatibility and the internal stability of the core and filter. The criterion for the assessment of internal stability of granular filters applied was based on methodology from Kenny and Lau (1985) and Rönnqvist (2007). The results from these assessments provided the likelihood of internal erosion for these soils within the dam. Since the foundation was built over the base of a steel container, backward erosion at foundation was discarded as a failure mode (free surface). Other factors such as plasticity index, temperature or resistivity were not analysed in this experiment. However, voids and construction quality details were considered in the failure mode analysis, since it was believed that compaction rates or defects caused by instrumentation would make the embankment more susceptible to fail at different zones, e.g. cracks next to instrumentation or poorly compacted layers.
Dam Failure
Dam failure was the phase of the experiment where the hypothesis was verified, i.e. if the result from the failure mode analysis matched the actual dam failure at the experiment, the hypothesis was true. In other words, the failure mode analysis aimed to find what factors and where breaching mechanisms could occur. Whereas, the dam failure investigation aimed to find what factors caused the dam failure, and how.
22
RESULTS
The results are described following the steps of the methodology (See Figure 2).
Dam design
Firstly, the slope stability was assessed to guarantee that the experiment would not fail due to slope instability. The slope stability was assessed for three initial conditions: Empty reservoir, full reservoir and rapid drawdown (See Figure 18, 19, 20, 21).
The dam designed had a FOS higher than 1.3 applying Bishop’s method for all the cases. From this analysis it was concluded that the dam would not fail during the experiment due to slope instability.
Slope stability analysis
Figure 18. FOS Empty reservoir (upstream)
23 Figure 20. FOS full reservoir (upstream)
24
Monitoring and modelling internal erosion
In this section, the seepage and deformations monitored in the experiment were compared with the FEM results (or Built Model), using SVFlux and SVSolid.
Seepage monitoring
The piezometers and seepage flow measurements provided huge amounts of data each day. From all the results collected each day, only steady conditions were used for the analysis. Therefore, when steady-state conditions were observed each day, it was assumed that a queasy-steady state of seepage was reached. Thus, in Table 4 are shown the results at queasy-steady state of seepage each day of the experiment. From these results, there have been plotted graphs showing the variation of the pore-water pressure of all the piezometers at the core and at the filter, respectively (See Figure 22 and 23). Attending to the pore-water pressure, it was noticed and anomaly behaviour at the right piezometers with respect to the other piezometers. The anomaly was a higher pore water pressure than expected, because the tip of the piezometer at the right abutment was placed at the most forward position into the core, which would suppose the lowest PWP of the 3 piezometers in normal condition (See Figure 6). Regarding to the seepage measurements, the leakage increased in great fashion for the last 3 days of the experiment. The Thomson weir was assumed to provide low reliable data in compare with the manual measurements at low seepage flow. Thus, the manual measurements were considered the most reliable values, at low flow.
Table 4. Dam values monitored at queasy-steady state seepage
DAY CORE PIEZOMETERS (cm) FILTER PIEZOMETERS (cm) WL (cm)
SEEPAGE (liters/min)
LEFT CENTRAL RIGHT LEFT CENTRAL RIGHT THOMSON MANUAL
25 Figure 22. Monitoring results (Core).
Figure 23. Monitoring results (Filter).
Built model (SVFlux)
The following results in Table 5 were obtained with SVFlux for steady-state conditions. These seepage results show values of pore-water pressure within the numerical model at the same location of the piezometers installed. Note that to compare the results at steady-state, the same reservoir levels from monitoring were applied in SVFlux. Thus, the graphs of the results from Table 5 were also plotted (See Figure 24 and 25). In Table 6, there has been compared the Built Model (SVFlux results) with the Dam (monitoring results), the table shows that the pore water pressures at the experiment started to match with the model after the 4th day. However, there were still differences at the right abutment piezometers. Moreover, the leakage monitored did not match with the SVFlux results.
0 20 40 60 80 100 120 140 1 2 3 4 5 6 7 8 9 10 PW P (c m ) Time (days)
CORE PIEZOMETERS (cm) LEFT CORE PIEZOMETERS (cm) CENTRAL CORE PIEZOMETERS (cm) RIGHT WL (cm) 0 2 4 6 8 10 12 14 16 18 1 2 3 4 5 6 7 8 9 10 PW P (c m ) Time (days)
26 Table 5. Built Model- SVFlux results at steady-state seepage
DAY CORE PIEZOMETERS (cm) FILTER PIEZOMETERS (cm) WL (cm)
SEEPAGE (liters/min) LEFT CENTRAL RIGHT LEFT CENTRAL RIGHT
1 22.3 21.5 20.3 9.19 9.1 9.1 23.5 1.04 2 60.9 57.5 53 9.8 9.4 9.3 65.5 1.12 3 41.1 39.1 36.3 9.5 9.3 9.2 44 1.04 4 120.6 113.7 104.6 16.05 15.35 15.2 130 1.80 5 120.6 113.7 104.6 16.05 15.35 15.2 130 1.80 6 119 112 103 15.8 15.1 15 128 1.78 7 110.5 104.3 96 16.2 15.6 15.4 119 1.84 8 114.2 107.7 99.1 16.2 15.6 15.5 123 1.84 9 115.1 108.6 100 16.3 15.6 15.5 124 1.84 10 115.1 108.7 100 16.2 15.5 15.4 124 1.83
Figure 24. SVFlux results (Core).
Figure 25. SVFlux results (Filter).
0 20 40 60 80 100 120 140 0 1 2 3 4 5 6 7 8 9 10 PW P (c m ) Time (days)
CORE PIEZOMETERS (cm) LEFT CORE PIEZOMETERS (cm) CENTRAL
CORE PIEZOMETERS (cm) RIGHT WL (cm) 0 2 4 6 8 10 12 14 16 18 1 2 3 4 5 6 7 8 9 10 PW P (c m ) Time (days)
FILTER PIEZOMETERS (cm) LEFT FILTER PIEZOMETERS (cm) CENTRAL
27 Table 6. Relative differences of results DAM vs BUILT MODEL
DAY CORE PIEZOMETERS FILTER PIEZOMETERS SEEPAGE
RATES LEFT CENTRAL RIGHT LEFT CENTRAL RIGHT
1 -14.36% -30.30% -19.41% 20.09% -1.11% 20.87% N/A 2 -12.78% -26.37% -20.45% 14.78% -4.44% 19.13% N/A 3 -19.13% -26.95% 9.93% 17.39% -3.33% 20.00% 39.69% 4 -0.50% -2.43% 8.96% 2.73% -2.33% 5.00% 59.17% 5 0.99% 0.00% 10.60% 2.73% -2.33% 1.94% 54.54% 6 0.83% 0.71% 10.51% 4.24% -0.67% 6.25% 60.28% 7 1.87% 1.79% 11.19% 0.61% -1.96% 1.91% 49.00% 8 -0.79% -0.75% 8.24% 0.00% -1.96% 3.13% 92.67% 9 -0.70% -0.56% 8.68% -0.62% 0.00% 3.13% 96.74% 10 -0.79% -0.37% 8.84% 0.00% 0.00% 3.75% 96.85% Deformation monitoring
With the laser scanner it was measured the deformation of the dam after 10 days. The measurements of deformations were taken independently for the upstream and downstream faces, although the surveillance equipment still measured points of both sides due to a high location of the apparatus. Figure 26, shows deformations monitored at downstream face. Note that this is a 3D view from an upstream point of view. The maximum deformations are represented in red. However, these deformations were due to water level variations upstream. Therefore, the maximum deformations within the dam are actually located downstream, and these were lower than 1.5 cm (green dots downstream slope). There were also deformations at the sidewalls of the container. In Figure 27, deformations monitored upstream are shown in a 3D view from upstream, the maximum displacements were lower than 10 cm. It indicates clearly that the maximum settlements occurred at the crest on the right abutment. The red and grey areas at the slope upstream do not indicate deformations of the dam, these areas only indicated water level variation.
28 Figure 26. Deformations monitored downstream (point of view from upstream)
29 Figure 28. Deformation monitored upstream and downstream (point of view from downstream).
Built model (SVSolid)
With the displacements obtained in SVSolid (See Figure 29) and the deformations monitored, the results were compared with in Table 7. In Figure 30, the comparison of the results was based on the maximum deformations monitored at different zones of the dam (crest, upstream and downstream) distinguishing between right, central and left parts of the dam. There were also drawn linear trend lines that indicated that the maximum deformations monitored were higher at the right abutment. In fact, deformations monitored at the right abutment matched closer to the calculation with
SVSolid, at a 20-30% relative error between all the results. Therefore, the results from the model and the experiment were considered to be close enough for further analysis.
30 Table 7. Maximum deformations DAM vs BUILT MODEL
MAXIMUM DEFORMATIONS MONITORED(cm) SVSOLID (cm)
ZONE LEFT CENTRAL RIGHT LEFT CENTRAL RIGHT
DEFORMATIONS UPSTREAM 8 5 10 8 8 8 DEFORMATIONS CREST 8 2,5 10 8 8 8 DEFORMATIONS DOWNSTREAM 1,6 1,6 3 4 4 4
Figure 30. Comparison results SVSolid, DAM vs BUILT MODEL
Internal erosion factors
The results from the analysis of the internal erosion factors (material susceptibility, hydraulic load and critical stress condition) are mentioned below.
Material susceptibility
Following the diagram in Figure 17, the soils were assessed for initiation and development of internal erosion due to: filter incompatibility and internal instability. The results were based on four grain size distributions attached in Figure 31 with a brief soil description. Then, with these results the filter criteria was applied following the method from Vattenfall (1988), which resulted to be fulfilled (See Table 8).
The method of Kenny and Lau (1985) was applied to determine the internal stability of granular filters, core and pipe (See Figure 32, 33 and 34). The samples of soil taken from the filter and the
0 2 4 6 8 10 12 1 2 3 Y Di sp lac e m e n ts (c m )
1=LEFT; 2=CENTRAL; 3=RIGHT
Maximum Deformations DAM vs BUILT MODEL
DEFORMATIONS UPSTREAM DEFORMATIONS CREST DEFORMATIONS DOWNSTREAM SVSOLID Max Deformations Downstream
SVSOLID Max Deformations at Crest and Upstream
31 pipe resulted to be internally unstable, whereas the core was stable since it was only possible to evaluate the fraction smaller than 20% (F<20%).
Finally, the methodology from Rönnqvist (2007) to assess the potential for internal erosion in glacial till core embankment dams was also applied for the filter incompatibility. The result of the assessment provided a neutral risk of continuation of erosion at the core, and an increased risk of continuation at the filter.
Soil description:
- Core (2 samples, to contrast results): Coarse glacial till with almost fifty-fifty distribution of sand and gravel.
- Filter (1 sample): Coarse material (gravel) with small fraction of fine material (sand <10 %). - Pipe (1 sample): Gap graded grain size distribution for the fine particles, and uniformly
graded for coarser material.
Figure 31. Grain size distribution
FILTER CRITERIA FINE MAT. <30% FINES (<0.06mm))
Requirements Value Limits Filter criteria
Permeability D15/d15 18.6 4<D15/d15>40 OK
Piping D15/d85 0.4 D15/d85<4 OK
Parallel curves D50/d50 12.0 D50/d50<25 OK
Separation Dmax 50 mm Dmax<60mm OK
Table 8. Filter criteria
0,0 10,0 20,0 30,0 40,0 50,0 60,0 70,0 80,0 90,0 100,0 0,001 0,010 0,100 1,000 10,000 100,000 P e rc e nt a ge pas s ing Particle size (mm)
Core filter pipe core 2
SAND GRAVEL
32 Figure 32. Filter Internal stability
Figure 33. Core internal stability
Figure 34. Pipe internal stability
0 1 2 3 4 5 6 7 8 9 10 0 1 2 3 4 5 6 7 8 9 10 H% F% H-F
Critical line internal stability Unstable 0 5 10 15 20 25 30 35 40 0 5 10 15 20 25 30 35 40 H% F% H/F
Critical line stability
Stable 0 2 4 6 8 10 12 14 0 2 4 6 8 10 12 14 H% F% H/F Critical line stability
33
FILTER ASSESSMENT CHECK
D15 7 mm D15<1.4mm
Core Stability Stable Fig 33 Pipe stability Unstable Fig 34 Filter Stability Unstable Fig 32 RISK of CE(core) NEUTRAL RISK of CE(pipe) INCREASED
Table 9. Filter assessment
Hydraulic load
With the model created in SVFlux, all the factors of hydraulic load were calculated at a water level upstream of 124 cm, the reason was because the PWP results between the model and the experiment matched, also because a queasy steady-state condition was reached at day 10, since there were no changes in the PWP from day 8. The pore water pressure distribution can be seen in Figure 35. The piezometers are represented with green triangles and vertical black lines. The PWP distribution indicated that the experiment did not reach the final steady-state seepage. That could occur in a longer test. However, it was still possible to analyse the experimental hydraulic load factors at the experiment. These factors indicated that the hydraulic gradient was i=3 within the saturated zone, and i=5 at the unsaturated, but since there was an anomaly at the right abutment the gradients could be different at this abutment (See Figure 36). Regarding with the water head and head pressure, the 124 cm were mainly distributed upstream at the core and the maximum head pressure at the bottom, upstream. These results were used for the stress/deformation analysis (See Figures 37 and 38). Furthermore, seepage flow (fluxes) pointed out an anomaly since were very small in compare with the monitored results (See Figure 39). The conclusions of the results of hydraulic load factors were:
Steady-state of seepage was not fully achieved at the experiment according to PWP distribution.
The right abutment piezometer indicated a different behaviour than monitoring results. Hydraulic gradients at the core were too high (gradients of 3 at saturated zone, and 5 at
unsaturated)
The water head and head pressure were loading mainly the upstream side of the core. Maximum flux velocity was 1.54 cm/min at the toe. The rest of the dam indicated a seepage
velocity of about 0.06 cm/min.
34 Figure 35. Pore-water pressure (kPa)
35 Figure 37. Water head (m)
36 Figure 39. Seepage velocity (m/s)
Critical stress condition
In Figure 40, there is a general picture of the stress state of the dam. It is shown that arching effect occurred; with the centre acting right downstream the filter foundation (blue zone; 𝛔max= 31.3 kPa).
Another zone of high vertical stress is out of the arching effect at the core foundation, where the pore-water pressure was at its highest (green zone; 20 KPa). Thus, due to the arching effect, slopes and crest were at a low stress state. It can be seen a decomposition of the horizontal vertical components of total stress in Figures 44 and 45. The following conclusions from the results are mentioned below.
The results of deformations with the model seemed to agree with the experiment. The maximum XY deformations were mainly located within the crest upstream side of the rock fill and rock fill-core interface (See Figure 41).
Vertical cumulative effective stress exerted maximum compressive stress (31 kPa) at the filter-rock fill interface downstream, which seemed to be normal. However, at the upstream part of the core the effective stresses were low between 3-6 KPa, which indicate a weak zone (See Figure 42).
There were small zones of negative shear stress within the core, at the crest, upstream and downstream (See Figure 43). The local factor of safety calculation with SVSolid indicated that it could be a shear failure mode at the top of the crest (See Figure 47). Moreover, considering the higher deformation of the rock fill, the top part of the core at the crest would be exposed to local shear failure mode, which agreed with observations at the experiment.
37 to that, minimum principle stresses (S3) decrease with the height at the core, where if the pore water pressure becomes higher than S3, hydraulic fracture may occur. The horizontal stresses are plotted in a clearer diagram called minimum principle stresses (S3), (See Figure 46).
Vibration at the experiment was monitored, and even though the impounding of water through the pipeline could generate small vibrations, the result did not show any relevance, and hence, it was disregarded as a factor of internal erosion in this experiment.
Figure 40. Total stress Sy (kPa)
38 Figure 42. Vertical effective stresses (kPa)
39 Figure 44. X total stresses (kPa)
40
Figure 46. Total minimum principle stress (S3) (kPa)
Figure 47. Local Factor of Safety
Failure mode analysis (Critical zones)
41 Figure 48 Critical zones of failure mode analysis
Dam failure
In the dam failure investigation, all the monitoring data collected was analysed, from the first day of the experiment until the dam breached, at day 10. There results of dam failure pointed out three phases (impounding, piping and breaching). Impounding was initiated at 13:41:41 at maximum inflow (1440 l/min) into the container. From 13:43:26, piping was initiated and progressed until the crest collapsed at the right abutment at 13:59:31. Note that the water level inside the container was limited to 147 cm, so overtopping did not occur. The following results from different instrumentation show where and how the dam breached, and at what time.
Turbidity
42 Figure 49. Turbidity
Seepage
Seepage flow reached daily values of at least 10 l/min, except at day 4 when values were lower than 7 l/min. Maximum seepage values of over 60 l/min were reached at days 6, 9 and 10. These values were measured manually (See Figure 50). However, at day 10, due to a high seepage flow the manual measurements were not as reliable as the Thomson’s weir logs, because the flow was becoming the same as the inflow from the pump (See Figure 51). Note that there were no manual reading the first 2 days of the experiment.
Figure 50. Seepage flow, 10 days (Manual readings)
43 Figure 51. Seepage flow at day 10 (Thomson weir)
Pore-water pressure
Piezometers installed within the core were automatically logged during the whole length of the experiment. However, only results at dam failure are shown in this section. The PWP at the core for the whole length of the experiment can be found in Figure 22. In Figure 52, when impounding started, the right abutment had higher PWP than it should be. Where, the central and left piezometers followed together a different behaviour. When the leakage was observed (piping) at the right abutment, the right piezometer increased at a higher rate than the other piezometers surpassing even the left piezometer. When the right core reached 145 cm of PWP at 14:14:58, which corresponded with the water level, the right part of the crest collapsed.
Figure 52. Pore-water pressure at day 10
0 20000 40000 60000 80000 100000 120000 140000 160000 13: 28:01 13: 29:44 13: 31:26 13: 33:09 13: 34:51 13: 36:34 13: 38:16 13: 39:58 13: 41:41 13: 43:2 3 13: 45:05 13: 46:48 13: 48:3 0 13: 50:13 13: 51:55 13: 53:38 13: 55:20 13: 57:02 13: 58:45 14: 00:27 14: 02:09 14: 03:52 14: 05:34 14: 07:17 14: 08:59 14: 10:42 14: 12:24 14: 14:06 14: 15:49 14: 17:31 14: 19:13 14: 20:56 14: 22:38 14: 24:21 14: 26:03 14: 27:46 Se e page (C l/m in) Time (hour) 100 105 110 115 120 125 130 135 140 145 150 13: 30:35 13: 33:09 13: 35:42 13: 38:16 13: 40:50 13: 43:23 13: 45:57 13: 48:3 0 13: 51:04 13: 53:38 13: 56:11 13: 58:45 14: 01:18 14: 03:52 14: 06:26 14: 08:5 9 14: 11:33 14: 14:06 14: 16:40 14: 19:13 14: 21:47 14: 24:21 14: 26:54 14: 29:28 PW P (c m ) Time (hour) Right core Left core Central core
IMPOUNDING PIPING BREACHING
PIPING BREACHING
44 Acoustic emissions
The acoustic sensor did not register relevant vibrations until the dam failed at day 10. Longitudinal, transversal and vertical vibrations were detected by the acoustic emission sensor giving the exact time of initiation of the breaching failure at 13:59:49. The vibration stopped when the acoustic sensor was retired from the water after the collapse of the pipe at this point of the crest (See Figure 53).
Figure 53. Acoustic emissions, day 10. Video surveillance
The following pictures were taken with the cameras installed upstream and downstream the embankment recording the exact times of failure. Pictures in Figure 54 show the same time of the breaching’s sequence at two different viewpoints, starting from impounding (a-b) to piping (c-d) and dam failure (d-e), respectively.
45 Figure 54. Dam Failure
46
DISCUSSION
Summary of the experimental results
From all the data collected during 10 days of monitoring, one queasy steady-state per day was selected to set up the numerical model. The results from monitoring after 4 days were starting to get closer to the ones solved with the Built Model; this is due to the consolidation process, where steady-state conditions cannot be applied. However, seepage results with SVFlux differed with the monitoring values in 2 orders of magnitude. This is because there was leakage at the bottom and sidewalls of the container which was not considered in the model. Nevertheless, the Built Model provided approximately the same results of pore-water pressure at 5 out of 6 piezometers installed within the dam at the 10th day, giving a 9% relative error of the pore-water pressure at the right core piezometer. The pore water pressure at the right core piezometer was presumably higher because the piezometers pipelines were seeping water from the right sidewall, i.e., leakage (See Figure 5 and 6). Since the other two core piezometers were further from the right sidewall, the water coming from the right side wall did not seep until those points. It was this anomaly what determined the location of the leakage. SVSolid, provided nearly (See Figure 29) similar results of maximum deformation obtained with laser scanning after 10 days, even though triaxial tests were not performed to set up the hyperbolic model of the soils.
Summary of the results from the analysis of the internal erosion factors
Having verified the model with the experimental results, the factors of internal erosion were analysed, providing also the location where the dam failure could occur due to a combination of all the factors. The results are summarized below.
Material susceptibility
47 Hydraulic load
On the one hand, hydraulic gradients were ascendant with the height of the core, reaching a maximum of 5.15 at 147 cm, at the unsaturated top layer. So, considering that tests performed with glacial tills by Hunter and Fell (2012), initiated and progressed backward erosion at hydraulic gradients higher than 5. On the other hand, the saturated area at the right abutment had higher seepage forces. Hence, the right abutment at the crest is potentially a critical zone of failure. The pipe inserted to test development of GBE did not provide relevant results in the seepage analysis with FEM; hence it was unlikely to develop internal erosion mechanisms within the time of the experimentation.
Critical stress state
The maximum vertical total stress was concentrated downstream at the filter foundation (arching effect occurs); hence no critical condition was detected at the foundation in this case. Thus, slopes and crest were at low stress state, being the crest the main area of concern since the slopes were assessed at design’s phase. The upstream core indicated low local factor of safety. So, there was risk of slope instability of small external slices at crest level upstream, moreover maximum deformations were located in the rock fill upstream at the abutments. Thus, the core was exposed to shear failure at the top 7-10 cm. Furthermore, minimum principle stresses (S3) decrease with the height at the core, where if the pore water pressure becomes higher than S3, hydraulic fracture can occur. Therefore, there was a flaw within the crest zone, particularly at the right abutment.
Failure Mode Analysis
At the failure mode analysis, it was analysed which failure mechanism would breach the dam, and where; for three different cases of the experiment: 1) constant water level; 2) slow filling; and 3) rapid filling (tested). The assessment concluded that the most likely failure mode was for a rapid filling. The failure mode analyses are explained below:
Firstly, if the experiment was kept at constant water level (h=124 cm). In this case, initiation of internal erosion was detected during monitoring, indicating high turbidity, seepage and deformations, particularly at the right abutment. However, the risk of development of a pipe at this water level was low for the short-term of the experiment, because the hydraulic gradient was lower than 3, the pore-water pressure was low to overcome the stress state conditions and there was a filter downstream the current seepage path.
48 Finally, the risk of hydraulic fracture (Sherard, 1986) is higher if the water level is suddenly increased because then the core cannot leak off the water at the same rate is passing through the pores spaces. This will easily increase the pore-water pressure to surpass the effective stress within the poorly compacted soil, specifically on the right abutment at the crest.
As a result of the assessment for a rapid filling (final test performed at day 10), the failure mode stands on the right abutment, at the crest, due to three factors: 1)high seepage rate at high hydraulic gradients, 2) low stress condition with high deformations, and 3)internally stable, but with initiation records, cohesionless material with no filter downstream, and badly compacted with potential concentrated leaks (cracks).
[1] Shear stress ratio (η=q/p’) , q is the deviatoric stress (𝛔1 - 𝛔3); and p’ is the mean principal stress (𝛔1 + 2 𝛔3)/3.
Dam failure and event tree (Hypothesis verified)
The before mentioned failure mode analysis determined the location of the zone where the risk of internal erosion could lead to piping and breach the dam. Thus, by breaching the dam it was verified that piping occurred exactly where and how it was determined in the failure mode analysis (See Figure 55). The dam failure is represented in an event tree, (See Figure 53) based on the generic internal erosion failure mode of Fell et al., (2008).
Figure 55. Event tree of dam failure
Conclusion
It has been tested an embankment dam breaching due to internal erosion mechanisms. The breaching mechanism was visible just 15 minutes prior to dam failure. With the analysis of the factors of internal erosion, it has been possible to determine the exact location of the most likely zone of internal erosion prior to breaching, confirming the hypothesis. However, only short-term risks for a rapid filling have been tested to be detectable by this method. Long-term and other risks were detected but not verified during the time of the experiment. For instance, low stress zones could have been eroded more in a longer experiment without rapid filling (Bruthans J. S., 2014).
Reservoir rises • Rapidly!
Initiation was already visible
• Settlement • High seepage • Turbidity
Continuation (no filter at crest)
• PWP is higher at right abutment • Seepage flow
increases
Progression visible at the right
abutment (crest)
• Roof forms to support a pipe
Dam breaches
• Collapse of the pipe • Uncontrolled
49 Moreover, material susceptibility, hydraulic conditions and stress condition were not investigated in depth. This will require further research such as:
Laboratory experiments of triaxial tests considering internal erosion of Swedish glacial tills (moraine) for stress analysis.
Transient seepage analysis. 3D modelling.
Temperature, resistivity and other parameters that can be considered to influence the factors of internal erosion.
After completion of the experiment, potential findings can be described; First of all, according to the hypothesis, it would be possible to analyse the risks of internal erosion within an existing embankment dam. Second of all, this approach has determined that internal erosion may develop at the core even if the assessment of the grain size distribution indicated that the soil was internally stable (See Figure 33). Third of all, surveillance, soil testing and modelling can allow creating reliable models of dams. Finally, from the literature review, it can be concluded that by analysing the factors of internal erosion, a more accurate prediction of the failure mechanism can be obtained. Thus, decide whether or not, safety measures should be taken into consideration at this respect. Hence, safety measures can face more realistic consequences of internal erosion, and therefore reduce potential risks and costs derived from conservative assumptions that do not guarantee the solution of the problem.
On the other hand, many adversities need to be considered before to reach any potential findings using these numerical methods. The programmer assumptions are always going to be predominantly the main uncertainty while trying to extrapolate the interpretation of the results from any model to reality. However, prior to breaching of any dam, uncertainties are primary the fact that it is not possible to ensure exactly what occurs within the dam before and during a breach, only interpretations from indirect measurements of parameters within the dam structure. For instance, this failure mode analysis has been performed post-hoc, which allows always confirming uncertainties rose during the experiment and discard others. In reality, there is no opportunity to discard other uncertainties which usually leads to take conservative decisions in the risk analysis. Inasmuch as the aim of the results was to identify the failure mechanisms prior to breaching. It is more than likely that other failure mechanisms were missed in the failure mode analysis and were developed in a longer duration of the experiment. Moreover, even if results showed those risks it was not possible to guarantee the reliability of those interpretations at this stage.
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