# Method for Assessing a Deformed Spillway Gate

When permanent deformation was found on a gate at Mercury’s Karapiro plant, Quest Integrity performed a number of assessments to determine whether it needed to be replaced, or if it still met criteria to continue operation.

By: Vitor Lopes Garcia and David Osuna, Quest Integrity

As seen in the July 2017 issue of Hydro Review Magazine.

Overview

When
personnel at the 96-MW Karapiro hydropower plant removed one of the four
spillway gates from service in late 2014, they discovered the lower section of
the gate had undergone permanent deformation and had suffered corrosion on the
internal and external gate surfaces. Concerned about the ability of the gate to
operate reliably when returned to service, plant owner Mercury (formerly Mighty
River Power) commissioned a fitness-for-service (FFS) assessment. This article
covers the methods used to determine if the spillway gate was fit for continued
service and the results of the assessment.

Background on the Situation
Commissioned in 1947, the 96-MW Karapiro hydropower plant is the last
in a series of nine located on the Waikato River on the North Island of New
Zealand. The facility houses three vertical Kaplan turbine-generator units and
has a net head of 30 meters. The dam is a 52-meter-tall, 335-meter-long
concrete arch structure, with a spillway located on the right abutment.

The spillway has four gates, each of which is 6.1 meters wide and rated
to pass 3.77 cubic meters per second of water. The gates are of the Stoney
roller design and were originally operated one-at-a-time by a gantry crane
until 1979, when a dedicated winch system was installed, allowing the gates to
be opened simultaneously. In 1998, the staunching bars were replaced with music
note seals and the gates were reinforced for seismic events.

In late 2014, Gate 2 was removed from service for installation of bird
netting. After removing the gate, Mercury personnel determined that the lower
section had undergone permanent deformation. Corrosion was also reported on the
gate's internal and external surfaces, prompting fitness-for-service (FFS) assessment,
which was undertaken by Quest Integrity.

Deflection discovered at the bottom of Spillway Gate No. 2 at the Karapiro facility in late 2014.

Inspecting the Gate

Two
on-site visits were carried out by Quest Integrity engineers, with the aim of quantifying the level
of superficial corrosion, using a Panametrics 36DL-Plus UT thickness meter.
These measurements (see Table 1) were taken at four locations between
the spillway gate's seven girders, designated A, B, C and D, with A being the lowest
location and D being the top section of the gate (see Figure 1).

Table 1. Thickness Measurement Results

Plate nominal thickness: 15.875mm (5/8 in.)

Location A showed the highest level of metal
loss with respect to the nominal gate thickness of 15.875 mm. Meanwhile, D
showed the minimum metal loss, with a value very close to the skinplate nominal
thickness. It was found that the metal loss magnitude was related to the
location of the skinplate section with respect to the spillway gate height. The
bottom sections showed higher degrees of metal loss compared to the top sections.

Figure 1. Spillway Gate No. 2

This schematic shows the position of Spillway Gate No. 2's seven horizontal girders in relation to the four locations selected for measurement.

*Finite Element Analysis*

A
finite element analysis (FEA) was performed by Quest Integrity with the purpose of estimating the stresses
at the spillway gate due to hydrostatic loading. Two different scenarios were
considered:

- Deformation load: To determine the
possible maximum loading that caused the current deflection in the gate. An
as-designed model with no corrosion was used; and
- Fitness-for-Service: To demonstrate the
current gate is fit for service in accordance with the plastic collapse and
local failure guidelines of the American Society of Mechanical Engineers FFS
standard. A deformed model with superficial corrosion was used.

*Geometry Modeling*

The geometry of the spillway gate was
generated based on engineering drawings provided by Mercury and photographic documentation taken
during the site visits. The models were generated using the finite element
modeling software Abaqus CAE 6.12-1. Two different models were generated:

- As-designed
model with no corrosion.
- Deformed
model based on reported vertical deflection with superficial corrosion.

To reduce computational cost of the finite
element analysis, some non-load bearing features of the spillway gate were not included
as part of the modelled geometry. These included the diagonal reinforcement
plate between beams A1 and A2 (see Figure 1); latching racks; and rope
retainers, guides and anchor brackets.

*Material Properties*

Based on engineering drawings provided by Mercury, the skinplate material was specified as BS 4360:1968:
Grade 43A, with a minimal tensile strength of 430 MPa, yield strength of 230
MPa, and elongation of 20%. Based on these properties, an elastic-plastic stress-strain
curve was generated based on the Ramberg-Osgood methodology found in the ASME FFS-1
standard.

*Loads
and Boundary Conditions*

The applied hydrostatic load was based on a
maximum operating level of 52.9 meters, per the *Hydraulic Structures Hydrological Data Book*.

Boundary conditions were applied to the side
joists to represent their interaction with the spillway gate slots. Only
rotation with respect to their own axes was allowed.

Stress Results

Stress results were obtained for the two
different scenarios considered. The highest level of stresses occurred at the
bottom of the gate and was due to hydrostatic loading. The locations that
exhibit the highest levels of tensile stresses are at the top plates of the two
bottom I-beams. The deformed model with superficial corrosion undergoes a
higher level of stresses, especially at the center of the top plate of beam A3.

Sensitivity Analysis

Mercury requested an additional assessment to
evaluate the possible effect of the gate deformation and corrosion on its
operation. Therefore, reaction forces at the side joists were also extracted, using
both models, from the results for comparison purposes.

The direction and magnitude of the extracted
reaction forces was determined for both models, and no difference was found
between the two.

Deformation Load Estimation
The stress results were subsequently used to
estimate the required load to cause the current spillway gate deformation. The
process of estimating this deformation load was done in two steps by:

- Calculating the strain that corresponds to
the reported maximum vertical deflection of 23 mm at beam A3; then
- Calculating the necessary load to reach
the strain level from Step 1.

A strain of 0.13% was found to be required to
cause a vertical deformation of 23 mm at the center of beam A3.

For the deformation load estimation, the
maximum operating load was incrementally increased to reproduce the observed
configuration. It was determined that for a vertical deflection of 23 mm, a
load 2.4 times the maximum operating load is required.

Fitness-for-Service (FFS) Assessment
To determine the acceptability of
the spillway gate for protection against plastic collapse, a FFS assessment was
carried out. An elastic-plastic stress analysis was performed on the
as-deformed model with corrosion damage. The acceptability of the spillway gate
using an elastic-plastic analysis was determined by satisfying the following
criteria: global collapse and local failure.

*Global Collapse Criterion*

To satisfy the global collapse
criterion, the finite element model was subjected to a load factor of 3.6 and
is required to reach the converged solution. The load factor was determined
based on Equation 1, in which the remaining strength factor (RSF), defined as
the ratio of the limit load of the damaged component to the limit load of the
undamaged component, is 0.9.

Equation 1

Load factor coefficient (β) = 4.0
x RSF

The as-deformed model of the spillway
gate subjected to a load factor of 3.6 reached a converged solution. Therefore,
the as-deformed model with corrosion damage satisfied the global criterion for
protection against plastic collapse following the ASME FFS-1 guidelines.

*Local Failure Criterion*

In accordance with the local
failure criterion guidelines found in the ASME FFS-1 standard, the model that
included the permanent deformation and surface corrosion is required to satisfy
the failure criterion against the applied loading condition with a load factor
of 1.5. High-stressed locations were identified for the assessment.

For the component to satisfy the local failure criterion,
the total equivalent plastic strain must be less than the limiting triaxial
strain ().
Total equivalent plastic strain at the assessed locations was extracted from
the results of the elastic-plastic analysis with a load factor of 1.5.

The limiting triaxial strain was calculated based on the
guidelines found in the ASME FFS-1 standard, using the following equation.

Equation 2

where:

is the limiting triaxial strain;

is the uniaxial strain limit;

is the material factor for multiaxial strain
limit;

, and are the principal stresses;

is the equivalent (von Mises) stress.

The acceptability per the local failure criterion was assessed
by calculating the ratio between equivalent plastic strain and triaxial strain
limit. Ratio values in the modeled gate that were less than one satisfy
equation 2 (i.e. equivalent plastic strain is less than triaxial strain limit).
As all the areas showed a ratio of less than one (see Figure 2) the spillway gate satisfied the local failure
criterion.

Additionally, it was determined that under the current
levels of deformation and metal loss, the most critical location corresponds to
the top plate at the center of beam A3.

Figure 2. 2014 Analysis of Gate No. 2

The von Mises distribution of the converged solution, with a load factor of 3.6.

Conclusions

Based on the results of the FFS assessment, it was
concluded that the spillway gate was fit for service as it met both the global
collapse and local failure requirements.

Replacing
a gate would include costs for design, manufacture and re-assembly at the
original location (which could require an additional overhaul in order to adapt
the original fixations to the new gate). Therefore, avoiding the substitution
of the gate resulted in significant cost savings, which covered the investments
on the FFS assessment and re-painting the original gate.

This
assessment showed that the lack of design information (e.g. corrosion allowance
was not known) can be overcome by engineering assessments compliant with
recognized standards, allowing for an informed decision.

Resources

American Society of
Mechanical Engineers, *Fitness-for-Service
Standard*,
Mercury Energy, Waikato Hydro System: Hydraulic Structures
Hydrological Data Book