Risk based analysis of RHPP penstock structural integrity

Risk based analysis of reverse hydro power plant penstock structural integrity is performed using fracture mechanics parameters. To assess its structural integrity, extensive testing of the full-scale prototype had been performed, including hydrostatic over-pressurizing, during the design phase. More recently, the Failure Assessment Diagram has been used to evaluate probability, whereas phenomenological analysis has been used to estimate consequence, in the scope of common risk estimation. It is shown that over-pressuring has potential detrimental effect on pipeline safety, i.e. structural integrity.


INTRODUCTION
eversible Hydro Power Plant (RHPP) "Bajina Basta" is in operation since 1982, [1,2]. Taking into account that the failure of its most critical part, the penstock, Fig. 1, would cause water overflow of the surge hub in the surrounding area, and the collapse of the entire plant, it is clear that special attention is still needed to prove its structural integrity. R This is especially important when it comes to the proof testing, now scheduled for 2022, since it has been shown that overpressure can cause significant damage and bring no benefit, [3]. Therefore, the basic aim of this paper is to make risk based analysis of the penstock structural integrity with focus of overpressure effect. Toward this aim, a simple engineering tool will be used to estimate probability, [4][5][6][7][8][9][10], and simple reasoning will be used to estimate consequence, [7,11], so that risk will be evaluated as the product of these two. This approach is also adopted in the scope of ESIS TC12 activities, [12].  aving in mind the importance of the penstock, special design procedure has been used, combined with extensive testing of the full-scale prototype, Fig. 2, including static, dynamic and fracture mechanics testing, based on the request to construct only one pipeline, made of steel with yield strength significantly higher than for the common structural steels. Therefore, SUMITEN HT80 was chosen, quenched and tempered weldable High Strength Low Alloyed (HSLA) steel, with nominal Yield Strength (YS) above 700 MPa, and Tensile Strength (TS) cca 800 MPa. Anyhow, welded joints made of such steels are well known for their susceptibility to cracking, making three stages hydrostatic proof testing of the model inevitable: 1. Loading from 0 to 3 MPa to check the measuring system. 2. Loading from 0 to 9.02 MPa, to reach the service stress. 3. Overloading (33.3%) from 0 to 12.05 MPa, as required by the regulation. Full-scale model strains were measured by Strain Gages (SG) and Moiré grids, as described in details in [1,2]. In the base metal (BM) response was dominantly elastic, whereas plastic strain (0,24%) was registered in welded joint LS1 (SG2, SG34), indicating non-uniform, even strange behavior due to stress concentration and weld mismatching, as shown in [4]. Concern and reaction at the international level. Table 1: Descriptive risk matrix, taken from [11]. H RISK MATRIX hen observing the risk, possible consequences for the people, property, environment and reputation of the company should be considered. In the suggested model, we proposed a combination of qualitative and quantitative approach to the assessment of potential consequences, as given in Tab. 1 in the form of risk matrix, [7,11]. Other aspects of risk based structural integrity assessment is given in [3][4][5][6][7][8][9][10][11]. As already shown in the case of pressure vessels that would cause air strike and significant damage, probably with fatalities, [7,11], this is the case also with eventual penstock failure. The indirect damage would be the total stoppage of a reversible hydroelectric power plant for long period of time. Therefore, potential consequence in the case of penstock failure is certainly the highest one, category 5, since it would cause the collapse of the entire power plant. Anyhow, the approach adopted here will not consider event frequency when probability is evaluated, since it has no relevance to the case considered. Instead, engineering approach will be applied, based on fracture mechanics concept, i.e. Failure Assessment Diagram (FAD), as described for different applications in [3][4][5][6][7][8][9][10][11].

FAILURE ASSESSMENT DIAGRAM APPLICATION
ailure Assessment Diagram, in its simplest form, i.e. level 1 as shown Fig. 3, enables one of the most efficient ways to assess structural integrity of a cracked component made of elastic-plastic material, such as HSLA steel. Basically, FAD indicates safe and unsafe position of a point corresponding to a given stress state for a cracked component, divided by so-called limit curve, Fig. 3: where S r =S n /S c and K r =K I /K Ic , S n stands for stress in net cross section, S c for the critical stress (Yield Strenght, Tensile Strength or any value in-between), KI for the stress intensity factor and KIc for its critical value, i.e. fracture toughness.  MPa and a/t=0.5.  K Ic =(EJ Ic /(1-ν 2 )=8548 MPamm (J Ic =316.6 N/mm [13]).  Kr=KI/KIc=3402/8548=0.40 (p=9.02, ¼), 4536/8548=0.53 (p=12.05, 1/4), 9380/8548=1.08 (p=9.02, 1/4), 12507/ 8548=1.44 (p=12.05, ½). Therefore, the FAD coordinates obtained for cracks treated as through thickness cracks with depths being ¼ and ½ half of thickness, are as follows, Fig. 1 1.43, 1.44). Clearly, this is overconservative estimation since both material and crack geometry are presented in conservative way. Anyhow, even this simple analysis indicates detrimental effect of over-pressurizing, since the points corresponding with it are way out of the safe region (1/2 crack), or very close to the limit curve (1/4 crack), Fig. 3. Less conservative assumption would be to consider cracks as they are, i.e. treat them as surface cracks. In that case reduction of cross-section is negligible, so Sn and Sr are calculated as follows:  Sn=pR/t= 9.02x2.1/0.047=402 MPa,  S n =pR/t=12.05x2.1/0.047=536 MPa.  Sr=Sn/Sc=402/750=0.54  S r =S n /S c =538/750=0.72 Stress intensity factor for surface edge crack in a plate can be evaluated using the following procedure from [14]. Plate is taken as better approximation than thin cylinder, since the ratio B/r i is just 47/2100=0.023, i.e. much closer to 0 than to 0.1, which is the lowest value for cylinders in [14]. Geometry parameters F and Q are calculated for tensile plate with a surface crack (a/2c=0.13 for ¼ crack and ≤1) at the point of maximum stress intensity factor (φ=900) as follows:

DISCUSSION
he approach so far presented is the simplest one which takes into account crack geometry and material behaviour.
Being the simplest it is not the most accurate one, lacking precise stress distribution, especially in weld joint zones. Namely, as shown previously, [1,2], stress concentration can cause local plastic deformation in welded joints made by SAW, in the case of overpressure, since they have the lowest YS (687 MPa). To take into account such effects, more sophisticated approach is needed, e.g. Japp vs. J-R curve analysis, based on more complex analytical solutions for J, [1,2]. Here, such an analysis is briefly presented, as shown in Fig. 5. Corresponding critical values (0.91·YS for WM and 0.92·YS for BM in the case of ¼ crack, or 0.82·YS for WM and 0.85·YS for BM in the case of ½ crack, can be taken as inverse of T probability, but this is beyond the scope of this approach since its basic advantage, simplicity, would be lost. Anyhow, one can notice that overpressure in weld metal can reach the critical state, since only 563 MPa would cause unstable crack growth in SAW weld metal with ½ crack, whereas operating pressure would not jeopardize penstock integrity even in that case.

CONCLUSIONS
ased on the results shown here, one can conclude the following  Risk based analysis using fracture mechanics parameters, as presented here, is efficient engineering method to assess structural integrity of a cracked component, especially if its geometry is relatively simple.  Effect of over-pressure is detrimental from the point of view of structural integrity since it can cause unnecessary damage of welded joints, as the most crack sensitive regions. Both simple engineering method, as presented here, and previously performed more complex fracture mechanics analysis, lead to that conclusion.