FR0200506 Proceedings of ICONE 9 9 th International Conference e on Nuclear Engineering April 8-12, 2001, Nice Acropolis, France ICONE-645 ANALYSIS AND DESIGN OF DRY CASK STORAGE PADS FOR PLANT HATCH ISFSI P. HSU, SOUTHERN COMPANY SERVICES Southern Company, 42 Inverness Center Parkway, Birmingham, Alabama, USA 35242 G. V. JONES, SOUTHERN COMPANY SERVICES Southern Company, 42 Inverness Center Parkway, Birmingham, Alabama, USA 35242 D. S. WALDEN, SOUTHERN COMPANY SERVICES Southern Company, 42 Inverness Center Parkway, Birmingham, Alabama, USA 35242 Keywords: Facilities - Fuel - Storage INTRODUCTION An independent spent fuel storage installation (ISFSI) at Southern Company's Edwin I. Hatch Nuclear Plant (HNP) was completed, licensed, and put in service in the summer of 2000. Currently this dry cask on-site storage facility provides a temporary spent fuel storage for three Holtec HI-STAR 100 system casks (Figure 1). After reracking and rod consolidation efforts, the HNP ISFSI was necessary to maintain a full core discharge capacity of its spent nuclear fuel pools and also to temporarily delay a need for a permanent off-site spent nuclear fuel repository. The HNP ISFSI was carried out to meet the following three main criteria established at the beginning of the HNP Spent Fuel Storage Project. These three criteria were 1) to use the general license approach which utilizes the license of the cask vendor rather than obtaining a site-specific license, 2) to select only dry cask products that are intended for dual purpose licensing, and 3) to acquire sufficient dry cask storage capacity to fully meet the plant's need. The HNP ISFSI was designed to accommodate the dry cask systems furnished by Holtec International. The dry cask system consists of Multi Purpose Canisters (MPC's) and overpacks. The MPC is a sealed metal canister in which the spent fuel is placed. The MPC is then placed in the overpack (Figure 2). The overpack consists of Hl- STORMs (storage only) and HI-STARs (storage and transportation). The HI-STORM constructed of steel and concrete is a spent fuel storage system designed to be in full compliance with the requirements of 10 CFR 72 (Ref. 1). The steel constructed 33/11
OGO HI-STAR system is a spent fuel storage system designed to be in full compliance with the US Department of Energy's design procurement specification for multi-purpose canisters and large transportation casks. Since the MPC meets the requirements of both 10 CFR 71 (Ref. 2) and 10 CFR 72 for transportation and storage, respectively, the HI-STORM (Ref. 3) system allows required decommissioning of the ISFSI by simply transferring the loaded MPCs directly into the HI-STAR (Ref. 4) overpacks with impact limiters for off-site transport. Major activities in the design of pads were impact analysis, seismic evaluations, and analysis and design of the concrete storage pads. A paper summarizing each of these activities, in addition to the project design criteria and licensing objectives, was presented at ICONE 8 in Baltimore, Maryland, USA (Ref. 5). A companion paper (Ref. 6) was also presented at ICONE 8 to discuss the seismic evaluations in detail. The current paper on the analysis and design of the storage pads is to supplement the previous summary paper. ISFSI PAD SITE LAYOUT The ISFSI pad site is located immediately outside the HNP power block fenced area. Its layout allows a total of 19 pads if needed. Presently, four pads have been completed to meet the current need. Each pad was designed to accommodate up to twelve Holtec HI-STAR or twelve Holtec HI-STORM casks with a minimum center to center spacing of 15'-6" between the casks. The pads are 31' wide, 96'-6" long, and 2' thick. Figure 3 shows a plan and elevation view of a single pad. It is important to note in Figure 3 that each cask location is numbered to denote the sequence of cask placement on the pad. The location sequence was chosen to minimize differential settlement. Mixing of the both types of cask on a single pad is not allowed. DESIGN AND CONSTRUCTION REQUIREMENTS The governing design and construction requirements for the concrete pads are provided in the concrete pad specification furnished by the cask vendor (Ref.7). Adherence to the design criteria given in the cask vendor's specification will ensure that design of the pads envelops the cask design basis described in the cask vendor's Safety Analysis Report (SAR) and the regulatory criteria for the types of cask systems at the pads. The primary function of the HNP ISFSI pads is to provide a level and stable foundation support surface for placement and storage of the free standing cylindrical Holtec HI- STORM or HI-STAR storage casks loaded with spent fuel. In order to provide an appropriate level of quality assurance, design and analysis of the concrete pads was required to comply with ACI 349-97 (Ref. 8) where applicable. However, ACI 318-95 (Ref. 9) was followed for material selection, testing, and construction of the pads. The temperature loading arises from the decay heat of the nuclear spent fuel emitting through the bottom footprint of the cask. The concrete design temperature loading was calculated by a heat transfer analysis using the design temperature at the bottom of the cask and the environmental temperature surrounding the cask and concrete pads. The
oooe enveloping design temperature loading at the concrete pads included both the average (bulk) pad temperature and temperature gradient through the pad thickness. The HNP ISFSI pads were also designed to withstand the effects of natural phenomena (severe environmental conditions) including design basis tornado and design basis earthquake. SOIL INVESTIGATION Since ISFSI site is located immediately outside the HNP power block restricted fenced area there was no sufficient existing soils information to support the required analysis and design. A soil investigation of the ISFSI site was therefore performed to characterize its static and dynamic soil properties. Based on standard penetration test (SPT) soil boring data, two locations were chosen for a seismic cross-hole survey to obtain the measured shear wave velocities. The measured shear wave velocities were then discretized to obtain an average of the two locations at the comparable elevations. This process resulted in a low-strain best-estimate shear wave velocity profile. To account for uncertainty and variations in the measured soil properties, lower bound and upper bound low-strain shear wave velocity profiles were also developed. The measured low-strain shear wave velocity (Vs), weight density (p), and Poisson's ratio (v) were used to calculate the soil shear modulus (G) and soil Young's modulus of elasticity (E). However, the strain and strain rate of the soils anticipated during the various phases of cask operations will be significantly higher than those experienced during the soil seismic cross-hole testing. A correction of the above low-strain soil properties (G and E) was necessary to obtain strain and strain-rate compatible soil properties for the static analysis of the pads. Based on the soil strength degradation curves developed from the soil boring data, reduction factors of 2.0 and 1.5 were used to obtain strain and strain-rate compatible soil properties. LOAD AND LOAD COMBINATIONS Dead Load (DL) is defined as the self-weight of the structure. The dead weight of the pad was not considered in determining the shears and moments acting on the pad but was considered in determining soil pressures and settlement. Live loads (LL) are defined as all equipment not permanently installed and include loads such as loaded casks, snow loads, and loaded crawler. Snow was defined as 100 pound per square foot. A dynamic impact factor of 1.25 was applied to the crawler live load to account for any impact effect during placement of the loaded casks. Normal Wind Load (WL) was selected on the basis of a 100-year recurrence interval based on ANSI/ANS-57.9 (Ref. 10). Using a wind speed conversion factor of 1.105, the 95 miles per hour wind at the HNP ISFSI site, per ASCE 7-95 (Ref. 11), was increased to about 105 miles per hour. Tornado loads (W t ) included tornado wind load and tornado generated missile loads. The tornado loads at the concrete pad were enveloped by the seismic analysis. The missile spectrum used in the analysis was developed to envelop those from NUREG- 1536 (Ref. 12), NUREG-0800 (Ref. 13), HNP FSAR, and the vendor Design Specification.
oooo Thermal Loads (T o ) - Thermal loads include temperature loads from the average temperature through the pad thickness, i.e., bulk temperature of the pad, and from the temperature gradients through the pad thickness. Both bulk temperature and temperature gradient are based on the maximum pad surface temperature at the overpack concrete circle on the pad. The design forces and moments for the concrete pad included the effects of summer and winter ambient air temperatures on the response of the concrete pad. Design Earthquake Loads (DE) - The maximum responses at the e.g. of the HI-STAR and HI-STORM were obtained from the seismic soil-structure interaction (SSI) analyses for the two enveloping conditions, i.e., the three-cask case, and the all-casks case. The maximum accelerations in a given orthogonal direction are the SRSS of the co-linear maximum accelerations in that direction due to the N-S, E-W, and vertical input. Accident Thermal Load (T a ) - Since the temperatures at the cask vent exits will be inspected, no accident temperature load was given in the cask vendor concrete design specification. Accident Loads (AL) - Although no accident loads were considered in the design of the HNP ISFSI pads, the pads were demonstrated to absorb the impact energy from the handling accident or the non-mechanistic tip-over event. This was assured by demonstrating that the deceleration of the cask was within the design basis deceleration set by the applicable SARs. Load Combinations - The HNP ISFSI concrete pad design considered the following load combinations as included, or derived from ANSI/ANS-57.9 and ACI 349-97: Normal Conditions Off-Normal Conditions 1.4DL + 1.7LL 1.05DL + 1.3LL + 1.05T 0 1.4DL + 1.7LL + 1.7WL 1.05DL + 1.3LL + 1.05T 0 Accident Conditions and Natural Phenomena Events DL + LL + DE DL + LL + T o + DE DL+ LL + T o +W t DL + LL + T a In order to minimize long-term settlement effects, the casks will be placed on the ISFSI concrete pad in the sequence shown in Figure 3. HEAT TRANSFER ANALYSIS As previously mentioned, the temperature loading arises from the long-term storage of the cask at the concrete pad. Such decay heat causes steady-state temperature conditions at the bottom contact circle of the cask overpack. The vendor specification provides a steady-state temperature profile with peak temperature being at the center of the contact circle. Separate temperature profiles are provided for HI-STORM and HI- STAR casks to depict differences in peak temperature and diameter of the contact circle. A composite temperature profile, which has a constant temperature throughout
oooe the contact circle, was constructed from the peak temperature of the HI-STAR and the contact circle diameter of the HI-STORM. This approach bounds the thermal loads of both different casks and therefore is conservative. In summary, the following temperature profiles were used in the subsequent heat transfer analysis: Winter Conditions constant temperature over the cask/pad contact circle: ambient air temperature: soil temperature at 60' below grade Summer Conditions constant temperature over the cask/pad contact circle: ambient air temperature: soil temperature at 60' below grade 165 degrees F 32 degrees F 60 degrees F 213 degrees F 80 degrees F 60 degrees F The purpose of a heat transfer analysis was to establish the bulk temperature for pad expansion analysis and the temperature gradient across the thickness of the pad for shear and bending moment calculations. ANSYS computer program was utilized to construct a 3-D solid element model of the concrete pad and soil system. By assuming adiabatic boundary conditions at the edges of the model, it was only necessary to model one quarter of the pad (approximately, 16' by 48') and the supporting soil. The soil was modeled to a depth of 10', but properties equivalent to a 60' depth were used. Figure 4 depicts the ANSYS 3-D solid model utilized in the heat transfer analysis. The material thermal properties associated with the thermal conductivity (k) and specific heat (c) were estimated from the reference values cited in two textbooks (Refs. 14 and 15). As such, the following realistic thermal properties were used in the heat transfer investigations. Material Concrete Soil Thermal Conductivity, k (BTU/(hr ft F)) 0.60 0.25 Specific Heat, c (BTU/(lb F)) 0.20 0.44 To account for equivalent effects of the 60-foot thick soil layer, the thermal conductivity ( k ) and specific ( c ) of the soil were multiplied by factors of 1/6 and 6, respectively. This scaling basis is similar to the equivalent spring and mass in the dynamic applications. The heat transfer film coefficient (h) at the pad surface was taken to be 3.0 BTU per hour per square foot per degree F for free air convection. Both steady-state and transient heat transfer analyses were performed using the ANSYS 3-D finite element model to determine the bulk temperature and temperature gradient at the concrete pad, respectively. Results of heat transfer analysis provided the following temperature loading conditions to be used for the stress analysis of the concrete pad. Region Within Cask Footprint Outside Cask Footprint Bulk Temp U F 213 80 Summer Condition Temp Gradient U F 133 0 Bulk Temp U F 165 32 Winter Condition Temp Gradient U F 133 0
oooe ANSYS FINITE ELEMENT MODEL While it is common to model a concrete pad as a plate supported by springs, referred to as Winkler foundation, the preferred approach is to use a 3-D model of the pad/soil system. The ANSYS (Ref. 17) 3-D finite element model used the explicit soil properties (E s, n), rather than the subgrade modulus (ks) which is dependent on the pad size and shape, and is also load dependent. The 3-D finite element model of the pad/soil system used for this project has the following key features. The soil model extended to a distance of B (31') on each side of the concrete pad and to a depth of 4B (125'), where B is the width of the pad. The depth of the model is consistent with the recommendations of ACI 336.2R-88 (Ref. 16). The soil model was divided into 25 layers in order to provide an accurate representation of the measured soil characteristics. The pad was represented by a TYPE 63 quadrilateral shell element (thin plate) having 4 corner nodes with 6 degrees of freedom per node while the soil was represented by SOLID45 elements. MATERIAL PROPERTIES USED IN ANSYS 3-D MODEL The specified compressive strength f c ' of the concrete used in the pad design was 3000 psi. The elevated temperature at the bottom of the casks was estimated to reduce the E c by about 5%. This 5% reduction in E c was not expected to significantly affect the results of the analysis and was therefore ignored. It should be noted that the effects of elevated temperature, i.e., above 150 degrees F, were taken into account when evaluating the concrete strength capacities in shear and moment. The soil system beneath the concrete pads was modeled as a linear elastic isotropic material for a given soil layer. For conservatism, the lower bound soil properties were used in modeling of properties of the soil system supporting the pad. CONCRETE SECTION PROPERTIES The gross concrete section properties were used in the static analysis except for the loading conditions associated with the thermal loading and for the settlement effects analysis. The self-relieving nature of thermal stresses due to cracking and deformation of the concrete was considered in the thermal stress analysis. ACI 349-97 recommends that all loads concurrent with the thermal load be considered in the evaluation. ACI 349-85 states, "Although this approach probably is the most accurate and generally result in the largest degrees of self-relieving thermal stress, it is very complex, involving non-linear analysis and iterative solutions not readily available to the Engineer." Therefore, an alternate approach was used, which considered the concrete pad structure uncracked under the mechanical loads such as dead load, live loads, wind, and seismic loads, and cracked under the thermal loading conditions. Iterative analyses were performed until the tensile cracking was stabilized. To evaluate the settlement effects on the pad, the cracked section properties (l cr ) in conjunction with the gross cross-sectional area (Ag r0s s) were used. Use of the gross cross-sectional area (A gro ss) was justified because the axial forces resulting from settlement effects were small in magnitude.
oooo STATIC ANALYSIS A routine static analysis was performed using the ANSYS finite element model described above. The responses from the dead load, live load, wind load, and seismic loads were obtained and used in load combination with the results from the thermal stress analysis and settlement evaluation. SETTLEMENT EFFECTS ANALYSIS The procedure to incorporate the soil settlement effects into the ANSY finite element model is analogous to that suggested in ACI 336.2R-88. The ACI 336.2R-88 (Ref. 16) settlement computation is iterated on the soil subgrade modulus k s, whereas the procedure used in the design of the Hatch pads iterates on the soil Young's modulus in the 3-D soil model. The procedure followed consists of the following steps: 1. Perform an initial pad analysis using the lower bound soil Young's modulus for each layer of soil. Obtain displacements and pressures in the soil (Figure 5). 2. Compute the consolidation settlement 8 C Po,i : Jr 1 + e,,i Pa A.<Jv,i where Aa v,i = average vertical soil pressure Hi = thickness of the soil layer P 0,i = pressure due to weight of overburden soil C r,i eo.i = soil consolidation constants i = ith consolidation layer 8 Cl i = soil consolidation settlement at soil layer i 3. Compute the reduced consolidation Young's modulus T-I J~l O 0,1 J-/c,i JL/o.i ~ r* Ooi + Oci where E 0,i = so/7 elastic Young's modulus E c j = reduced soil consolidation Young's modulus 8 0,i = elastic displacement at soil layer i 4. Re-run the pad static analysis with these new reduced soil Young's moduli. 5. Repeat the above steps until the soil settlement converges. 6. The forces and moments from the last run to combine with other loading conditions for ACI 349-97 code check. The procedure was carried out using twelve zones representing 12 storage casks as shown in Figure 2. The selected point(s) for monitoring the consolidation settlements was the centroid of each zone. For load combination purposes, the consolidation
oooe settlement was treated as a dead load as recommended by the ACI 349-97 code. Settlement was considered for combined dead and live loads only. Table 1 shows the sample iterative results of soil Young's modulus of elasticity at panel 1. Table 2 summarizes the soil Young's modulus of elasticity and the corresponding settlement estimates at all 12 panels for loading the case associated with the four-cask case (Cask sequence 2, 3, 10, and 11). Similar results were also performed for the settlement for the all-casks case. Table 3 summarizes the estimated settlements at the pad. CONCRETE PROPERTIES HNP ISFSI pads were constructed as foundation structures and are classified as important to safety, class C in consistent with the cask vendor specification and regulatory requirements. As a result, based on NUREG-1536, no tests to prove capability for elevated temperatures or reduction of concrete strength are required, if concrete temperatures exceed 200 degrees F but do not exceed 300 degrees F. The maximum expected concrete temperature is 213 degrees F based on the cask vendor concrete specification. However, for conservatism, the effect of elevated temperature on concrete strength was considered in determining concrete design capacities. The cask vendor SAR shows that the temperature distribution across the bottom of the cask is not uniform and in fact, is decreasing from the cask center towards the outside edge of the cask. For the purpose of evaluating temperature effects, a uniform temperature was deemed more appropriate and used. From the cask vendor SAR, the reduction of the concrete compressive strength was estimated to be less than 10%. For conservatism, a 10% reduction in strength was used in the determination of concrete section design capacities including shear and bending moments. CONCRETE DESIGN CAPACITY CHECK To evaluate the structural adequacy of the pads, the concrete section forces and moments from the analysis were compared against the concrete section capacities, which are represented by an axial force/moment interaction diagrams. A sample result of such comparison for the governing loading combination is presented below. In addition, structural adequacy of the pad section with regard to punching shear, transverse shear, and deflection was also investigated and found acceptable. Furthermore, concrete sections were also evaluated to ensure the effects of tornado missiles would not impair the safety function of the pads.
oooo Hatch ISFSI Concrete Storage Pad d' = 4.692 inches A's= 2 in2 / ft. d = 20.436 Inches 7 A As(top) = 2 h= 24 in d = 20.436 Fy= 60 ka in2 As(bot) = 2 in2 b= 12 in " d'= 4.692 in Pc = 2.7 ks ips( ft 0 Load Combination 1.05D+1.3L(AI cks)+1.05td{gr)+1.3w(s-n)+sbtt1ement: FWMx Factored NominalCapacly A Loading Data CONCLUSION This paper describes the major steps of analysis and design of dry cask storage pads for Plant Hatch ISFSI. Results showed that HNP ISFSI met the applicable codes, regulatory and cask vendor requirements. REFERENCES [1] United States Code of Federal Relations Title 10, Part 72, Licensing Requirements for the Independent Storage of Spent Nuclear Fuel and High-Level Radioactive Waste. [2] United States Code of Federal Regulations Title 10, Part 71, Packaging and Transportation of Radioactive Material. [3] Holtec International, Topical Safety Analysis Report for the Holtec International Storage and Transfer Operation Reinforced Module Cask System (HI-STORM 100 Cask System), NRC Docket No. 72-1014, Holtec Report HI-951312. [4] Holtec International, Topical Safety Analysis Report for the Holtec International Storage, Transport and Repository Cask System (HI-STAR 100 Cask System), NRC Docket No. 71-1008, Holtec Report HI-941184. [5] Hsu. P., Jones, G. V., Moore, D. P., Springfield, T. H., Walden, D. S., "Design of Plant Hatch Independent Spent Fuel Storage Installation Pads," paper 8498, Proceedings of ICONE8, 8 International Conference on Nuclear Engineering, Baltimore MD, April 2-6, 2000. [6] Bjorkman, G. S., Kennedy, R. P., Moore, D. P., "Seismic Analysis of Plant Hatch ISFSI Pad and Stability Assessment of Dry Casks," paper 8499, Proceedings of
oooe ICONE8, 8th International Conference on Nuclear Engineering, Baltimore MD, April 2-6, 2000. [7] Holtec International, "Specification Document for ISFSI Concrete Pad at E. I. Hatch," Holtec Report No. H1-981878, Revision 3. [8] American Concrete Institute, "Code Requirements for Nuclear Safety Related Concrete Structures (ACI 349-97) and Commentary-ACI 349R-97," ACI 349-97. [9] American Concrete Institute, "Building Code Requirements for Structural Concrete (ACI 318-95) and Commentary-ACI 318R-95," ACI 318-95. [10] American National Standards Institute, American Nuclear Society, "Design Criteria for an Independent Spent Fuel Storage Installation (Dry Type)," ANSI/ANS 57.9. [11] American Society of Civil Engineers, "Minimum Design Loads for Buildings and Other Structures," ASCE 7-95. [12] U.S. Nuclear Regulatory Commission, "Standard Review Plan for Dry Cask Storage Systems," NUREG-1536. [13] U.S. Nuclear Regulatory Commission, "Standard Review Plan for Nuclear Power Plants," NUREG-0800. [14] F. Kreith, Heat Transfer, International Book Company, 1958 [15] B.V. Karlekarand R.M. Desmond, Heat Transfer Second Edition, West Publishing Company, 1982 [16] American Concrete Institute, "Suggested Analysis and Design Procedures for Combined Footings and Mats," ACI 336.2R-88. [17] ANSYS Incorporated, ANSYS Users Manual, Revision 5.4, Houston, PA. Table 1 - Typical Iterative Analysis for Settlement at Panel No. 1 - Iteration No. 4 Panel No. 1 SOIL Layer No. Node No. @ Top of Layer Disp @ Top of Layer Node No. @ Bottom of Layer Disp @ Bottom of Layer, ft Pressure @ Top of Layer, ksf Pressure @ Bottom of Layer, ksf Elastic Disp of Layer, ft Initial Elastic Disp of Layer, ft Average Pressure of Layer, ksf Layer Thickness, H Cr eo P0, ksf Layer Settlement, ft Calibration Constant Initial Young/s Modulus, ksf Consolidation Modulus, ksf 1 2432 1.60E-02 2410 9.24E-03-0.40373-0.38408 0.00677 0.00194 0.39391 10 0.0165 0.63 1.27 0.0119 0.141 2418.3 339.88 2 2399-8.40E-03 2388-6.86E-03-0.295555-0.295443 0.00155 0.00088 0.29550 5 0.0224 1.07 2.8 0.0024 0.272 2418.3 656.72 3 2366-5.85E-03 2355-4.97E-03-0.205728-0.205688 0.00088 0.00053 0.20571 5 0.0224 1.07 4.4 0.0011 0.330 3240 1068.36
OGO Table 2 - Typical Iterative Analysis for Settlement - Iteration No. 4 Soil Young's Modulus of Elasticity Values at Pad Panels (ksf) Panel No. 1 3 5 7 11 Soil Layer 339.88 404.38 292.54 249.66 321.67 428.42 1 656.72 627.49 600.72 587.70 627.25 664.85 2 1068.36 1027.18 1020.96 1022.96 1031.18 1070.99 3 Panel No. 428.42 664.85 1070.99 321.67 627.25 1031.18 249.66 587.70 1022.96 292.54 600.72 1020.96 404.38 627.49 1027.18 339.88 656.72 1068.36 10 12 1 2 3 Soil Consolidation Values at Pad Panels (inches) Panel No 1 0.184 3 0.263 5 0.159 7 0.134 9 0.205 11 0.244 3 anel No. 0.244 2 0.205 4 0.134 6 0.159 8 0.263 10 0.184 12 Table 3 - Summary of Settlement Analysis Settlement @ centroid of cask location Cask No. 9 Cask No. 3 Cask No. 1 Cask No. 7 Cask No. 11 Cask No. 5 Cask No. 6 Cask No. 12 Cask No. 8 Cask No. 2 Cask No. 4 Cask No. 10 4-casks case (inches) 0.184 0.244 0.263 0.205 0.159 0.134 0.134 0.159 0.205 0.263 0.244 0.184 All-cask case (inches) 0.358 0.358 0.437 0.437 0.448 0.448 0.448 0.448 0.437 0.437 0.358 0.358 Figure 1. HNP ISFSI Facility
OGOO CaskLoadingSeqi 1 { J, Hi " \ ^ IIIIII Figure 2: HI-STORM Overpack with MPC Partially Inserted Figure 3: ISFSI Pad, Cask Array and Cask Loading Sequence Concrete Pad v--- ;I-AB-^S W7/777/.. 1 ZONE 1 i 4 Top Layer Button Laye J ZONE 2 2 22 ZONES 77777777} Figure 4: 3-D Finite Element Model of Concrete Pad and Soil Figure 5: Schematic Diagram for Settlement Analysis