Judul: Review of Morning Glory Type Service Spillway Dimensions Considering the Seroja Tropical Cyclone at Manikin Dam
Abstrak: Munculnya siklon tropis seroja pada tanggal 5 – 12 April 2021 menyebabkan bencana alam banjir bandang dan angin puting beliung di pulau Timor. Kejadian siklon tropis seroja tersebut perlu dipertimbangkan dalam desain Bendungan Manikin dan infrastruktur lainnya untuk mengantisipasi potensi melimpasnya air di atas main dam. Desain bendungan harus aman dari kegagalan hidrolis dengan cara membangun bangunan pelimpah yang mampu mengalirkan debit banjir. Tujuan penelitian ini adalah untuk melakukan kajian ulang dalam perhitungan debit rencana dengan mempertimbangkan kejadian siklon tropis seroja. Metode yang dilakukan terdiri atas analisis curah hujan, analisis debit banjir rencana bangunan pelimpah utama, penelusuran banjir, dan analisis dimensi pelimpah utama (morning glory). Hasil perhitungan debit banjir rencana QPMF sebesar 949.19 m3/detik. Dengan besaran debit rencana tersebut, nilai elevasi muka air banjir setinggi +152.10 mdpl serta debit outflow maksimal yang dapat dialirkan sebesar 540.25 m3/detik. Hasil kaji ulang menunjukkan bahwa dimensi bangunan pelimpah utama yang direncanakan cukup memadai untuk mengalirkan QPMF yang diakibatkan siklon tropis seroja, The emergence of seroja tropical cyclone on 5-12 April 2021 caused natural disasters of flash floods and tornadoes on the island of Timor. The seroja tropical cyclone event needs to be considered in the design of the Manikin Dam and other infrastructure to anticipate the potential for water overtopping the main dam. The design of the dam must be safe from hydraulic failure by constructing a spillway that is capable of conveying the flood discharge. The purpose of this research is to conduct a reassessment in the calculation of the discharge plan by considering the seroja tropical cyclone event. The method consists of rainfall analysis, flood discharge analysis of the service spillway building plan, flood tracing, and dimension analysis of the service spillway (morning glory). The result of the calculation of the design flood discharge QPMF is 949.19 m3/second. With the amount of the design discharge, the value of the flood water level is as high as +152.10 masl and the maximum outflow discharge that can be flowed is 540.25 m3/second. The review results show that the planned dimensions of the service spillway building are adequate to drain the QPMF caused by tropical cyclone Seroja.
Keyword: design discharge, morning glory, seroja tropical cyclone

Judul: Stability Slope Analysis of Main Dam Planning
Abstrak: Main dam merupakan salah satu bangunan hidrolika pada suatu waduk/bendungan yang berfungsi sangat penting dalam menahan tampungan air, sehingga perlu diperhitungkan kekuatan dan keamanannya secara cermat. Penelitian ini bertujuan untuk melakukan kaji ulang stabilitas lereng pada perencanaan main dam berdasarkan muka air normal (MAN) dan muka air banjir (MAB). Hasil analisis debit inflow menunjukkan bahwa pada kondisi volume tampungan normal sebesar 10.40 juta m3/detik, elevasi muka air normal bendungan pada 94.27 mdpl. Pada elevasi tersebut, kedalaman bendungan adalah 29.27 m dari dasar bendungan. Hasil analisis debit banjir terpilih menggunakan metode HSS Nakayasu dengan distribusi hujan durasi 6 jam sebesar 189.82 m3/detik, sehingga diperoleh elevasi muka air banjir bendungan sebesar 95.72 mdpl. Pada elevasi tersebut, kedalaman bendungan setinggi 30.37 m dari dasar bendungan. Berdasarkan parameter muka air, beban akibat angin, kenaikan muka air akibat abnormal operasional pintu bangunan, dan tambahan tinggi jagaan berdasarkan tipe bendung, tinggi jagaan main dam yang diperoleh sebesar 2.97 m. Stabilitas lereng main dam aman dengan analisis faktor keamanan (FK) menggunakan software rocscience untuk kondisi MAN diperoleh sebesar 1.37 dan MAB diperoleh sebesar 1.25. Kondisi tersebut memenuhi syarat faktor keamanan minimum stabilitas dengan tambahan beban gempa (FK ≥ 1.2)., Main dam is one of the hydraulic structures in a dam which has a very important function in holding water reservoirs, so its strength and safety need to be carefully calculated. This study aims to review slope stability in main dam planning based on normal water level (MAN) and flood water level (MAB). Results of the discharge inflow analysis showed that normal conditions were 10.40 million m3/ sec, normal water level at 94.27 mdpl. At this elevation, the depth of the dam was 29.27 m from the bottom of the dam. The result of selected flood discharge analysis using the Nakayasu HSS method with a rainfall distribution of 6 hours duration was 189.82 m3/second, so that the flood water level of the dam was obtained at 95.72 mdpl. At this elevation, the depth of the dam was 30.37 m from the bottom of the dam. Based on water level parameters, wind loads, water level rise due to abnormal building door operations, and additional guard height based on the type of dam, guard height main dam obtained was 2.97 m. Slope stability of the main dam was considered good by factor of safety analysis (FK) using rocscience software for MAN conditions obtained by 1.37 and MAB obtained by 1.25. This condition met the requirements for the minimum safety factor of stability with additional earthquake loads (FK ≥ 1.2).
Keyword: discharge, flood, stability, water level

Judul: Penentuan Nilai Eigen dan Vektor Eigen dari Matriks Tridiagonal 2-Toeplitz dengan Pendekatan Polinomial Chebyshev
Abstrak: The eigenvalues and eigenvectors of a matrix can be determined by finding its characteristic polynomials. The characteristic polynomials of a tridiagonal 2-Toeplitz matrix is shown to be closely connected to polynomials which satisfy the Chebyshev recurrence relationship. If the order of the matrix is odd, then the eigenvalues are found explicitly in terms of the Chebyshev zeros and the eigenvectors are found in terms of the polynomials satisfying the recurrence relationship. For even ordered matrices, the situation is more complicated. The problem in these cases is that although the Chebyshev recurrence formula is still applied, its initial values are not generating Chebyshev polynomials
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