Optimizacija težnostnih podpornih konstrukcij

Lah, Luka (author), Pulko, Boštjan (mentor)

Podporni in oporni zidovi so gradbene konstrukcije, namenjene podpiranju horizontalnih ali nagnjenih zaledij iz zemljine, kamnine, nasutega materiala ali vode. Njihov namen je zagotoviti stabilnost tal in preprečiti zdrs ali posedanje terena. Oporni in podporni zidovi zmanjšujejo erozijo, omogočajo dreniranje in stabilizirajo pobočja, kar je koristno na območjih z omejenim prostorom. Poleg lastne teže predstavljajo glavno obtežbo konstrukcije zemeljski pritiski, ki jih v splošnem delimo na mirne, aktivne in pasivne zemeljske pritiske. Izračun mirnih zemeljskih pritiskov temelji na teoriji elastičnosti, aktivnih in pasivnih pa na teoriji mejnih napetostnih stanj. Glavni namen naloge je bila določitev najmanjše možne površine oporne oziroma podporne težnostne konstrukcije, ki ustreza podanim geometrijskim pogojem in izpolnjuje pogoje mejnega stanja nosilnosti. Obravnavali smo dve obliki težnostnih konstrukcij: težnostni oporni zid s peto naprej in težnostni podporni zid s peto nazaj. Za oba primera smo, ob spreminjajoči geometriji zidu in s ciljem določiti minimalno potrebno površino prečnega prereza zidu, izračunali horizontalne in vertikalne komponente in koordinate prijemališč vseh delujočih sil, normalno in strižno komponento ter ekscentričnost rezultante vseh delujočih sil na dno temelja in izvedli kontrolo nosilnosti temeljnih tal in kontrolo odpornosti proti zdrsu. V okviru naloge smo v Excelu pripravili orodje, ki za dane geometrijske pogoje (višina zidu, naklon zaledja …) in materialne lastnosti tal (prostorninska teža, strižni kot) omogoča optimizacijo oblike in površine zidu s ciljem določitve minimalne površine prereza. Za optimizacijo geometrije zidov smo uporabili Excelov reševalnik z uporabo nelinearne metode optimizacije »Generalized Reduced Gradient (GRG)« (Lasdon et al., 1978), ki ob upoštevanju vseh podanih geometrijskih in geostatičnih omejitev izračuna najmanjšo še ustrezno površino opornega ali podpornega zidu.

• Language: Slovenian
• Keywords: težnostni podporni zid, težnostni oporni zid, zemeljski pritiski, geotehnična analiza, Evrokod 7, optimizacija
• Work type: Bachelor thesis/paper
• Organization: FGG - Faculty of Civil and Geodetic Engineering
• Year: 2024
• Publication date in RUL: 05.09.2024

Secondary language

• Language: English
• Title: Optimisation of gravity retaining walls

Abstract

Retaining walls are structures designed to support horizontal or inclined slopes made of earth, rock, fill or water. They are intended to ensure the stability of the ground and prevent the terrain from slipping or sinking. Retaining walls reduce erosion, allow drainage and stabilise slopes, which is an advantage in areas with limited space. In addition to its own weight, the main load on the structure is represented by earth pressures, which are generally divided into at-rest, active, and passive earth pressures. The calculation of at-rest earth pressure is usually based on the theory of elasticity, while the calculation of active and passive pressure is based on the theory of limit stress states. The main objective of this thesis was to determine the smallest possible cross-sectional area of a gravity retaining wall that meets given geometric conditions and fulfils the conditions of ultimate limit state. We examined two types of gravity structures: a gravity retaining wall with a toe in front and a gravity support wall with a toe at the back. In both scenarios, considering varying wall geometries and aiming to establish the minimal necessary wall cross-section area, we computed the horizontal and vertical force components, as well as the coordinates of their points of application. Additionally, we evaluated the normal and shear force components, assessed the eccentricity of the resultant forces at the foundation base, and conducted checks for ground bearing capacity and resistance against sliding. As part of this task, an Excel tool was developed to optimize the shape and area of the wall, aiming to determine the minimum cross-sectional area. This tool considers geometric conditions such as wall height and backfill slope, along with soil properties like unit weight and shear angle. To optimize the wall geometry, we utilized the Excel solver with the non-linear optimization method "Generalized Reduced Gradient (GRG)" (Lasdon et al, 1978). This method calculates the smallest appropriate area for the retaining wall, while accounting for all specified geometric and geostatic constraints.

• Keywords: gravity retaining walls, earth pressures, geotechnical analysis, Eurocode 7, optimisation