陡 is primarily used for physical steepness (roads, slopes, stairs). For 'sudden/abrupt,' it appears in the literary expression 陡然 (dǒurán, suddenly). Common compound: 陡峭 (dǒuqiào, steep and precipitous).
memory
The left radical 阝(阜) means hill/mound. The right side 走 means walk. Imagine trying to walk up a hill — it's steep (陡)!
Left-side mound radical, the side form of 阜 used whenever a hill or earthen rise sits on the left. Carries the meaning: 陡 describes the sharp pitch of a slope. Indexes the character in the terrain family alongside 险 dangerous, 阶 steps, 陵 mausoleum, 阴 shady side.
Right 走 supplies the sound — zǒu → dǒu in an old initial-stop alternation. The 'walking' meaning is not active; 走 is a sound tag, though the picture of a person climbing the mound on the left does fit a steep ascent. Same phonetic in 徒 on foot, 途 path.