It's D+5: Russian troops have consolidated positions on the flanks of Avdeevka in the face of AFU counterattacks and resumed attacks. It's likely at at this point we've seen the completion of Phases I (attack to isolate) and II (defeat counterattack) of the Russian battle plan.
Allow me to explain what's going on in the battle with the help of something that most mappers don't use - an elevation map. This allows us to see what the intervisibility lines are around Avdeevka - essentially the ridgelines beyond which you can see into the terrain beyond. Control of intervisibility lines allows observation and direct fire beyond them, and allows friendly forces to take cover behind them.
I've marked what are currently Russian-held positions and key IV lines in red and Ukrainian ones in blue, with Russian tactical positions in gray. Before the Russian attack went in last week, the IV lines at what are currently the Russian tactical positions were all Ukrainian-held, the Russian position in Krasnogorovka north of Avdeevka (immediately east of the marked Security Position) was probably far more tenuous than was generally believed, and Avdeevka was so secure the AFU could still supply it by rail.
Fast forward to today and reports are coming in that Avdeevka has been isolated, with the one remaining supply road - marked AFU MSR - too dangerous to use thanks to effective Russian fire. So what happened?
Well, on October 10th the Russian "114th Brigade" launched a battalion attack out of Krasnogorovka to seize SBF 1 ("support by fire") and the Security Position - this dramatic armored attack was completely successful and took both areas in a matter of hours, with Russian forces rapidly getting into direct-fire engagements with Ukrainian troops in the northern village belt and the industrial zone. This led to panic reports that those areas in turn were being stormed despite there being little evidence of Russian troops operating west of the railroad in that area. The 114th was after the high ground, not the villages. The seizure of these positions allowed Russian armor and AT teams to dominate the north half of the Western Village Belt, fire on the MSR, and begin softening up the usual AFU stronghold in the industrial zone.
Meanwhile, different Russian battalions attacked to seize SBF 2 in the south and the Assault Position - something that took longer due, I believe, to the need to clear minefields and the dense entrenchments immediately south of Avdeevka. Russian troops appear to have consolidated on SBF 2 yesterday, allowing them to dominate the south half of the village belt with fire and engage the MSR from the south as well. At that time a flurry of reports came out that the city had been cut off.
Immediate Ukrainian counterattacks appear to have done little beyond push Russian troops off the exposed face of the slag heap on the south side of SBF 1. Russian troops in turn have begun expanding their foothold around the slag heap in the last couple days.
So, right now the Russians are in a position around Avdeevka where they can move troops into combat via covered routes, and have essentially no positions that are "hanging" and exposed to enemy direct fire, while Ukrainian supplies and reinforcements will need to run a gauntlet of direct fire to get in and their entire defensive belt west of town is in full view of Russian armor.
* Just as a note, the distance between both SBF 1 and SBF 2 and the MSR is about four kilometers - a long but quite reasonable distance to engage for tank guns and antitank missiles, particularly against soft targets that can be destroyed with HE shells.
I suspect that Russian forces will now fight south to north from the Assault Position to secure the Residential Zone before making another rural push to collapse the village belt - which will necessarily see the withdrawal of Ukrainian troops from the fortified Industrial Zone. They may also attack the AFU-held "Redoubt" east of town to bolster their general position in the north, which is somewhat interdicted by this Ukrainian-held hill.
Their pace of progress really depends on the forces they're willing to commit - thus far only a single brigade's worth of troops appears to have actually gone into action. Contra to Ukrainian propaganda, losses have been modest compared to the results achieved - trading one or two companies to isolate an enemy brigade battle position is an excellent showing, and Russian industry stamps out enough equipment for a motor rifle regiment every week regardless.
