How to break through a stubborn Semi-Slav? With every other middlegame formation, I know more or less what I would do if I were given a load of free tempi, and thus, what I should aim for in the present. However, concerning a highly defensive Semi-Slav still with "fangs," it seems like there's not much I can do but twiddle my thumbs and hope Black opens up the position for me (which is of course a terrible strategy):

r1bq1rk1/ppn1bpp1/2p1pn1p/8/3P3B/2NBPN2/PPQ2PPP/R3K2R w KQ - 6 13


Black currently has five (!) defenders locking down d5, with the possibility of bringing in an additional rook or fianchettoed bishop if the current defenders were relocated/exchanged. Thus, I wouldn't have any idea how to launch a successful central takeover (in particular, whenever I push e3-e4 in these situations, my center pawns only seem to turn into a liability for me).

As well, the kingside is without any real defect to exploit, and starting a kingside pawn storm would (afaict) be to bet my whole position on an attack with less-than-ideal odds.

So, it seems to me that at present the queenside is White's best option to secure a weakness-free advantage. Let's say I get the opportunity for free to push my pawns and reposition my rook. The issue is that it seems Black often has the ability to liquidate the queenside at his will in his favor, for example:

[FEN "r1bq1rk1/ppn1bpp1/2p1pn1p/8/PP1P3B/2NBPN2/2Q2PPP/1R2K2R b KQ - 0 1"]

1... a5 2. bxa5 Ncd5 3. Nxd5 Nxd5 4. Bxe7 Qxa5+ 5. Nd2 Nxe7


Usually, however, Black commits to some expansion before White has the time to engineer a true queenside pawn storm, often in the form of a fianchetto for his weak bishop. This in turn tends to create a weakness on c6 that, personally, I'm glad to see, because it's at least something for White to begin to target.

But from my tabiya in the first diagram, how does White ideally want to take advantage of Black's position in the Semi-Slav, without giving himself weaknesses in the process, and without relying on Black's cooperation to loosen his own position?
The position you are looking at is indeed very common in the semi-Slav defense and the solid control of the d5 square is exactly the underlying idea for Black, often after having played ...dxc4 at some point in the opening. Looking at White's piece placement, in particular at the e pawn on e3 and the White dark squared bishop on the king's side, this seems to have originated from the classic Moscow variation, namely

[fen ""]
[Event "Merano defense, Moscow variation"]

1.d4 d5 2.c4 e6 3.Nc3 Nf6 4.Nf3 c6 5.Bg5 h6 6.Bh4 dxc4


At this point White has to play aggressively to avoid Black keeping both the pawn and maintaining the initiative: the standard continuation for White is 7.e4 (that you have not played) to threaten the knight on f6 and force Black to play 7...g5 and weaken their king's side. Playing 7.e3 instead gives Black the possibility to continue developing their pieces calmly; they played possibly something like 7...Be7 but could have played instead 7...b5, pushing on the queen's side and threatening ...b4 at some point.

However, given your position on the board, White usually pursues the plan of the minority attack on the queen's side rather than going for control of the d5 square, pushing the a and b pawns to threaten b5 or c6. In order to do so it is fundamental to give rook support on the c-file with something like 0-0 followed by Rfc1. Stockfish gives the following idea, after castling:

[fen ""]
[Event "Merano defense, Moscow variation: Stockfish analysis"]

1.d4 d5 2.c4 e6 3.Nc3 Nf6 4.Nf3 c6 5.Bg5 h6 6.Bh4 dxc4 7.e3 Be7 8.Bxc4 Na6 9.Bd3 O-O 10. Qc2 Nc7 11.O-O b6 12.Rfc1 Bb7 13.Ne5 Rc8 14.a3 Nce8 15.b4


and White can play trying to break on the b-c files somehow. Perhaps you want to play 12.Rfd1 instead, to avoid ...c5; dxc5 and already having control of the d-file instead.

As an example let us have a look at a famous match Topalov-Kramink, one of the many regarding (semi)-Slav variations and Queen's gambit declined as in the fashion of two amongst the most productive players of those lines:

[fen ""]
[Event "Corus"]
[Site "Wijk aan Zee NED"]
[Date "2008.01.22"]
[EventDate "?"]
[Round "9"]
[Result "1-0"]
[White "Veselin Topalov"]
[Black "Vladimir Kramnik"]
[ECO "D44"]
[WhiteElo "?"]
[BlackElo "?"]
[PlyCount "89"]

1.d4 d5 2.c4 c6 3.Nf3 Nf6 4.Nc3 e6 5.Bg5 h6 6.Bh4 dxc4 7.e4 g5
8.Bg3 b5 9.Be2 Bb7 10.O-O Nbd7 11.Ne5 Bg7 12.Nxf7 Kxf7 13.e5
Nd5 14.Ne4 Ke7 15.Nd6 Qb6 16.Bg4 Raf8 17.Qc2 Qxd4 18.Qg6 Qxg4
19.Qxg7+ Kd8 20.Nxb7+ Kc8 21.a4 b4 22.Rac1 c3 23.bxc3 b3 24.c4
Rfg8 25.Nd6+ Kc7 26.Qf7 Rf8 27.cxd5 Rxf7 28.Rxc6+ Kb8 29.Nxf7
Re8 30.Nd6 Rh8 31.Rc4 Qe2 32.dxe6 Nb6 33.Rb4 Ka8 34.e7 Nd5
35.Rxb3 Nxe7 36.Rfb1 Nd5 37.h3 h5 38.Nf7 Rc8 39.e6 a6 40.Nxg5
h4 41.Bd6 Rg8 42.R3b2 Qd3 43.e7 Nf6 44.Be5 Nd7 45.Ne6 1-0