In several Points in Half-Life, the Gargantua physically breaks Barricades so that it can get to and attack the Player.
Surface Tension[]
In Surface Tension, after reaching the Tactical Map to call down Airstrikes, the Gargantua breaks apart a Gate in a single Hit.

Gordon: 343px = 168.2cm
Gate Width: 1636px = 802.26cm (8.0226m)

Gate Width: 901px = 802.26cm
Gate Height: 678px = 603.7cm (6.037m)

Gordon: 346px = 168.2cm
Gate Depth: 158px = 76.8cm (0.768m)
So the Gate is ~8m Wide, ~6m High and ~0.77m in Depth. This gives us 37196111.0016cc.
It's likely violent Fragmentation, given that many small Pieces appear from destroyed Objects in these Games. Material is likely Steel, which has Value of 568.5 j/cc.
This gives us: 21145989104.4096 Joules or 5.05 Tons of TNT (High 8-C)
Recalc[]
It's more likely standard Fragmentation (as pointed out in the Comments). Steel Fragmentation is 208 j/cc
With a Volume of 37196111.0016cc, this gets us...
7736791088 Joules or 1.85 Tons of TNT (8-C+) ACCEPTED
Well that went down a Tier. 2.73x below the previous result.
Interloper[]
In Interloper, an Unavoidable Gargantua breaks through 3 Rocks from just walking into them (Each vary in Size, one smaller and one larger).
Calc 1[]
Using the Rock close to the Exit as reference to get the Value. I'm gonna assume their all perfect Rectangles.

Gordon: 342px = 168.2cm
Rock Width: 717px = 352.63cm
Rock Height: 530px = 260.66cm

Gordon: 338px = 168.2cm
Rock Depth: 627px = 312cm
With this we get the Volume of 28677959.1696cc. The Gargantua violently fragments this Rock, which is 69 j/cc. With this we get... 1978779182.7024 Joules
For Multipliers, 2x will be Mid-End and 3x will be High-End (Due to destroying Multiple Rocks, though all different sizes)
Low End (1 Rock): 1978779182.7024 Joules or 0.473 Tons of TNT (8-C)
Mid End (2 Rocks): 3957558365.4048 Joules or 0.946 Tons of TNT (8-C)
High End (3 Rocks): 5936337548.1072 Joules or 1.42 Tons of TNT (8-C+)
Calc 2[]
Using the Tall Rock as reference to get the Value. Basically same as above.

Gordon: 335px = 168.2cm
Rock Height: 733px = 368cm
Rock Width: 488px = 245cm

Gordon: 341px = 168.2cm
Rock Depth: 584px = 288cm
With these, we get the Volume of 25966080cc. With 69 j/cc we get 1791659520 Joules. With Multipliers we get...
Low End: 1791659520 Joules or 0.428 Tons of TNT (8-C)
Mid End: 3583319040 Joules or 0.856 Tons of TNT (8-C)
High End: 5374978560 Joules or 1.285 Tons of TNT (8-C+)
Results[]
Surface Tension: 1.85-5.05 Tons of TNT (Building+ to Large Building)
Interloper Calc 1: 0.473-1.42 Tons of TNT (Building to Building+)
Interloper Calc 2: 0.428-1.285 Tons of TNT (Building to Building+)