This porch was the length of the women's court, approximately 150 feet long, forming at that time, the eastern boundary of the temple area.

With deep valleys on the west and east of the threshing floor that King David had purchased, Solomon had to come up with some pretty ingenious ideas to increase the top of the mount.  We can see that work today but it is hard to recognize because it is buried deep beneath a now flat surface of the temple mount, which is many times larger then what was there in Solomon's time.

Warren and Wilson's maps show substructures that would have, at one time, been on the edge of the cliff of the Kidron Valley.

The cistern shaped like an E on the map below was clearly constructed at the time of Solomon's on the side of this steep hill.
It lays below Triple Gate on the south wall.  In fact its purpose is as support for the building that rest on it.
This cistern was not dug deep under the surface, but a structure built into the side of the steep hill.

The vaulted passage from the Triple Gate lies appoxamatly 5 feet under the surface of the Temple Mount.  Directly below that is cistern #11. The bottom of the cistern is 61 feet 6 inches below the surface of the ground.  It consists of three tanks, each about 26 feet by 40 feet, lying east and west, connected by a passage 14 feet wide, running north and south. The roof is cut in rock, in the form of arches. Steps cut in the rock run up along the west side, and issue close to the mouth of the cistern. There is the foundation of a massive wall on the rock to west of steps.

When Solomon built a portico east of the Temple it had to be built on the side of a steep rocky hill.    This was called Solomon's Porch/portico: the kings entrance. His palace was between the city and this entrance, built on the Ophel south east of the temple.
 

Below I have drawn a horizontal perspective of the purpose of the big E structure under the triple gate passages as it would have been viewed from the Mount of Olives.

When I lay my diagram of the Temple in Solomon's time over Warren's map the western passage and arch  of the triple passages is within the eastern wall of the compound and the two eastern passages are outside the wall.

Solomon's Temple according to Josephus Flavius

War of the Jews - BOOK 5, CH. 5

A DESCRIPTION OF THE TEMPLE.

1. NOW this temple, as I have already said, was built upon a strong hill. At first the plain at the top was hardly sufficient for the holy house and the altar, for the ground about it was very uneven, and like a precipice; but when king Solomon, who was the person that built the temple, had built a wall to it on its east side, there was then added one cloister founded on a bank cast up for it,  and on the other parts the holy house stood naked.
But in future ages the people added new banks, (12) and the hill became a larger plain.

This cloister/portico on the east was called Solomon's porch or colonnade. According to Josephus the portico was built upon a bank cast up for it, which would be the big E shaped structure underneath it.  This structure allowed the portico to be built on the edge of the hill over looking the kidron valley.

 It is written that;
Solomon's Porch was on the east side of the courtyard adjacent  to the many porticoes surrounding the courtyard.   Jesus walked in Solomon's Porch (John 10:23); Peter and John healed a lame man at Solomon's Porch (Acts 3:1-11); the early church met on Solomon's Porch (Acts 5:12).
2986 \Porch, Solomon's\ - a colonnade on the east of the temple, so called from a tradition that it was a relic of Solomon's temple left standing after the destruction of Jerusalem by the Babylonians. (Comp. 1 Kings 7:6.) The word "porch" is in the New Testament the rendering of the Greek word: por'-ti-ko- Stoa, meaning a portico or verandah (John 5:2; 10:23; Acts 3:11; 5:12).

In architecture a "porch" is strictly an exterior structure forming a covered approach to the entrance of a building; a "portico" is an ambulatory, consisting of a roof supported by columns placed at regular intervals--a roofed colonnade.

The portico bearing Solomon's name was that running along the eastern wall. The portico was the scene of Christ's teaching at the Feast of the Dedication (John 10:23), and was flocked to by the multitude after the healing of the lame man (Acts 3:11 "the porch that is called Solomon's"). There the apostles preached and wrought other miracles (Acts 5:12).
 

Herod did not rebuild Solomon's porch, called eastern cloisters.

 Josephus FlaviusAnt. 20:9, section 7
Quote;....so they persuaded him to rebuild the eastern cloisters. These cloisters belonged to the outer court, and were situated in a deep valley, and had walls that reached four hundred cubits, and were built of square and very white stones, the length of each of which stones was twenty cubits, and their height six cubits. This was the work of king Solomon. (The request was denied)
A portion of the temple which according to Josephus (B. J. 5:5, section 1; Ant. 20:9, section 7) remained from Solomon's time. It rose from a great depth, occupying part of the valley, and supported by a wall 400 cubits high, formed of white, immense stones, some 20 cubits long. The Chaldaeans spared it. Our Lord walked in its shelter in winter.

This Porch would have been built as a covered area for entering the eastern gate of the Temple complex, needed because of the steepness of the hill and the high elevation of the complex wall above the Kidron Valley. The Porch was entered from  a southern entrance, and from the porch, the King would then enter the Temple Compound through the East gate.
 

The three openings on the wall show where the gates are.

Below I have drawn the gates in place.

Notice the western gate is on the west side of the wall and the other two gates are on the eastern side of the wall. This means that the western passageway was within Solomon's temple compound, past of the eastern court of the gentiles and the other two were the porch outside the temple compound.  The  row of arches between the two vaulted passages actually acted as the eastern wall for this section of the temple compound.

Only the top portion of the arches can be seen above the dirt and rubble in these passages.
 

Below excerpts from:

Ordnance Survey Office,
Southampton, 29th March 1866.

HENRY JAMES,
Colonel Royal Engineers

Italic font in parentheses added by me.

(Part of the survey concerning Triple gate from outside the south wall);

"The " triple gateway" is closed with small masonry, its arches are semicircular, with a span of 13 feet, and the stones in both piers and arches have plain chiseled faces. In front of the gateway are some large fiat slabs of stone, which appear to have formed part of a flight of steps leading up to it; an excavation was made here, and three passages discovered by Monsr. De Saulcy explored, a description of which will be given in another place. To the west of the gateway there are two courses of (Herod) stones with the draft, and one of these can be traced to the " double gateway," where it abruptly terminates; this course is of some height, 5 feet 5 inches being seen above ground, and the blocks are finely finished with plain picked faces, and 3.25 inch draft chiseled round the margins; one of these stones, which forms part of the left jamb of the western entrance of the "triple gateway," has a molding worked on it, which seems to have been intended as a sort of architrave, (a beam; a beam resting on the top of a column ) and to have been worked at the time the gateway was built, certainly after the stone was set; on its face the characters shown in Sketch 4, Plate XI can be traced.

(Note:  The excerpt below is part of the description Warren gave after being led through the substructure of the terraced area of the south east corner called Solomon's Stables. Warren is then lead into the area of the Triple Gate ruins from the inside):

"The remaining part of the substructure is made up of the three vaulted passages leading from the "Triple Gateway," (leading north) these appear to have been built at the same time as the other vaults; but having been intended as an entrance, the eastern boundary is of solid masonry, through which there is an entrance from the other substructures, by a slightly elliptical doorway, the arch having a span of 5 feet 9 inches, and rise of 3 feet 4 inches.

There is a large accumulation of rubbish in the passages, especially the two eastern ones, which cannot be traced far.

"The jambs of the "Triple Gateway" seen from the inside, (Note; Warren now facing south viewing the three arches in the south wall from the inside) are made out of old material, the one on the west has a portion of an engaged column, similar to those at the Golden Gate, built into it at the bottom, but there was too much rubbish to see whether this was a portion of an older building "in situ," (meaning original construction) or merely a stone taken from some other gateway; it may be mentioned that several of these stones are found lying about and built in, in the immediate neighborhood.

On examining the west wall or boundary of these passages, the pilaster (a supporting column projecting slightly from a wall) were found to be cut out of the solid masonry of an older building, so as to correspond with the piers supporting the vaults.

 Not far from the gateway a hole in the ground opens into a short passage which, passing beneath the western wall, leads to a cistern (No. X.); the first part of the passage is through rubbish, and is roofed with large flat stones, but the latter part is cut in the solid rock;

higher up there is a hole on the right-hand side, partly excavated in the rock, and beyond this on the left there is, in the side of the wall, either a large stone or a portion of the natural rock which looks very like the lintel of an old doorway. The surface of the rubbish rises to the under side of this, but a stick between three and four feet long could be pushed in horizontally, and the ground beneath appeared to be soft; the distance between the vertical joints was 18 feet 2 inches.
A little higher up the passage are the remains of a water pipe (partly embedded in a groove cut in the wall), for conducting surface drainage into the cisterns ; from this point to the end of the passage, the western wall is formed of the natural rock scarped down.  Some of the arches near the gateway have been supported by columns placed under their centres, and others look as if they would soon need it, the roots of trees having in several places forced their way through.
 

------------
In my opinion the reason the western most  passage has less rubbish and dirt in it is because it was cleaned out  after the destruction of the temple in 70 AD by the same Jews that did the work on the double gate passages in 325 and 365 AD. Over the last 1700 years silt from water drainage has filled it back in somewhat.  They would have also been the people that "scarped out" the  tunnel at the end of the western passage, possibly trying to reach to the end of Solomon's temple area along the outer court.

From what I could glean concerning the Porch is that  it had at least partially open arches on the western wall, which would have let in all the rubble and dirt as Titus's men covered the remaining ruins with dirt and rubbish after 70 AD.   That to me makes sense, since the passages are covered with a solid roof to this day, and explains how the rubbish filled it almost to the top of the vaults.
 

Also see "Reconstructing Substructure Seven"
 

Quote: After building the Temple, Solomon also erected a palace, a hall of justice, an armory, and other administrative buildings on Mount Moriah.

The armory (the treasury of the Temple) was an exedra, (Hebrew, siderot, "arrangement of columns") a three-story, semi-circular building (perhaps with one long side and three shorter sides at the back rather than a truly curved back) whose roof was supported by three rows of columns, giving the appearance of its interior an effect something like that of a forest. It's rear wall continued this motif, having murals of trees. Because of this motif, the armory was called the House of the Forest of Lebanon. It was a place for judges to meet and discuss cases.

Solomon's palace was built at a lower elevation. Somewhere between them was the king's throne room, where he would pronounce judgment in those matters of law that were brought before him.
These three buildings lay outside the square of the Temple Mount.

From 1968 to 1977, large-scale excavations took place in Jerusalem along the southern wall of the Temple Mount and the southern portion of the western wall. In the area of the Ophel, south of the eastern Hulda Gate (Triple Gate), remains of a royal building complex of the First Temple period were discovered.
 

Major construction units of this area from the outset of construction in the First Temple period: two towers, a gate, and an adjacent royal building, apparently first built in the 9th century BCE.

Further evidence of the Davidic dynasty was found in 1986 by archaeologist Eilat Mazar. Digging on the southeast Ophel slope, she discovered an eighth-century B.C. gate that may well have led to the First Temple area. Beyond it: an area that appears to have been a royal administrative center.
-----------

At the bottom of this picture is a very large bath and north of it appears to be a semicircle building. The Palace was at a lower level than the hall of justice, and the armory.

There is a stepped walkway between these ruins and the Temple complex ruins. Immediately inside the gate was a guard room for a sentry.

It is likely that this section of Mount Moriah is where Solomon built His Palace and the East gate became the Kings entrance to the Temple Complex.