I have 1 doubt about that LTD settings in Static trip breakers.
If the fault current or overload current line crosses the TCC at the LTD segment then it will show tripping time near about 120 or 130 seconds though your LTD settings are at 9 or 10 seconds. Then what is the use of LTD?. Or breaker will wait until 120 seconds?

The Long Time Delay (LTD) was never intended for arc flash mitigation. This function has been around for decades and is primarily used to adjust the time current curve for protection and coordination in the "long time" region i.e. hundreds of seconds. The setting of 9X and 10X that you mention correspond to a multiple of current (sensor or plug).

If LTD used to adjust the time current curve for protection and coordination in the "long time" region i.e. hundreds of seconds.
What is the reason behind to keep delay in hundreds of seconds?

A couple of reasons:
Provide for overload protection for conductors
Allow for adjustment to coordinate with other protective devices
Allow time delay to override transient overloads
protection for high resistance faults that have low short circuit current
ground fault large enough to trip breaker

It takes a long time to melt copper at moderate overloads. NEMA class 20 overload curve is specified as something like tripping in under 600 seconds at 200% of full load current. If we use a pure electromechanical protection system and try to achieve “no damage“ to the starter {Type II protection in IEC terminology} we use a solder pot aka eutectic overload relay and a current limiting fuse. The fuse curve is too fast to give overload protection and the eutectic overload is too slow to respond to arcing and short circuit events. If a single phase fault occurs, the fuse trips then the current roughly doubles on the two remaining phases at which point the eutectic overload triggers .

Most breakers can be set to at mlst 9x to 10x of the rating on any given trip setting. Two reasons for this. Until about 10 years ago a common method for engineering was to calculate short circuit current using transformer and motor data only and set breakers to trip at about 50-80% of this value. This is very fast and can be done with a pen and calculator in the field. It ignores upstream current limiting but stiff buses were common along with very oversized transformers. It ignores cable impedance but most of the time, it works. Then just grade breaker or fuse curves 0.5-2 seconds apart for coordination. It results in high settings with virtually no arcing fault tripping except as a happy accident. Today the goal is generally to set everything as low as possible without causing nuisance trips so incident energy is minimized. This is the opposite strategy and requires a much deeper analysis.

The second reason is often that following Code {assuming it is followed} the procedure for setting up a breaker is to set it at the lowest setting above the motor name plate stall current for instance which is usually around 6xFLA. Then increase until no more nuisance trips or reaching Code maximum, whichever comes first. Obviously there is a real temptation to short circuit this process and go to Code maximum for motors, or anything else for that matter. In years past this again might mess up coordination (more jacking up settings) but got the production guy off your back since measuring motor inrush and timing is tricky at best even today.

Worse still most motors were well behaved. Today we try to minimize losses in motors which always results in higher inrush currents. NEMA specs call for stall current labels but neither NEMA nor IEC put limits on inrush. I now write that motors must meet NEC limits on inrush (17xFLA) specifically because Siemens and Toshiba in particular relabel motors meant for IEC-only markets where there are no restrictions but there ais political sensitivity to increasing motor efficiency by 0.01%. I have measured inrush as high as 21-23xFLA and it appears theoretical maximum is about 23-26x. This specification effectively bans Toshiba and Siemens motors but is the only practical solution to meet Code without a soft start or VFD to control inrush. Anyone not aware of this will again jack up breakers to maximum or even go up 1-2 frame sizes or even starter sizes.

A third reason is a lot of molded case breakers have no way to disable LTD in particular but it may not matter. This happens a lot in MCCs. The correct device for a motor starter ks a magnetic only breaker aka motor circuit protector but a thermal magnetic breaker or microprocessor breaker can be used if the LTD is high enough to avoid miscoordination with the overload. This is often less expensive, keeps parts inventories low, and usually MCPs don't come with any features like a shunt trip input. At around 100-400 A frames in particular, electronic breakers from some manufacturers are cheaper and more reliable than MCP's but the LTD is set to a maximum to protect the breaker and can't be changed.

So any time you see this be aware that it is a red flag that it can be a correct setting but more often than not it was done for all the wrong reasons in the pas but there are still valid reasons for very high LTD.