同学你好，该知识点来自沪江网校《英语零基础直达大学六级【全额奖学金班】》的课程，想要更系统的学习，欢迎进入课程学习。不仅可以和更多的同学一起学习，而且还有老师、助教随时的学习指导和知识点解答哦。

同学你好~
因为这里整体都是讲的过去的事情，可以都统一为过去时态。

During the rescue operations there was a loud explosive noise and a big vibrations.
big前的a去掉，后面的名词是复数

The mine muse have been collapsed.
muse在这里要指什么呢

Suddenly, the microphone, which has enabled the men to keep in touch with their relatives, was silent and their relatives were very worry.
worried，用形容词形式

Hearing that the men were alive, the work continued drilling.
work改成workers

As the collapse exploded through the hard layer of rock, their works got easier.
这里意思不是很明确，可以改成：As the hard layers of rock were broken by the collapse, the work was made easier.
work是不可数名词。

While the men were brought to the surface, their relatives were eager to see them.
while改成when，这里谓语是瞬间性的。

At last, the relatives kissed the men's face and went home together.
faces 复数，went前面可以加个they

祝同学学习进步~