Symbolism of walking by foot to Karbala

 (Kamil al-Ziyarat, page 255) 

“Aba Abdilah [al-Sadiq] said: 

Whomever goes to the grave of Husayn by foot, Allah writes for him for each step - 1000 good deeds and removes from him 1000 bad deed, and raises his status (by) 1000 degrees.”

سمعت أبا عبد الله (عليه السلام) وهو يقول:

من أتى قبر الحسين (عليه السلام) ماشيا كتب الله له بكل خطوة الف حسنة ومحا عنه الف سيئة ورفع له الف درجة.

As we know, ziyara to Husayn equals going to a hajj - in thawab.

(Kamil al-Ziyarat, page 294)

“I said to Imam al-Sadiq, “May I be sacrificed on you, I cannot afford to go to Hajj every year.” The Imam replied: If you ever wanted to go to the Hajj but could not afford it, go to the Ziyarat of Imam Husayn, for indeed it will be recorded as a Hajj for you.”

483] 3 - حدثني أبي رحمه الله، عن سعد بن عبد الله، عن الحسن بن علي بن عبد الله بن المغيرة، عن عباس بن عامر، قال: أخبرني عبد اللهبن عبيد الأنباري، قال:

قلت لأبي عبد الله (عليه السلام): جعلت فداك انه ليس كل سنة يتهيأ لي ما اخرج به إلى الحج، فقال: إذا أردت الحج ولم يتهيأ لك فائت قبرالحسين (عليه السلام) فإنها تكتب لك حجة،

Now - it was sunnah of our Imams to go to hajj by foot, something their companions imitated them. Thus, because ziyara of Husayn equals hajj in reward - mustahab acts of hajj like walking to al-Masjid al-Haram by foot from other cities was made applicable to Imam Husayn’s ziyara. 

As an example, Imam al-Hasan went to Hajj by foot over 20 times. 

(Al-Kafi, vol 1, page 461)

“When al-Hasan was on his deathbed, he cried. 

So it was said to him: O Son of Rasul Allah, how do you cry when your status with regards to Rasul Allah is the way it is?

And he said about you what he said (from praise), and you have partaken in Hajj twenty times by foot..”

محمد بن يحيى، عن الحسين بن إسحاق، عن علي بن مهزيار، عن الحسين ابن سعيد، عن النضر بن سويد، عن عبد الله بن سنان، عمنسمع أبا جعفر عليه السلام يقول لما حضرت الحسن عليه السلام الوفاة بكى، فقيل له: يا أبن رسول الله تبكي ومكانك من رسول الله صلى اللهعليه وآله الذي أنت به؟ وقد قال فيك ما قال، وقد حججت عشرين حجة ماشيا وقد قاسمت مالك ثلاث مرات حتى النعل بالنعل؟ فقال: إنماأبكي لخصلتين: لهول المطلع وفراق الأحبة.