Hi. According to what is exposed first step should be knowing the composition of the soil in site by soil investigation then a general stability analysis has to be carried to ensure the system is safe against sliding situation. Once those are covered a local stability analysis can be made for each foundation. 

Having been a geotechnical engineer for 50 years, and working in many different countries on major infrastructure projects, I must warn that geotechnical engineering is not learned by asking questions like this on line. I am sorry but it involves some text book learning, and a lot of learning through experience by working under and with more experienced engineers. There are many unusual behaviours to try to understand, and things can easily go badly wrong. In the last 18 months I have worked on two significant building projects where qualified and experienced geotechnical engineers were not employed at the right time, and the resulting losses were about $300 million!

The interaction between an under-construction parking structure and a railway foundation is a complex design task. To approach it effectively:

1. Parking Design and Monitoring:

   • Gather information about the parking structure design and monitor its construction progress.
   • Understand any potential impacts on the adjacent railway foundation.

2. Geotechnical Soil Investigation:

   • Conduct thorough soil investigations to characterize the site's soil properties.
   • Use this data to select an appropriate soil behavior model for numerical analysis.

3. Foundation Modeling Software:

   • Utilize specialized software to model the foundation during parking construction stages.
   • Consider factors like load distribution, settlement, and interaction effects.

4. MGR Rail Foundation Requirements:

   • Understand the specific requirements for the railway foundation (e.g., allowable settlement, lateral stability).
   • These requirements guide your design decisions.

Remember that foundation design is challenging, and I recommend consulting an experienced geotechnical engineer to review and approve the design. If you provide more detailed information, I would be happy to assist further