I would like to read how to use caching effectively, optimize my database schema and queries, apply partitioning and load balancing. There are pretty much resources on optimizing code and low-level stuff but not the other.
I've read Building Scalable Web Sites by Cal Henderson and besides a single chapter actually on scaling, which barely scratches the surface, there is nothing interesting inside.
Is there any decent book or another resource on web application performance optimization?
When we talk about performance improvement of a web application two must read books are High Performance Websites and Even faster websites, both of them focus on Improving the load time of a website and other client side optimizations techniques.
For the database side of things you can look at SQL Performance tuning.
Take a look at the Patterns and Practices Guide - http://www.codeplex.com/PerfTestingGuide
If you are using an Oracle database, this guide may also help.
http://download.oracle.com/docs/cd/B28359_01/server.111/b28274/toc.htm
It sounds like your bottleneck is the database? Is it? Then read prevayler to decide if an RDBMS provides the right architecture.