Nginx – Work with multiple codeigniter installation

I have a Nginx server (1.6), with PHP-FPM on my local server.
I have multiple webapps in my "/var/www/" folder, like site01, site02…

My applications use CodeIgniter.

I want to have /var/www/site01 called on default location, and /var/www/site02 called when I go :

http://server/site02.

Here is my nginx default.conf :

server {
listen 80;
server_name localhost;
access_log off;
client_body_buffer_size 1M;
proxy_max_temp_file_size 0;
disable_symlinks off;

# Site 01
location / {
    root   /var/www/site01;
    index index.html index.php index.htm;

    try_files $uri $uri/ /index.php;

    location = /index.php {
        fastcgi_pass    127.0.0.1:9000;
        fastcgi_read_timeout 10000;
        fastcgi_param SCRIPT_FILENAME $document_root$fastcgi_script_name;
        fastcgi_buffer_size 16K;            
        fastcgi_buffers 256 16k;        
        include fastcgi_params; 
    }
}

# Site 2
location /site02 {
    root /var/www/;
    index index.htm;

    try_files $uri $uri/ /index.php;

    location ~ ^/site02/index.php {
        try_files $uri =404;
        root /var/www/;
        fastcgi_pass    127.0.0.1:9000;
        fastcgi_index index.php;
        fastcgi_read_timeout 10000;
        fastcgi_param SCRIPT_FILENAME   $document_root$fastcgi_script_name;
        fastcgi_buffer_size 16K;            
        fastcgi_buffers 256 16k;        
        include /etc/nginx/fastcgi_params;  
    }
}

I have multiple errors, firstly, when I don't put "index.php" in my site02 URL, I have a 403 error. Then, I can't go any controller, it redirects me to /site01.

What is the best way to handle multiple PHP apps folders ? Why do I have these redirections ? Thanks.