在ASP.NET Core 3.1中使用仓储模式实现多对多关系，可以按照以下步骤进行操作：

1. 创建数据库上下文类

public class ApplicationDbContext : DbContext
{
    public ApplicationDbContext(DbContextOptions options)
        : base(options)
    {
    }

    public DbSet Users { get; set; }
    public DbSet Roles { get; set; }

    protected override void OnModelCreating(ModelBuilder modelBuilder)
    {
        modelBuilder.Entity()
            .HasKey(ur => new { ur.UserId, ur.RoleId });

        modelBuilder.Entity()
            .HasOne(ur => ur.User)
            .WithMany(u => u.UserRoles)
            .HasForeignKey(ur => ur.UserId);

        modelBuilder.Entity()
            .HasOne(ur => ur.Role)
            .WithMany(r => r.UserRoles)
            .HasForeignKey(ur => ur.RoleId);
    }
}

2. 创建实体类

public class User
{
    public int Id { get; set; }
    public string Name { get; set; }
    public ICollection UserRoles { get; set; }
}

public class Role
{
    public int Id { get; set; }
    public string Name { get; set; }
    public ICollection UserRoles { get; set; }
}

public class UserRole
{
    public int UserId { get; set; }
    public User User { get; set; }

    public int RoleId { get; set; }
    public Role Role { get; set; }
}

3. 创建仓储接口和实现类

public interface IUserRepository
{
    Task AddUser(User user);
    Task> GetAllUsers();
    Task GetUserById(int id);
}

public class UserRepository : IUserRepository
{
    private readonly ApplicationDbContext _context;

    public UserRepository(ApplicationDbContext context)
    {
        _context = context;
    }

    public async Task AddUser(User user)
    {
        await _context.Users.AddAsync(user);
        await _context.SaveChangesAsync();
    }

    public async Task> GetAllUsers()
    {
        return await _context.Users.Include(u => u.UserRoles).ThenInclude(ur => ur.Role).ToListAsync();
    }

    public async Task GetUserById(int id)
    {
        return await _context.Users
            .Include(u => u.UserRoles)
            .ThenInclude(ur => ur.Role)
            .FirstOrDefaultAsync(u => u.Id == id);
    }
}

4. 注册仓储服务

在Startup.cs文件的ConfigureServices方法中，注册仓储服务：

services.AddScoped();

现在，你可以在需要使用多对多关系的地方注入IUserRepository来对用户和角色进行操作了。

public class UserController : Controller
{
    private readonly IUserRepository _userRepository;

    public UserController(IUserRepository userRepository)
    {
        _userRepository = userRepository;
    }

    public async Task Index()
    {
        var users = await _userRepository.GetAllUsers();
        return View(users);
    }

    // 其他操作方法...
}

以上就是在ASP.NET Core 3.1中使用仓储模式实现多对多关系的解决方法，通过仓储模式可以方便地进行数据访问和管理。